tag:blogger.com,1999:blog-90450152171358855872024-03-19T04:48:23.391-04:00Intermediate Physics for Medicine and BiologyIntermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.comBlogger906125tag:blogger.com,1999:blog-9045015217135885587.post-29505927341906061092024-03-15T05:00:00.512-04:002024-03-15T06:31:58.953-04:00A New Version of Figure 10.13 in the Sixth Edition of IPMB<p><a href="https://scholar.google.com/citations?user=58ZyTnEAAAAJ&hl=en">Gene Surdotovich</a> and I are hard at work preparing the 6<sup>th</sup> edition of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>. One change compared to the 5<sup>th</sup> edition is that we are redrawing most of the figures using <a href="https://en.wikipedia.org/wiki/Wolfram_Mathematica">Mathematica</a>. It’s a lot of work, but the revised figures look great and many are in color.
<br /><br />
One advantage of redrawing the figures is that it forces us to rethink what the figure is all about and if it makes sense. This brings me to Figure 10.13 in the chapter about <a href="https://en.wikipedia.org/wiki/Feedback">feedback</a>. Specifically, it is from Section 10.6 about a negative feedback loop with two time constants. Without going into detail, let me outline what this figure is describing.
<br /><br />
Chapter 10 centers around one particular feedback loop, relating the amount of carbon dioxide in your lungs (which we call <i>x</i>) to your breathing rate (<i>y</i>). The faster you breath, the more CO<sub>2</sub> you blow out of your lungs, so an increase in <i>y</i> causes a decrease in <i>x</i>. But your body detects when CO<sub>2</sub> is building up and reacts by increasing your breathing rate, so an increase in <i>x</i> causes an increase in <i>y</i>. There is one additional parameter, your metabolic rate, <i>p</i>. If your metabolic rate increases, so does the amount of CO<sub>2</sub> in your lungs.
<br /></p><p style="text-align: left;">Our book emphasizes <a href="https://en.wikipedia.org/wiki/Mathematical_model">mathematical modeling</a>, so we develop a <a href="https://en.wikipedia.org/wiki/Toy_model">toy model</a> of how <i>x</i> and <i>y</i> behave. We assume that initially <i>x</i> and <i>y</i> are in steady state for some <i>p</i>, and call these values <i>x</i><sub>0</sub>, <i>y</i><sub>0</sub>, and <i>p</i><sub>0</sub>. At time <i>t</i> = 0, <i>p</i> increases from <i>p</i><sub>0</sub> to <i>p</i><sub>0</sub> + Δ<i>p</i>, which could represent you starting to exercise. How do <i>x</i> and <i>y</i> change with time? We define two new variables, <i>ξ</i> and <i>η</i>, that represent the deviation of <i>x</i> and <i>y</i> from their steady state values, so <i>x</i> = <i>x</i><sub>0</sub> + <i>ξ</i> and <i>y</i> = <i>y</i><sub>0</sub> + <i>η</i>. We then develop two differential equations for <i>ξ</i> and <i>η</i>, </p><p style="text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2N42-txDytNflrszSy4kh2u5JILJXL35gGlL9SwVZbTIq_aLRBDyzJSIn-3HwSVpVNBxxYjQLq8_3Kd1BmZO2ehmY6mkz-hkdjbxrrITvy7Gi4FTs63PWD-rYpuWiLQ_2aGQK3hNTOFDTK3Pjg3NWm8EnUM4roKP9LHl2DW501zf42hqjdiZkd82dCdjM/s263/Eq1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="68" data-original-width="263" height="68" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj2N42-txDytNflrszSy4kh2u5JILJXL35gGlL9SwVZbTIq_aLRBDyzJSIn-3HwSVpVNBxxYjQLq8_3Kd1BmZO2ehmY6mkz-hkdjbxrrITvy7Gi4FTs63PWD-rYpuWiLQ_2aGQK3hNTOFDTK3Pjg3NWm8EnUM4roKP9LHl2DW501zf42hqjdiZkd82dCdjM/s1600/Eq1.jpg" width="263" /></a></p>
<div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB75ksff6o2oXJKSXqK4Lxbxxs_LKG0T7Tt_3_s4x_WM533UhgLPlzvsJv3yFmTc2j9dN5eOzqoPfo1DbavL6kHLPqK6ZCgKRVQX2nQREhY_pq8C63e9u8ayc4gcJUOk-a5z5PzQXfDF4laYeVBMpciz_vaMHqNBsbQga6GJLegpOI8ulCUXcGtCXfUjWs/s256/Eq2.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="64" data-original-width="256" height="64" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhB75ksff6o2oXJKSXqK4Lxbxxs_LKG0T7Tt_3_s4x_WM533UhgLPlzvsJv3yFmTc2j9dN5eOzqoPfo1DbavL6kHLPqK6ZCgKRVQX2nQREhY_pq8C63e9u8ayc4gcJUOk-a5z5PzQXfDF4laYeVBMpciz_vaMHqNBsbQga6GJLegpOI8ulCUXcGtCXfUjWs/s1600/Eq2.jpg" width="256" /></a><br /></div><p>
The variables <i>ξ</i> and <i>η</i> have different time constants, <i>τ</i><sub>1</sub> and <i>τ</i><sub>2</sub>. The parameters <i>G</i><sub>1</sub> and <i>G</i><sub>2</sub> are the “gains” of the system, determining how much <i>ξ</i> changes in response to <i>η</i>, and how much <i>η</i> changes in response to <i>ξ</i>. In our model, <i>G</i><sub>1</sub> is negative (an increase in breathing rate causes the amount of CO<sub>2</sub> in the lungs to decrease) and <i>G</i><sub>2</sub> is positive (an increase in CO<sub>2</sub> causes the rate of breathing to increase). The “open loop gain” of the feedback loop is the product <i>G</i><sub>1</sub><i>G</i><sub>2</sub>. Finally, the constant <i>a</i> is simply a factor to get the units right.
<br /><br />
All is good so far. But now let’s look at the 5<sup>th</sup> edition’s version of Fig. 10.13. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeXGVHkBx2aArZxfEqhJ2csjMPu0L5VWhzN4ihAAaQGo0OLQZqUknUmSZ35neAwUy-jzYDTnLEXvgilePECL3xV_R2upeNNwAU9mc2DffVdk-8aD48wNSR4hjFoGqCx6Hbnzk7BpXZ-J1MGAxwsenNFoofovzQkX4BiGGqRL-OClk0z62NwU2t_XeSyha/s825/Fig10_13_old.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="Fig. 10.13 from the 5th edition of Intermediate Physics for Medicine and Biology." border="0" data-original-height="413" data-original-width="825" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaeXGVHkBx2aArZxfEqhJ2csjMPu0L5VWhzN4ihAAaQGo0OLQZqUknUmSZ35neAwUy-jzYDTnLEXvgilePECL3xV_R2upeNNwAU9mc2DffVdk-8aD48wNSR4hjFoGqCx6Hbnzk7BpXZ-J1MGAxwsenNFoofovzQkX4BiGGqRL-OClk0z62NwU2t_XeSyha/w400-h200/Fig10_13_old.jpg" title="Fig. 10.13 from the 5th edition of Intermediate Physics for Medicine and Biology." width="400" /></a></div><p></p><p></p><p>What’s wrong with it? First, the calculation uses a positive value of <i>G</i><sub>1</sub> and a negative value of <i>G</i><sub>2</sub>, so it doesn’t correspond correctly to our model, which has negative <i>G</i><sub>1</sub> and positive <i>G</i><sub>2</sub>. Second, the calculation uses Δ<i>p</i> = 0, so the steady state values of <i>x</i> and <i>y</i> don’t change and <i>ξ</i> and <i>η</i> both approach zero. That’s odd. I thought the whole point of the model was to look at how the system responds to changes in <i>p</i>. Finally, the initial values of <i>ξ</i> and <i>η</i> are not zero. What’s up with that? We know their values are zero for <i>t</i> < 0, when <i>x</i> = <i>x</i><sub>0</sub> and <i>y</i> = <i>y</i><sub>0</sub>. How could they suddenly change at <i>t</i> = 0?
<br /><br />
In the 6<sup>th</sup> edition, the new version of Figure 10.13 is going to look something like this: </p><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdvprcrzC1LcfFMOsk3ttzXlEqhzeJxiUmCeGp64Ryr2CJy8Om1BwMPionPM2wt1c89a3D5VkpmF7mkG47SbfkIP2Wi5fIFnEFsco168rEg6iozb9WvZMvuOqhGMy1sXRozAZMK8hGcTIz8uVqmoNsO1xDgHWVfTD0ouRtBd9lbhKS1aFTCKMi8fAqYOvs/s2430/Fig10_13_new.jpg"><img alt="Fig. 10.13 for the 6th edition of Intermediate Physics for Medicine and Biology." border="0" data-original-height="2430" data-original-width="1208" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdvprcrzC1LcfFMOsk3ttzXlEqhzeJxiUmCeGp64Ryr2CJy8Om1BwMPionPM2wt1c89a3D5VkpmF7mkG47SbfkIP2Wi5fIFnEFsco168rEg6iozb9WvZMvuOqhGMy1sXRozAZMK8hGcTIz8uVqmoNsO1xDgHWVfTD0ouRtBd9lbhKS1aFTCKMi8fAqYOvs/w199-h400/Fig10_13_new.jpg" title="Fig. 10.13 for the 6th edition of Intermediate Physics for Medicine and Biology." width="199" /></a></div><p></p><p>The figure has color and switches from landscape to portrait orientation. Those changes are trivial. Here are the important differences: <br /></p><ol style="text-align: left;"><li>
I made <i>G</i><sub>1</sub> negative and <i>G</i><sub>2</sub> positive, like in our breathing model. Now an increase in CO<sub>2</sub> causes the body to increase the breathing rate, rather than decrease it as in the 5<sup>th</sup> edition figure.
</li><li>
The parameter Δ<i>p</i> is no longer zero. To be simple, I set <i>a</i>Δ<i>p</i> = 1. The person starts exercising at <i>t</i> = 0.
</li><li>
Because there is a change in metabolic rate, the new steady state values of <i>ξ</i> and <i>η</i> are not zero. In fact, they are equal to <i>ξ</i> = <i>a</i>Δ<i>p</i>/(1-<i>G</i><sub>1</sub><i>G</i><sub>2</sub>) and <i>η</i> = <i>G</i><sub>2</sub><i>a</i>Δ<i>p</i>/(1-<i>G</i><sub>1</sub><i>G</i><sub>2</sub>). Notice how the factor of 1-<i>G</i><sub>1</sub><i>G</i><sub>2</sub> plays a big role. Since the product <i>G</i><sub>1</sub><i>G</i><sub>2</sub> is negative, this means that 1-<i>G</i><sub>1</sub><i>G</i><sub>2</sub> is a positive number greater than one. It’s in the denominator, so it makes <i>ξ</i> smaller. That’s the whole point. The feedback loop is designed to keep <i>ξ</i> from changing much. It’s a control system to suppress changes in <i>ξ</i>. To make life simple, I set <i>G</i><sub>1</sub> = −5 and <i>G</i><sub>2</sub> = 5 (the same values from the 5<sup>th</sup> edition except for the signs), so the open loop gain is 25 and the steady state value of <i>ξ</i> is only 1/26 of what it would be if no feedback were present (in which case, <i>ξ</i> would rise monotonically to one while <i>η</i> would remain zero).
</li><li>
The initial values of <i>ξ</i> and <i>η</i> are now zero, so there is no instantaneous jump of these variables at <i>t</i> = 0.</li></ol><p>
When revising the <a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">5<sup>th</sup></a> edition of <i>IPMB</i>, I began wondering why <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I never worried about the units for the time constants, the gains, <i>a</i>, or Δ<i>p</i>. This motivated me to write a new homework problem for the 6<sup>th</sup> edition, in which the student is asked to rewrite the model equations in nondimensional variables <i>Ξ</i>, <i>Η</i>, and <i>T</i> instead of <i>ξ</i>, <i>η</i>, and <i>t</i>. Interestingly, such a switch results in a pair of differential equations for <i>Ξ</i> and <i>Η</i> that depend on only two nondimensional parameters: the ratio of time constants and the open loop gain. So, our plot in the 5<sup>th</sup> edition has the qualitative behavior correct (except for the signs of <i>G</i><sub>1</sub> and <i>G</i><sub>2</sub>). The system oscillates because the open loop gain is so high. The correct units for the various parameters would only rescale the horizontal and vertical axes. </p><p>Is the new version of Figure 10.13 in this blog post what you’ll see in the 6<sup>th</sup> edition of <i>IPMB</i>? I don’t know. I haven’t passed the figure by Gene yet, and he’s my Mathematica guru. He might make it even better.<br /><br />
What’s the moral of this story? THINK BEFORE YOU CALCULATE! That’s the motto I often would tell my students, but it applies just as well to textbook authors. The plot should not only be correct but also make physical sense. You should be able to explain what’s happening in words as well as pictures. If you can’t tell the story of what’s taking place by looking at the figure, something’s wrong.
<br /><br />
Finally, is there really no physical problem that the original version of Fig. 10.13 describes? Actually, there is. Imagine you are resting throughout this “event”; you sit in your chair and don’t change your metabolic rate, so Δ<i>p</i> = 0 meaning <i>p</i> is the same before and after <i>t</i> = 0. However, at time <i>t</i> = 0, your “friend” sneaks up on you, shoves a <a href="https://en.wikipedia.org/wiki/Fire_extinguisher">fire extinguisher</a> in front of your face, and gives you a quick, powerful blast of CO<sub>2</sub>. Except for the sign issue on <i>G</i><sub>1</sub> and <i>G</i><sub>2</sub>, the original figure shows how your body would respond.</p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNKS6EGqGUhBOfUZ3nXkTtZ8LjnqtYHgpYPg9EAPglWcG2wQ6JDJA5GHwZlZh270luauR6EWzgafOzhhYt9IrdcnA3xZqJfF4bglO7ODQVtpCCd86VwwHOQgESTlaLW4O-Q0LoOorGVIw3bxrKCH5cnLwoKYIZic1v3hpfMoCrz6rauTRY6W4aG0fvTXcU/s600/FireExtinguisher.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="600" data-original-width="308" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNKS6EGqGUhBOfUZ3nXkTtZ8LjnqtYHgpYPg9EAPglWcG2wQ6JDJA5GHwZlZh270luauR6EWzgafOzhhYt9IrdcnA3xZqJfF4bglO7ODQVtpCCd86VwwHOQgESTlaLW4O-Q0LoOorGVIw3bxrKCH5cnLwoKYIZic1v3hpfMoCrz6rauTRY6W4aG0fvTXcU/s320/FireExtinguisher.jpg" width="164" /></a></div><p></p><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-51077474969475277032024-03-08T05:00:00.448-05:002024-03-08T05:00:00.311-05:00Stirling's Approximation<p>I've always been fascinated by <a href="https://en.wikipedia.org/wiki/Stirling%27s_approximation">Stirling’s approximation</a>,</p><p style="text-align: center;">ln(<i>n</i>!) = <i>n</i> ln(<i>n</i>) − <i>n</i>,</p><p>where <i>n</i>! is the <a href="https://en.wikipedia.org/wiki/Factorial">factorial</a>. <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I mention Stirling’s approximation in Appendix I of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>. In the homework problems for that appendix (yes, <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i> does has homework problems in its appendices), a more accurate version of Stirling’s approximation is given as<br /></p><p style="text-align: center;">ln(<i>n</i>!) = <i>n</i> ln(<i>n</i>) − <i>n</i> + ½ ln(2π<i> n</i>) .</p><p>There is one thing that’s always bothered me about Stirling’s approximation: it’s for the logarithm of the factorial, not the factorial itself. So today, I’ll derive an approximation for the factorial. </p><p>The first step is easy; just apply the <a href="https://en.wikipedia.org/wiki/Exponential_function">exponential function</a> to the entire expression. Because the exponential is the <a href="https://en.wikipedia.org/wiki/Inverse_function">inverse</a> of the <a href="https://en.wikipedia.org/wiki/Natural_logarithm">natural logarithm</a>, you get</p><p style="text-align: center;"><i>n</i>! = e<sup><i>n</i> ln(<i>n</i>) − <i>n</i> + ½ ln(2π <i>n</i>)</sup></p><p>Now, we just use some <a href="https://en.wikipedia.org/wiki/Exponentiation#Identities_and_properties">properties of exponents</a></p><p style="text-align: center;"><i>n</i>! = e<sup><i>n </i>ln(<i>n)</i></sup> e<sup>−<i>n</i></sup> e<sup>½ln(2π<i> n</i>)</sup></p><p style="text-align: center;"><i>n</i>! = (e<sup>ln(<i>n</i>)</sup>)<sup><i>n </i></sup>e<sup><i>−n</i></sup> √(e<sup>ln(2π<i> n</i>)</sup>)</p><p style="text-align: center;"><i>n</i>! = <i>n</i><sup><i>n</i></sup> e<sup>−<i>n</i></sup> √(2π<i> n</i>) </p><p>And there we have it. It’s a strange formula, with a really huge factor (<i>n</i><sup><i>n</i></sup>) multiplied by a tiny factor (e<sup>−<i>n</i></sup>) times a plain old modestly sized factor (√(2π<i> n</i>)). It contains both e = 2.7183 and π = 3.1416.<br /></p><p>Let's see how it works. <br /></p>
<table style="margin-left: auto; margin-right: auto; text-align: left;">
<tbody><tr align="center">
<th><i style="font-weight: normal;">n</i></th>
<th><span style="font-weight: normal;"><i>n</i>!</span></th>
<th><span style="font-weight: normal;"><i>n<sup>n</sup></i> </span><span style="font-weight: normal;">e<sup><i>−n</i></sup></span><span style="font-weight: normal;"> √(2π<i> n</i>)</span></th>
<th><span style="font-weight: normal;"> fractional error (%)</span></th>
</tr>
<tr align="center">
<td>1</td>
<td>1</td>
<td>0.92214</td>
<td>7.8</td>
</tr>
<tr align="center">
<td>2</td>
<td>2</td>
<td>1.9190</td>
<td>4.1</td>
</tr>
<tr align="center">
<td>5</td>
<td>120</td>
<td>118.02</td>
<td>1.7</td>
</tr>
<tr align="center">
<td>10</td>
<td>3.6288 × 10<sup>6</sup></td>
<td>3.5987 × 10<sup>6</sup></td>
<td>0.83</td>
</tr>
<tr align="center">
<td>20</td>
<td>2.4329 × 10<sup>18</sup></td>
<td>2.4228 × 10<sup>18</sup></td>
<td>0.42</td>
</tr>
<tr align="center">
<td>50</td>
<td>3.0414 × 10<sup>64</sup></td>
<td>3.0363 × 10<sup>64</sup></td>
<td>0.17</td>
</tr>
<tr align="center">
<td>100</td>
<td> 9.3326 × 10<sup>157</sup></td>
<td> 9.3249 × 10<sup>157</sup></td>
<td>0.083</td>
</tr>
</tbody></table><p style="text-align: left;">For the last entry (<i>n</i> = 100), my calculator couldn’t calculate 100<sup>100 </sup>or 100!. To get the first one I wrote</p><p style="text-align: center;">100<sup>100</sup> = (10<sup>2</sup>)<sup>100</sup> = 10<sup>2 × 100</sup> = 10<sup>200</sup>.</p><p style="text-align: left;">The calculator was able to compute e<sup>−100</sup> = 3.7201 × 10<sup>−44</sup>, and of course the square root of 200π was not a problem. To obtain the actual value of 100!, I just asked <a href="https://www.google.com/">Google</a>.</p><p>Why in the world does anyone need a way to calculate such big factorials? Russ and I use them in Chapter 3 about <a href="https://en.wikipedia.org/wiki/Statistical_mechanics">statistical dynamics</a>. There you have to count the number of states, which often requires using factorials. The beauty of statistical mechanics is that you usually apply it to macroscopic systems with a large number of particles. And by large, I mean something like <a href="https://en.wikipedia.org/wiki/Avogadro_constant">Avogadro’s number</a> of particles (6 × 10<sup>23</sup>). The interesting thing is that in statistical mechanics you often need not the factorial, but the logarithm of the factorial, so Stirling's approximation is exactly what you want. But it’s good to know that you can also approximate the factorial itself. </p><p>Finally, one last fact from Mr. Google. 1,000,000! = 8.2639 × 10<sup>5,565,708</sup>. Wow!</p><p><br /></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/IJ5N28-Ujno" width="320" youtube-src-id="IJ5N28-Ujno"></iframe></div><p style="text-align: center;">Stirling’s Approximation</p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=IJ5N28-Ujno">https://www.youtube.com/watch?v=IJ5N28-Ujno</a><br /></p><p><br /></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oaklanad University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-62987184504101692412024-03-01T05:00:00.016-05:002024-03-01T05:39:10.493-05:00A Text-Book on Medical Physics<i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a> </i>provides, <i>for the first time</i>, a textbook about the role that physics plays in medicine.
<br /><br />
Well… no.
<br /><br />
I recently found a textbook that preceded <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i> by over a century. Below is its preface.
<br /><blockquote>
The fact that a knowledge of Physics is indispensable to a
thorough understanding of Medicine has not yet been as fully
realized in this country as in Europe, where the admirable
works of <a href="https://books.google.com/books?id=V4WovYoq0OEC&printsec=frontcover&source=gbs_book_other_versions_r&cad=4#v=onepage&q&f=false">Desplats and Gariel</a>, of Robertson, and of numerous
German writers, constitute a branch of educational literature
to which we can show no parallel. A full appreciation of
this, the author trusts, will be sufficient justification for placing
in book form the substance of his lectures on this department
of science, delivered during many years at the <a href="https://en.wikipedia.org/wiki/New_York_University">University of the City of New York</a>.
<br /><br />
Broadly speaking, this work aims to impart a knowledge
of the relations existing between Physics and Medicine in
their latest state of development, and to embody in the
pursuit of this object whatever experience the author has
gained during a long period of teaching this special branch
of applied science. In certain cases topics not strictly embraced
in the title have been included in the text—for example, the directions for section-cutting and staining; and in other instances exceptionally full descriptions of apparatus
have been given, notably of the microscope; but in view of
the importance of these subjects, the course pursued will
doubtless be approved. Attention may be called to the paragraph
headings and italicized words, which suggest a system
of questions facilitating a review of the text.
<br /><br />
In conclusion, the author will feel that his labor has not
been in vain if the work should serve to call deserved
attention to a subject hitherto slighted in the curriculum of
medical education.
</blockquote>
Readers of <i>IPMB</i> might be interested in a brief table of contents for this earlier book.
<br /><blockquote>
I. Matter <br /></blockquote><blockquote><span> </span> 1. Properties of matter <br /></blockquote><blockquote><span> </span> 2. Solid matter <br /></blockquote><blockquote><span> </span>3. Liquid matter <br /></blockquote><blockquote><span> </span> 4. Gaseous matter <br /></blockquote><blockquote> <span> </span>5. Ultragaseous and radiant matter <br /></blockquote><blockquote>II. Energy
</blockquote><p> <span> </span><span> </span><span> </span> 1. Potential energy </p><p><span> </span><span> </span><span> </span> 2. Kinetic energy </p><p><span> </span><span> </span><span> </span><span> </span>3. Machines and instruments </p><p><span> </span><span> </span><span> </span><span> </span>4. Translatory molecular motion </p><p> 5. Acoustics </p><p> 6. Optics </p><p> 7. Heat </p><p> 8. Electricity </p><p> 9. Dynamic electricity </p><p> 10. Magnetism </p><p> 11. Electrobiology
</p>
Many of these topics are familiar to readers of <i>IPMB</i>. Yet, the list and the language seem quaint and just a little old-fashioned.
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxAduthl6Hq5ccl26RcsGN1lmVU9pST74zd_VNNCZOfNWiLCo3hpfa6mTRqdUvA3pa-nN2mZqYyeh8-VYCWIOjadYOQuDvMLRycfW1Qes4JrmPe3LML8qxJXER6Zfq3kR7xOS82uL_jZGDP-qJf2W9VdpSTcg5r5pxxEoKWCsD4vZY8gMSlzROLSP7e1mD/s895/Draper.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="895" data-original-width="788" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxAduthl6Hq5ccl26RcsGN1lmVU9pST74zd_VNNCZOfNWiLCo3hpfa6mTRqdUvA3pa-nN2mZqYyeh8-VYCWIOjadYOQuDvMLRycfW1Qes4JrmPe3LML8qxJXER6Zfq3kR7xOS82uL_jZGDP-qJf2W9VdpSTcg5r5pxxEoKWCsD4vZY8gMSlzROLSP7e1mD/w176-h200/Draper.jpg" width="176" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://www.amazon.com/Text-Book-Medical-Physics-Students-Practitioners/dp/1017642710"><i>A Text-Book on Medical Physics</i></a>,<br />by <a href="https://onlinebooks.library.upenn.edu/webbin/book/lookupname?key=Draper%2C%20John%20C%2E%20%28John%20Christopher%29%2C%201835%2D1885">John C. Draper</a>.<br /></td></tr></tbody></table><p>This should not be surprising. The book was titled <i><a href="https://books.google.com/books?id=S7TBNY0ds0oC&printsec=frontcover#v=onepage&q&f=false">A Text-Book on Medical Physics</a></i>, written by <a href="https://en.wikipedia.org/wiki/John_Christopher_Draper">John C. Draper</a>, and published in 1885. <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I are following a long tradition of applying physics to medicine and biology. In nearly 140 years much has changed, but also much has stayed the same. The last sentence of the preface could serve as our call to arms, and the subtitle of Draper’s book could be our own: “For the Use of Students and Practitioners of Medicine.” </p><p>Below I post the definition of medical physics in the <i>Text-Book</i>. I love it. Draper should have written a blog! <br /></p><div class="separator" style="clear: both; text-align: center;"> </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1iTEaraV-2lpV9CmO7kU0u9B_fsEYopYSz4RiTZHTHZJgFdqQxs7zYTV9E9PHGrxnAYnbl4I1lKzzzy349VH1ozyze52MrK4aSer-uar56akfI2hPX7Ptc4oBwFmQ7WZJjalCelehEA_wnx6Jc2jldzyMokBAfx93L-HIDeW8Zirmui8MSDDFtTuODehf/s492/MedicalPhysics1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="492" data-original-width="451" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1iTEaraV-2lpV9CmO7kU0u9B_fsEYopYSz4RiTZHTHZJgFdqQxs7zYTV9E9PHGrxnAYnbl4I1lKzzzy349VH1ozyze52MrK4aSer-uar56akfI2hPX7Ptc4oBwFmQ7WZJjalCelehEA_wnx6Jc2jldzyMokBAfx93L-HIDeW8Zirmui8MSDDFtTuODehf/w366-h400/MedicalPhysics1.jpg" width="366" /></a></div> <p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHSkXBen-JxNDZ6HwNvy9OHyGko1BwH-LETpbT7AugfmAAsszj9XVQnID1WIDoxNl_m0Q8sI-jpnE0EA0yw6qfaw1SUA8f8ue0ayQlAMrpHAqtTFtJAWiRqc6pas7UyZqHnVUT2o8BWRPfglKP0lS2dOH66_ElCq-5SM9R99mC3b3T9wYSkhbiyQtGeVBQ/s577/MedicalPhysics2.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="577" data-original-width="452" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhHSkXBen-JxNDZ6HwNvy9OHyGko1BwH-LETpbT7AugfmAAsszj9XVQnID1WIDoxNl_m0Q8sI-jpnE0EA0yw6qfaw1SUA8f8ue0ayQlAMrpHAqtTFtJAWiRqc6pas7UyZqHnVUT2o8BWRPfglKP0lS2dOH66_ElCq-5SM9R99mC3b3T9wYSkhbiyQtGeVBQ/w314-h400/MedicalPhysics2.jpg" width="314" /></a></div><br />Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com2Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-44149597026141143842024-02-23T05:00:00.124-05:002024-02-23T05:00:00.452-05:00The Rest of the Story 4<p>Allan was born in <a href="https://en.wikipedia.org/wiki/Johannesburg">Johannesburg</a>, the youngest of three children. He spent his teenage years in <a href="https://en.wikipedia.org/wiki/Cape_Town">Cape Town</a>, and was interested in debating, tennis, and acting. He also loved astronomy, which triggered an interest in physics and mathematics.
<br /><br />
At the <a href="https://en.wikipedia.org/wiki/University_of_Cape_Town">University of Cape Town</a> he studied <a href="https://en.wikipedia.org/wiki/Electrical_engineering">electrical engineering</a>, following in the footsteps of his father and brother. But he soon abandoned engineering to learn <a href="https://en.wikipedia.org/wiki/Physics">physics</a> and to engage in <a href="https://en.wikipedia.org/wiki/Mountaineering">mountaineering</a>. After he obtained his undergraduate degree, he went to England and studied physics at the <a href="https://en.wikipedia.org/wiki/Cavendish_Laboratory">Cavendish Laboratory</a> in <a href="https://en.wikipedia.org/wiki/University_of_Cambridge">Cambridge</a>. </p><p>He didn’t finish his PhD, however, because in <a href="https://en.wikipedia.org/wiki/Paul_Dirac">Paul Dirac</a>’s <a href="https://en.wikipedia.org/wiki/Quantum_mechanics">quantum mechanics</a> class he fell in love with one of his classmates, an American physics student named Barbara Seavey. He wanted to marry her but he had no money. As fortune would have it, there was a teaching position available back in Cape Town. He married Barbara and returned home to <a href="https://en.wikipedia.org/wiki/South_Africa">South Africa</a>. There he was happy, but isolated from cutting edge research. He didn’t seem posed for success in the high-power and competitive world of physics.
<br /><br />
Page 2
<br /><br />
At Cape Town Allan eventually qualified for a <a href="https://en.wikipedia.org/wiki/Sabbatical">sabbatical</a>, which Barbara wanted to spend in the United States. So they traveled to the <a href="https://en.wikipedia.org/wiki/Harvard_Cyclotron_Laboratory">Harvard cyclotron</a>, where he worked on <a href="https://en.wikipedia.org/wiki/Nucleon">nucleon</a>-nucleon scattering with <a href="https://en.wikipedia.org/wiki/Norman_Ramsey_Jr.">Norman Ramsey</a> and <a href="https://en.wikipedia.org/wiki/Richard_Wilson_(physicist)">Richard Wilson</a>. While on sabbatical leave, he was offered a position at <a href="https://en.wikipedia.org/wiki/Tufts_University">Tufts University</a>.
<br /><br />
Allan became interested in a computer imaging problem: how to make a 2-d image of the inside of an object based on <a href="https://en.wikipedia.org/wiki/Projection_(mathematics)">projections</a> taken at different angles. He published the results of this work, but it didn’t make a splash. No one seemed to care about his algorithm. So he went back to his research on high energy physics.
<br /><br />
Several years latter, researchers suddenly began to pay attention to Allan’s imaging work. Medical doctors were interested in forming two- or even three-dimensional images of the body using <a href="https://en.wikipedia.org/wiki/X-ray">X-rays</a> applied from different directions. Allan’s algorithm was exactly what they needed.
<br /><br />
These studies became fundamental to the emerging field of <a href="https://en.wikipedia.org/wiki/Medical_imaging">medical imaging</a>. It was so important, that in 1979 he—<a href="https://en.wikipedia.org/wiki/Allan_MacLeod_Cormack">Allan MacLeod Cormack</a>—and <a href="https://en.wikipedia.org/wiki/Godfrey_Hounsfield">Godfrey Hounsfield</a> shared the <a href="https://en.wikipedia.org/wiki/Nobel_Prize_in_Physiology_or_Medicine">Nobel Prize in Physiology or Medicine</a> for the invention of <a href="https://en.wikipedia.org/wiki/CT_scan">computed tomography</a>.
<br /><br />
And now you know the rest of the story.
<br /><br />
Good day!
<br /><br />
***************************
<br />
</p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkWubKD-gly2HeFtzqtS8tn_5S5rt8g4KD2TV0Ofq_7stdxBjEyf85llvxv-JDkKNXP_ImHnrXgqkp5aHAbxTK1x4xoDsJntTMa_Dh39s8p4hJW3-vD1xC9StGBcLiOIt1S6kJE7j5BMjkg-WuiaIWf8Vox_soJVruMgzK2Y2GddB-klHVGXM30fhILp3p/s4032/ImaginingTheElephant.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Imaging the Elephant: A biography of Allan MacLeod Cormack. by Christopher Vaughan, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="4032" data-original-width="3024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgkWubKD-gly2HeFtzqtS8tn_5S5rt8g4KD2TV0Ofq_7stdxBjEyf85llvxv-JDkKNXP_ImHnrXgqkp5aHAbxTK1x4xoDsJntTMa_Dh39s8p4hJW3-vD1xC9StGBcLiOIt1S6kJE7j5BMjkg-WuiaIWf8Vox_soJVruMgzK2Y2GddB-klHVGXM30fhILp3p/w150-h200/ImaginingTheElephant.jpg" title="Imaging the Elephant: A biography of Allan MacLeod Cormack. by Christopher Vaughan." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://www.amazon.com/Imagining-Elephant-Biography-MacLeod-Cormack/dp/1860949886/ref=sr_1_1?crid=2WXIUUWFW2YW8&keywords=Imaging+the+Elephant%3A+A+biography+of+Allan+MacLeod+Cormack&qid=1704321795&s=books&sprefix=imaging+the+elephant+a+biography+of+allan+macleod+cormack%2Cstripbooks%2C345&sr=1-1&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc">Imagining the Elephant:<br />A Biography of Allan MacLeod Cormack</a></i>.<br />by <a href="https://en.wikipedia.org/wiki/Kit_Vaughan">Christopher Vaughan</a>.<br /></td><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table><p>This blog post was written in the style of <a href="https://en.wikipedia.org/wiki/Paul_Harvey">Paul Harvey</a>’s “<a href="https://en.wikipedia.org/wiki/The_Rest_of_the_Story">The Rest of the Story</a>” radio program. You can find three other of my “The Rest of the Story” blog posts <a href="https://hobbieroth.blogspot.com/2016/02/the-rest-of-story.html">here</a>, <a href="https://hobbieroth.blogspot.com/2021/03/the-rest-of-story-2.html">here</a>, and <a href="https://hobbieroth.blogspot.com/2018/12/the-rest-of-story-2.html">here</a>.<br /></p><p>The content is based on Cormack’s <a href="https://www.nobelprize.org/prizes/medicine/1979/cormack/biographical">biography on the Nobel Prize website</a>. You can read about tomographic reconstruction techniques in Chapter 12 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>.
<br /><br />
<a href="https://www.joh.cam.ac.uk/1979-allan-macleod-cormack-1924-1998">Allan MacLeod Cormack</a> was born on February 23, 1924, exactly 100 years ago today. </p><p></p><p>Happy birthday Allan!
</p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-73961724503996454802024-02-16T05:00:00.070-05:002024-02-16T05:00:00.312-05:00Forman Acton (1920 – 2014)<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglwcdsCecw-ZxGLtGsUNQxAMJcE_LCl6WBmlesTA4lxtb-RplVwRJtgpnsH9msBIIAHUMOQIMhW845mvijcdKaWfMSPdausYZR5KyVtR2aiKLqDuYxCVNMcPXDwP89VggCvcTulnszxNRtEOaYrVSwUUgVLrN8pXE57Y492nSTKtQMK6K1A9zxBNrR8SeR/s4032/NumericalMethodsThatWork.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Numerical Methods That Work, by Forman Acton superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="4032" data-original-width="3024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglwcdsCecw-ZxGLtGsUNQxAMJcE_LCl6WBmlesTA4lxtb-RplVwRJtgpnsH9msBIIAHUMOQIMhW845mvijcdKaWfMSPdausYZR5KyVtR2aiKLqDuYxCVNMcPXDwP89VggCvcTulnszxNRtEOaYrVSwUUgVLrN8pXE57Y492nSTKtQMK6K1A9zxBNrR8SeR/w150-h200/NumericalMethodsThatWork.jpg" title="Numerical Methods That Work, by Forman Acton." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://bookstore.ams.org/spec-2/">Numerical Methods That Work</a></i>,<br />by Forman Acton.<br /></td></tr></tbody></table>The American computer scientist <a href="https://en.wikipedia.org/wiki/Forman_S._Acton">Forman Acton</a> died ten years ago this Sunday. In <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I cite Acton’s <i><a href="https://www.amazon.com/Numerical-Methods-that-Work-Spectrum/dp/0883854503/ref=sr_1_1?keywords=Numerical+Methods+That+Work&qid=1704367710&s=books&sr=1-1">Numerical Methods That Work</a></i>. For readers interested in using computers to model biological processes, I recommend this well written and engaging book.
<br /><br />
Before he died, Acton donated funds to establish the <a href="https://www.formanscholars.org/">Forman Acton Foundation</a>. Here is how their website describes his life:
<br /><blockquote>
Forman Sinnickson Acton was born in <a href="https://en.wikipedia.org/wiki/Salem,_New_Jersey">Salem City</a>, and he went on to change the world.
<br /><br />
Born on August 10, 1920, he began his education in the <a href="https://en.wikipedia.org/wiki/Salem_City_School_District_(New_Jersey)">Salem City school system</a> before attending private boarding school at <a href="https://en.wikipedia.org/wiki/Phillips_Exeter_Academy">Phillips Exeter Academy</a> and college at <a href="https://en.wikipedia.org/wiki/Princeton_University">Princeton University</a>. He graduated with two degrees in engineering toward the end of <a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a>, during which he served in the <a href="https://en.wikipedia.org/wiki/United_States_Army_Corps_of_Engineers">Army Corps of Engineers</a> and worked on a team involved in the <a href="https://en.wikipedia.org/wiki/Manhattan_Project">Manhattan Project</a>.
<br /><br />
After his service, he earned his doctorate in mathematics from <a href="https://en.wikipedia.org/wiki/Carnegie_Mellon_University">Carnegie Institute of Technology</a>, helped the Army develop the world’s first anti-aircraft missiles and became a pioneer in the evolving field of <a href="https://en.wikipedia.org/wiki/Computer_science">computer science</a>.
<br /><br />
Acton conducted research and taught at Princeton from 1952 to 1990, during which time he wrote textbooks on mathematics at his cabin on Woodmere Lake in Quinton Township, Salem County. When he turned 80, he joined the Lower Alloways Creek pool to stay in shape, swimming six days a week for 14 years.
<br /><br />
He died on February 18, 2014, in <a href="https://en.wikipedia.org/wiki/Woodstown,_New_Jersey">Woodstown, New Jersey</a>, but not before he anonymously donated thousands of dollars toward scholarships for Salem City School District students, some of whom were just then graduating from college. Before he passed, he made it clear to friends and confidants that he wanted these students to have access to the incredible educational experiences he enjoyed.
<br /><br />
Eight months after his passing, the Forman S. Acton Educational Foundation was officially incorporated to ensure that all of Salem’s youth also have a chance to change the world.
</blockquote>
Sometimes I will read a passage and say to myself “That’s exactly what students studying from <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i> need to hear.” I feel this way about Acton’s preface to <i><a href="https://books.google.com/books/about/Numerical_Methods_that_Work.html?id=cGnSMGSE5Y4C">Numerical Methods That Work</a></i>. Russ and I include many homework problems in <i>IPMB</i> so the student can gain experience with the art of mathematical modeling. Below, in Acton’s words, is why we do that. Just replace phrases like “solving equations numerically” with “building models mathematically” and his words apply equally well to <i>IPMB</i>.
<br /><blockquote>
Numerical equation solving is still largely an art, and like most arts it is learned by practice. Principles are there, but even they remain unreal until you actually apply them. To study numerical equation solving by watching someone else do it is rather like studying portrait painting by the same method. It just won’t work. The principle reason lies in the tremendous variety within the subject…
<br /><br />
The art of solving problems numerically arises in two places: in choosing the proper method and in circumventing the main road-blocks that always seem to appear. So throughout the book I shall be urging you to go try the problems—mine or yours.
<br /><br />
I have tried to make my explanations clear, but sad experience has shown that you will not really understand what I am talking about until you have made some of the same mistakes I have made. I hesitate to close a preface with a ringing exhortation for you to go forth to make fruitful mistakes; somehow it doesn’t seem quite the right note to strike! Yet, the truth it contains is real. Guided, often laborious, experience is the best teacher for an art. <br /></blockquote><p> </p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-6423271613364554732024-02-09T05:00:00.002-05:002024-02-09T05:00:00.134-05:00Robert Kemp Adair (1924–2020)—Notes on a Friendship<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgufTpjak0U_bEIHhJm0daVdD-7rM6ZOzCTPrvUQHab4jMYkTZf1sDaSz2NFyZDbhoIrnOblxPJVrip4ZWRR1oetOm4kpgU6GKpHPhNEjJAYVAVeIBeWLaVSdLnb18XmFblt1mylYqXasea43qRyKEriWUb0saRu8E2B3tqAClCrIR0N6NarQxX9C2YRwri/s500/Adair.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Robert Adair." border="0" data-original-height="500" data-original-width="350" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgufTpjak0U_bEIHhJm0daVdD-7rM6ZOzCTPrvUQHab4jMYkTZf1sDaSz2NFyZDbhoIrnOblxPJVrip4ZWRR1oetOm4kpgU6GKpHPhNEjJAYVAVeIBeWLaVSdLnb18XmFblt1mylYqXasea43qRyKEriWUb0saRu8E2B3tqAClCrIR0N6NarQxX9C2YRwri/w224-h320/Adair.jpg" title="Robert Adair." width="224" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Robert Adair.<br />Photo credit: <a href="https://michaelmarslanddev.com">Michael Marsland</a>/<a href="https://en.wikipedia.org/wiki/Yale_University">Yale University</a>.</td><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table>I try to write obituaries of scientists who appear in <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, but for some reason I didn’t write about <a href="https://en.wikipedia.org/wiki/Robert_Adair_(physicist)">Robert Adair</a>’s death in 2020. Perhaps the <a href="https://en.wikipedia.org/wiki/COVID-19_pandemic">covid pandemic</a> over-shadowed his demise. In Chapter 9 of <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I cite seven of his publications. He was a leader in studying the health effects (or, lack of heath effects) from <a href="https://en.wikipedia.org/wiki/Electromagnetic_field">electric and magnetic fields</a>.
<br /><br />
Recently, I read a charming article subtitled “N<a href="https://quillette.com/2024/01/12/robert-kemp-adair-notes-on-a-friendship/">otes on a Friendship</a>” about <a href="https://www.legacy.com/us/obituaries/nhregister/name/robert-adair-obituary?id=7876570">Adair</a>, written by <a href="https://en.wikipedia.org/wiki/Geoffrey_Kabat">Geoffrey Kabat</a>, the author of <i><a href="https://www.amazon.com/Getting-Risk-Right-Understanding-Science-ebook/dp/B01MAXIL21/ref=sr_1_1?crid=43LDOP7R67RT&dib=eyJ2IjoiMSJ9.IuPYbyKlCOQprQlqP9rpuA.aLvSIA7XwfcYECq3LwjQL5JcewDTOGHyGSJPcrkvxiI&dib_tag=se&keywords=Getting+Risk+Right%3A+Understanding+the+Science+of+Elusive+Health+Risks&qid=1705243742&s=books&sprefix=getting+risk+right+understanding+the+science+of+elusive+health+risks%2Cstripbooks%2C343&sr=1-1">Getting Risk Right: Understanding the Science of Elusive Health Risks</a></i>. I have <i>Getting Risk Right</i> on my to-read list. It sounds like my kind of book.<br /><br />
I admire <a href="https://www.pnas.org/doi/10.1073/pnas.2026037118">Adair</a>’s service in an infantry rifle <a href="https://en.wikipedia.org/wiki/Platoon">platoon</a> during <a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a>. I loved his <a href="https://www.amazon.com/Physics-Baseball-3rd-Robert-Adair/dp/0060084367/ref=sr_1_1?crid=17O0G5BH30V7V&dib=eyJ2IjoiMSJ9.NtgMrqlfvYmtYoySU4KProwXD7weNaV2EkMcQBdwiVCyuJ0OAva9fQCj4q-2di8-59i-bQw95xkg62LRaBXG7FIYtVBk6DkcR17Lebgf6LJIaccm0ecO6atMLlGG-qPTGyIkDjLQQJMc4Q_MYzoBiw.FCoYgV1BT8akv_iuGnGWZEt4kqXgPZgBYJA1GXQ8BU0&dib_tag=se&keywords=robert+adair&qid=1705254033&s=books&sprefix=robert+adair%2Cstripbooks%2C137&sr=1-1">book about baseball</a>. I respect his independent assessment of the seriousness of <a href="https://en.wikipedia.org/wiki/Climate_change">climate change</a>, although I don’t agree with all his conclusions. He certainly was a voice of reason in the debate about <a href="https://en.wikipedia.org/wiki/Electromagnetic_radiation_and_health">health risks of electric and magnetic fields</a>. He led a long and useful life. We need more like him.
<br /><br />
I will give <a href="https://www.geoffreykabat.com/">Kabat</a> the final word, quoting the last paragraph of his article.
<br /><blockquote>
In early October 2020, Bob’s daughter Margaret called me to tell me that Bob had died. I looked for an obituary in the <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">New York Times</a></i>, and was shocked when none appeared, likely due to the increased deaths from the pandemic. I wrote to an <a href="https://en.wikipedia.org/wiki/Epidemiology">epidemiologist</a> colleague and friend, who knew Bob’s work on ELF-EMF [<a href="https://en.wikipedia.org/wiki/Extremely_low_frequency">extremely low frequency</a> electromagnetic fields] and <a href="https://en.wikipedia.org/wiki/Microwave">microwave</a> energy, and who had served on a committee to assess possible health effects of the <a href="https://en.wikipedia.org/wiki/PAVE_PAWS">Pave Paws</a> radar array on <a href="https://en.wikipedia.org/wiki/Cape_Cod">Cape Cod</a>. My friend Bob Tarone wrote back, “Very sad to hear that. Adair was not directly involved in the Pave Paws study, but we relied heavily on his superb published papers on the biological effects of radio-frequency energy in our report. He and <a href="https://hobbieroth.blogspot.com/2013/05/eleanor-adair-1926-2013.html">his wife</a> were superb scientists. Losing too many who don’t seem to have competent replacements. Too bad honesty and truth are in such short supply in science today.” He concurred that there should have been an obituary in the <i>Times</i>.
</blockquote>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-57062012333483406742024-02-02T05:00:00.023-05:002024-02-02T05:00:00.147-05:00“Havana Syndrome”: A post mortem<div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwy1cqvItL8ySBo_nMaGnnzEka_1jJb9BCFObbaKipDqSryN3GiZsYafTcTqb0f6TJrzB5wUAHpJ1AN9-AxkaKj4_9RyV2N_hDKpH699GJphCKTVSUbKFhBUbgGeszDsAPW6vTZeD4YkoILQRCMlTWLlqsmEIFhHU5BfNMvKuqT7X8lp5ziFjHDD9aRElY/s827/HavanaSyndrome.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="“Havana Syndrome”: A Post Mortem, by Bartholomew and Baloh, superimposedo on Intermediate Physics for Medicine and Biology." border="0" data-original-height="827" data-original-width="735" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwy1cqvItL8ySBo_nMaGnnzEka_1jJb9BCFObbaKipDqSryN3GiZsYafTcTqb0f6TJrzB5wUAHpJ1AN9-AxkaKj4_9RyV2N_hDKpH699GJphCKTVSUbKFhBUbgGeszDsAPW6vTZeD4YkoILQRCMlTWLlqsmEIFhHU5BfNMvKuqT7X8lp5ziFjHDD9aRElY/w178-h200/HavanaSyndrome.jpg" title="“Havana Syndrome”: A Post Mortem, by Bartholomew and Baloh." width="178" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">“Havana Syndrome”: A Post Mortem,<br />by Bartholomew and Baloh.<br /></td></tr></tbody></table>Remember the <a href="https://en.wikipedia.org/wiki/Havana_syndrome">Havana Syndrome</a>? You don’t hear much about it anymore. Recently I read an article titled “<a href="https://journals.sagepub.com/doi/full/10.1177/00207640231208374">‘Havana Syndrome’: A Post Mortem</a>,” by <a href="https://en.wikipedia.org/wiki/Robert_Bartholomew">Robert Bartholomew</a> and <a href="https://people.healthsciences.ucla.edu/institution/personnel?personnel_id=7900">Robert Baloh</a>. These two researchers are long-time skeptics who don’t believe that the Havana Syndrome was caused by a physical attack on US and Canadian diplomats. They are also critical of the <a href="https://nap.nationalacademies.org/catalog/25889/an-assessment-of-illness-in-us-government-employees-and-their-families-at-overseas-embassies">National Academies report</a> that suggested <a href="https://en.wikipedia.org/wiki/Directed-energy_weapon">microwave weapons</a> might be responsible for the Havana Syndrome. <a href="https://medium.com/intuition/two-reports-about-the-havana-syndrome-which-should-we-believe-7cf8f94bd4d1">I came to a similar conclusion</a> in my book <i><a href="https://link.springer.com/book/10.1007/978-3-030-98774-9">Are Electromagnetic Fields Making Me Ill?</a></i>, where I wrote
<br /><blockquote>
At this time, we have no conclusive explanation for the Havana syndrome. We need
more evidence. Measuring intense beams of microwaves should be easy to do and
would not be prohibitively expensive. Until someone observes microwaves associated
with the onset of this illness, I will remain skeptical of the <a href="https://hobbieroth.blogspot.com/2021/01/an-assessment-of-illness-in-us.html">National Academies’conclusion</a>.
</blockquote>
Bartholomew and Baloh believe that the Havana Syndrome is <a href="https://en.wikipedia.org/wiki/Psychogenic_disease">psychogenic</a>. In my book, I make an analogy to <a href="https://en.wikipedia.org/wiki/Post-traumatic_stress_disorder">post traumatic stress syndrome</a>: it’s a real disease, but not one with a simple physical cause. Below I quote the abstract from Bartholomew and Baloh’s paper.
<br /><blockquote>
<b>Background</b>: Since 2016, an array of claims and public discourse have circulated in the medical community over the
origin and nature of a mysterious condition dubbed “Havana Syndrome,” so named as it was first identified in Cuba. In March 2023, the United States intelligence community concluded that the condition was a socially constructed catch-all category for an array of health conditions and stress reactions that were lumped under a single label. <br /></blockquote><blockquote><b>Aims</b>: To examine the history of “Havana Syndrome” and the many factors that led to its erroneous categorization as a novel clinical entity. <br /></blockquote><blockquote> <b>Method</b>: A review of the literature. <br /></blockquote><blockquote><b>Results/Conclusions</b>: Several factors led to the erroneous classification of “Havana Syndrome” as a novel entity
including the failure to stay within the limitations of the data; the withholding of information by intelligence agencies, the prevalence of popular misconceptions about psychogenic illness, the inability to identify historical parallels; the role of the media, and the mixing of politics with science.
</blockquote><p>
In <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss the health effects of electromagnetic fields. It’s crucial to understand the physics that underlies tissue-field interactions before postulating a nefarious role for electromagnetic fields in human health. If you suggest an idea that is not consistent with physics, prepare to be proved wrong.</p><p style="text-align: left;">A final note: Baloh and Bartholomew write
<br /></p><blockquote>
In September
2021, the head of a U.S. Government panel investigating
“Havana Syndrome,” <a href="https://en.wikipedia.org/wiki/Pamela_L._Spratlen">Pamela Spratlen</a>, was forced to
resign after refusing to rule out [mass psychogenic illness] as a possible cause... A former senior C.I.A.
operative wrote that Spratlen’s position was “insulting to
victims and automatically disqualifying.”
</blockquote>I think we all owe Pamela Spratlen an apology. Thank you for your service. <br /><p></p><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/ljf1TVWTSlQ" width="320" youtube-src-id="ljf1TVWTSlQ"></iframe></div><p></p><p style="text-align: center;"> Was “Havana Syndrome” a case of mass hysteria? DW News.</p><p style="text-align: center;"><a href="https://www.youtube.com/embed/ljf1TVWTSlQ">https://www.youtube.com/embed/ljf1TVWTSlQ </a><br /></p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/4IWnhmqVsPc" width="320" youtube-src-id="4IWnhmqVsPc"></iframe></div><div style="text-align: center;"> </div><div style="text-align: center;">Havana Syndrome: Tilting at Windmills?</div><p></p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=4IWnhmqVsPc">https://www.youtube.com/watch?v=4IWnhmqVsPc</a><br /> </p><p style="text-align: center;"></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/izeVdfkYnIo" width="320" youtube-src-id="izeVdfkYnIo"></iframe></div><br /></div><div style="text-align: center;"> The Havana Syndrome: A Disorder of Neuropolitics?</div><p></p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=izeVdfkYnIo">https://www.youtube.com/watch?v=izeVdfkYnIo</a><br /></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-18869045441928612912024-01-26T05:00:00.187-05:002024-01-26T05:00:00.147-05:00Craig Henriquez (1959–2023)<p>I just learned that my friend <a href="https://en.wikipedia.org/wiki/Craig_Henriquez">Craig Henriquez</a> passed away last summer. <a href="https://today.duke.edu/2023/08/duke-flags-lowered-craig-henriquez-biomedical-engineer-and-associate-vice-provost-faculty">Craig</a> earned his PhD at <a href="https://en.wikipedia.org/wiki/Duke_University">Duke University</a> in their Department of Biomedical Engineering under the guidance of the renowned bioelectricity expert <a href="https://en.wikipedia.org/wiki/Robert_Plonsey">Robert Plonsey</a>. His 1988 dissertation, titled “Structure and Volume Conductor Effects on Propagation in Cardiac Tissue,” was closely related to work I was doing at that time. <a href="https://facultyadvancement.duke.edu/news/memoriam-craig-s-henriquez-0/">Craig</a> sent me a copy of his dissertation after he graduated. I really wanted to read it, but I was swamped with my my new job at the <a href="https://en.wikipedia.org/wiki/NIH_Intramural_Research_Program">National Institutes of Health</a> and helping care for my newborn daughter Stephanie. There wasn’t time to read it at work, and when I got home it was my turn to watch the baby, as my wife had been with her all day. The solution was to read <a href="https://www.hallwynne.com/obituaries/Craig-Henriquez?obId=28817385">Craig</a>’s dissertation out loud to Stephanie as she crawled around in her play pen. She seemed to like the attention and I got to learn about Craig’s work.
<br /><br />
Craig and I are nearly the same age. He was born in 1959 and I in 1960. Our careers progressed along parallel lines. After he graduated he stayed at Duke and joined the faculty. I recall he told me at the time that he didn’t know if he would make a career in academia, but he certainly did. He was on the Duke faculty for 35 years. In the early 1990s three young researchers at Duke—Craig, <a href="https://en.wikipedia.org/wiki/Natalia_Trayanova">Natalia Trayanova</a>, and <a href="https://bme.duke.edu/faculty/wanda-neu">Wanda Krassowska</a>—were all from my generation. They were my friends, collaborators, and sometimes competitors as we worked to establish the <a href="https://en.wikipedia.org/wiki/Bidomain_model">bidomain model</a> as the state-of-the-art representation of the electrical properties of cardiac tissue.
<br /><br />
In my <a href="https://pubs.aip.org/aip/bpr/article-abstract/2/4/041301/134308/Bidomain-modeling-of-electrical-and-mechanical?redirectedFrom=fulltext">recent review about bidomain modeling</a> (<i><a href="https://pubs.aip.org/aip/bpr">Biophysics Reviews</a></i>, Volume 2, Article 041301, 2021) , I wrote (referring to myself in third person, as required by the journal; in the quotes below references are removed):</p><p></p><blockquote>Roth’s calculation was not the first attempt to solve the active
bidomain model using a numerical method. In 1984, Barr and Plonsey
had developed a preliminary algorithm to calculate action potential
propagation in a sheet of cardiac tissue. Simultaneous with Roth’s
work, Henriquez and Plonsey were examining propagation in a perfused
strand of cardiac tissue. For the next several years,
Henriquez continued to improve bidomain computational methods
with his collaborators and students at Duke. His 1993 article published
in <i>Critical Reviews of Biomedical Engineering</i> remains the definitive
summary of the bidomain model.
</blockquote>
I’ve cited his 1993 review article (<i>Crit. Rev. Biomed. Eng., </i>Volume 21, Pages 1–77) many times, including in <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>. It’s a classic.
<br /><br />
Craig and I were both interested in determining if <a href="https://scholars.duke.edu/person/cspach">Madison Spach</a>’s electrical potential data from cardiac tissue samples should be interpreted as evidence of discontinuous propagation (<a href="https://www.ahajournals.org/doi/10.1161/01.RES.48.1.39">Spach’s hypothesis</a>) or a bath effect.
<br /><blockquote>
The original calculations of action potential propagation in a continuous
bidomain strand perfused by a bath hinted at different
interpretations of Spach’s data. As discussed earlier, the wave front is
not one-dimensional because its profile varies with depth below the
strand surface. The same effect occurs during propagation
through a perfused planar slab, more closely resembling Spach’s experiment.
The conductivity of the bath is higher than the conductivity
of the interstitial space, so the wave front propagates ahead on the surface
of the tissue and drags along the wave front deeper below the surface,
resulting in a curved front. The extra electrotonic load
experienced at the surface slows the rate of rise and the time constant
of the action potential foot. Plonsey, Henriquez, and
Trayanova analyzed this effect, and subsequently so did Henriquez
and his collaborators and Roth.
</blockquote><p>
Craig became an associate editor of the <i><a href="https://www.embs.org/tbme/">IEEE Transactions on Biomedical Engineering</a></i>, and he would often send me papers to review. He was a big college basketball fan. We would email each other around March, when our alma maters—my <a href="https://kuathletics.com/sports/mbball/">Kansas Jayhawks</a> and his <a href="https://goduke.com/sports/mens-basketball">Duke Blue Devils</a>—would face off in the <a href="https://en.wikipedia.org/wiki/NCAA_Division_I_men%27s_basketball_tournament">NCAA tournament</a>. His research interests turned to nerves and the brain, and he co-directed a <a href="https://dibs.duke.edu/centers/center-neural-engineering-neurotechnology/">Center of Neuroengineering</a> at Duke. He eventually chaired Duke’s biomedical engineering department, and at the time of his death he was an Associate Vice Provost.
<br /><br />
I found out about Craig’s death when I was submitting a paper to a journal. This publication asks authors to suggest potential reviewers, and I was about to put Craig’s name down as a person who would give an honest and constructive assessment. I googled him to get his current email address, and discovered the horrible news. What a pity. I will miss him. </p><p></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDaACUjgMnWxV_CAE1cEKm7lBEBvIq1jhvqgCBr-bwjjKb4zLqodeUSAeENrY2MoXWJV3JLEKVaqpch5esnsEdc_oOcDP7J1dU_8Eh_KZZrXIjgd0T5kC3F9rJvYQyg0sNgPvrQS7ylILjr0iNvwPgMXq81WI2c0J2pr4bfzof2pldPk9r_VCsco9MO0tS/s531/Henriquez.jpg" style="margin-left: auto; margin-right: auto;"><img alt="Short bio published in the IEEE Transactions on Biomedical Engineering in January, 1990." border="0" data-original-height="278" data-original-width="531" height="210" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDaACUjgMnWxV_CAE1cEKm7lBEBvIq1jhvqgCBr-bwjjKb4zLqodeUSAeENrY2MoXWJV3JLEKVaqpch5esnsEdc_oOcDP7J1dU_8Eh_KZZrXIjgd0T5kC3F9rJvYQyg0sNgPvrQS7ylILjr0iNvwPgMXq81WI2c0J2pr4bfzof2pldPk9r_VCsco9MO0tS/w400-h210/Henriquez.jpg" title="Short bio published in the IEEE Transactions on Biomedical Engineering in January, 1990." width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Short bio published in the <i>IEEE Transactions on Biomedical Engineering</i> in January, 1990.</td></tr></tbody></table><br /><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/OiSiLwP1ZPo" width="320" youtube-src-id="OiSiLwP1ZPo"></iframe></div><p></p><p style="text-align: center;"> Craig Henriquez talking about cardiac tissue and the bidomain model.</p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=OiSiLwP1ZPo">https://www.youtube.com/watch?v=OiSiLwP1ZPo</a><br /></p><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-58843057395619416372024-01-19T05:00:00.385-05:002024-01-19T05:00:00.137-05:00The Alaska Airlines Boeing 737 Max Accident<p>Last week, the plug door panel on an <a href="https://en.wikipedia.org/wiki/Alaska_Airlines">Alaska Airlines</a> <a href="https://en.wikipedia.org/wiki/Boeing_737_MAX">Boeing 737 Max</a> airplane detached during flight, leaving a gaping hole in the side of the <a href="https://en.wikipedia.org/wiki/Fuselage">fuselage</a>. Fortunately, the plane was able to land safely and no one was seriously injured in the accident. I thought it would be fun to analyze this event from the point of view of physics in medicine and biology. Let me stress that I have no inside information about this accident, and I am not an aviation expert. I’m just an old physics professor playing around trying to make sense of information reported in the press.
<br /><br />
Let’s calculate the pressure difference between the normal cabin pressure of a 737 Max and the outside air pressure. The typical pressure at sea level is 1 <a href="https://en.wikipedia.org/wiki/Standard_atmosphere_(unit)">atmosphere</a>, which is about 100,000 <a href="https://en.wikipedia.org/wiki/Pascal_(unit)">pascals</a>. However, in most planes the <a href="https://en.wikipedia.org/wiki/Cabin_pressurization">cabin pressure</a> is maintained somewhat lower than an atmosphere. Usually the cabin pressure corresponds to the air pressure at about 6000 feet, which is 1800 <a href="https://en.wikipedia.org/wiki/Metre">meters</a>. The air pressure falls <a href="https://en.wikipedia.org/wiki/Exponential_decay">exponentially</a> with height. Problem 42 in Chapter 3 of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i> asks the reader to calculate the length constant corresponding to this decay. If you solve that problem, you get a length constant of about 8700 meters. So, the cabin pressure in the plane should have been around <a href="https://en.wikipedia.org/wiki/Exponential_function">exp</a>(–1800/8700) = 0.81 atm before the door panel blew out.
<br /><br />
The mid-air depressurization occurred at about 16,000 feet (4900 meters). I assume this means 16,000 feet above <a href="https://en.wikipedia.org/wiki/Sea_level">sea level</a>. Therefore, the air pressure outside the plane just before the door panel failed was about exp(–4900/8700) = 0.57 atmosphere. Thus, the pressure difference between the inside and outside was approximately 0.81 – 0.57 = 0.24 atmospheres, or 24,000 pascals.
<br /></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqidbGmSxZRmaBKS6LvgnZUO5gxAimNTdNG42gsn0RJIzgGO8u3Ipi5gmkcpj_hV5FOlwi3Lqni6LnFtbBaRLGFLyX4IhS55Sx22UrqaqCLPVXPOq_rk_KTU24D_fuxJ9M8r5_wYyJLx7NU55bT0oJuvVuXk5kEIqYR4nPQ_vvynqGvGpFN4ynj9DLFByZ/s1023/Magdeburg.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Otto von Guerick’s Magdeburg hemispheres experiment." border="0" data-original-height="825" data-original-width="1023" height="161" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqidbGmSxZRmaBKS6LvgnZUO5gxAimNTdNG42gsn0RJIzgGO8u3Ipi5gmkcpj_hV5FOlwi3Lqni6LnFtbBaRLGFLyX4IhS55Sx22UrqaqCLPVXPOq_rk_KTU24D_fuxJ9M8r5_wYyJLx7NU55bT0oJuvVuXk5kEIqYR4nPQ_vvynqGvGpFN4ynj9DLFByZ/w200-h161/Magdeburg.jpg" title="Otto von Guerick’s Magdeburg hemispheres experiment." width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Otto von Guerick’s famous <br /><a href="https://en.wikipedia.org/wiki/Magdeburg_hemispheres">Magdeburg hemispheres</a> experiment.</td></tr></tbody></table><p style="text-align: left;">The door looks to me like it is about 5 feet by 3 feet, or 15 square
feet, which is 1.4 square meters. So, the force acting on the door was
(24,000 pascals)×(1.4 square meters) = 34,000 <a href="https://en.wikipedia.org/wiki/Newton_(unit)">newtons</a>, or 7600 <a href="https://en.wikipedia.org/wiki/Pound_(force)">pounds</a>
(almost 4 <a href="https://en.wikipedia.org/wiki/Short_ton">tons</a>). That’s why it’s so important that the door panel be
attached securely to the fuselage; air pressure differences can produce
large forces, even if the pressure difference is only a quarter of an
atmosphere. If you don’t believe me, just ask <a href="https://en.wikipedia.org/wiki/Otto_von_Guericke">Otto von Guericke</a>, who in 1654 showed how <a href="https://en.wikipedia.org/wiki/Magdeburg_hemispheres">two hemispheres</a> held together by air pressure could not be pulled apart by two teams of eight horses.
<br /></p><div><div>
What sort of biological effects would a sudden drop of air pressure have? I expect the biggest effect would be on the ears. The <a href="https://en.wikipedia.org/wiki/Eardrum">eardrum</a> separates the outside air from an air-filled region in the middle ear. Normally there’s no pressure difference across the ear drum, except for the tiny pressures associated with sound. But pop that door off the plane and you suddenly have a quarter atmosphere pressure difference. Some of the people on the plane complained of plugged ears following the accident. Your <a href="https://en.wikipedia.org/wiki/Eustachian_tube">Eustachian tubes</a> that connect your ears to your throat will eventually allow you to equilibrate the air pressure across the eardrum, but it may take a while, especially if you have a cold so your tubes are congested.
<br /><br />
How significant is an abrupt change of 0.24 atmospheres? The <a href="https://en.wikipedia.org/wiki/Empire_State_Building">Empire State Building</a> is 1250 feet tall (380 meters), which means the top and bottom of the building have a pressure difference of only about 0.04 atm. If you hop on an express elevator and zoom to the observation deck at the top of the skyscraper, you won’t cry out in pain, but you might notice your ears pop. The cabin pressure in a plane typically falls from 1 atm to about 0.8 atm as the plane rises. That’s why our ears feel uncomfortable. But that change occurs slowly, so it is not too bothersome. Normal <a href="https://en.wikipedia.org/wiki/Parachuting">skydivers</a> jump at about 10,000 feet (3000 meters), so during their descent they experience a drop in pressure of about 0.3 atm. Skydivers often experience noticeable ear pressure, but any associated pain is not severe enough to keep them from jumping again. Unfortunately, the pressure decompression on the 737 Max happened much more quickly than the decompression during a parachute jump, so I would expect any ear problems would have been greater for the passengers on the plane than for a typical skydiver.
<br /><br />
Pressures under water are much greater than those in the air, because water is more dense than air. Dive into a pool to a depth of 32 feet (10 meters) and the pressure on your eardrum increases by one atmosphere. Swimmers typically have worse ear problems than airplane passengers. It is one reason why you have to use <a href="https://en.wikipedia.org/wiki/Scuba_diving">scuba</a> equipment if you’re diving deep. It’s also why submarine accidents are so much more severe than airplane depressurizations. Remember last year when that <a href="https://en.wikipedia.org/wiki/Submersible">submersible</a> was going down to the wreckage of the <a href="https://en.wikipedia.org/wiki/Titanic">Titanic</a> and suffered the catastrophic implosion? It was going to a depth of 13,000 feet (4000 meters), which means the pressure difference between the inside and outside of the sub was about 400 atmospheres! You can survive a hole in the wall of a 737 Max, but not one in a Titanic-visiting submersible.
<br /><br />
The <a href="https://en.wikipedia.org/wiki/Emergency_oxygen_system">airplane’s oxygen masks</a> dropped when the hole opened in the 737 Max. Did people really need the oxygen? The airplane altitude was 16,000 feet when the accident occurred. <a href="https://en.wikipedia.org/wiki/Mount_Everest">Mount Everest</a> is 29,000 feet high (8800 meters). A few people have climbed to the peak of Everest without using <a href="https://en.wikipedia.org/wiki/High_altitude_breathing_apparatus">supplemental oxygen</a>, but most carry an oxygen tank. The <a href="https://en.wikipedia.org/wiki/Everest_base_camps">Everest base camp</a> is 17,600 feet (5300 meters). Climbers often experience mild symptoms of altitude sickness at base camp, but for most it is not debilitating. I suspect that if the passengers on that 737 Max flight hadn’t put on their mask they would have survived, but it might have had an impact on their ability to think straight. And everyone is different; some are more susceptible to mild <a href="https://en.wikipedia.org/wiki/Asphyxia">oxygen deprivation</a> than others. Certainly, the safe thing to do was to put on the mask.
<br /><br />
What would have happened if the door hadn’t blow out until the plane reached its cruising altitude of 35,000 feet (11,000 meters). Now you are well above the height of Mount Everest. The outside air pressure would be about 0.28 atmospheres. You would go unconscious (and probably die) if you didn’t promptly put on your mask. The pressure difference between the outside pressure and the cabin pressure would be over half an atmosphere. The odds of being sucked out of the plane during rapid decompression would have been higher. Yikes! The passengers on that 737 Max were lucky that door was very insecurely
attached, and not just modestly insecurely attached. If you are going to
have a in-flight disaster, it is best to have it as soon after takeoff
as possible, before your altitude gets too high. <br /></div><div> </div><div><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzMqG8j6lWKih3VS3HLqjmaroeD3cKKgHGB7LdM4CW6fzcu5vOQOxtSVatNmS9I56wbaFLTT0Qj6gNAjZ2OZKLa1zznXs3DdbaHFpiMgNUXULo48v_7USisPZCZ_LxTU-7T6GvborapyuikI-7Gf79uPMfLnqKoD2CVaQCC_uAxOmZ0RjpMcy-dp7BqfHH/s4032/PhysicsWithIllustrativeExamples1.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="4032" data-original-width="3024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgzMqG8j6lWKih3VS3HLqjmaroeD3cKKgHGB7LdM4CW6fzcu5vOQOxtSVatNmS9I56wbaFLTT0Qj6gNAjZ2OZKLa1zznXs3DdbaHFpiMgNUXULo48v_7USisPZCZ_LxTU-7T6GvborapyuikI-7Gf79uPMfLnqKoD2CVaQCC_uAxOmZ0RjpMcy-dp7BqfHH/w150-h200/PhysicsWithIllustrativeExamples1.jpg" width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://www.amazon.com/Physics-Illustrative-Examples-Medicine-Biology/dp/1461270510/ref=sr_1_5?keywords=Physics+With+Illustrative+Examples+From+Medicine+and+Biology&qid=1705320226&s=books&sr=1-5&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc">Physics With Illustrative Examples<br />From Medicine and Biology</a></i>.<br />by Benedek and Villars.<br /></td></tr></tbody></table><a href="https://en.wikipedia.org/wiki/George_Benedek">George Benedek</a> and <a href="https://en.wikipedia.org/wiki/Felix_Villars">Felix Villars</a>, in the first volume of their classic textbook <i><a href="https://hobbieroth.blogspot.com/2012/09/benedek-and-villars-volume-1.html">Physics With Illustrative Examples From Medicine and Biology</a></i>, discuss the effects of low oxygen.<br /></div><div></div><blockquote><div>Below 10,000 ft (3150) there is no detectable effect on performance and respiration and heart rates are unaffected. Between 10,000 and 15,000 ft (3150–4570 m) is a region of so-called "compensated <a href="https://en.wikipedia.org/wiki/Hypoxia_(environmental)">hypoxia</a>"... There is a measurable increase in heartbeat and breathing rate, but only a slight loss in efficiency in performing complex tasks. Between 15,000 and 20,000 ft (4570–6100 m), however, dramatic changes start to occur. The respiratory and heart rates increase markedly; there is a loss of critical judgment and muscular control, and a dulling of the senses. Emotional states can vary widely from lethargy to excitation with euphoria and even hallucinations... The final fatal regime is the altitude region from 20,000 to 25,000 ft (6100–7620 m).<br /></div></blockquote><p>Perhaps those few Mount Everest climbers who don’t carry an oxygen tank can only survive their ordeal by <a href="https://en.wikipedia.org/wiki/Altitude_training">training their body to adapt to high altitudes</a>.</p><p>Benedek and Villars also recount a fascinating story about oxygen deprivation from the early years of <a href="https://en.wikipedia.org/wiki/Hot_air_ballooning">ballooning</a>, based on an account written by <a href="https://en.wikipedia.org/wiki/Gaston_Tissandier">Gaston Tissandier</a>. <br /></p><p></p><blockquote>These various symptoms are shown very clearly in the tragic balloon ascent of the “Zenith” carrying the balloon pioneers Tissandier, Sivel, and Croce-Spinelli on April 15, 1875... The balloon’s maximum elevation as recorded on their instruments was 8600 m. Though gas bags containing 70% oxygen were carried by the balloonists, the rapid and insidious effect of hypoxia reduced their judgment and muscular control and prevented their use of the oxygen when it was most needed. Though these balloonists were indeed trying to establish an altitude record, their account shows clearly that their judgment was severely impaired during critical moments near the maximum tolerable altitudes. As they were on the verge of losing consciousness at 7450 m they decided to throw out the ballast and rise even higher. They lost consciousness above this altitude, but by good fortune the balloon descended rapidly after reaching 8600 m. On falling to about 6500 m the balloonists revived and—under the influence of the hypoxia did exactly the wrong thing once again—they threw out ballast! The second rise to high elevation killed Croce-Spinelli and Sivel.<br /></blockquote><p></p><div>Let us hope we have no more 737 Max door panels detaching in flight. I think we were lucky that no one was hurt this time. </div><div> </div><div>I’ll end with a <a href="https://upjoke.com/737-max-jokes">737 Max joke</a>. What's the difference between the <a href="https://en.wikipedia.org/wiki/SARS-CoV-2">covid-19 virus</a> and the 737 Max? Covid is airborne. (<a href="https://en.wikipedia.org/wiki/Rimshot">Rimshot</a>).<br /></div><div> </div><div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/yMmQ-v0izPk" width="320" youtube-src-id="yMmQ-v0izPk"></iframe></div><br /></div><div style="text-align: center;"> A video from inside the plane after the 737 Max door panel detached.<br /></div></div>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-86346841352734869562024-01-12T05:00:00.108-05:002024-01-12T05:00:00.148-05:00The First Log-Log Plot<p>In Chapter 2 of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss <a href="https://en.wikipedia.org/wiki/Log%E2%80%93log_plot">log-log plots</a>. Have you ever wondered who made the first log-log plot? The honor goes to French mathematician and engineer <a href="https://en.wikipedia.org/wiki/L%C3%A9on_Lalanne">Léon Lalanne</a> (1811–1892), who was interested in using <a href="https://en.wikipedia.org/wiki/Infographic">infographics</a> to aid in <a href="https://en.wikipedia.org/wiki/Computation">computation</a>. Let me take you through his idea.
<br /><br />
Start with a sheet of <a href="https://incompetech.com/graphpaper/logarithmic/">log-log graph paper</a>, one cycle in each direction. </p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Fc3jIVDfWKk9CLxVLxQFl6JaapU_seE3dyQ65qr9c81HiwLwIdnPnGxRZUspwBwowqwT6qIJ5xcq-fQA3UmazZR66rJiWS2EyXIFE9FivewNEUJcjUcZVKMRfmDdnH83Bv9OrVD6brlcxX5JiXdfHTpu1MwYyijqHw5-aF2emVfIyyuNwntT59f_yWR-/s1419/Lalanne1.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A sheet of log-log graph paper, one cycle in each direction." border="0" data-original-height="1419" data-original-width="1418" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg1Fc3jIVDfWKk9CLxVLxQFl6JaapU_seE3dyQ65qr9c81HiwLwIdnPnGxRZUspwBwowqwT6qIJ5xcq-fQA3UmazZR66rJiWS2EyXIFE9FivewNEUJcjUcZVKMRfmDdnH83Bv9OrVD6brlcxX5JiXdfHTpu1MwYyijqHw5-aF2emVfIyyuNwntT59f_yWR-/w320-h320/Lalanne1.jpg" title="A sheet of log-log graph paper, one cycle in each direction." width="320" /></a><br /></p><p style="text-align: left;">
The lines in the bottom left are far apart, so let’s add a few more so it’s easier to make accurate estimates. </p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAfjifXL8rnp749leUOw49OUctjSy7Q7fRImxzSWJ4sEcEWFnl7NkIOld1JCimwg8D66u_MmzZ3n8jXm85vykducFkyuBZRGb_szpYXBDr7qHMwwURxR_FbQTZjPMKpmM2F5T1xvhCPPgZjqzp_2JwHKBLaEs5tvKvjoZZ41GjiPglaJ6pbDauFFzPUPpk/s1415/Lalanne2.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A sheet of log-log graph paper, one cycle in each direction, with added lines." border="0" data-original-height="1389" data-original-width="1415" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAfjifXL8rnp749leUOw49OUctjSy7Q7fRImxzSWJ4sEcEWFnl7NkIOld1JCimwg8D66u_MmzZ3n8jXm85vykducFkyuBZRGb_szpYXBDr7qHMwwURxR_FbQTZjPMKpmM2F5T1xvhCPPgZjqzp_2JwHKBLaEs5tvKvjoZZ41GjiPglaJ6pbDauFFzPUPpk/w320-h314/Lalanne2.jpg" title="A sheet of log-log graph paper, one cycle in each direction, with added lines." width="320" /></a><br /></p><p style="text-align: left;">Next, following Lalanne, add a bunch of diagonal lines connecting points of equal value on the vertical and horizontal axes. Label them, so they’re easy to read. </p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqDHcu7SVOeY_2vY_kqpDIOLgiQS9oa4SxS0PFh5YPFCLjkNmgjbl8T4VXVcEoCaf8JIS5ISb0bTi68gcfHdTAF_h2D80Mngb7OalfF0lY0GEJphjlA1nXdf51pDbBbPnLL9zWtUtc9pkQIf-apVZ7l6fgiBq5IBJSA516bBjfjcWn3-es_Rd4Y3vaVm5-/s1415/Lalanne3.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A multiplication table, created using log-log graph paper." border="0" data-original-height="1389" data-original-width="1415" height="314" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgqDHcu7SVOeY_2vY_kqpDIOLgiQS9oa4SxS0PFh5YPFCLjkNmgjbl8T4VXVcEoCaf8JIS5ISb0bTi68gcfHdTAF_h2D80Mngb7OalfF0lY0GEJphjlA1nXdf51pDbBbPnLL9zWtUtc9pkQIf-apVZ7l6fgiBq5IBJSA516bBjfjcWn3-es_Rd4Y3vaVm5-/w320-h314/Lalanne3.jpg" title="A multiplication table, created using log-log graph paper." width="320" /></a></div><p style="text-align: left;">What we’ve just invented is a log-log plot to do multiplication. For example, suppose we want to multiply 3.2 by 6.8. We find the value of 3.2 on the vertical axis, and draw a horizontal line (solid red). Then we find 6.8 on the horizontal axis and draw a vertical line (dashed red). Where the two lines intersect gives the product. We estimate it by seeing what are the closest diagonal lines. The intersection is between 20 and 22.5. I would guess it’s a little closer to 22.5 than 20, so I’ll estimate the product as 22.0. I’m pretty confident that I have the result correct to within ± 0.5. If I do the calculation on an electronic calculator, I get 21.76. My answer is off by 1.1%. Not bad.</p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrSDKJk2iCah0uqKozTi_ZKASaA1Mth5uGgBiZpx5oPDwaNlhnCxRzHgro0wQcwFGVfmMbfvyK2S-ac9wSxTGI-IBrMIRwsmAgM3RU1zoOYESVLISwYJyxSwa-Y_OocHWlyAExv8xUta9wxj_0ytJEMRXMdovrNkU11kcv8Pi2HGsW4LmoG09FbaEXVS7k/s1407/Lalanne4.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="An example using a multiplication table, created using log-log graph paper." border="0" data-original-height="1386" data-original-width="1407" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrSDKJk2iCah0uqKozTi_ZKASaA1Mth5uGgBiZpx5oPDwaNlhnCxRzHgro0wQcwFGVfmMbfvyK2S-ac9wSxTGI-IBrMIRwsmAgM3RU1zoOYESVLISwYJyxSwa-Y_OocHWlyAExv8xUta9wxj_0ytJEMRXMdovrNkU11kcv8Pi2HGsW4LmoG09FbaEXVS7k/w320-h315/Lalanne4.jpg" title="An example using a multiplication table, created using log-log graph paper." width="320" /></a><br /></p><p style="text-align: left;">You can do other sorts of calculations with this one sheet of log-log paper. For instance, below I plot a green line with a slope of one half, which lets me calculate square roots. Really, this is just a plot of <i>y</i> = <i>x</i><sup>1/2</sup> on log-log paper. Because my log-log plot is only one cycle in each direction, the green line lets me calculate square roots of the numbers one through ten. To get the roots of ten through one hundred, I need to add a second, parallel line (green dashed). </p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVbd8lJEke8TNbmLm9uQB4sR3pmYo4kcTrbKyEqd-H4PMTagsaVGC3rIp_9m0nJPwCYTtN0VFbfd5kuXqJ6Sua7LWjHBseppTdAGhAGwPvuWZYQd1P7ZBqbW2g1xKHBrTXPj97R45SeI7jCXXa_Qba7rUjxC9oJiOYk4h60hK-nTeuwLj9P-JyrstlLprN/s1419/Lalanne5.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A square root calculator, created using log-log graph paper." border="0" data-original-height="1383" data-original-width="1419" height="312" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVbd8lJEke8TNbmLm9uQB4sR3pmYo4kcTrbKyEqd-H4PMTagsaVGC3rIp_9m0nJPwCYTtN0VFbfd5kuXqJ6Sua7LWjHBseppTdAGhAGwPvuWZYQd1P7ZBqbW2g1xKHBrTXPj97R45SeI7jCXXa_Qba7rUjxC9oJiOYk4h60hK-nTeuwLj9P-JyrstlLprN/w320-h312/Lalanne5.jpg" title="A square root calculator, created using log-log graph paper." width="320" /></a><br /></p><p style="text-align: left;"><br />
To calculate the square root of 77, I find 7.7 on the horizontal axis, go up to the dashed line, and then extrapolate over to the vertical axis. I estimate the result is about 8.8. When I use my electronic calculator, I get 8.775, so my estimate was accurate to about 0.3%. </p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3gcIrOktiLC9dlRI0CIFu-tMEm9ku_nm2Jk4WN9ErM3__sXe8h0fv59PuN7twKzvbTQbVsLEfoSO8ro3wu0mluiDxNo-0wknidmd3H-cWgfCnkezCS30BmBYnmGEmzJjL_mwDH5Uv10n_emn6DDF0g4C9THqSWhhIsaFOGhUW-fRbzyoxvGrqSjv_wvCd/s1410/Lalanne6.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="An example using a square root calculator, created using log-log graph paper." border="0" data-original-height="1387" data-original-width="1410" height="315" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3gcIrOktiLC9dlRI0CIFu-tMEm9ku_nm2Jk4WN9ErM3__sXe8h0fv59PuN7twKzvbTQbVsLEfoSO8ro3wu0mluiDxNo-0wknidmd3H-cWgfCnkezCS30BmBYnmGEmzJjL_mwDH5Uv10n_emn6DDF0g4C9THqSWhhIsaFOGhUW-fRbzyoxvGrqSjv_wvCd/w320-h315/Lalanne6.jpg" title="An example using a square root calculator, created using log-log graph paper." width="320" /></a><br /></p><p style="text-align: left;"><br />
Of course, you could do all sorts of other calculations. Lalanne included many in his “universal calculator” that he had printed and posted in public places. Basically, the universal calculator is meant to compete with the <a href="https://en.wikipedia.org/wiki/Slide_rule">slide rule</a> (see my discussion of <a href="https://link.springer.com/book/10.1007/978-3-319-12682-1"><i>IPMB</i></a> and the slide rule <a href="https://hobbieroth.blogspot.com/2023/09/the-slide-rule.html">here</a>). His charts never were as popular as the slide rule, perhaps because it’s more fun to slide the little rules than it is to look at a busy chart.
</p><br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKNZ8kzQGba1TQ-OeG9tcNF4MuKGdJxBwzrL-hoGJ6VvV-ED7Y7srKudDf-uSkZBo6Wtb41nQoCmrVO3p0sjoAzAuP95ZV-zDQtYIz1-iSHnI8xsmxJxoZVtAHXHeh-4Yr_u0RgvLZVQMlrtA9c3x6cKpbw54zuW1TnN4kQh6e1ZA7JCbqri5RrrC1LF36/s1511/Lalanne7.jpg" style="margin-left: auto; margin-right: auto;"><img alt="Léon Lalanne’s“Universal Calculator,” or “Abacus” (1843)." border="0" data-original-height="1511" data-original-width="1218" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgKNZ8kzQGba1TQ-OeG9tcNF4MuKGdJxBwzrL-hoGJ6VvV-ED7Y7srKudDf-uSkZBo6Wtb41nQoCmrVO3p0sjoAzAuP95ZV-zDQtYIz1-iSHnI8xsmxJxoZVtAHXHeh-4Yr_u0RgvLZVQMlrtA9c3x6cKpbw54zuW1TnN4kQh6e1ZA7JCbqri5RrrC1LF36/w323-h400/Lalanne7.jpg" title="Léon Lalanne’s“Universal Calculator,” or “Abacus” (1843)." width="323" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Léon Lalanne’s “Universal Calculator,”<br />or “Abacus” (1843).<br /></td></tr></tbody></table><br />Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-4399146763457761752024-01-05T05:00:00.113-05:002024-01-05T05:00:00.245-05:00Basic Rheology for Biologists<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgI5TxIdOHZ7ukuPLBYjgOS6SW2jSPI8NsgAJLN-bxr1rS3ZaZh8bzX4WlhpN_dTE6hT68cmQdbNHg-OZnTlVP779_avX7O7n7_tt-kr9FqEmQy3HgobK5rkOLEISh1rUwAkrrbROTli520S7rzlSbxLvDujLGz5Y2FlW4fGs5MrXk2qKtIJs9FxKBxjw7p/s841/CellMechanics.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="841" data-original-width="757" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgI5TxIdOHZ7ukuPLBYjgOS6SW2jSPI8NsgAJLN-bxr1rS3ZaZh8bzX4WlhpN_dTE6hT68cmQdbNHg-OZnTlVP779_avX7O7n7_tt-kr9FqEmQy3HgobK5rkOLEISh1rUwAkrrbROTli520S7rzlSbxLvDujLGz5Y2FlW4fGs5MrXk2qKtIJs9FxKBxjw7p/w180-h200/CellMechanics.jpg" width="180" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://shop.elsevier.com/books/cell-mechanics/wang/978-0-12-370500-6"><i>Cell Mechanics</i></a>.<br /></td></tr></tbody></table>In Chapter 1 of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss ideal solids and ideal liquids. Ideal solids are covered in Section 1.10, which introduces <a href="https://en.wikipedia.org/wiki/Stress_(mechanics)">stress</a>, <a href="https://en.wikipedia.org/wiki/Strain_(mechanics)">strain</a>, and their relationship through an <a href="https://en.wikipedia.org/wiki/Elastic_modulus">elastic modulus</a>. Ideal fluids are discussed in Section 1.16, which introduces a <a href="https://en.wikipedia.org/wiki/Newtonian_fluid">Newtonian fluid</a> where the shear force is related to the flow rate by the <a href="https://en.wikipedia.org/wiki/Viscosity">coefficient of viscosity</a>.
<br /><br />
In the book <a href="https://www.amazon.com/Cell-Mechanics-Methods-Biology-Book-ebook/dp/B008B5LLOU/ref=sr_1_3?crid=1P56UXT0HGMUL&keywords=Cell+Mechanics&qid=1702385730&s=books&sprefix=cell+mechanics%2Cstripbooks%2C190&sr=1-3"><i>Cell Mechanics</i></a>, the chapter “Basic Rheology for Biologists,” by <a href="https://cdb.med.upenn.edu/people/paul-a-janmey-ph-d/">Paul Janmey</a>, <a href="https://cst.princeton.edu/people/penelope-georges">Penelope Georges</a>, and <a href="https://forskning.ruc.dk/en/persons/hvidt">Søren Hvidt</a>, focuses on materials that are not ideal solids or liquids.
<br /><blockquote>
Real materials are neither ideal solids nor ideal liquids nor even ideal mixtures of the
two. There are always effects due to molecular rearrangements and other factors that
complicate deformation, transforming elastic and viscous constants to functions of
time, and extent of deformation. Real materials, and especially biological materials,
exhibit both elastic and viscous responses and are therefore called <a href="https://en.wikipedia.org/wiki/Viscoelasticity">viscoelastic</a>. They are
also often highly <a href="https://en.wikipedia.org/wiki/Anisotropy">anisotropic</a>, showing different viscoelastic properties when deformed
in one direction than when deformed in other directions. The goal of rheological
experiments is to quantify the viscoelasticity of a material over as wide a range of
time and deformation scales as possible, and ultimately to relate these viscoelastic
properties to the molecular structure of the material.
</blockquote>
<i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i> examines only briefly the subject of <a href="https://en.wikipedia.org/wiki/Rheology">rheology</a>: the study of how nonideal materials deform and flow.
<br /><blockquote>
In some materials, the stress depends not only on the
strain, but on the rate at which the strain is produced. It may
take more stress to stretch the material rapidly than to stretch
it slowly, and more stress to stretch it than to maintain a fixed
strain. Such materials are called <i>viscoelastic</i>.
</blockquote><p>
Some materials are even more complicated, and the stress is not proportional to the strain or flow, but instead the relationship is nonlinear, demonstrating strain softening or strain stiffening. <br /></p><blockquote>Most materials will exhibit strain softening with a smaller [elastic modulus] at large strains.
However, some systems exhibit strain stiffening where [the elastic modulus] increases above a critical
strain.</blockquote><p>Russ and I show an example of strain softening in <i>IPMB</i>’s Fig. 1.21. When
stress is plotted versus strain, the stress first rises linearly and
then bends over and becomes flatter. <br /></p><p>
One rheological concept Russ and I never discuss is <a href="https://en.wikipedia.org/wiki/Creep_(deformation)">creep</a>.
Janmey et al. write<br /></p><blockquote>
Many biological systems experience
a sustained force such as gravity or blood pressure. It is therefore useful to
monitor how such systems deform under a constant load or stress. This type of
measurement is called a creep experiment, and in such an experiment the strain is monitored as a function of time for a fixed stress.
</blockquote><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-yX4HuhY095Kx-96imfXT0kgM8pyMTQXy84GHFZaj0EOu5SRlkX2qeCvtmuNoMl0YUtF17yzv8FKcNfqQ6zLXNqo5UPfZRReAp9Ygd0Y9JGRIGc1MkIGEvVlk4greBXV9VlgJ_EkeZhXH-wgKhyGaE9aPJaBDVVUxKOLWvmAXZgCnbIi4SOfj5yHzXpWE/s799/CreepRecoveryExperiment.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="387" data-original-width="799" height="155" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-yX4HuhY095Kx-96imfXT0kgM8pyMTQXy84GHFZaj0EOu5SRlkX2qeCvtmuNoMl0YUtF17yzv8FKcNfqQ6zLXNqo5UPfZRReAp9Ygd0Y9JGRIGc1MkIGEvVlk4greBXV9VlgJ_EkeZhXH-wgKhyGaE9aPJaBDVVUxKOLWvmAXZgCnbIi4SOfj5yHzXpWE/s320/CreepRecoveryExperiment.jpg" width="320" /></a><br /></div><div style="text-align: center;">A creep-recovery experiment.</div><div><br />
Another type of stress-relaxation experiment is to keep the strain constant and measure the stress.
<br /><blockquote>
Stress–relaxation measurements can be performed in both simple shear and
simple elongation, and they are of special interest for viscoelastic systems. In a
stress–relaxation experiment, the sample is rapidly deformed and the stress is
monitored as a function of time, keeping the sample in the deformed state.
</blockquote><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM1B66vVMaRxSYIkCkRqw0wYaq1qmM-04NDYocCToDZmUzoxeKTiglaPFfUkULKds4Cy96Ejfbj5LvOK7K6DRKmGUJn6eWTtCTU6W2OdDWNi0ZqeRaPeKTyJxfdWD1xNDEdu6gH-kEYAwi0as7fmAivI5G0UtjtvzZI8UunmgWdjVba2kVcjhyl9tVHgty/s795/StressRelaxationExperiment.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="383" data-original-width="795" height="154" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhM1B66vVMaRxSYIkCkRqw0wYaq1qmM-04NDYocCToDZmUzoxeKTiglaPFfUkULKds4Cy96Ejfbj5LvOK7K6DRKmGUJn6eWTtCTU6W2OdDWNi0ZqeRaPeKTyJxfdWD1xNDEdu6gH-kEYAwi0as7fmAivI5G0UtjtvzZI8UunmgWdjVba2kVcjhyl9tVHgty/s320/StressRelaxationExperiment.jpg" width="320" /> </a></div><div style="text-align: center;">A stress-relaxation experiment. <br /></div></div><div><br />
Janmey et al. point out that oscillatory behavior is particularly useful when studying nonideal materials.
<br /><blockquote>
Rheological information for viscoelastic systems is
often obtained by applying small amplitude oscillatory strains or stresses to the
sample rather than steady flows.
</blockquote>
When a oscillating deformation is applied to a material, the part of the stress in phase with the strain contains information about the material’s elastic behavior and the out-of-phase part contains information about the viscosity. </div><div></div><div></div><div></div><div></div><div><br />Rheology is an advanced topic and probably doesn't belong in an intermediate textbook like <i>IPMB</i>. Yet, in the messy, wet, and sticky world of biology, rheology can often play a major role. Janmey et al. conclude
<br /><blockquote>
As cell and tissue mechanics become more of an integral part of basic cell
biologic studies, a comprehensive understanding of micro- and macrorheology
may help develop a unified model for how specific structural elements are used
to form the soft but durable and adaptable materials that make up most organisms.
The results of these studies also have potential for developing materials and
methods for wound healing, cell differentiation, artificial organ development, and
many other applications in biomedical research.</blockquote></div>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-88947406610765252872023-12-29T05:00:00.012-05:002023-12-29T05:00:00.137-05:00Special Relativity in IPMB<p>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMe-iXh7oI3BJeRdsyhDIpudY9JSmnJJoS37D_yLxiBtuBJfx6bd8RQ8SbM_Wr8nRFmxMHKt7q6Xqpyb76aZhcS1qPpGTNU2FdHJSI8_-LqYlQjipGPAoxCybsAVlFarBuIJce4jTfey0wtX3T5WQ1fr6ft77XrxyqgzE83cPrAURws_jWPWy6qLSzSuCg/s4032/ElectricityAndMagnetism.jpg" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Electricity and Magnetism, by Edward Purcell, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="4032" data-original-width="3024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhMe-iXh7oI3BJeRdsyhDIpudY9JSmnJJoS37D_yLxiBtuBJfx6bd8RQ8SbM_Wr8nRFmxMHKt7q6Xqpyb76aZhcS1qPpGTNU2FdHJSI8_-LqYlQjipGPAoxCybsAVlFarBuIJce4jTfey0wtX3T5WQ1fr6ft77XrxyqgzE83cPrAURws_jWPWy6qLSzSuCg/w150-h200/ElectricityAndMagnetism.jpg" title="Electricity and Magnetism, by Edward Purcell." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Electricity and Magnetism</i>,<br />by Edward Purcell.<br /></td></tr></tbody></table>In <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I rarely discuss <a href="https://en.wikipedia.org/wiki/Special_relativity">special relativity</a>. We briefly mention that <a href="https://en.wikipedia.org/wiki/Magnetism">magnetism</a> is a consequence of relativity in Chapter 8 (<a href="https://en.wikipedia.org/wiki/Biomagnetism">Biomagnetism</a>) but we don’t develop our study of magnetic fields from this point of view. (If you want to see magnetism analyzed in this way, I suggest looking at the textbook <a href="https://www.amazon.com/Electricity-Magnetism-Edward-M-Purcell/dp/0070048592/ref=sr_1_5?crid=1JZPE3Y3R4HHN&keywords=Electricity+and+Magnetism+Purcell&qid=1700912133&s=books&sprefix=electricity+and+magnetism+purcel%2Cstripbooks%2C493&sr=1-5"><i>Electricity and Magnetism</i></a>, by <a href="https://en.wikipedia.org/wiki/Edward_Mills_Purcell">Edward Purcell</a>, which is Volume 2 of the <a href="https://en.wikipedia.org/wiki/Berkeley_Physics_Course"><i>Berkeley Physics Course</i></a>). We use the relationship between the energy and momentum of a photon, <i>E</i> = <i>pc</i>, in Chapter 15 (Interaction of <a href="https://en.wikipedia.org/wiki/Photon">Photons</a> and <a href="https://en.wikipedia.org/wiki/Charged_particle">Charged Particles</a> with Matter) when analyzing <a href="https://en.wikipedia.org/wiki/Compton_scattering">Compton scattering</a> and <a href="https://en.wikipedia.org/wiki/Pair_production">pair production</a>. And we use <a href="https://en.wikipedia.org/wiki/Albert_Einstein">Einstein</a>’s famous equation <i>E</i> = <i>mc</i><sup>2</sup>, relating a particles energy to its <a href="https://en.wikipedia.org/wiki/Invariant_mass">rest mass</a>, when calculating the <a href="https://en.wikipedia.org/wiki/Nuclear_binding_energy">binding energy of nuclei</a> in Chapter 17 (<a href="https://en.wikipedia.org/wiki/Nuclear_physics">Nuclear Physics</a> and <a href="https://en.wikipedia.org/wiki/Nuclear_medicine">Nuclear Medicine</a>).
<br /><br />
The most relativisticish equation we present is in Chapter 15 when analyzing how charged particles (such as <a href="https://en.wikipedia.org/wiki/Proton">protons</a>, <a href="https://en.wikipedia.org/wiki/Electron">electrons</a>, or <a href="https://en.wikipedia.org/wiki/Alpha_particle">alpha particles</a>) lose energy when passing through tissue at relativistic speeds.
We write<br /></p><blockquote><p>
The <a href="https://en.wikipedia.org/wiki/Stopping_power_(particle_radiation)">stopping powers</a> are plotted vs particle speed in the form <i>β</i> = <i>v</i>/<i>c</i>. At low energies (<i>β</i> ≪ 1) <i>β</i> is related to kinetic energy by </p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsUi9lRucmrDjfgvN_hWvu-pLLrUdJmrvOiKhAKVelmleFmlJvsGR6VTGtv-FTTwn7AryJVMNnlev_GZD1xLdFhcqWwYdGflUKdR2ZfyNuMoA0R_XR5t88AZ17aq22hN0LB5Xgmi2roJP4HKXi57I1r-q5qhLVsIOIEilGjpCyWLGQxzeUQIOgi_SgvhxN/s257/Eq15-47.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="53" data-original-width="257" height="53" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsUi9lRucmrDjfgvN_hWvu-pLLrUdJmrvOiKhAKVelmleFmlJvsGR6VTGtv-FTTwn7AryJVMNnlev_GZD1xLdFhcqWwYdGflUKdR2ZfyNuMoA0R_XR5t88AZ17aq22hN0LB5Xgmi2roJP4HKXi57I1r-q5qhLVsIOIEilGjpCyWLGQxzeUQIOgi_SgvhxN/s1600/Eq15-47.jpg" width="257" /></a><br /></p><p><br />For larger values of <i>β</i>, the relativistically correct expression </p></blockquote><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvxBTbwvR146x8-RPkzaxmvwWDL4ABoULeUj6q1TRYnWrRWw2jwK9N95jW8mMVv7bM9nL800i23EbKOVaCFY67trjvNfx2ZkRMTVP4djmPo0WnRsSOW9hpHovr2gKsTEEdRXyOl_gJRzM_ivSUZJvU2KFEeH3oq_4HhVn0kwjUCWTQCRb73JPSLw8cJ0Rf/s319/Eq15-48.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="66" data-original-width="319" height="66" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvxBTbwvR146x8-RPkzaxmvwWDL4ABoULeUj6q1TRYnWrRWw2jwK9N95jW8mMVv7bM9nL800i23EbKOVaCFY67trjvNfx2ZkRMTVP4djmPo0WnRsSOW9hpHovr2gKsTEEdRXyOl_gJRzM_ivSUZJvU2KFEeH3oq_4HhVn0kwjUCWTQCRb73JPSLw8cJ0Rf/s1600/Eq15-48.jpg" width="319" /></a></div><p></p><blockquote>
was used to convert Fig. 15.17 to 15.18. </blockquote><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrRgteQrh_zW3YWnYkD5RaI9ezsrmxODYMVgZBFnPa-bNtw4aFhYeg6BmsEYFHnBg47IKEVopE3cDV7WxtrU2MfwrEXxa7eHYrJQ56oG0cShPqwVUbKYevf3lFhY7YEl7u2-uh4jDrat-9lHO4y4_gOHqj0-LmRqRmQKv9Ek9Ioy0pi30Zc63kPVemN37t/s361/Fig15-17.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="282" data-original-width="361" height="250" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrRgteQrh_zW3YWnYkD5RaI9ezsrmxODYMVgZBFnPa-bNtw4aFhYeg6BmsEYFHnBg47IKEVopE3cDV7WxtrU2MfwrEXxa7eHYrJQ56oG0cShPqwVUbKYevf3lFhY7YEl7u2-uh4jDrat-9lHO4y4_gOHqj0-LmRqRmQKv9Ek9Ioy0pi30Zc63kPVemN37t/s320/Fig15-17.jpg" width="320" /></a></div><p></p><p style="text-align: center;">Fig. 15.17<br /></p><p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdMC6Aratn5WYDgTvMixVhwKTzCQcN9fUn31BWf9x8BFzct5bpyiiTgNQ3x2tL5o9xOcFknxGQmDlFLuOZt5iQ4rV4yOlAAlNumyfkoKyJgVpmPoK9juwr3E6N1qET1hmfZ0PwYvw4mDSleLUaNy3IwA7J7pBGfXMUvBJ15fPcBxHhT4yaKOKpg5r8C8lz/s362/Fig15-18.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="362" height="292" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdMC6Aratn5WYDgTvMixVhwKTzCQcN9fUn31BWf9x8BFzct5bpyiiTgNQ3x2tL5o9xOcFknxGQmDlFLuOZt5iQ4rV4yOlAAlNumyfkoKyJgVpmPoK9juwr3E6N1qET1hmfZ0PwYvw4mDSleLUaNy3IwA7J7pBGfXMUvBJ15fPcBxHhT4yaKOKpg5r8C8lz/s320/Fig15-18.jpg" width="320" /></a></div><p></p><p style="text-align: center;">Fig. 15.18<br /></p><p>Here<a href="https://en.wikipedia.org/wiki/Albert_Einstein"></a>’s a new homework problem examining the relationship between a particle<a href="https://en.wikipedia.org/wiki/Albert_Einstein"></a>’s speed and kinetic energy when its speed is near the speed of light.
<br /></p><blockquote>
<b>Section 15.11
</b><br /><br />
<b>Problem 41 ½</b>. A charged particle’s kinetic energy, <i>T</i>, is related to its mass <i>M</i> and its speed, <i>v</i>. We often express speed in terms of the parameter <i>β</i> = <i>v</i>/<i>c</i>, where <i>c</i> is the speed of light.
<br /><br />
(a) At low energies (<i>T</i> ≪ <i>Mc</i><sup>2</sup>, or equivalently <i>β</i> ≪ 1), show that Eq. 15.47 is consistent with the familiar expression from classical mechanics, <i>T</i> = ½ <i>mv</i><sup>2</sup>.
<br /><br />
(b) Show that Equation 15.48 (the relativistically correct relationship between <i>β</i> and <i>T</i>) reduces to Eq. 15.47 when <i>T</i> ≪ <i>Mc</i><sup>2</sup>.
<br /><br />
(c) Plot <i>β</i> versus <i>T</i>/<i>Mc</i><sup>2</sup>, both in a linear plot (0 < <i>T</i>/<i>Mc</i><sup>2</sup> < 3) and in a log-log plot (0.0001 < <i>T</i>/<i>Mc</i><sup>2</sup> < 100).
<br /><br />
(d) Take a few data points from Fig. 15.17 for a proton, replot them in Fig. 15.18, where the dependent variable is <i>β</i>, not <i>T</i>. See how well they match. Be sure to adjust for the different units for Stopping Power in the two plots. </blockquote>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-47670424933077332422023-12-22T05:00:00.724-05:002024-03-01T15:22:22.666-05:00An IPMB Episode of Meeting of Minds<p>A few weeks ago, I published a <a href="https://hobbieroth.blogspot.com/search?q=Meeting+of+Minds">blog post</a> about the television show <i><a href="https://en.wikipedia.org/wiki/Meeting_of_Minds">Meeting of Minds</a></i>. That show from the late 1970s was created and hosted by <a href="https://en.wikipedia.org/wiki/Steve_Allen">Steve Allen</a> and featured historical figures as guests in a talk show format. In my earlier post, I wrote that if I were going to have an episode of <i>Meeting of Minds</i> based on <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, it would include guests <a href="https://en.wikipedia.org/wiki/Alan_Hodgkin">Alan Hodgkin</a>, <a href="https://en.wikipedia.org/wiki/Willem_Einthoven">Willem Einthoven</a>, <a href="https://en.wikipedia.org/wiki/Paul_Lauterbur">Paul Lauterbur</a>, and <a href="https://en.wikipedia.org/wiki/Marie_Curie">Marie Curie</a>.</p><p>As your Christmas present, I offer you a script for the <i>IPMB</i> episode of <i>Meeting of Minds</i>.</p><p>Enjoy!<br /></p><p>***********************************************************</p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu-DAqL8VuZU0Q1_3k9yY2Icd9Ul_47_w0J6ylpc19zx_bLj-4C0z_0PCqMBvS4g4SzpbBMMCkfuNp2uTpRYOXU3AbT-ih_OHFGl4Mwbz92nsz3bCsnzjoWbBSw37yeVOC_Am4jPLk4QbEKcWcX1jh0gJ044ieZphK5ygogrQx5-hYWpbLahKQtHj0b39y/s1502/MeetingOfMindsIPMB.jpg" style="margin-left: auto; margin-right: auto;"><img alt="Meeting of Minds, IPMB episode, with Intermediate Physics for Medicine and Biology laying on the table." border="0" data-original-height="718" data-original-width="1502" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgu-DAqL8VuZU0Q1_3k9yY2Icd9Ul_47_w0J6ylpc19zx_bLj-4C0z_0PCqMBvS4g4SzpbBMMCkfuNp2uTpRYOXU3AbT-ih_OHFGl4Mwbz92nsz3bCsnzjoWbBSw37yeVOC_Am4jPLk4QbEKcWcX1jh0gJ044ieZphK5ygogrQx5-hYWpbLahKQtHj0b39y/w400-h191/MeetingOfMindsIPMB.jpg" title="Meeting of Minds, IPMB episode." width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Meeting of Minds</i>, <a href="https://link.springer.com/book/10.1007/978-3-319-12682-1"><i>IPMB</i></a> episode.<br /></td></tr></tbody></table><p><b>Allen</b>: Good evening. I’m Steve Allen and I’d like to welcome you to this week’s episode of <i>Meeting of Minds</i>. Our guests will all be drawn from the field of physics applied to medicine and biology. We have the French physicist Marie Curie, the English physiologist Alan Hodgkin, the Dutch medical doctor Willem Einthoven, and the American chemist Paul Lauterbur. I’d first like to introduce Alan Hodgkin. [applause]
<br /><br />
<b>Hodgkin</b>: [Hodgkin enters from stage right, and sits at the table.] Thank you, thank you. It’s such a pleasure to be here, Mr. Allen.
<br /><br />
<b>Allen</b>: The pleasure’s all mine, Dr. Hodgkin. Tell me, I understand you were born in the market town of <a href="https://en.wikipedia.org/wiki/Banbury">Banbury, England</a> in 1914, the son of <a href="https://en.wikipedia.org/wiki/Quakers">Quakers</a>. How did a Quaker upbringing influence your early life?
<br /><br />
<b>Hodgkin</b>: It had a huge influence. As you know, Quakers are <a href="https://en.wikipedia.org/wiki/Pacifism">pacifists</a>, and I was born just as <a href="https://en.wikipedia.org/wiki/World_War_I">World War I</a> began. When I was only two, my father, George Hodgkin, traveled to <a href="https://en.wikipedia.org/wiki/Armenia">Armenia</a> to try to help the many refuges trying to escape <a href="https://en.wikipedia.org/wiki/Armenian_genocide">genocide</a> committed by the <a href="https://en.wikipedia.org/wiki/Ottoman_Empire">Ottoman Empire</a>. He tried to return to to Armenia two years later, but ended up dying of dysentery in <a href="https://en.wikipedia.org/wiki/Baghdad">Baghdad</a>. This was just a few weeks after my brother Keith was born. I was only four when dad died.
<br /><br />
<b>Allen</b>: But your Quaker roots didn’t stop you from participating in <a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a>?
<br /><br />
<b>Hodgkin</b>: No, not at all. In fact, I was eager to do my part against the <a href="https://en.wikipedia.org/wiki/Nazism">Nazis</a>. I had visited Germany in 1932 and that experience destroyed any pacifist beliefs I might’ve held. During World War II, I worked on <a href="https://en.wikipedia.org/wiki/Radar">radar</a>. In fact, I was on one of the first test flights of a <a href="https://en.wikipedia.org/wiki/Bristol_Blenheim">Bristol Blenheim</a> light bomber when it was fitted with our airborne <a href="https://en.wikipedia.org/wiki/Radar_in_World_War_II">centimetric radar system</a>.
<br /><br />
<b>Allen</b>: Going back to your childhood, were there any influences that led you to a scientific career?
<br /><br />
<b>Hodgkin</b>: Oh yes. My mother encouraged my scientific interests and so did my Aunt Katie, who used to take me bird watching. In high school, I even got a job surveying <a href="https://en.wikipedia.org/wiki/Rookery">rookeries</a> and <a href="https://en.wikipedia.org/wiki/Heronry">heronries</a>. I spent many hours wading around in the salt marshes watching birds. This experience kindled my love for science.
<br /><br />
<b>Allen</b>: I see you started your career in the biological sciences. Where did you gain the knowledge of the physical sciences that allowed you to work on radar?
<br /><br />
<b>Hodgkin</b>: When at college at <a href="https://en.wikipedia.org/wiki/University_of_Cambridge">Cambridge</a>, one of my <a href="https://en.wikipedia.org/wiki/Zoology">zoology</a> professors gave me some good advice: study as much math and physics as you can! I also picked up a lot doing student research. And of course, during the war I learned on the job. I’m very interested in learning how my esteemed colleague Willem Einthoven made a similar transition from biology to physics.
<br /><br />
<b>Allen</b>: In that case, let’s welcome the father of clinical <a href="https://en.wikipedia.org/wiki/Electrocardiography">electrocardiography</a>, Willem Einthoven. [applause]
<br /><br />
<b>Einthoven</b>: [Einthoven enters from stage left and sits at the table across from Hodgkin] So good to meet you Mr. Allen. And it is truly a delight to meet the famous Alan Hodgkin, of Hodgkin and Huxley fame.
Dr. Hodgkin, I see we have something in common.<br /><br />
<b>Hodgkin</b>: Oh, what’s that?
<br /><br />
<b>Einthoven</b>: We both lost our fathers early in our life. My father, Jacob Einthoven, was a doctor, and died when I was only six. I was not born in the <a href="https://en.wikipedia.org/wiki/Netherlands">Netherlands</a>, but in <a href="https://en.wikipedia.org/wiki/Java">Java</a>, which at that time was part of the <a href="https://en.wikipedia.org/wiki/Dutch_East_Indies">Dutch East Indies</a>. After dad died, we returned to the Netherlands and settled in <a href="https://en.wikipedia.org/wiki/Utrecht">Utrecht</a>.
<br /><br />
<b>Allen</b>: I understand you studied medicine.
<br /><br />
<b>Einthoven</b>: Yes, Mr. Allen. When I was 25 I received my medical degree from the <a href="https://en.wikipedia.org/wiki/Utrecht_University">University of Utrecht</a>. Then I became a professor at the <a href="https://en.wikipedia.org/wiki/Leiden_University">University of Leiden</a>, where I spent my career. At that time, I married my first cousin Frédérique Jeanne Louise de Vogel.
<br /><br />
<b>Hodgkin</b>: First cousin! [giggles from the audience]
<br /><br />
<b>Einthoven</b>: Yes, a wonderful woman. [frowning]
<br /><br />
<b>Allen</b>: Like Dr. Hodgkin, your biological and medical research required knowledge of physics and math. How did you learn these subjects?
<br /><br />
<b>Einthoven</b>: Through self study, Mr. Allen.
<br /><br />
<b>Hodgkin</b>: The best type of learning.
<br /><br />
<b>Einthoven</b>: I obtained a textbook by the Dutch physicist <a href="https://en.wikipedia.org/wiki/Hendrik_Lorentz">Hendrik Lorentz</a> and taught myself differential and integral <a href="https://en.wikipedia.org/wiki/Calculus">calculus</a>. Thirty years later, I gave a copy of that book to the American cardiologist <a href="https://en.wikipedia.org/wiki/Frank_Norman_Wilson">Frank Wilson</a> (of the Wilson central terminal) with the inscription “May I send you the excellent book of Lorentz’ Differential- und Integralrechnung? I have learned my mathematics from it after my nomination as a professor in this University and I hope you will have as much pleasure and profit by it as I have had myself.” I also benefited from talks with my brother-in-law Julius, a physics professor at Utrecht. My training and degree was in medicine, but in my heart of hearts I was a physicist.
<br /><br />
<b>Hodgkin</b>: Fascinating.
<br /><br />
<b>Einthoven</b>: What is truly fascinating is how all the guests tonight contributed to the study of <a href="https://en.wikipedia.org/wiki/Bioelectromagnetics">bioelectricity and biomagnetism</a>. I developed the electrocardiogram, and you Dr. Hodgkin figured out how nerves work. I am anxious to meet Dr. Lauterbur, who invented <a href="https://en.wikipedia.org/wiki/Magnetic_resonance_imaging">magnetic resonance imaging</a>.
<br /><br />
<b>Allen</b>: Then without further ado, let me invite Dr. Paul Lauterbur to join our stimulating discussion. [applause]
<br /><br />
<b>Lauterbur</b>: [Lauterbur enters from stage right, and sits next to Hodgkin.] Steve Allen [shakes hand]. Drs. Hodgkin and Einthoven [nods]. So happy to be here. Willem, my ancestors came from over in your neck of the woods. They’re from <a href="https://en.wikipedia.org/wiki/Luxembourg">Luxembourg</a>.
<br /><br />
<b>Einthoven</b>: Interesting. Luxembourg is more closely related to France and Germany than the Netherlands, but….
<br /><br />
<b>Hodgkin</b>: Ha!
<br /><br />
<b>Lauterbur</b>: Yeah, we Americans are a little weak on our <a href="https://en.wikipedia.org/wiki/Geography">geography</a>. I was born and raised in the small town of <a href="https://en.wikipedia.org/wiki/Sidney,_Ohio">Sidney, Ohio</a>, just north of <a href="https://en.wikipedia.org/wiki/Dayton,_Ohio">Dayton</a>.
<br /><br />
<b>Einthoven</b>: And how did you become interested in science, Dr. Lauterbur?
<br /><br />
<b>Lauterbur</b>: As a teenager I built my own chemistry laboratory in the basement of our house.
<br /><br />
<b>Hodgkin</b>: Nice.
<br /><br />
<b>Lauterbur</b>: My high school chemistry teacher realized that I liked experimenting, so he let me do my own chemistry experiments in the back of the room during class.
<br /><br />
<b>Einthoven</b>: Such a wise teacher.
<br /><br />
<b>Lauterbur</b>: I got my bachelor’s degree in industrial chemistry form Case Institute of Technology in <a href="https://en.wikipedia.org/wiki/Cleveland">Cleveland</a>, which is now part of <a href="https://en.wikipedia.org/wiki/Case_Western_Reserve_University">Case Western Reserve University</a>. Like Dr. Hodgkin, I served in the army. In the early 1950s I was assigned to the army chemical center in <a href="https://en.wikipedia.org/wiki/Edgewood,_Maryland">Edgewood, Maryland</a>. They let me spend part of my time using an early <a href="https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance">nuclear magnetic resonance</a> machine. It didn’t do imaging…
<br /><br />
<b>Allen</b>: Of course not! You invented imaging.
<br /><br />
<b>Lauterbur</b>: …but NMR machines are important for chemical identification. I actually published four papers by the time I was discharged.
<br /><br />
<b>Hodgkin</b>: And where did you do your famous work on imaging?
<br /><br />
<b>Lauterbur</b>: I was at <a href="https://en.wikipedia.org/wiki/Stony_Brook_University">Stony Brook University</a> for 22 years.
<br /><br />
<b>Einthoven</b>: On <a href="https://en.wikipedia.org/wiki/Long_Island">Long Island</a>?
<br /><br />
<b>Lauterbur</b>: Yes, Willem, your geography’s better than mine [quiet laughter from the audience].
<br /><br />
<b>Allen</b>: I look forward to hearing about your development of MRI later in our discussion, but now I would like to introduce our last guest, Marie Curie [enthusiastic applause, louder than for any of the other scientists].<br /><br />
<b>Curie</b>: [Curie enters from stage left and sits next to Einthoven] Thank you. Thank you so very much. <br /><br />
<b>Einthoven</b>: The honor is ours, Dr. Curie. Why, you are the only one of us who has an element named for them.
<br /><br />
<b>Curie</b>: Yes, element 96 is named <a href="https://en.wikipedia.org/wiki/Curium">curium</a>.
<br /><br />
<b>Lauterbur</b>: While on the topic of geography, I seem to associate you with two countries, Marie: <a href="https://en.wikipedia.org/wiki/France">France</a> and <a href="https://en.wikipedia.org/wiki/Poland">Poland</a>. Which is your home?
<br /><br />
<b>Curie</b>: Well, I was born and raised in <a href="https://en.wikipedia.org/wiki/Warsaw">Warsaw</a>, which at that time was part of the <a href="https://en.wikipedia.org/wiki/Russian_Empire">Russian Empire</a>. It was only when I was 24 that I went to <a href="https://en.wikipedia.org/wiki/Paris">Paris</a>, and I spent the rest of my life in France. But I never lost my Polish heritage. I made sure my daughters learned the Polish language, and we went on trips to Poland. And Dr. Einthoven, you will be interested to know that I managed to get an element, <a href="https://en.wikipedia.org/wiki/Polonium">polonium</a>, named after my beloved homeland [scattered applause from the audience].
<br /><br />
<b>Einthoven</b>: Nicely done.
<br /><br />
<b>Hodgkin</b>: And how did you get started in science, Dr. Curie?
<br /><br />
<b>Curie</b>: “Dr. Curie.” That still seems strange to hear. You see, it wasn’t as easy for a young lady to start a career in science as it was for you men.
<br /><br />
<b>Allen</b>: I’m sure it wasn’t.
<br /><br />
<b>Curie</b>: Also, my education was difficult because my parents were involved in uprisings to gain Polish independence. We lost much of the family fortune. My father was a physics teacher. When Russia eliminated laboratory instruction from Polish schools, dad brought all the lab equipment home for us kids to use. The Russians finally fired my father. Like Drs. Hodgkin and Einthoven, I lost a parent when I was young. For me, it was my mother, who died of <a href="https://en.wikipedia.org/wiki/Tuberculosis">tuberculosis</a> when I was ten.
I couldn’t pursue higher education then, because I was a woman…<br /><br />
<b>Einthoven</b>: So unfair.
<br /><br />
<b>Curie</b>: I did become involved with the clandestine <a href="https://en.wikipedia.org/wiki/Flying_University">Flying University</a>, a Polish patriotic institution that admitted women. Eventually my sister Bronislawa and I made a deal. I stayed in Poland and made money to pay for her medical studies in Paris. In exchange, she agreed to help me pay for my education two years later.
<br /><br />
I got a job tutoring for some wealthy relations of my father. I fell in love with one of the sons, <a href="https://en.wikipedia.org/wiki/Kazimierz_%C5%BBorawski">Kazimierz</a>, but his family wouldn’t allow a marriage to a poor tutor. Kazimierz later became a famous mathematician. When he was an old man and I had died, he would come sit and stare at my statue at the <a href="https://en.wikipedia.org/wiki/Maria_Sklodowska-Curie_National_Research_Institute_of_Oncology">Radium Institute</a>.
<br /><br />
I eventually was able to go to Paris and join my sister. Still, life was hard. I studied so hard I often forgot to eat! I hit the books all day and tutored in the evenings to pay the bills.
<br /><br />
<b>Hodgkin</b>: How did you meet your husband <a href="https://en.wikipedia.org/wiki/Pierre_Curie">Pierre Curie</a>?
<br /><br />
<b>Curie</b>: We met through our mutual love of science. When Pierre proposed, I was reluctant to accept because I planned to return to Poland. Pierre said he would give up his distinguished physics career to join me! [applause from the audience]. We eventually were married. One smart aleck called me “Pierre’s greatest discovery” but <a href="https://en.wikipedia.org/wiki/Curie_temperature">his work in magnetism</a> was very important in its own right.
<br /><br />
<b>Allen</b>: Now I would like to switch the conversation to the science that made each of you famous. Dr. Hodgkin, you first. Tell us a little about your work with the <a href="https://en.wikipedia.org/wiki/Squid_giant_axon">squid nerve axon</a>.
<br /><br />
<b>Hodgkin</b>: I’d love to. Yes, Dr. Curie, some people think they’re so witty. In my case, one wise guy said that “it’s the squid who really deserved the Nobel Prize” [polite laughter from the audience]. I must admit he had a point. We conducted our experiments using the giant axon of the squid, which is up to one millimeter in diameter.
<br /><br />
<b>Einthoven</b>: One millimeter!? For a nerve axon, that is huge!
<br /><br />
<b>Hodgkin</b>: Yes, that’s the point. It was big enough that we could stick electrodes down its length.
<br /><br />
<b>Curie</b>: Who is “we,” Dr. Hodgkin?
<br /><br />
<b>Hodgkin</b>: I worked mainly with my collaborator, <a href="https://en.wikipedia.org/wiki/Andrew_Huxley">Andrew Huxley</a>. He was a little younger than me and started as my student, but eventually became a true collaborator. He was an excellent experimentalist, but one of his greatest strengths was his skill in mathematics.
<br /><br />
<b>Lauterbur</b>: Do go on, Alan. What did ya do with those axons?
<br /><br />
<b>Hodgkin</b>: We developed a technique called the “<a href="https://en.wikipedia.org/wiki/Voltage_clamp">voltage clamp</a>” in which we used two electrodes, one to measure the voltage across the axon membrane and the other to pass current across the membrane. The electrodes were attached to a <a href="https://en.wikipedia.org/wiki/Negative_feedback">feedback</a> circuit, which applied whatever current was necessary to keep the voltage constant. With this device, we could monitor both the current and voltage, and thus determine the membrane conductance.
<br /><br />
<b>Allen</b>: But Dr. Hodgkin, wasn’t the voltage clamp originally invented by <a href="https://en.wikipedia.org/wiki/Kenneth_Stewart_Cole">Kenneth Cole</a> at <a href="https://en.wikipedia.org/wiki/Woods_Hole_Oceanographic_Institution">Woods Hole</a> in the United States?
<br /><br />
<b>Hodgkin</b>: Yes, he did some of the early work. And it’s true I visited Woods Hole and learned the technique from Cole. But some of his measurements were questionable. He reported action potentials that went positive by over 100 millivolts!
<br /><br />
<b>Einthoven</b>: Oh my.
<br /><br />
<b>Hodgkin</b>: An action potential that positive would have invalidated the idea that the membrane depolarized until it reached the <a href="https://en.wikipedia.org/wiki/Reversal_potential">sodium equilibrium voltage</a>, which was the basis for the Hodgkin and Huxley model. In any case, we were able to calculate the membrane conductance and could determine how the membrane changed its conductance for both sodium and potassium individually.
<br /><br />
<b>Lauterbur</b>: Because the sodium and potassium ions passed through selective <a href="https://en.wikipedia.org/wiki/Ion_channel">ion channels</a>?
<br /><br />
<b>Hodgkin</b>: Yes, but we didn’t know it at the time. We just knew that two ions were involved: sodium and potassium. At rest the axon was primarily permeable to potassium and during the action potential it became permeable to sodium. We imagined that “gates” allowed the current to pass through the membrane: the <i>m</i> and <i>h</i> gates for sodium, and the <i>n</i> gate for potassium. It may sound a bit ad hoc, but our Hodgkin and Huxley model was really a gigantic curve-fitting exercise.
<br /><br />
When the membrane was slightly depolarized—that is, when the membrane voltage was made slightly positive compared to its resting value—the <i>m</i> gate began to open, letting in sodium. The positive charge of the sodium ions raised the membrane voltage further, resulting in the <i>m</i> gate opening more, allowing more sodium to enter…
<br /><br />
<b>Einthoven</b>: <a href="https://en.wikipedia.org/wiki/Positive_feedback">Positive feedback</a>!
<br /><br />
<b>Hodgkin</b>: Yes, the upstroke of the action potential is a positive feedback loop.
<br /><br />
<b>Lauterbur</b>: But Alan, positive feedback can be explosive. What stopped the rise in membrane voltage?
<br /><br />
<b>Hodgkin</b>: When the membrane voltage reached the sodium equilibrium voltage, there was no longer a tendency for sodium to enter the nerve. Even though there was more sodium outside the axon than inside, the high positive voltage in the <a href="https://en.wikipedia.org/wiki/Axoplasm">axoplasm</a> prevented any more positive sodium ions from diffusing in. That’s why Cole’s huge action potentials didn’t make any sense. Their reported action potentials went <i>above</i> the sodium equilibrium voltage.
<br /><br />
<b>Curie</b>: But Dr. Hodgkin, what then caused the voltage to return to rest?
<br /><br />
<b>Hodgkin</b>: Well, the <i>n</i> gate slowly opened, allowing potassium to leave the axon (carrying positive charge with it). But more importantly, the <i>h</i> gate slowly closed, preventing any further sodium current.
<br /><br />
<b>Einthoven</b>: But if the <i>h</i> gate closes, would not that destroy the positive feedback loop of the action potential?
<br /><br />
<b>Hodgkin</b>: Yes indeed. The closing of <i>h</i> made the axon “<a href="https://en.wikipedia.org/wiki/Refractory_period_(physiology)">refractory.</a>” It couldn’t fire another action potential until the <i>h</i> gate finally opened again and the membrane returned to its resting state.
<br /><br />
<b>Allen</b>: Interesting, Dr. Hodgkin. And you made a mathematical model of this?
<br /><br />
<b>Hodgkin</b>: Yes. Much of that was Andrew’s work.
<br /><br />
<b>Lauterbur</b>: Don’t some people call Huxley the “greatest mathematical biologist ever”?
<br /><br />
<b>Hodgkin</b>: They do. Our model required solving a set of <a href="https://en.wikipedia.org/wiki/Nonlinear_system">nonlinear</a> <a href="https://en.wikipedia.org/wiki/Differential_equation">differential equations</a>. This was back in the days before <a href="https://en.wikipedia.org/wiki/Computer#Digital_computers">digital computers</a> were available. You should’ve seen Andrew working that hand-held <a href="https://en.wikipedia.org/wiki/Mechanical_calculator">mechanical calculating machine</a> to solve those equations numerically. Boy, did his fingers fly!
<br /><br />
<b>Allen</b>: Dr. Einthoven, you also worked in bioelectricity. Perhaps you could tell us about your discoveries?
<br /><br />
<b>Einthoven</b>: Well, I was the first to record the electrocardiogram, which is the electrical signal produced by the <a href="https://en.wikipedia.org/wiki/Heart">heart</a>.
<br /><br />
<b>Lauterbur</b>: I often had an ECG taken during my yearly physical.
<br /><br />
<b>Einthoven</b>: Yes, it has become one of the most important diagnostic tools of modern medicine. But unlike Dr. Hodgkin, I didn’t have fancy voltmeters and <a href="https://en.wikipedia.org/wiki/Oscilloscope">oscilloscopes</a> that I could use to measure electrical current. I had to invent an improved “<a href="https://en.wikipedia.org/wiki/String_galvanometer">string galvanometer</a>.”
<br /><br />
<b>Hodgkin</b>: Yes, yes. You passed a current through a wire in a <a href="https://en.wikipedia.org/wiki/Magnetic_field">magnetic field</a>, causing a <a href="https://en.wikipedia.org/wiki/Lorentz_force">force</a> on the wire proportional to the current.
<br /><br />
<b>Enithoven</b>: Indeed, Dr. Hodgkin. We could not measure currents that changed too rapidly or that were too weak, but the device was sufficient to record the electrocardiogram. Unlike Hodgkin and Huxley, I could not insert an electrode into a heart cell, so I had to be content with measuring the voltage produced on the body surface by the electrical activity of the distant heart.
<br /><br />
<b>Curie</b>: And wasn’t it you, Dr. Einthoven, who assigned the names <a href="https://en.wikipedia.org/wiki/P_wave">P-wave</a>, <a href="https://en.wikipedia.org/wiki/QRS_complex">QRS-complex</a>, and <a href="https://en.wikipedia.org/wiki/T_wave">T-wave</a> to the various electrocardiogram deflections?
<br /><br />
<b>Enithoven</b>: Yes it was. The P-wave corresponded to the <a href="https://en.wikipedia.org/wiki/Atrium_(heart)">atria</a> depolarizing, the QRS-complex to the <a href="https://en.wikipedia.org/wiki/Ventricle_(heart)">ventricles</a> depolarizing, and the T-wave to the ventricles repolarizing.
<br /><br />
<b>Allen</b>: And what about the atria repolarizing?
<br /><br />
<b>Einthoven</b>: That tiny signal was buried in the QRS-complex.
<br /><br />
<b>Lauterbur</b>: And how did ya interpret your data?
<br /><br />
<b>Einthoven</b>: I imagined that the heart produced a <a href="https://en.wikipedia.org/wiki/Electric_dipole_moment">dipole</a>, which just means current passed out of the heart cells at one point and reentered the cells at another, like an electric dipole made from two charges separated by a distance. Really, the ECG is produced by tiny dipoles associated with each cardiac cell, but there are billions of cells so I simplified the situation by representing the current source as a single dipole.
<br /><br />
<b>Hodgkin</b>: A “toy model”!
<br /><br />
<b>Einthoven</b>: Yes, sometimes we must make approximations to simplify a complicated situation so we can understand it better. A dipole is a <a href="https://en.wikipedia.org/wiki/Euclidean_vector">vector</a>, meaning it has a magnitude and a direction. To determine its direction, I placed <a href="https://en.wikipedia.org/wiki/Electrode">electrodes</a> on the left arm, right arm, and left leg. These three electrodes roughly form an <a href="https://en.wikipedia.org/wiki/Equilateral_triangle">equilateral triangle</a>…
<br /><br />
<b>Lauterbur</b>: <a href="https://en.wikipedia.org/wiki/Einthoven%27s_triangle">Einthoven’s triangle</a>!
<br /><br />
<b>Einthoven</b>: Some people started calling it that, which was quite an honor. The signal from the three electrodes forming “Einthoven’s” triangle, if you will, determine the dipole direction.
<br /><br />
<b>Curie</b>: Can’t the electrocardiogram be used to treat diseases?
<br /><br />
<b>Einthoven</b>: Not really treat, but diagnose. The details of the electrical signal provide information about heart <a href="https://en.wikipedia.org/wiki/Arrhythmia">arrhythmias</a>. Once you know the type of arrhythmia, then you can treat it properly.
<br /><br />
<b>Allen</b>: I believe that our modern <a href="https://en.wikipedia.org/wiki/Artificial_cardiac_pacemaker">artificial pacemakers</a> and <a href="https://en.wikipedia.org/wiki/Defibrillation">defibrillators</a> are what you are referring to.
<br /><br />
<b>Einthoven</b>: Yes. These miraculous devices can use ECG recordings to determine the correct place and time to stimulate the heart to overcome the arrhythmia. It is all quite wonderful, but those devices were invented long after I had left the scene.
<br /><br />
<b>Curie</b>: But they’re based on your work, Dr. Einthoven. We all owe you a great debt of gratitude.
<br /><br />
<b>Einthoven</b>: And to you, Dr. Curie, for your work on…
<br /><br />
<b>Allen</b>: Before we discuss Dr. Curie’s research, I would like to hear from Dr. Lauterbur about his studies that led to magnetic resonance imaging.
<br /><br />
<b>Lauterbur</b>: Steve, I’d love to talk about it. Some n<a href="https://en.wikipedia.org/wiki/Atomic_nucleus">uclei</a> have a property called “<a href="https://en.wikipedia.org/wiki/Spin_(physics)">spin</a>.” A nucleus with spin, such as that of the <a href="https://en.wikipedia.org/wiki/Hydrogen_atom">hydrogen atom,</a> <a href="https://en.wikipedia.org/wiki/Larmor_precession">precesses</a>, or rotates, about a magnetic field, with its precession <a href="https://en.wikipedia.org/wiki/Frequency">frequency</a> proportional to the magnetic field strength. This precession is the basis for nuclear magnetic resonance.
<br /><br />
Now, the secret to magnetic resonance imaging is to apply a large, static magnetic field that causes the spins to precess, plus a <a href="https://en.wikipedia.org/wiki/Physics_of_magnetic_resonance_imaging">magnetic field gradient</a> that you can turn on and off. The gradient makes the magnetic field larger in one location than another; it maps magnetic field strength to position. This causes the precession frequency to also vary with position. It’s the frequency that we measure during MRI. Therefore, the gradient maps frequency to position, allowing you to determine a nucleus’s location from its frequency.
<br /><br />
<b>Hodgkin</b>: Wonderful! Why didn’t they call the method “nuclear magnetic resonance imaging”?
<br /><br />
<b>Lauterbur</b>: Ha! People are so afraid of the word “nuclear” that they dropped it and renamed the technique “magnetic resonance imaging,” or MRI. Some people have such irrational fears of anything having to do with the nucleus or radiation.
<br /><br />
<b>Curie</b>: I know what you mean, I remember when…
<br /><br />
<b>Allen</b>: Yes, but let Dr. Lauterbur finish his story.
<br /><br />
<b>Lauterbur</b>: I remember the day I came up with the idea of using gradient fields to do MRI. I was sitting in a <a href="https://en.wikipedia.org/wiki/Big_Boy_Restaurants">Big Boy restaurant</a> and it just came to me: <a href="https://en.wikipedia.org/wiki/Eureka_(word)">Eureka</a>! I immediately scribbled the thought down on the only thing I had available: a paper napkin.
<br /><br />
<b>Hodgkin</b>: I’m glad they didn’t use cloth napkins.
<br /><br />
<b>Lauterbur</b>: Ha. Not likely at a Big Boy. I would’ve walked out with it if they had. So I built the first simple MRI machine and started creating images. I tried to publish my initial results in the journal <i><a href="https://en.wikipedia.org/wiki/Nature_(journal)">Nature</a></i>…
<br /><br />
<b>Einthoven</b>: Ah, that English journal is one of the finest in all of science.
<br /><br />
<b>Lauterbur</b>: Perhaps, but they initially rejected my manuscript.
<br /><br />
<b>Curie</b>: Goodness!
<br /><br />
<b>Lauterbur</b>: They thought my images were too fuzzy. But they were the very first magnetic resonance images, for crying out loud. I persisted and asked them to review it again. It was finally published in <i>Nature</i>, and the article became a classic. I believe you could write the entire history of science in the last 50 years in terms of papers rejected by <a href="https://en.wikipedia.org/wiki/Science_(journal)"><i>Science</i></a> or <i>Nature</i>.
<br /><br />
<b>Allen</b>: Really?
<br /><br />
<b>Lauterbur</b>: Yes. I tried to <a href="https://en.wikipedia.org/wiki/Patent">patent</a> my ideas, but Stony Brook decided not to pursue it. Patents are expensive, and they didn’t expect the potential earnings justified the cost of the lawyers and filing fees.
<br /><br />
<b>Curie</b>: What a mistake.
<br /><br />
<b>Allen</b>: Can you tell us a little about your controversy with <a href="https://en.wikipedia.org/wiki/Raymond_Damadian">Raymond Damadian</a> regarding the invention of MRI.
<br /><br />
<b>Lauterbur</b>: Steve, I thought ya might bring that up [audience laughs awkwardly]. Yes, Damadian also was working on imaging using MRI. He was particularly interested in finding if signals from a tumor were different from normal tissue. It was nice work, but it didn’t contain the idea of using a magnetic field gradient to map frequency to position, which is the essence of my method. When <a href="https://en.wikipedia.org/wiki/Peter_Mansfield">Peter Mansfield</a> and I each received the <a href="https://en.wikipedia.org/wiki/Nobel_Prize">Nobel Prize</a> for developing MRI, Damadian took out a full-page ad in the <i><a href="https://en.wikipedia.org/wiki/The_New_York_Times">New York Times</a></i> claiming the prize should have gone to him too! He was bitter about it all his life. But I think history is on my side.
<br /><br />
<b>Einthoven</b>: What about <a href="https://en.wikipedia.org/wiki/Herman_Carr">Herman Carr</a>?
<br /><br />
<b>Lauterbur</b>: Carr’s work was a precursor to mine and he probably had a better claim to the Nobel Prize than Damadian did. I should’ve cited Carrr’s work. And Mansfield thought <a href="https://en.wikipedia.org/wiki/Erwin_Hahn">Erwin Hahn</a> deserved a piece of the prize for his discovery of <a href="https://en.wikipedia.org/wiki/Spin_echo">spin echo</a>. Scientific discoveries and inventions are complex processes, and the credit must often be shared among many researchers.
<br /><br />
<b>Hodgkin</b>: Yes, I know. Besides Huxley, my work was assisted by <a href="https://en.wikipedia.org/wiki/Bernard_Katz">Bernard Katz</a> and <a href="https://en.wikipedia.org/wiki/W._A._H._Rushton">William Rushton</a> among others.
<br /><br />
<b>Allen</b>: Including Kenneth Cole.
<br /><br />
<b>Hodgkin</b>: [Sighs] And Cole.
<br /><br />
<b>Allen</b>: Now, Dr. Curie, could you tell us a little of your important work.
<br /><br />
<b>Curie</b>: Yes. I’ve been waiting patiently for my turn [quiet laughter]. First a little background. I lived in an exciting time for science…
<br /><br />
<b>Einthoven</b>: I believe all times are exciting for science.
<br /><br />
<b>Curie</b>: I agree, but the end of the 19th century was a particularly exciting time for physics. In 1895 <a href="https://en.wikipedia.org/wiki/Wilhelm_R%C3%B6ntgen">Wilhelm Rontgen</a> discovered <a href="https://en.wikipedia.org/wiki/X-ray">x-rays</a> (a type of very high frequency <a href="https://en.wikipedia.org/wiki/Electromagnetic_radiation">electromagnetic radiation</a>) and then in 1896 <a href="https://en.wikipedia.org/wiki/Henri_Becquerel">Henri Becquerel</a> discovered <a href="https://en.wikipedia.org/wiki/Radiation">radiation</a> from <a href="https://en.wikipedia.org/wiki/Uranium">uranium</a>. I decided to examine uranium in more detail.
<br /><br />
<b>Lauterbur</b>: Didn’t you find three types of radiation: <a href="https://en.wikipedia.org/wiki/Alpha_decay">alpha</a>, <a href="https://en.wikipedia.org/wiki/Beta_decay">beta</a>, and <a href="https://en.wikipedia.org/wiki/Gamma_ray">gamma</a>?
<br /><br />
<b>Curie</b>: No, Dr. Lauterbur, that was found by my good friend <a href="https://en.wikipedia.org/wiki/Ernest_Rutherford">Ernest Rutherford</a>. But back to my work. I started with a ton of <a href="https://en.wikipedia.org/wiki/Uraninite">pitchblende</a> (an ore containing uranium) and analyzed it chemically, separating the radioactive and nonradioactive parts. My husband Pierre was so interested in this work that he abandoned his own research to help me. After years of analysis, we finally ended up with less than a gram of a new element we named <a href="https://en.wikipedia.org/wiki/Radium">radium</a>. It was highly radioactive. Along the way, we also discovered another element, <a href="https://en.wikipedia.org/wiki/Polonium">polonium</a>, which I mentioned previously.
<br /><br />
<b>Hodgkin</b>: Those discoveries must’ve made you very famous.
<br /><br />
<b>Curie</b>: Well, it did allow me to finally obtain my doctorate from the <a href="https://en.wikipedia.org/wiki/University_of_Paris">University of Paris</a>. I was then invited to the <a href="https://en.wikipedia.org/wiki/Royal_Institution">Royal Institution</a> in <a href="https://en.wikipedia.org/wiki/London">London</a> to lecture about radioactivity. But since I was a woman, I was not allowed to speak, and Pierre alone gave the presentation [indignant murmur from the audience]. The committee that decides the Nobel Prize was going to award it to only Pierre and Henri Becquerel, but Pierre put a stop to that. I miss Pierre so much. In 1906, he was killed in a road accident. It was devastating…
<br /><br />
<b>Allen</b>: I’m so sorry, Dr. Curie [Allen pats Curie on the shoulder].
<br /><br />
<b>Curie</b>: But I soldiered on. Almost immediately x-rays and radium began to be used in medicine, creating the new discipline of <a href="https://en.wikipedia.org/wiki/Medical_physics">medical physics</a>. During the First World War, my daughter <a href="https://en.wikipedia.org/wiki/Ir%C3%A8ne_Joliot-Curie">Irene</a> and I developed x-ray imaging equipment mounted on trucks that could be used as mobile radiography units at the front. They were known as “petites Curies,” or “Little Curies.” [Curie smiles.]<br /><br />
<b>Einthoven</b>: Was not Irene herself a famous scientist?
<br /><br />
<b>Curie</b>: Yes, Irene and her husband won their own Nobel Prize for discovering <a href="https://en.wikipedia.org/wiki/Induced_radioactivity">artificial radioisotopes</a>.
<br /><br />
<b>Allen</b>: I know this may be a delicate subject, but could you tell us about your relationship with physicist <a href="https://en.wikipedia.org/wiki/Paul_Langevin">Paul Langevin</a>?
<br /><br />
<b>Curie</b>: Mr. Allen, I’m surprised you have so little tact [audience laughs nervously]. But I suppose if you must know, Paul was a former student of Pierre’s. He was married, but was estranged from his wife. After Pierre died, Paul and I were lovers. The press got a hold of the news (by that time I was quite famous) and started calling it the “Langevin affair.” They tortured me about that relationship.
<br /><br />
<b>Allen</b>: Thank you, Dr. Curie, for sharing that difficult part of your past. [Looking up at the entire group] There is one thing all four of you have in common. You all won a Nobel Prize.
<br /><br />
<b>Lauterbur</b>: Yes, you’ve already heard my embarrassing story about the prize. I received mine, jointly with Mansfield, for Physiology and Medicine.
<br /><br />
<b>Hodgkin</b>: I also received mine in Physiology or Medicine, along with Huxley and neurophysiologist <a href="https://en.wikipedia.org/wiki/John_Eccles_(neurophysiologist)">John Eccles</a>.
<br /><br />
<b>Einthoven</b>: Mine was for Physiology or Medicine too, but it was a solo award.
<br /><br />
<b>Curie</b>: I’m so proud of you all. But gentlemen, do any of you have <i>two</i> Nobel Prizes [all laugh]?
<br /><br />
<b>Hodgkin</b>: Yes, Dr. Curie, you were the first woman to receive a Nobel Prize, and you ended up with two: one in physics and one in chemistry [several young female members of the audience start stomping their feet and cheering for Curie; one yells “<a href="https://en.wikipedia.org/wiki/Girl_power">girl power</a>!”].
<br /><br />
<b>Allen</b>: [Laughing] With that thought, my friends, I fear we have run out of time. I hope you will join us again next week for another episode of <i>Meeting of Minds</i>.
</p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-66462254179149479102023-12-15T05:00:00.000-05:002023-12-15T05:00:00.143-05:00The Three Laws of Thermodynamics<a href="https://en.wikipedia.org/wiki/Thermodynamics">Thermodynamics</a> is often summarized in three laws. Do <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss the <a href="https://en.wikipedia.org/wiki/Laws_of_thermodynamics">three laws of thermodynamics</a> in <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>? Yes!<br /><h4 style="text-align: left;">
The First Law
</h4>
We state the first law on page 58.
<br /><blockquote>
The most general way the <a href="https://en.wikipedia.org/wiki/Energy">energy</a> of a system can change [<i>ΔU</i>] is
to have both <a href="https://en.wikipedia.org/wiki/Work_(thermodynamics)">work</a> [<i>W</i>] done by the system and <a href="https://en.wikipedia.org/wiki/Heat">heat</a> [<i>Q</i>] flow into the
system. The statement of the <a href="https://en.wikipedia.org/wiki/Conservation_of_energy">conservation of energy</a> in that
case is called the <a href="https://en.wikipedia.org/wiki/First_law_of_thermodynamics"><i>first law of thermodynamics</i></a>:
<i>ΔU</i> = <i>Q</i> − <i>W</i>.
</blockquote><h4 style="text-align: left;">
The Second Law
</h4><p>
</p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ2iuOKplugHZCjlHtN9GKmseFpdywth-xlQjZ84xM9vtLymzSIbPv2fILPfQ7o3n7HuBv3us42MKZIklTfcuKhhEsoKWU36Wkv8w3TsZCuz0cCQ61ZaPmP_E6ZqJRdmQra0kdV-Av-1jdFpPsH3kqai3Ml4QnwgwCgrhVioVtE4FZWmkwYyFUPJMfpke4/s1024/TheSecondLaw.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1024" data-original-width="768" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjZ2iuOKplugHZCjlHtN9GKmseFpdywth-xlQjZ84xM9vtLymzSIbPv2fILPfQ7o3n7HuBv3us42MKZIklTfcuKhhEsoKWU36Wkv8w3TsZCuz0cCQ61ZaPmP_E6ZqJRdmQra0kdV-Av-1jdFpPsH3kqai3Ml4QnwgwCgrhVioVtE4FZWmkwYyFUPJMfpke4/w150-h200/TheSecondLaw.jpg" width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>The 2nd Law</i>, by Peter Atkins.<br /></td></tr></tbody></table>On page 75 of <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i>, Russ and I write<p></p><p></p><blockquote>The total <a href="https://en.wikipedia.org/wiki/Entropy">entropy</a> [of a system] remains the same or increases. This is one form of the <a href="https://en.wikipedia.org/wiki/Second_law_of_thermodynamics"><i>second law of thermodynamics</i></a>.
For a fascinating discussion of the second law, see
Atkins (1994).
</blockquote><p>The book we cite by <a href="https://en.wikipedia.org/wiki/Peter_Atkins">Peter Atkins</a>, <i><a href="https://www.amazon.com/Second-Law-Scientific-American-Library/dp/071675004X/ref=sr_1_1?keywords=The+2nd+Law%3A+Energy%2C+Chaos+and+Form&qid=1698344574&s=books&sr=1-1&ufe=app_do%3Aamzn1.fos.006c50ae-5d4c-4777-9bc0-4513d670b6bc">The 2nd Law: Energy, Chaos and Form</a></i> (Scientific American, 1994) is excellent and I highly recommend it. <br /></p><p></p><p></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_iBxJ9_vH04GzSqTMNbNmKUhu0Qk_uYl1etDN0BqN36wQUKiY9j7VZ3mcpmWfPkM67idYWVrk6NrHaLprL1SaZlxkdE3Od6IzGLfr9Fuwte7lANR1frSpx12aWmpwASuLp-EF9460K8AHMt24UssJpckjVWbNEQitYWIDMSh3bGoDc9IAESBwWKJNUZax/s2016/AnIntroductionToThermalPhysics.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_iBxJ9_vH04GzSqTMNbNmKUhu0Qk_uYl1etDN0BqN36wQUKiY9j7VZ3mcpmWfPkM67idYWVrk6NrHaLprL1SaZlxkdE3Od6IzGLfr9Fuwte7lANR1frSpx12aWmpwASuLp-EF9460K8AHMt24UssJpckjVWbNEQitYWIDMSh3bGoDc9IAESBwWKJNUZax/w150-h200/AnIntroductionToThermalPhysics.jpg" width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>An Introduction to<br />Thermal Physics</i>, <br />by Daniel Schroeder.<br /></td><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table>When <a href="https://physics.weber.edu/schroeder/">Daniel Schroeder</a> talks about the efficiency of a <a href="https://en.wikipedia.org/wiki/Heat_engine">heat engine</a> in his textbook <a href="https://www.amazon.com/Introduction-Thermal-Physics-Daniel-Schroeder/dp/0192895559/ref=sr_1_1?crid=7APPI4S54Z05&keywords=An+Introduction+to+Thermal+Physics&qid=1698344641&s=books&sprefix=an+introduction+to+thermal+physics%2Cstripbooks%2C96&sr=1-1"><i>An Introduction to Thermal Physics</i></a>, he states the first two laws this way:
<br /><p></p><blockquote>
In deriving the limit… on the efficiency of an engine, we used both the first and second laws of thermodynamics. The first law told us that… we can’t get more work out than the amount of heat put in. In this context, the first law is often paraphrased, “You can’t win.” The second law, however, made matters worse. It told us that we can’t even achieve [an efficiency of one, meaning all the heat is converted to work] unless [the heat engine operates between a cold reservoir at zero absolute temperature and a hot reservoir at an arbitrarily high absolute temperature], both of which are impossible in practice. In this context, the second law is often paraphrased, “You can’t even break even.”
</blockquote>
The second law is one of the most famous principles of science. In his book <a href="https://en.wikipedia.org/wiki/The_Two_Cultures"><i>The Two Cultures</i></a>, <a href="https://en.wikipedia.org/wiki/C._P._Snow">C. P. Snow</a> writes
<br /><blockquote>
A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of <a href="https://en.wikipedia.org/wiki/William_Shakespeare">Shakespeare</a>’s?
</blockquote><p></p><h4 style="text-align: left;">
The Third Law</h4><p>
Russ and I don’t state the <a href="https://en.wikipedia.org/wiki/Third_law_of_thermodynamics">third law of thermodynamics</a>, but it is inherent in the definition of entropy we give on page 62.
<br /></p><blockquote>
The entropy <i>S</i> is defined by <i>S</i> = <i>k<sub>B</sub></i> ln <i>Ω</i>.
</blockquote>In this equation, <i>k<sub>B</sub></i> is <a href="https://en.wikipedia.org/wiki/Boltzmann_constant">Boltzmann's constant</a> and <i>Ω</i> is the number of possible states of the system.
<br /><br />
Here is what Schroeder writes.
<br /><blockquote>
At <a href="https://en.wikipedia.org/wiki/Absolute_zero">zero temperature</a> [absolute zero] a system should settle into its unique lowest-energy state, so [the number of states is one] and [the entropy, which is proportional to the <a href="https://en.wikipedia.org/wiki/Natural_logarithm">logarithm</a> of the number of states, is therefore zero]. This fact is often called the <i>third law of thermodynamics</i>.
</blockquote><p>
The third law was discovered by the German physicist <a href="https://en.wikipedia.org/wiki/Walther_Nernst">Walther Nernst</a>, whose <a href="https://en.wikipedia.org/wiki/Nernst_equation">Nernst equation</a> for the <a href="https://en.wikipedia.org/wiki/Reversal_potential">equilibrium potential</a> across a membrane plays such a big role <i>IPMB</i>’s analysis of bioelectricity.
<br /></p><h4 style="text-align: left;">Summary<br /></h4><p>To summarize, the three laws of thermodynamics are
<br /></p><ol style="text-align: left;"><li>
Energy is conserved
</li><li>
Entropy increases
</li><li>
The entropy is zero at absolute zero.
</li></ol><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-90582445388664965672023-12-08T05:00:00.064-05:002024-03-01T15:22:37.864-05:00One Hot Summer: Dickens, Darwin, Disraeli, and the Great Stink of 1858<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoV32OJmq5vDKEsgwjX13080gEpuwEfYqjgqh9f7B_uAJnBdAygJlKubkMCph9POEeRAVjwCoCRVC-8AVLMueWyz26lbBTWHj1u3VEYaeMMK_4Jo8IqRTmmrWktQRUYs91AbsTinyN5M1MMjtaUhbkbVm_S3OVkxTzRmWZA4czj0d7q9GA0YJNLqiJwW7H/s2016/OneHotSummer.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="One Hot Summer, by Rosemary Ashton, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjoV32OJmq5vDKEsgwjX13080gEpuwEfYqjgqh9f7B_uAJnBdAygJlKubkMCph9POEeRAVjwCoCRVC-8AVLMueWyz26lbBTWHj1u3VEYaeMMK_4Jo8IqRTmmrWktQRUYs91AbsTinyN5M1MMjtaUhbkbVm_S3OVkxTzRmWZA4czj0d7q9GA0YJNLqiJwW7H/w150-h200/OneHotSummer.jpg" title="One Hot Summer, by Rosemary Ashton." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://yalebooks.yale.edu/book/9780300238662/one-hot-summer/">One Hot Summer</a></i>,<br />by <a href="https://www.ucl.ac.uk/english/people/rosemary-ashton">Rosemary Ashton</a>.<br /></td></tr></tbody></table>I recently finished <a href="https://en.wikipedia.org/wiki/Rosemary_Ashton">Rosemary Ashton</a>’s book <a href="https://www.amazon.com/One-Hot-Summer-Dickens-Disraeli/dp/0300227264/ref=sr_1_1?crid=10PA8QYJPIG2G&keywords=One+Hot+Summer%3A+Dickens%2C+Darwin%2C+Disraeli%2C+and+the+Great+Stink+of+1858&qid=1701788733&s=books&sprefix=one+hot+summer+dickens%2C+darwin%2C+disraeli%2C+and+the+great+stink+of+1858%2Cstripbooks%2C610&sr=1-1"><i>One Hot Summer: Dickens, Darwin, Disraeli, and the Great Stink of 1858</i></a>. Her prologue begins<br /><blockquote>
What was it like to live in <a href="https://en.wikipedia.org/wiki/London">London</a> through one of the hottest summers on record, with the <a href="https://en.wikipedia.org/wiki/River_Thames">Thames</a> <a href="https://en.wikipedia.org/wiki/Great_Stink">emitting a sickening smell as a result of the sewage of over two million inhabitants being discharged into the river</a>? How did people cope with the extraordinary heat leading up to the hottest recorded day, Wednesday, 16 June 1858? What did those living or working near the Thames—including at the <a href="https://en.wikipedia.org/wiki/Palace_of_Westminster">Houses of Parliament</a> and the law courts in <a href="https://en.wikipedia.org/wiki/Westminster_Hall">Westminster Hall</a>—do when they found their circumstances intolerable? What did the newspapers say?
</blockquote>
Ashton proposes to examine London for just a few months in the summer of 1858, providing a snapshot of one moment in <a href="https://en.wikipedia.org/wiki/Victorian_era">Victorian England</a>. Such a <a href="https://en.wikipedia.org/wiki/Microhistory">microhistory</a> provides insight into the life of mid-19th century Britain.
<br /><blockquote>
Microhistory, the study in depth and detail of historical phenomena, can uncover hitherto hidden connections, patterns, and structures. Some events and incidents are revealed over time to have been life changing or nation building. Examples from 1858 are the tackling of London’s sewage and the resultant improvement of public health, <a href="https://en.wikipedia.org/wiki/Isambard_Kingdom_Brunel">Brunel</a>’s engineering feats, the initial laying of the <a href="https://en.wikipedia.org/wiki/Transatlantic_telegraph_cable">Atlantic telegraph cable,</a> the beginnings of a long process of attaining justice and equality in the matter of marriage and divorce, and <a href="https://en.wikipedia.org/wiki/Medical_Act_1858">the transformation of the miscellaneous medical practice into a proper profession</a>.
</blockquote>
She focuses on the novelist <a href="https://en.wikipedia.org/wiki/Charles_Dickens">Charles Dickens</a>, biologist <a href="https://en.wikipedia.org/wiki/Charles_Darwin">Charles Darwin</a>, and politician <a href="https://en.wikipedia.org/wiki/Benjamin_Disraeli">Benjamin Disraeli</a>.
<br /><blockquote>
A comparatively neglected time in Disraeli’s career can be shown to have been remarkably important in bringing him to prominence. The attention of historians and biographers has focused hitherto on his reckless youth, his racy novels, his controversial journalism, and his late-won success from 1868, when he finally became <a href="https://en.wikipedia.org/wiki/Prime_Minister_of_the_United_Kingdom">prime minister</a>. His hard work in the parliamentary session of 1858, particularly in the hectic weeks before the summer break beginning on 2 August, and his success in turning round a hostile press and distrustful colleagues by his efforts, deserve to be acknowledged. In Dickens’s case his painful and self-exposing actions in connection with his failed marriage have been fully discussed, but no detailed account exists of the day-to-day struggles he faced in the long summer which followed his catastrophic error of judgment in advertising his separation from his wife in the early days of June. As for Darwin, though much has been written about his abrupt shock and change of plans on receiving in mid-June <a href="https://en.wikipedia.org/wiki/Alfred_Russel_Wallace">Wallace</a>’s letter outlining natural selection, little attention has been paid to the interaction between his family life and scientific work in summer 1858.
</blockquote><p>
This idea of a microhistory sounds fun, and I thought readers of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i> might be interested in learning about events in the summer of 1858 that influenced physics, biology, and medicine. So, in this blog post I augment Ashton’s analysis by adding incidents from the world of science.
<br /><br />
<a href="https://www.nhm.ac.uk/discover/charles-darwin-most-famous-biologist.html">Charles Darwin</a> (age 48, all ages are as of summer 1858) had been developing his theory of <a href="https://en.wikipedia.org/wiki/Evolution">evolution</a> by <a href="https://en.wikipedia.org/wiki/Natural_selection">natural selection</a> for twenty years, since returning to England in 1836 after his famous voyage on the <a href="https://en.wikipedia.org/wiki/Second_voyage_of_HMS_Beagle">HMS Beagle</a>. Over the years he had told his friends <a href="https://en.wikipedia.org/wiki/Joseph_Dalton_Hooker">Joseph Hooker</a> (age 41) and <a href="https://en.wikipedia.org/wiki/Charles_Lyell">Charles Lyell</a> (age 61) about his ideas, but had never published them. Ashton describes how on June 18, 1858 Darwin received a letter from <a href="https://www.nhm.ac.uk/discover/who-was-alfred-russel-wallace.html">Alfred Russel Wallace</a> (age 35), containing a draft of a paper describing the same idea of natural selection as the mechanism of biological evolution, written while Wallace was collecting biological specimens in the <a href="https://en.wikipedia.org/wiki/Malay_Archipelago">Malay Archipelago</a>. Hooker and Lyell arranged to have some early private writings of Darwin’s, along with the paper by Wallace, published on July 1 at a meeting of the <a href="https://en.wikipedia.org/wiki/Linnean_Society_of_London">Linnean Society of London</a>. </p><p></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC63LrhzuB-NHd92tPDaka09RkVxGQQT6F08HfZs6PmV2K9JPnKzCtjMOAJasJw1yc7_ybBl4QC7zGvqAhSOFfavP-grzmPBqy1z4ARVOXlNQeYzaBR0EY5NeAx4m1QR9yqUSkcpM0jod0UqDGnhzzwmTXpRVE1FB98_NmkTb4TMnMu-GeXMvh2I_Aq2Vl/s2016/TheOriginOfSpecies.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="On the Origin of Species, by Charles Darwin, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiC63LrhzuB-NHd92tPDaka09RkVxGQQT6F08HfZs6PmV2K9JPnKzCtjMOAJasJw1yc7_ybBl4QC7zGvqAhSOFfavP-grzmPBqy1z4ARVOXlNQeYzaBR0EY5NeAx4m1QR9yqUSkcpM0jod0UqDGnhzzwmTXpRVE1FB98_NmkTb4TMnMu-GeXMvh2I_Aq2Vl/w150-h200/TheOriginOfSpecies.jpg" title="On the Origin of Species, by Charles Darwin." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>On the Origin of Species</i>,<br />by Charles Darwin.<br /></td></tr></tbody></table>The following year, Darwin published his much more detailed book <a href="https://en.wikipedia.org/wiki/On_the_Origin_of_Species"><i>On the Origin of Species</i></a>, changing biology forever. One of the most pugnacious of the advocates for natural selection was his young friend <a href="https://en.wikipedia.org/wiki/Thomas_Henry_Huxley">Thomas Henry Huxley</a> (age 33), known as “Darwin’s Bulldog.” In 1858 Huxley was the <a href="https://en.wikipedia.org/wiki/Fullerian_Professor_of_Physiology">Fullerian Professor of Physiology</a> at London's <a href="https://en.wikipedia.org/wiki/Royal_Institution">Royal Institution</a>, and on June 17, 1858 he gave the <a href="https://en.wikipedia.org/wiki/Royal_Society">Royal Society</a>’s annual <a href="https://en.wikipedia.org/wiki/Croonian_Medal">Croonian Lecture</a>. Darwin’s friend Charles Lyell—winner of the Royal Society’s prestigious <a href="https://en.wikipedia.org/wiki/Copley_Medal">Copley Medal</a> in 1858 for his contributions to <a href="https://en.wikipedia.org/wiki/Geology">geology</a>—never completely embraced natural selection.<br /><br />
On June 10, 1858 the botanist <a href="https://en.wikipedia.org/wiki/Robert_Brown_(botanist,_born_1773)">Robert Brown</a> died in London, at age 84. In Chapter 4 of <a href="https://link.springer.com/book/10.1007/978-3-319-12682-1"><i>IPMB</i></a>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I write
<br /><p></p><blockquote>
This movement of microscopic-sized particles, resulting
from bombardment by much smaller invisible atoms, was
first observed by the English botanist Robert Brown in 1827
and is called <a href="https://en.wikipedia.org/wiki/Brownian_motion"><i>Brownian motion</i></a>.
</blockquote>
Brown’s death had an interesting impact on the Darwin/Wallace publications. Ashton writes
<br /><blockquote>
By a stroke of luck the death of the former president Robert Brown had induced the [Linnean] society to postpone its summer meeting from 17 June, the day before Darwin received Wallace’s letter, to Thursday, 1 July. This meant that Darwin (and Wallace) would not have to wait until September to have their papers made public.
</blockquote>
One of the most famous scientists in England during 1858 was <a href="https://en.wikipedia.org/wiki/Michael_Faraday">Michael Faraday</a> (age 65). In Chapter 8 of <i>IPMB</i>, Russ and I discuss <a href="https://en.wikipedia.org/wiki/Electromagnetic_induction">electromagnetic induction</a>, which underlies <a href="https://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation">transcranial magnetic stimulation</a> of the brain.
<br /><blockquote>
In 1831 Michael Faraday discovered that a changing magnetic
field causes an electric current to flow in a circuit.
</blockquote>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9kKPp24o9c9xYRU856bIDPsVGHrU6Zwbeg0q-X3-0IlX35f0WKh-Lz3DjV7zv8qDI-w3pjAP0ewupVI00U4BD1nvSnUAI_RhLKNJDi-LmMGVz7j_osx44zUGCdZycEi_zKujoZOQS2eHzjDdmOZHtWGHTkW-FCfjAiJf2fbqimgtnhfCl08BWbJBkKP0U/s2016/FaradayMaxwellAndTheElectromagneticField.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Faraday, Maxwell, and the Electromagnetic Field, by Forbes and Mahon, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj9kKPp24o9c9xYRU856bIDPsVGHrU6Zwbeg0q-X3-0IlX35f0WKh-Lz3DjV7zv8qDI-w3pjAP0ewupVI00U4BD1nvSnUAI_RhLKNJDi-LmMGVz7j_osx44zUGCdZycEi_zKujoZOQS2eHzjDdmOZHtWGHTkW-FCfjAiJf2fbqimgtnhfCl08BWbJBkKP0U/w150-h200/FaradayMaxwellAndTheElectromagneticField.jpg" title="Faraday, Maxwell, and the Electromagnetic Field, by Forbes and Mahon." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="http://prometheusbooks.com/books/9781633886070">Faraday, Maxwell, and the<br />Electromagnetic Field</a></i>,<br />by Forbes and Mahon.<br /></td><td class="tr-caption" style="text-align: center;"><br /></td></tr></tbody></table>After a long career at the Royal Institution, Faraday moved from his home at the RI to a house at <a href="https://en.wikipedia.org/wiki/Hampton_Court_Palace">Hampton Court</a> in 1858. In their book <a href="https://www.amazon.com/Faraday-Maxwell-Electromagnetic-Field-Revolutionized/dp/1616149426/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=1701793193&sr=1-1"><i>Faraday, Maxwell, and the Electromagnetic Field</i></a>, <a href="https://awis.org/historical-women/nancy-forbes/">Nancy Forbes</a> and <a href="https://www.goodreads.com/author/show/16539.Basil_Mahon">Basil Mahon</a> write
<br /><blockquote>
As Faraday’s health and mental faculties declined, he began to relinquish his various responsibilities at the Royal Institution, finally handing over the directorship to <a href="https://en.wikipedia.org/wiki/John_Tyndall">John Tyndall</a> in 1865. The consequent loss of income, and of his flat, would have been a worry, but in 1858 <a href="https://en.wikipedia.org/wiki/Prince_Albert_of_Saxe-Coburg_and_Gotha">Prince Albert</a>, a great admirer, had asked the queen to put a house at Hampton Court at his disposal. Faraday had refused at first, fearing the high cost of repairs, but the queen said she would pay. He and Sarah [his wife] moved in, and the new house became his last home.
</blockquote>
Although his research career was winding down, Faraday was still a great science communicator. On June 12, 1858 he gave a RI lecture “<a href="https://www.whipplemuseum.cam.ac.uk/explore-whipple-collections/microscopes/michael-faradays-microscope-slide">On the relation of gold to light,</a>” about light scattering from <a href="https://en.wikipedia.org/wiki/Colloidal_gold">gold colloids</a> (nowadays we would call them gold <a href="https://en.wikipedia.org/wiki/Nanoparticle">nanoparticles</a>). He was also famous for his <a href="https://en.wikipedia.org/wiki/Royal_Institution_Christmas_Lectures">Christmas lectures</a>, which he gave annually throughout the 1850s.
<br /><br />
Faraday’s work in <a href="https://en.wikipedia.org/wiki/Electromagnetism">electricity and magnetism</a> was carried on by the young <a href="https://en.wikipedia.org/wiki/James_Clerk_Maxwell">James Maxwell</a> (age 27), who was married on June 2, 1858 in <a href="https://en.wikipedia.org/wiki/Aberdeen">Aberdeen</a>, Scotland. That year, Maxwell published his paper “<a href="https://en.wikipedia.org/wiki/On_Physical_Lines_of_Force">On Faraday’s Lines of Force</a>” (although it had been read before the <a href="https://en.wikipedia.org/wiki/Cambridge_Philosophical_Society">Cambridge Philosophical Society</a> in late 1855 and early 1856). Forbes and Mahon write
<br /><blockquote>
In February 1857, [Maxwell] decided to send a copy of his paper “On Faraday’s Lines of Force” to the great man [Faraday]. No doubt, he did so with some trepidation… He needn’t have worried. As we’ve seen, Faraday’s response was grateful, gracious, and charming. The two had at once formed a rare bond.
</blockquote>
In the 1860s Maxwell continued his research on electromagnetism, and eventually developed the four <a href="https://en.wikipedia.org/wiki/Maxwell%27s_equations">Maxwell’s equations</a> that rival Darwin’s theory of evolution as the most significant <a href="https://en.wikipedia.org/wiki/19th_century_in_science">scientific contribution of the 19th century</a>.
<br /><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA4Fxgd-QMcX4j-BSFTkYH691-BpoqULny0QhNjqhdgqQHMFbLBZTOpzPns6UOJ0rWQL31Ngg_pftjTl4yRwfAhxMM9SFX8l1SwgOdoG6-YUx7UG93PeXAeLg4SlGvvnoJZJPsjsptmYrk0CgXWjabq_31IfizwBYTopURYSFRkus91rdHw7zbgFG5IHfr/s2016/AThreadAcrossTheOcean.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="A Thread Across the Ocean, by John Steele Gordon, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgA4Fxgd-QMcX4j-BSFTkYH691-BpoqULny0QhNjqhdgqQHMFbLBZTOpzPns6UOJ0rWQL31Ngg_pftjTl4yRwfAhxMM9SFX8l1SwgOdoG6-YUx7UG93PeXAeLg4SlGvvnoJZJPsjsptmYrk0CgXWjabq_31IfizwBYTopURYSFRkus91rdHw7zbgFG5IHfr/w150-h200/AThreadAcrossTheOcean.jpg" title="A Thread Across the Ocean, by John Steele Gordon." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://www.harpercollins.com/products/a-thread-across-the-ocean-john-steele-gordon?variant=32116705853474">A Thread Across the Ocean</a></i>,<br />by <a href="http://www.johnsteelegordon.com/bio.html">John Steele Gordon</a>.<br /></td></tr></tbody></table>Besides Faraday and Maxwell, a third great Victorian physicist was <a href="https://en.wikipedia.org/wiki/Lord_Kelvin">William Thomson</a> (age 34), who was one of the main scientists involved in developing the transatlantic telegraph. As part of that effort, in February of 1858 Thomson patented the <a href="https://en.wikipedia.org/wiki/Mirror_galvanometer">mirror galvanometer</a>, which is an instrument to measure electrical current. In his book <i><a href="https://www.amazon.com/Thread-Across-Ocean-Heroic-Transatlantic/dp/B001RFOHWE/ref=sr_1_1?keywords=A+Thread+Across+the+Ocean&qid=1701803857&s=books&sr=1-1">A Thread Across the Ocean</a></i>, <a href="https://en.wikipedia.org/wiki/John_Steele_Gordon">John Steele Gordon</a> describes this device.
<br /><blockquote>
In a long submarine cable, immersed in a conducting medium—saltwater—the current if often very low, sometimes no more than ten <a href="https://en.wikipedia.org/wiki/Ampere">mircoamperes</a>. (The current in a standard <a href="https://en.wikipedia.org/wiki/Incandescent_light_bulb">incandescent lightbulb</a> is about 100,000 times as great.) The standard galvanometers then available were often inadequate to detect a signal coming through a cable that would be two thousand miles long. So Thomson—half <a href="https://en.wikipedia.org/wiki/Albert_Einstein">Einstein</a>, half <a href="https://en.wikipedia.org/wiki/Thomas_Edison">Edison</a>—developed a much better one. He took a very small magnet and attached a tiny mirror to it. Both together weighed no more than a <a href="https://en.wikipedia.org/wiki/Grain_(unit)">grain</a>. He suspended the magnet from a silk thread and set it in the middle of the coil of very thin insulated copper wire.
<br /><br />
When the faint current flowing through the cable was allowed to flow through the copper coil, it created a magnetic field. This caused the magnet, with its attached mirror, to deflect. Thomson simply directed a beam of light from a shaded lamp onto the mirror and allowed it reflection to hit a graduated scale.
</blockquote><p>
In June of 1858 two ships—the <a href="https://en.wikipedia.org/wiki/HMS_Agamemnon_(1852)">Agamemnon</a> and the <a href="https://en.wikipedia.org/wiki/USS_Niagara_(1855)">Niagara</a>—attempted to meet in the middle of the <a href="https://en.wikipedia.org/wiki/Atlantic_Ocean">Atlantic Ocean</a>,
splice together the two halves of the cable, and then each pay out the cable as they sailed toward shore: the Niagara toward <a href="https://en.wikipedia.org/wiki/Newfoundland_and_Labrador">Newfoundland</a> and the Agamemnon toward <a href="https://en.wikipedia.org/wiki/Ireland">Ireland</a>. However, a terrible storm struck the North Atlantic that month, nearly capsizing the Agamemnon with Thomson on board and aborting the mission. <br /></p><p></p><blockquote>On Sunday, June 20, the storm unleashed a fury such as few sailors ever see and even fewer live to tell about. The caption feared that the coil on the deck, working against its restraints, might break lose and smash through the side, undoubtedly causing the ship to founder. </blockquote><p></p><p>A second try several weeks later proved more successful. On August 16, the first transatlantic telegraph message was sent between <a href="https://en.wikipedia.org/wiki/Queen_Victoria">Queen Victoria</a> in England and President <a href="https://en.wikipedia.org/wiki/James_Buchanan">James Buchanan</a> in the United States. Unfortunately, the cable soon failed, and it was not until some years later that reliable telegraph service was established across the Atlantic.
<br /><br />
Based on his basic research discoveries and his contributions to the telegraph, Thomson became a scientific hero. Gordon writes
<br /></p><blockquote>
In 1892, William Thomson became the first British scientist to be raised to the <a href="https://en.wikipedia.org/wiki/Peerages_in_the_United_Kingdom">peerage</a>, when Queen Victoria created him Lord Kelvin of Largs. He has been known ever since as Lord Kelvin. In 1908, the year after he died, the <a href="https://en.wikipedia.org/wiki/Kelvin">Kelvin temperature scale</a>, devised by him in the 1850s, was named in his honor.
</blockquote><p>The absolute temperature scale, with Kelvin’s name attached to <a href="https://en.wikipedia.org/wiki/Kelvin">the unit of temperature</a>, appears throughout <i>IPMB</i>. <br /></p><p>Still another notable Victorian physicist was <a href="https://en.wikipedia.org/wiki/Sir_George_Stokes,_1st_Baronet">George Stokes</a> (age 36), who at that time was the <a href="https://en.wikipedia.org/wiki/Lucasian_Professor_of_Mathematics">Lucasian Professor</a> at <a href="https://en.wikipedia.org/wiki/University_of_Cambridge">Cambridge University</a> (a position held earlier by <a href="https://en.wikipedia.org/wiki/Isaac_Newton">Isaac Newton</a> and later by <a href="https://en.wikipedia.org/wiki/Stephen_Hawking">Stephen Hawking</a>). <i>IPMB</i> often uses <a href="https://en.wikipedia.org/wiki/Stokes%27_law">Stokes’ law</a> for the viscous force of a small sphere in a fluid. Stokes and Thomson were close friends, and <a href="https://hobbieroth.blogspot.com/2014/03/the-correspondence-between-sir-george.html">their many letters are preserved</a>. I provide a few excerpts from these letters during late 1857 and 1858.</p><p></p><blockquote><p>2 College, Glasgow</p><p>Dec. 23, 1857</p><p>My Dear Stokes</p><p>That principle, in the <a href="https://en.wikipedia.org/wiki/Fluid_dynamics">hydrodynamics</a> of a “<a href="https://en.wikipedia.org/wiki/Perfect_fluid">perfect liquid</a>”, which I first learned from you, is something that I have always valued as one of the great things of science, simple as it is, and I now see more than ever its importance. One conclusion from it is that <a href="https://en.wikipedia.org/wiki/Turbulence">instability,</a> or a tendency to run to eddies, or any kind of dissipation of energy, is impossible in a perfect liquid (a fluid with neither <a href="https://en.wikipedia.org/wiki/Viscosity">viscosity</a> nor <a href="https://en.wikipedia.org/wiki/Compressibility">compressibility</a>)... [several pages follow with many equations]...Some of the simplest applications of the theory are very interesting: for instance the... case of a circular disc or oblate spheroid, moving... in a perfect [liquid]...</p><p>As to <a href="https://en.wikipedia.org/wiki/Faraday_effect">Faraday’s magneto-optic experiment</a>, I think my argument that it must depend on a peculiar state of motion induced by magnetic influence (<a href="https://en.wikipedia.org/wiki/Proceedings_of_the_Royal_Society"><i>Proceedings R. S.</i></a> June or July 1856) is unanswerable. Have you considered it?...</p><p>It seems like old times for me to be writing you so long a letter, and I am afraid you will be less disposed to be so bored. Your redress simply be not to read it.</p><p>With best wishes for a “Merry Christmas” of which there can be no doubt now, I remain</p><p></p><p>Yours always truly</p><p>William Thomson</p></blockquote><p></p><p>Stokes responded,</p><p></p><blockquote><p>69 Albert Street <a href="https://en.wikipedia.org/wiki/Regent%27s_Park">Regent's Park</a> London N.W. <br /></p></blockquote><blockquote><p>Feb. 12, 1858 <br /></p></blockquote><blockquote><p>My Dear Thomson,</p><p>I have been so very busy of late that your letter has remained for a long time unanswered. I now set to answer it, though I have still got plenty of work before me...</p><p>Without having a decided opinion either way I have always inclined to the belief that the motion of a perfect incompressible liquid, primitively at rest, about a solid which continually progressed, was unstable... [pages of math...]</p><p>In speculating a good while ago (in fact no great time after Faraday’s discovery) as to the cause of magnetic rotation I naturally tried rotations of the <a href="https://en.wikipedia.org/wiki/Luminiferous_aether">luminiferous ether</a> as suggested by <a href="https://en.wikipedia.org/wiki/Andr%C3%A9-Marie_Amp%C3%A8re">Ampere’s</a> theory...</p><p>Yours very truly</p><p>G. G. Stokes</p></blockquote><p></p><p>Finally, late in 1858, Stokes wrote<br /></p><blockquote><p><a href="https://en.wikipedia.org/wiki/Athenaeum_Club,_London">The Athenaeum</a></p><p>Oct 5/58</p><p>My Dear Thomson,</p><p>... It is a great pity to see the [transatlantic] cable in its present state after apparently so successful a laying down. Still the thing has been done and even if this should be utterly lost the matter will not I presume rest there.</p><p>I did not go to <a href="https://en.wikipedia.org/wiki/Leeds">Leeds</a> this meeting [The <a href="https://en.wikipedia.org/wiki/British_Science_Association">British Science Association</a> met in Leeds in 1858]. On the morning of the 27th my wife was safely delivered of a fine boy. She is going on very well but I am afraid her complete recovery will be slow.</p><p>Yours very truly</p><p>G. G. Stokes</p></blockquote><p><a href="https://en.wikipedia.org/wiki/James_Prescott_Joule">James Joule</a> (age 39) was yet another English physicist of the Victorian era. His name appears repeatedly in <i>IPMB</i> because the <a href="https://en.wikipedia.org/wiki/Joule">unit of energy</a> is named after him. In the 1840s Joule had done pioneering work on the <a href="https://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat">mechanical equivalent of heat</a> and the <a href="https://en.wikipedia.org/wiki/Conservation_of_energy">conservation of energy</a>, and in the 1850s had collaborated to explain the <a href="https://en.wikipedia.org/wiki/Joule%E2%80%93Thomson_effect">Joule-Thomson</a> effect. In 1858 he was in a train wreck while traveling home from London. Although unhurt, the accident made him reluctant to travel, somewhat isolating him from the scientific community.<br /></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5ARPgAFAfCMs4ZIoD3dKIpGbr2TXifR-U86yt4HaNw9yaUyj77dG5BxpivWu_FU2XNa6cKUmg9Lo4GeBQzTtR4NB4DwQ1bRwJfgACH8VG6IwBd0N6d1aLA3bnEjzU6FA9eMKJNXmlOkchwrIpm4PkWqKJ70cIWHPsaAxD9sZBu18fcqz2Pp-HPMThK4WI/s2006/GraysAnatomy.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Gray’s Anatomy, below Intermediate Physics for Medicine and Biology." border="0" data-original-height="2006" data-original-width="1473" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg5ARPgAFAfCMs4ZIoD3dKIpGbr2TXifR-U86yt4HaNw9yaUyj77dG5BxpivWu_FU2XNa6cKUmg9Lo4GeBQzTtR4NB4DwQ1bRwJfgACH8VG6IwBd0N6d1aLA3bnEjzU6FA9eMKJNXmlOkchwrIpm4PkWqKJ70cIWHPsaAxD9sZBu18fcqz2Pp-HPMThK4WI/w147-h200/GraysAnatomy.jpg" title="Gray’s Anatomy." width="147" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Gray’s Anatomy</i>.<br /></td></tr></tbody></table><p> A major event in medicine occurred during the summer of 1858: the publication of the first edition of <a href="https://en.wikipedia.org/wiki/Gray%27s_Anatomy"><i>Gray’s Anatomy</i></a>. In his article “<a href="https://www.tandfonline.com/doi/abs/10.1080/08998280.2009.11928553">Happy Birthday, Gray’s Anatomy</a>,” <a href="https://www.dmagazine.com/healthcare-business/2017/10/dr-adrian-e-flatt-1921-2017/">Adrian Flatt</a> (<i>Proc. Bayl. Med. Cent.</i>, 22:342–345, 2009) writes
<br /></p><blockquote>
<i>Anatomy Descriptive and Applied</i> was first published in London
in the summer of 1858 by two young demonstrators of
anatomy in <a href="https://en.wikipedia.org/wiki/St_George%27s_Hospital">St. George’s Hospital</a> at Hyde Park Corner…
These two young men were very different. <a href="https://en.wikipedia.org/wiki/Henry_Gray">Henry Gray</a> [age 31] wrote
the text; he was 4 years older than <a href="https://en.wikipedia.org/wiki/Henry_Vandyke_Carter">Henry Vandyke Carter</a> [age 27], who
drew all the illustrations…
</blockquote><blockquote>
The print number of 2000 books had been decided, page
size was fixed, and all the paper purchased. Considerable
adjustments were successfully made and by mid May 1857,
the work was going well but was to be interrupted by the
absence of Gray. He had received an invitation to “attend”
the Duke of Sutherland on his private yacht sailing around
England and Scotland and at the estate at <a href="https://en.wikipedia.org/wiki/Dunrobin_Castle">Dunrobin Castle</a>
for the next 6 months, from June to November 1857. This was
manna from heaven for Gray; service for such an aristocrat
would be of enormous help to his practice. Carter continued
work on the book, of which the final proof corrections were
done in late June or early July 1858, in time for the book to
be available for students arriving in September.
</blockquote>
Gray died at age 34, just three years after publication of his textbook, of <a href="https://en.wikipedia.org/wiki/Smallpox">smallpox</a>. Apparently the relationship between Gray and Carter was strained. Flatt states that
<br /><blockquote>
Gray never gave Carter one penny from all the royalties the early editions of the book earned.
</blockquote>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2xnIxnI8Bpv70jQ4l6Wv96DSttvyz4UKX4rFR-rcFZVcpanZk8MaeM9OqbddlGxk49ofOVsoxoc-0KjIUeadvGnXk5Z1ujanfLhRaTyFW36Zrjv-uB1FN6PlqUJbHQaTp4AGJqkjPulWdB5GaX4yfcNX8dH9lHFC6LXzdMqxp4RTTmUFbGWn2hbychfBx/s1024/NightingaleCoxcomb.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Diagram of the causes of mortality in the army in the East (1858)" border="0" data-original-height="560" data-original-width="1024" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2xnIxnI8Bpv70jQ4l6Wv96DSttvyz4UKX4rFR-rcFZVcpanZk8MaeM9OqbddlGxk49ofOVsoxoc-0KjIUeadvGnXk5Z1ujanfLhRaTyFW36Zrjv-uB1FN6PlqUJbHQaTp4AGJqkjPulWdB5GaX4yfcNX8dH9lHFC6LXzdMqxp4RTTmUFbGWn2hbychfBx/w320-h175/NightingaleCoxcomb.jpg" title="Diagram of the causes of mortality in the army in the East (1858)" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Diagram of the causes of mortality <br />in the army in the East (1858).<br /></td></tr></tbody></table><p>Another leading figure of Victorian health care was <a href="https://en.wikipedia.org/wiki/Florence_Nightingale">Florence Nightingale</a> (age 38), the founder of modern nursing. In 1858 Nightingale published <a href="https://wellcomecollection.org/works/jxwtskzc"><i>Notes on Matters Affecting the Health, Efficiency, and Hospital Administration of the British Army. Founded Chiefly on the Experience of the Late War. Presented by Request to the Secretary of State for War</i></a>. This work contained a color statistical illustration called “Diagram of the Causes of Mortality in the Army of the East” that showed that epidemic disease—which caused more British deaths during the <a href="https://en.wikipedia.org/wiki/Crimean_War">Crimean War</a> than battlefield wounds—could be controlled by nutrition, ventilation, and shelter. The <a href="https://en.wikipedia.org/wiki/Infographic">infographic</a> became known as Nightingale’s “coxcomb.” Her achievements in <a href="https://en.wikipedia.org/wiki/Statistics">statistics</a> were so remarkable that in 1858 she was selected as the first woman fellow of the <a href="https://en.wikipedia.org/wiki/Royal_Statistical_Society">Royal Statistical Society</a>. Two years later she established her nursing school at <a href="https://en.wikipedia.org/wiki/St_Thomas%27_Hospital">Saint Thomas’ Hospital</a> in London.
<br /><br />
Another noteworthy happening in medicine was the death of <a href="https://en.wikipedia.org/wiki/John_Snow">John Snow</a> (age 45) on June 16, 1858 (London’s hottest day of that steamy summer). Snow was best known for figuring out the source of the <a href="https://en.wikipedia.org/wiki/1854_Broad_Street_cholera_outbreak">Broad Street cholera outbreak</a> in 1854, when he demonstrated that cholera was being spread through contaminated water from one specific pump. He also studied using <a href="https://en.wikipedia.org/wiki/Ether">ether </a>as an <a href="https://en.wikipedia.org/wiki/Anesthesia">anesthesia</a> during surgery. </p><p></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbS4AfEp62iQmsCmJosXRY9Wmzx3JVbsEqo-ne-wG7onFCKafNJVYhF1EEqOWGQkqfWU6Y9YN2HbOcpFftNFfqJYczsiJ6up7Q_qF5rGSp2aPugMIEeT89zxoBmodlyxnynmKFUBDJiow1M5PDtasnTJTT76e1bWG8353n7oHhwYMGuFCtKHrT9X33qr0b/s2016/TheGhostMap.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="The Ghost Map, by Steven Johnson, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhbS4AfEp62iQmsCmJosXRY9Wmzx3JVbsEqo-ne-wG7onFCKafNJVYhF1EEqOWGQkqfWU6Y9YN2HbOcpFftNFfqJYczsiJ6up7Q_qF5rGSp2aPugMIEeT89zxoBmodlyxnynmKFUBDJiow1M5PDtasnTJTT76e1bWG8353n7oHhwYMGuFCtKHrT9X33qr0b/w150-h200/TheGhostMap.jpg" title="The Ghost Map, by Steven Johnson." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://www.penguinrandomhouse.com/books/295522/the-ghost-map-by-steven-johnson/">The Ghost Map</a></i>,<br />by Steven Johnson.<br /></td></tr></tbody></table>In his fascinating book <i><a href="https://www.amazon.com/Ghost-Map-Londons-Terrifying-Epidemic/dp/1594489254/ref=tmm_hrd_swatch_0?_encoding=UTF8&qid=1701863031&sr=1-1">The Ghost Map</a></i>, <a href="https://en.wikipedia.org/wiki/Steven_Johnson_(author)">Steven Johnson</a> writes about the prevailing belief that <a href="https://en.wikipedia.org/wiki/Miasma_theory">miasma</a> (bad air) caused disease.<p></p><p></p><blockquote>In June 1858, a relentless early-summer heat wave produced a stench of epic proportions along the banks of the polluted Thames. The press quickly dubbed it the “Great Stink”... [Yet] the rates of death from epidemic disease proved to be entirely normal. Somehow the most notorious cloud of miasmatic air in the history of London had failed to produce even the slightest uptick in disease mortality... It's easy to imagine John Snow taking great delight in [this] puzzling data... But he never got the opportunity. He had suffered a stroke in his office on June 10... and died six days later, just as the Great Stink was reaching its peak above the foul waters of the Thames.</blockquote><p></p><p><a href="https://en.wikipedia.org/wiki/Joseph_Lister">Joseph Lister</a> (age 31) was in <a href="https://en.wikipedia.org/wiki/Edinburgh">Edinburgh</a> in 1858, studying the <a href="https://en.wikipedia.org/wiki/Coagulation">coagulation of blood</a> and <a href="https://en.wikipedia.org/wiki/Inflammation">inflammation</a>. In the 1860s he developed <a href="https://en.wikipedia.org/wiki/Antiseptic">antiseptic surgery</a>, and later relocated to London. In their article “<a href="https://www.canjsurg.ca/content/55/5/E8.2">Joseph Lister: Father of Modern Surgery</a>” (<i>Can. J. Surg.</i>, 55:E8–E9, 2012), <a href="https://med.uottawa.ca/surgery/people/pitt-dennis">Dennis Pitt</a> and <a href="https://www.linkedin.com/in/jean-michel-aubin-ba585443/?originalSubdomain=ca">Jean-Michel Aubin</a> claim that </p><p></p><blockquote>it was Lister’s application of <a href="https://en.wikipedia.org/wiki/Germ_theory_of_disease">germ theory</a> to the care of surgical patients that laid the foundation for what surgeons do now. He directed the minds of physicians and surgeons to the vital necessity of keeping wounds clean and free of contamination. </blockquote><p></p><p>
Finally, in 1858 <a href="https://en.wikipedia.org/wiki/Elizabeth_Garrett_Anderson">Elizabeth Garrett Anderson</a> (age 22) was a young woman dreaming of making a career in medicine. She eventually became the first female doctor in the United Kingdom.
<br /><br />
Ashton believes that microhistory provides valuable insight into Victorian England. Near the end of her Prologue she concludes
<br /></p><blockquote>
Intense scrutiny of the lives of these men [Dickens, Darwin, and Disraeli, plus Brown, Faraday, Maxwell, Thomson, Stokes, Joule, Gray, Nightingale, Snow, and others] over a short period of a few months allows us to make fresh threads of connection between each of them and the larger society in which they lived, all at a time of public events which provided to be of lasting national importance.
</blockquote><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-75464331566143405762023-12-01T05:00:00.018-05:002023-12-01T05:00:00.157-05:00Louis Pasteur, Biological Physicist<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPilp-kNN83tQ1Ood6KctNQyvkne-h9HtESrU_2d1U7bGimAD3IldjYb-YylLvZr1swSz7CUtw0e42H58iKZeaup_E-9DYKyrXA2oT_ZxAmUUxrYBI03t9zT3uUWwkVRBpwNH-Fe0bYn_corvhRW6kt-10R-3zK0wfPgBc9z_mLraHafrTiVnmXoSgLhZd/s610/LouisPasteur.jpg" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="583" data-original-width="610" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPilp-kNN83tQ1Ood6KctNQyvkne-h9HtESrU_2d1U7bGimAD3IldjYb-YylLvZr1swSz7CUtw0e42H58iKZeaup_E-9DYKyrXA2oT_ZxAmUUxrYBI03t9zT3uUWwkVRBpwNH-Fe0bYn_corvhRW6kt-10R-3zK0wfPgBc9z_mLraHafrTiVnmXoSgLhZd/w200-h191/LouisPasteur.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Louis Pasteur (1822–1895)<br /></td></tr></tbody></table>One recurring theme in this blog is how scientists make the transition from working in the physical sciences to studying the biological sciences. Indeed, this theme is intimately related to <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>. Recently, I decided to consider a case study of how a prominent scientist straddled physics, biology, and medicine. So, I searched for someone famous who illustrates how one trained in physics can end up contributing to the life sciences. I selected <a href="https://en.wikipedia.org/wiki/Louis_Pasteur">Louis Pasteur</a>.
<br />
<br /><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBugGOzmLhs3xRsqbimhXxU8kj4U-wT9-1wWLub4JLjRREsk3I0qh9AWPJK-T9H-iT8kJ5E4Ls9dxsyJ0rNm-P8_w8vSLRNm1-MgzJq-VoM91VW64ToHMSI0JDzd1Leo4Xuy00A0l3XzAKAQqQdx4MJBsgC7AXzrFwKd-fWOZWwJMvhN4HRDQPH7rt1FES/s2008/LouisPasteur.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="763" data-original-width="2008" height="76" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBugGOzmLhs3xRsqbimhXxU8kj4U-wT9-1wWLub4JLjRREsk3I0qh9AWPJK-T9H-iT8kJ5E4Ls9dxsyJ0rNm-P8_w8vSLRNm1-MgzJq-VoM91VW64ToHMSI0JDzd1Leo4Xuy00A0l3XzAKAQqQdx4MJBsgC7AXzrFwKd-fWOZWwJMvhN4HRDQPH7rt1FES/w200-h76/LouisPasteur.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Louis Pasteur</i>, by Patrice Debré.<br /></td></tr></tbody></table><p>I base this study on the biography <i><a href="https://www.amazon.com/Louis-Pasteur-Patrice-Debr%C3%A9/dp/0801865298/ref=sr_1_1?keywords=Louis+Pasteur+by+Patrice+Debr%C3%A9&qid=1700138720&s=books&sr=1-1">Louis Pasteur</a></i> by <a href="https://www.press.jhu.edu/books/authors/patrice-debre">Patrice Debré</a> (translated from French to English by <a href="https://www.press.jhu.edu/books/authors/elborg-forster">Elborg Forster</a>). As I read this book, I focused on the key events in Pasteur’s education and early research when he made this transition. </p><p>Pasteur began his career as a physical scientist studying at the <a href="https://en.wikipedia.org/wiki/%C3%89cole_normale_sup%C3%A9rieure_(Paris)">École normale supérieure</a> in Paris.
<br /></p><blockquote>
For his doctorate, Pasteur had to submit two theses, one in physics and one in chemistry. The physics thesis brought together several studies concerning the use of the <a href="https://en.wikipedia.org/wiki/Polarimeter">polarimeter</a>… Pasteur’s first studies showed, or rather confirmed, that two isomorphic substances rotate polarized light to the same degree.
</blockquote>
Polarization was a new topic in physics at that time. <a href="https://en.wikipedia.org/wiki/%C3%89tienne-Louis_Malus">Étienne-Louis Malus</a>, a fellow Frenchman, discovered the <a href="https://en.wikipedia.org/wiki/Polarizer#Malus'_law_and_other_properties">Law of Malus</a>, governing how much light passes through two polarizers, in 1808, just 14 years before Pasteur’s birth. Pasteur’s friend and mentor <a href="https://en.wikipedia.org/wiki/Jean-Baptiste_Biot">Jean-Baptiste Biot</a> first showed that polarized light could be <a href="https://en.wikipedia.org/wiki/Optical_rotation">rotated</a> when passed through certain crystals. Pasteur’s contribution was to prove that crystals formed from <a href="https://en.wikipedia.org/wiki/Tartaric_acid">tartaric acid</a> could rotate polarized light either clockwise or counterclockwise, depending on the <a href="https://en.wikipedia.org/wiki/Chirality">chirality</a> of the crystal (this acid is asymmetric, having two forms that are mirror images of each other, like the left hand and the right hand). In a famous experiment, he inspected the structure of each crystal under a microscope and determined if it was left or right handed. When he then separated the two types of crystals he could obtain rotation in either direction, although a mixture of the two crystals did not rotate light. This discovery, made in 1848, at first appears to arise from physics and chemistry alone, but its relation to biology is that most biological molecules exist in only one version. Handedness matters in biology. Debré writes
<br /><blockquote>
In discovering the principles of molecular asymmetry, Pasteur had done nothing less than to forge a key—and this key has unlocked the door to the whole of modern biology… When Pasteur considered asymmetry on a cosmic scale, he went beyond the confines of physics and chemistry to confront the fundamental questions about life.
</blockquote><div style="text-align: left;">
Pasteur’s next step toward biology came when he was a young professor at the <a href="https://en.wikipedia.org/wiki/University_of_Lille">University of Lille</a>.
<br /><blockquote>
At the beginning of the academic year 1856, an industrialist of <a href="https://en.wikipedia.org/wiki/Lille">Lille</a>, M. Bigo, whose son Emile was taking Pasteur’s course at the Faculty of Sciences, came to see him. Many manufacturers of <a href="https://en.wikipedia.org/wiki/Beetroot">beet root</a> alcohol, he said, were having problems with their production…
</blockquote></div><div style="text-align: left;">
This led to Pasteur’s research on <a href="https://en.wikipedia.org/wiki/Fermentation">fermentation</a>, when a <a href="https://en.wikipedia.org/wiki/Microorganism">microorganism</a> such as <a href="https://en.wikipedia.org/wiki/Yeast">yeast</a> brings about a change to a food or beverage, such as producing alcohol. Fermentation and light polarization do not appear to have much in common, but they do.
<br /><blockquote>
The findings Pasteur presented to the Academy of Sciences of Lille, and subsequently that of Paris, seemed very different from the studies he had undertaken previously. He was known as a specialist on crystals, and now he had become a theoretician of fermentation. Ranging from polarized planes of light to culture media, his reagents had little in common. Yet the preoccupations that guided Pasteur’s thinking at that period were not really different from those that had haunted him for a long time: he wanted to understand the relationship between life and molecular asymmetry.
</blockquote>
The idea that a living microscopic organism was responsible for fermentation was one of Pasteur’s key insights. In fact, there were two types of yeast involved in beet root fermentation. The desirable one produced alcohol. The undesirable one, that led to all the problems, produced <a href="https://en.wikipedia.org/wiki/Lactic_acid">lactic acid</a>. Debré concludes
<br /><blockquote>
A few years after the request of industrialist Bigo, Pasteur had thus established beyond a doubt that the lactic acid in the vats in the rue d’Esquermes came from an unfortunate contamination with this yeast. He even suggested the means to get rid of this contamination… Pasteur’s research on fermentation created <a href="https://en.wikipedia.org/wiki/Microbiology">microbiology</a>.
</blockquote>
Pasteur’s work on fermentation led to the related question of <a href="https://en.wikipedia.org/wiki/Spontaneous_generation">spontaneous generation</a>. Many scientists at the time thought that living organisms could spontaneously arise in dead and decaying tissue, but Pasteur showed that such decay was always due to germs that entered the tissue from the air.
<br /><br />
Pasteur’s transition to biology became complete after <a href="https://en.wikipedia.org/wiki/Jean-Baptiste_Dumas">Jean-Baptiste Dumas</a> asked him to investigate a disease that was destroying the <a href="https://en.wikipedia.org/wiki/Bombyx_mori">silkworm</a> industry in France. To address this issue, he needed to learn more biology.
<br /></div><div style="text-align: left;"><blockquote>
Pasteur came from crystals. Owing to his scant knowledge of animal biology, he was somewhat apprehensive about experiments on animals. As soon as he accepted Dumas’s assignment, he therefore went, along with his assistant <a href="https://en.wikipedia.org/wiki/%C3%89mile_Duclaux">Emile Duclaux</a>, to the physiology course taught by <a href="https://en.wikipedia.org/wiki/Claude_Bernard">Claude Bernard</a> at the <a href="https://en.wikipedia.org/wiki/University_of_Paris">Sorbonne</a>. There he took notes and humbly relived his years of training in the halls of the university. But he found it difficult to learn a whole new field; and indeed, since he had neither the time nor the patience to do this, he soon preferred to form his own ideas on the problem at hand.
</blockquote>
Once again, Pasteur was successful in addressing a biological problem; this time <a href="https://en.wikipedia.org/wiki/Bacteria">bacteria</a> infecting silkworms (they are not really a worm, but a <a href="https://en.wikipedia.org/wiki/Caterpillar">caterpillar</a>).
<br /><blockquote>
The caterpillar of <a href="https://en.wikipedia.org/wiki/Al%C3%A8s">Alés</a> led Pasteur from microbiology to veterinary science to medicine… When Pasteur revolutionized the science of his era by discovering the germs and their role, it was only natural that he should become interested in medicine and hygiene.
</blockquote>
At this point, Pasteur had essentially completed his transition from physics to biology and medicine. I won’t discuss his later work on the use of <a href="https://en.wikipedia.org/wiki/Antiseptic">antiseptics</a> in surgery, <a href="https://en.wikipedia.org/wiki/Pasteurization">pasteurization</a>, <a href="https://en.wikipedia.org/wiki/Anthrax">anthrax</a> infection in sheep, or the development of a <a href="https://en.wikipedia.org/wiki/Rabies">rabies</a> <a href="https://en.wikipedia.org/wiki/Vaccine">vaccine</a>.
Debré summarizes,<br /><blockquote>
In his last studies, Pasteur recalled that he had started out as a chemist. First in the laboratory of the rue d’Ulm and then in his <a href="https://en.wikipedia.org/wiki/Pasteur_Institute">Institute</a>, his ultimate experiments indicate that he was trying to understand how the same microbe can either kill a person or stimulate his or her resistance. This is where <a href="https://en.wikipedia.org/wiki/Bacteriology">bacteriology</a> merged into <a href="https://en.wikipedia.org/wiki/Immunology">immunology</a>. Pasteur brought these neighboring disciplines together. Understanding the role of the molecules, the toxins, and the antitoxins involved both chemistry and biology.
</blockquote>
So what do I conclude about Pasteur’s transition from the physical to the biological sciences? It wasn’t part of a long-range plan. Nor was it primarily motivated by the desire to help the sick, at least initially. I see two key points. First, the rotation of polarized light when passed through an organic substance led him naturally from physics to biology; scientific problems don’t always respect academic boundaries. Second, requests to address industrial problems further accelerated this transition, and those problems happened to be biological in nature. There seems to be a lot of chance involved in this transition (I think there often is for many scientists). But, as Pasteur famously said, <a href="https://en.wikiquote.org/wiki/Louis_Pasteur">chance favors the prepared mind</a>. </div><div style="text-align: left;"> </div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/OXdbQ1JkX7c" width="320" youtube-src-id="OXdbQ1JkX7c"></iframe></div> </div><div style="text-align: left;">https://www.youtube.com/watch?v=OXdbQ1JkX7c<br /> </div><div style="text-align: left;"><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/1lLNZQVPpQA" width="320" youtube-src-id="1lLNZQVPpQA"></iframe></div><br /> https://www.youtube.com/watch?v=1lLNZQVPpQA</div>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com2Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999117.025961455354093 -118.36448469999999 68.3097949446459 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-43760733377667555632023-11-24T05:00:00.337-05:002023-11-24T05:00:00.124-05:00The Deadly Rise of Anti-Science<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIEmvP5ksfjRSJu2x7xLU0kCsce4zecQ2aXrBGPjrXe4-Oy2MEdPa-5LXfY_AI6opn5g8Ct8NlfnW0Nw63FUwy5fs2uuUfdnYv702-p0L3yV1c5H7MK4jl_-Bi2OtTpCf1Cw7NVfJg1y9sv7UDgROH1n-51Bli2CUjQ-Y5q1pNGNYDnwQjXPcXc85gZC8Z/s2016/TheDeadlyRiseOfAntiScience.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="The Deadly Rise of Anti-Science, by Peter Hotez, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjIEmvP5ksfjRSJu2x7xLU0kCsce4zecQ2aXrBGPjrXe4-Oy2MEdPa-5LXfY_AI6opn5g8Ct8NlfnW0Nw63FUwy5fs2uuUfdnYv702-p0L3yV1c5H7MK4jl_-Bi2OtTpCf1Cw7NVfJg1y9sv7UDgROH1n-51Bli2CUjQ-Y5q1pNGNYDnwQjXPcXc85gZC8Z/w150-h200/TheDeadlyRiseOfAntiScience.jpg" title="The Deadly Rise of Anti-Science, by Peter Hotez." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i><a href="https://www.press.jhu.edu/books/title/33293/deadly-rise-anti-science">The Deadly Rise of Anti-Science</a></i>,<br />by <a href="https://twitter.com/PeterHotez?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor">Peter Hotez</a>.<br /></td></tr></tbody></table>This week I read <i><a href="https://www.amazon.com/Deadly-Rise-Anti-science-Scientists-Warning/dp/1421447223/ref=sr_1_1?keywords=The+Deadly+Rise+of+Anti-Science%3A+A+Scientist%E2%80%99s+Warning&qid=1700391139&s=books&sr=1-1">The Deadly Rise of Anti-Science: A Scientist’s Warning</a></i>, by <a href="https://en.wikipedia.org/wiki/Peter_Hotez">Peter Hotez</a>. Every American should read this book. In his introductory chapter, <a href="https://www.bakerinstitute.org/expert/peter-j-hotez">Hotez</a> writes
<br /><blockquote>
This is a dark and tragic story of how a significant segment of the population of the United States suddenly, defiantly, and without precedent turned against biomedical science and scientists. I detail how anti-science became a dominant force in the United States, resulting in the deaths of thousands of Americans in 2021 and into 2022, and why this situation presents a national emergency. I explain why anti-science aggression will not end with the <a href="https://en.wikipedia.org/wiki/COVID-19_pandemic">COVID-19 pandemic</a>. I believe we must counteract it now, before something irreparable happens to set the country on a course of inexorable decline…
<br /><br />
The consequences are shocking: as I will detail, more than 200,000 Americans needlessly lost their lives because they refused a <a href="https://en.wikipedia.org/wiki/COVID-19_vaccine">COVID-19 vaccine</a> and succumbed to the virus. Their lives could have been saved had they accepted the overwhelming scientific evidence for the effectiveness and safety of COVID-19 immunization or the warnings from the community of biomedical scientists and public health experts about the dangers of remaining unvaccinated. Ultimately, this such public defiance of science became a leading killer of middle-aged and older Americans, more than gun violence, terrorism, nuclear proliferation, cyberattacks or other major societal threats.
</blockquote>
Where did this 200,000 number come from? On page 2 of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I claim that
<br /><blockquote>
One valuable skill in physics is the ability to make order-of-magnitude estimates, meaning to calculate something approximately right.
</blockquote><p>
Hotez gives a classic example of <a href="https://en.wikipedia.org/wiki/Estimation">estimation</a> when deriving the 200,000 number. First, he notes that 245,000 Americans died of covid between May 1 and December 31, 2021. Covid arrived in the United States in early 2020, but vaccines did not become widely available until mid 2021. Actually, the vaccines were ready in early 2021 (I had my first dose on March 20), but May 1 was the date when the vaccine was available to everyone. During the second half of 2021, about 80% of Americans who died of covid were unvaccinated. So, Hotez multiplies 245,000 by 0.8 to get 196,000 unvaccinated deaths. After rounding this off to one <a href="https://en.wikipedia.org/wiki/Significant_figures">significant figure</a>, this is where he gets the number 200,000.
<br /><br />
There are a few caveats. On the one hand, our estimate may be too high. The vaccine is not perfect. If all of the 200,000 unvaccinated people who died would have gotten the vaccine, some of them would still have perished from covid. If we take the vaccine as being 90% effective against death, we would multiple 196,000 times 0.9 to get 176,400. On the other hand, our estimate may be too low. Covid did not end on January 1, 2022. In fact, the <a href="https://en.wikipedia.org/wiki/SARS-CoV-2_Omicron_variant">omicron variant</a> swept the country that winter and at its peak over 2000 people died of covid each day. So, the total covid deaths since the vaccine became available—the starting point of our calculation—is certainly higher than 245,000.
<br /><br />
As Hotez points out, other researchers have also estimated the number of unnecessary covid deaths, using slightly different assumptions, and all the results are roughly consistent, around 200,000. (Hotez’s book appears to have been written in mid-to-late 2022; I suspect the long tail of covid deaths since then would not make much difference to this estimation, but I’m not sure.) </p><p>In the spirit of an order-of-magnitude estimate, one should not place too great an emphasis on the precise number. It was certainly more than twenty thousand and it was without a doubt less than two million. I doubt we’ll ever know if the “true” amount is 187,000 or 224,000 or any other specific value. But we can say with confidence that about a couple hundred thousand Americans died unnecessarily because people were not vaccinated. Hotez concludes<br /></p><blockquote>
That 200,000 unvaccinated Americans gave up their lives needlessly through shunning COVID-19 vaccines can and should haunt our nation for a long time to come.
</blockquote><p>
Infectious disease scientists such as <a href="https://www.bcm.edu/people-search/peter-hotez-23229">Peter Hotez</a>, <a href="https://en.wikipedia.org/wiki/Anthony_Fauci">Tony Faucci</a>, and others are true American heroes. That far-right politicians and journalists vilify these researchers is despicable and disgusting. We all owe these scientists so much. Last Monday was “<a href="https://www.researchamerica.org/phtyd/">Public Health Thank You Day</a>” and yesterday was <a href="https://en.wikipedia.org/wiki/Thanksgiving">Thanksgiving</a>. I can think of no one more deserving of our thanks than the scientists who led the effort to vaccinate America against covid. </p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/PbGfeksduGE" width="320" youtube-src-id="PbGfeksduGE"></iframe></div><p></p><p style="text-align: center;">Why Science Isn’t Up for Debate, with Peter Hotez.<br /></p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=PbGfeksduGE">https://www.youtube.com/watch?v=PbGfeksduGE</a> <br /></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-65937075195417893082023-11-17T05:00:00.084-05:002023-11-17T05:00:00.164-05:00Gustav Bucky and the Antiscatter Grid<p></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih-ZZYy_bgKACpuTkMcwPjpmuS0GD9VptmTCulNJu1CDcCVlBfxTIVV1uLKaqwwPlE_HIT7VJExueQTMSvuQCJgjwPmDh273h3qYXWcdwRzVoCavLuxe76kxaxD22kPwGGLSTZwI0pNlKsC9g1z3vEUfcf9MpQ4zwdWPP95YtQwclBAz9CA88neAyjG5Jy/s471/AntiscatterGrid.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="An antiscatter grid, as discussed in Intermediate Physics for Medicine and Biology." border="0" data-original-height="343" data-original-width="471" height="146" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEih-ZZYy_bgKACpuTkMcwPjpmuS0GD9VptmTCulNJu1CDcCVlBfxTIVV1uLKaqwwPlE_HIT7VJExueQTMSvuQCJgjwPmDh273h3qYXWcdwRzVoCavLuxe76kxaxD22kPwGGLSTZwI0pNlKsC9g1z3vEUfcf9MpQ4zwdWPP95YtQwclBAz9CA88neAyjG5Jy/w200-h146/AntiscatterGrid.jpg" title="An antiscatter grid." width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">An antiscatter grid.<br /><a href="https://commons.wikimedia.org/wiki/File:Lead_collimator.svg">Episcophagus, CC BY-SA 4.0, <br />via Wikimedia Commons</a>.<br /></td></tr></tbody></table>In Chapter 16 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss the <a href="https://en.wikipedia.org/wiki/Anti-scatter_grid">antiscatter grid</a> used in <a href="https://en.wikipedia.org/wiki/Radiography">radiography</a>.
<br /><p></p><blockquote>
Since the radiograph assumes that photons either travel in a straight line from the point source in the <a href="https://en.wikipedia.org/wiki/X-ray_tube">x-ray tube</a> to the detector or are absorbed, <a href="https://en.wikipedia.org/wiki/Compton_scattering">Compton-scattered</a> photons that strike the detector reduce the contrast and contribute an overall background darkening. This effect can be reduced by placing an antiscatter grid (or radiographic grid, or “bucky” after its inventor, <a href="https://en.wikipedia.org/wiki/Gustav_Peter_Bucky">Gustav Bucky</a>) just in front of the detector.
</blockquote>
Who is <a href="https://radiopaedia.org/articles/gustav-bucky?lang=us">Gustav Bucky</a>? We can learn more about his life and work by examining the chapter “<a href="https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwj7ov28zKWCAxWRjYkEHbTUAosQFnoECBYQAQ&url=http%3A%2F%2Fwww.bshr.org.uk%2FThe_Story_of_Radiology_Volume_2_LR.pdf&usg=AOvVaw0CXv3uetpspjycfj8Vf9JL&opi=89978449">Two Centenaries: William Coolidge & Gustav Bucky</a>,” by <a href="https://www.kcl.ac.uk/people/elizabeth-beckmann">Elizabeth Beckmann</a> and <a href="https://www.linkedin.com/in/adrian-thomas-1a47b539/?originalSubdomain=uk">Adrian Thomas</a>, in <i>The Story of Radiology (Volume 2)</i>, published by the <a href="https://en.wikipedia.org/wiki/European_Society_of_Radiology">European Society of Radiology</a>. Beckmann and Thomas begin
<br /><blockquote>
Gustav Peter Bucky was born on September 3, 1880 in <a href="https://en.wikipedia.org/wiki/Leipzig">Leipzig</a>, Germany. He wanted to be an engineer, however at the insistence of his parents he transferred to study medicine at the <a href="https://en.wikipedia.org/wiki/Leipzig_University">University of Leipzig</a>, graduating in1906.
The combination of his interest in photography at school, his ambition to be an engineer and his parent’s insistence that he study medicine would lead him into the relatively new technical branch of medicine which was to be called radiology.</blockquote>
I’ve seen many reasons for scientists to straddle between physics/engineering and biology/medicine. In Bucky’s case the reason was parental pressure.
<br /><br />
Beckmann and Thomas of course mention Bucky’s biggest contribution to science, his antiscatter grid.
<br /><blockquote>
It was Gustav Bucky who realised that the main problem was finding a way to reduce the scattered radiation that was responsible for the loss of definition of the radiological image from reaching the film. However, this had to be achieved with minimum impact on the primary x-ray beam. Bucky had his original idea on how to achieve this in 1909, but it took some years of experimenting for him to develop his design.
<br /><br />
Bucky described his original design for the ‘Bucky Diaphragm’ as a ‘honeycomb’ lead grid, but with individual elements being square in shape, rather than hexagonal. He used lead since it was a material which absorbed x-rays. In this design the lead strips were thick and spaced 2 cm apart, running both parallel to the length and width of the film. This resulted in the lines of the grid being visible on the x-ray film. Despite this, the grid was effective and did remove scatter and improve image contrast.
</blockquote>
You can eliminate those artifact lines by moving the grid.
<br /><blockquote>
In 1920, the American <a href="https://chicagoradiology.org/?page_id=523">Hollis Potter</a> further developed the grid. Potter aligned the lead strips so that they now ran in one direction only, and he also made the lead strips thinner so that they were less visible on the image. Potter also proposed moving the grid during exposure, which blurred out the image of the lead strips on the radiographic image... The resulting moving grid, based upon the work of Bucky and Potter, became known as the Potter-Bucky grid.
</blockquote>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtBEAJg2_C3M_zux9pyOHPoRsGlkmKe77xXaepzQDCCHCKIyslRY9qOy-XB435uLXuAagCLwNwyftVbLeYJkGZwkJL93vz-U-8UEZollfJNl13AUnajBRN9oLul4RKrhM2TbjxPdaHebdh5n8G77gGdKuZB8rUEI4kdSeyaVHzM6t06KVUUAXwbVNvyLuO/s1350/BuckyAndEinstein.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1233" data-original-width="1350" height="183" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhtBEAJg2_C3M_zux9pyOHPoRsGlkmKe77xXaepzQDCCHCKIyslRY9qOy-XB435uLXuAagCLwNwyftVbLeYJkGZwkJL93vz-U-8UEZollfJNl13AUnajBRN9oLul4RKrhM2TbjxPdaHebdh5n8G77gGdKuZB8rUEI4kdSeyaVHzM6t06KVUUAXwbVNvyLuO/w200-h183/BuckyAndEinstein.jpg" width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Albert Einstein and Gustav Bucky, <br /><a href="https://en.wikipedia.org/wiki/Leo_Baeck_Institute">Leo Baeck Institute</a>, F 5347B.</td></tr></tbody></table>Bucky moved from Germany to the United States in 1929. He became good friends with <a href="https://en.wikipedia.org/wiki/Albert_Einstein">Albert Einstein</a>.
<br /><blockquote>
In 1933, Bucky met up again with his friend Albert Einstein when he arrived in New York. When on holiday together Gustav and Albert would go for a long walk together each day, discussing and developing
new ideas…
<br /><br />
Probably the most famous collaboration between Bucky and Einstein was the idea of ‘a light intensity self-adjusting camera’ with a US patent granted on October 27, 1936... <br /><br />
It is a sign of the close relationship between Bucky and Einstein that Bucky visited Einstein every day during his final illness and was at the hospital only hours before Einstein’s death in April 1955.
</blockquote>
The story concludes
<br /><blockquote>
Gustav Bucky was a friendly, modest, undemanding person who made a lasting and significant contribution to radiology. For 21st century radiology the impact of the invention for which Gustav Bucky is most remembered – the Bucky Grid – continues. The grid is as important in modern digital detection systems, like computed radiography (CR) plates or digital radiography (DR) detector systems, as it was with x-ray film in the 1920s. <br /></blockquote><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com1Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-64706361117033557262023-11-10T05:00:00.010-05:002023-11-10T05:00:00.151-05:00Monet's Water Lilies<p>When my wife and I were in <a href="https://en.wikipedia.org/wiki/Paris">Paris</a> <a href="https://hobbieroth.blogspot.com/2010/07/paris.html">several years ago</a> we visited the <a href="https://en.wikipedia.org/wiki/Mus%C3%A9e_de_l%27Orangerie">Musée de l’Orangerie</a>, where <a href="https://en.wikipedia.org/wiki/Claude_Monet">Claude Monet</a>’s beautiful <a href="https://en.wikipedia.org/wiki/Water_Lilies_(Monet_series)">water lily murals</a> are displayed. <a href="https://www.claudemonetgallery.org/">Monet</a> (1840–1926) is the famous <a href="https://en.wikipedia.org/wiki/Impressionism">impressionist</a> painter who, during the last decades of his life, painted lilies floating on the surface of the pond at his home in <a href="https://en.wikipedia.org/wiki/Giverny">Giverny</a>. I remember sitting in one of the oval rooms staring at these giant paintings. It was so quiet and peaceful.
<br /></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsvhzYV_fNqvPjaUQSD1QjVZeN17ZEwUAT-gQlNakcPuiXb65i3U7uAvY_CFxGyaaSy3cAUOAIWTkAwUmX8CDlfpTuHz9QSwf4QUsdKsaavgKnV0pf_d3Bpq-txEFTCpJFp5LXRvM3B8NjjzW4nFE8oeIcX7xEbdadg3j_4HxGb9RAMk-T-rQ0B9OoJgzX/s5472/WaterLilies.jpg" style="margin-left: auto; margin-right: auto;"><img alt="Monet’s water lily murals in the Musée de l’Orangerie in Paris" border="0" data-original-height="3648" data-original-width="5472" height="213" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsvhzYV_fNqvPjaUQSD1QjVZeN17ZEwUAT-gQlNakcPuiXb65i3U7uAvY_CFxGyaaSy3cAUOAIWTkAwUmX8CDlfpTuHz9QSwf4QUsdKsaavgKnV0pf_d3Bpq-txEFTCpJFp5LXRvM3B8NjjzW4nFE8oeIcX7xEbdadg3j_4HxGb9RAMk-T-rQ0B9OoJgzX/w320-h213/WaterLilies.jpg" title="Monet’s water lily murals in the Musée de l’Orangerie in Paris" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Monet’s water lily murals in the <a href="https://www.musee-orangerie.fr/en">Musée de l’Orangerie</a> in Paris.<br />Brady Brenot, CC BY-SA 4.0 <https: by-sa="" creativecommons.org="" licenses="">, via Wikimedia Commons.</https:></td></tr></tbody></table><p><https: by-sa="" creativecommons.org="" licenses="">Water lilies take advantage of some interesting physics. First, their stalks and leaves contain air pockets, reducing their average density and making them <a href="https://en.wikipedia.org/wiki/Buoyancy">buoyant</a>. <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I compare the effect of buoyancy in terrestrial and aquatic animals. I quote this comparison below, but I have replaced the word “animals” by “plants”.
<br /></https:></p><blockquote>
Plants are made up primarily of water, so their density
is approximately 10<sup>3</sup> kg m<sup>−3</sup>. The buoyant force depends
on the plant’s environment. Terrestrial plants live in air,
which has a density of 1.2 kg m<sup>−3</sup>. The buoyant force on
terrestrial plants is very small compared to their weight.
Aquatic plants live in water, and their density is almost
the same as the surrounding fluid. The buoyant force almost
cancels the weight, so the plant is essentially “weightless.”
Gravity plays a major role in the life of terrestrial plants,
but only a minor role for aquatic plants. <a href="https://www.amazon.com/Air-Water-Mark-Denny/dp/0691087342/ref=sr_1_2?crid=2PPEV0YXJJ416&keywords=air+and+water&qid=1699359350&s=books&sprefix=air+%2Cstripbooks%2C1244&sr=1-2">Denny (1993)</a> explores
the differences between terrestrial and aquatic plants in more detail.
</blockquote><p>
Another piece of physics important to water lilies is <a href="https://en.wikipedia.org/wiki/Surface_tension">surface tension</a>,
a topic only briefly mentioned in the fifth edition of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>, but which (spoiler alert!) may play a larger role in the sixth edition. The lily’s leaf is waxy, which repels water and enhances its ability to remain on the water-air surface. In addition, small <a href="https://en.wikipedia.org/wiki/Cilium">cilia</a> increase the surface area.
<br /><br />
A last bit of physics has to do with the <a href="https://en.wikipedia.org/wiki/Surface-area-to-volume_ratio">surface-to-volume ratio</a>. Usually surface tension can’t support a large object, because its weight increases with the cube of its linear size, whereas the effect of surface tension increases with the object’s perimeter. Therefore, the impact of gravity increases with size more dramatically than does the impact of surface tension, so a large object sinks like a rock. The water lily’s leaf, however, is thin, and making the leaf larger increases its surface area but not its thickness. The weight only increases as the square of its linear size, not as the cube. If the leaf is large enough, gravity will still win out, but the leaf can be larger than you might expect and still float on the water surface.
<br /><br />Monet donated his water lily murals to France at the end of <a href="https://en.wikipedia.org/wiki/World_War_I">World War I</a>, to create a place where people could reflect on those who gave their life for the nation. When visiting them, you can also contemplate the role of physics in medicine and biology.</p><p>Happy <a href="https://en.wikipedia.org/wiki/Veterans_Day">Veterans Day</a>.<br /></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOosSIOzg16poYJjcSfGz90Uoj9vGkxmYcGiDq8gWdOwXV4QISMwObwn6Qf3eZaq5Xbo0dx-x_fn9uUcbVv9pCrdiRMkKi4geneSeOkEaYocO7pHX2u-JkO0iJR7E2Di-CgyuUWLXTTI_LKcGrYh2Y2GolMY-wCCw4qig3vfZ1iBfrE8AunHYhK7-kAHD0/s800/WaterLilyMural.jpg" style="margin-left: auto; margin-right: auto;"><img alt="One of Monet’s water lily murals at the Musée de l’Orangerie." border="0" data-original-height="274" data-original-width="800" height="138" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiOosSIOzg16poYJjcSfGz90Uoj9vGkxmYcGiDq8gWdOwXV4QISMwObwn6Qf3eZaq5Xbo0dx-x_fn9uUcbVv9pCrdiRMkKi4geneSeOkEaYocO7pHX2u-JkO0iJR7E2Di-CgyuUWLXTTI_LKcGrYh2Y2GolMY-wCCw4qig3vfZ1iBfrE8AunHYhK7-kAHD0/w400-h138/WaterLilyMural.jpg" title="One of Monet’s water lily murals at the Musée de l’Orangerie." width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">One of Monet’s water lily murals at the Musée de l’Orangerie.</td>
</tr></tbody></table><div class="separator" style="clear: both; text-align: center;">
</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/fd-Me3EBGYY" width="320" youtube-src-id="fd-Me3EBGYY"></iframe></div><div style="text-align: center;">Monet’s Water Lilies: Great Art Explained.</div><div style="text-align: center;"> <a href="https://www.youtube.com/watch?v=fd-Me3EBGYY&t=7s">https://www.youtube.com/watch?v=fd-Me3EBGYY&t=7s</a></div>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com1Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-56504013746041654432023-11-03T05:00:00.133-04:002023-11-03T05:00:00.146-04:00The Golay CoilLast week I introduced the <a href="https://en.wikipedia.org/wiki/Helmholtz_coil">Helmholtz coil</a> and the <a href="https://en.wikipedia.org/wiki/Maxwell_coil">Maxwell coil</a>. The Maxwell coil is useful for creating the magnetic field gradient needed for <a href="https://en.wikipedia.org/wiki/Magnetic_resonance_imaging">magnetic resonance imaging</a>. At the end of the post, I wrote
<br /><blockquote>
The Maxwell coil is great for producing the magnetic field gradient <i>dB<sub>z</sub>/dz</i> needed for slice selection in MRI, but what coil is required to produce the gradients <i>dB<sub>z</sub>/dx</i> and <i>dB<sub>z</sub>/dy</i> needed during MRI readout and phase encoding? That, my friends, is a story for another post.
</blockquote>Today, I will finish the story.
<br /><br />
First, let’s assume the gradient coils are all located on the surface of a cylinder. If this were a clinical MRI scanner, the person would lie on a bed that would be slid into the cylinder to get an image. The Maxwell coil consists of two circular coils, separated by a distance equal to the square root of three times the coil radius. The parts of the coil in the back that are hidden by the cylinder are shown as dashed. The two coils carry current in opposite directions, as shown below, creating a gradient <i>dB<sub>z</sub>/dz</i> in the imaging region midway between the two coils on the axis of the cylinder.<br /><p></p><p style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQg4SKOLUOdRJ4Doii-p6sQf7TSdYh1pDD13_yOKFcZOz9kPeWijGWi22OLqDZ0UuxqN3JopZKLLQKYLOdojEpJfYKkia_SIcYnDqsbHGv-LAwj4zihfN1WhHVyqREcw-0MoymzDGIaYcPT-ztKUMBOkKn5Y5BQ8qmFC65TngHlNlDLwggy2MQRY1pOxeV/s912/Gradient%20Coil%201.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A Maxwell coil." border="0" data-original-height="379" data-original-width="912" height="133" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQg4SKOLUOdRJ4Doii-p6sQf7TSdYh1pDD13_yOKFcZOz9kPeWijGWi22OLqDZ0UuxqN3JopZKLLQKYLOdojEpJfYKkia_SIcYnDqsbHGv-LAwj4zihfN1WhHVyqREcw-0MoymzDGIaYcPT-ztKUMBOkKn5Y5BQ8qmFC65TngHlNlDLwggy2MQRY1pOxeV/w320-h133/Gradient%20Coil%201.jpg" title="A Maxwell coil." width="320" /></a><br /></p><p>To perform imaging, however, you need gradients in the<i> x</i> and <i>y</i> directions too. To create <i>dB<sub>z</sub>/dx</i>, you typically use what is called a Golay coil. It consists of four coils wound on the cylinder surface as shown below. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5KT0EJavMevO8Fc4dZqbOB_UqnSmcvJN1qv-WkvljghOEI6Hf8zM_uLkVS0UCzfqw_QHfcI7q7LMuJtBx4jFexxhIch5_lM-xXS8wRoujB-MXANEfZ82-HbCk_c3BKHvNcCOZb-YScSnvCax4t6PLqYFXWmLllmwXQ7RsIdzvTDlMCUBEFAg81BqqnLQF/s900/Gradient%20Coil%202.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A Golay coil." border="0" data-original-height="372" data-original-width="900" height="132" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj5KT0EJavMevO8Fc4dZqbOB_UqnSmcvJN1qv-WkvljghOEI6Hf8zM_uLkVS0UCzfqw_QHfcI7q7LMuJtBx4jFexxhIch5_lM-xXS8wRoujB-MXANEfZ82-HbCk_c3BKHvNcCOZb-YScSnvCax4t6PLqYFXWmLllmwXQ7RsIdzvTDlMCUBEFAg81BqqnLQF/w320-h132/Gradient%20Coil%202.jpg" title="A Golay coil." width="320" /></a></div><p></p><p></p><p></p><p>The mathematics to determine the details of this design is too complicated for this post. Suffice to so, it requires setting the third derivative of <i>B<sub>z</sub></i> with respect to <i>x</i> equal to zero. The resulting coils should each subtend an angle of 120°. Their inner loops should be separated by 0.778 cylinder radii, and their outer loops by 5.14 radii.
<br /><br />
To create the gradient <i>dB<sub>z</sub>/dy</i>, simply rotate the Golay coil by 90°, as shown below. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhesV9_iSuvDrtYQzLXZ-iE9y8snv1-16Mev3-09MWEKd0NlOCQhf1I2nNqNriYjP0QdWOMRS3wlP70ZD0elymQ8t3wdu-zbDG6DlQA-bujz7T50NyPqCtswl89oEJ34d9aMk1GzQHRSv_GzvGZ3JOOJsNMAEJc23A3A4XdhgYvZxrsjaifkWum59h_3CID/s905/Gradient%20Coil%203.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A rotated Golay coil." border="0" data-original-height="385" data-original-width="905" height="136" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhesV9_iSuvDrtYQzLXZ-iE9y8snv1-16Mev3-09MWEKd0NlOCQhf1I2nNqNriYjP0QdWOMRS3wlP70ZD0elymQ8t3wdu-zbDG6DlQA-bujz7T50NyPqCtswl89oEJ34d9aMk1GzQHRSv_GzvGZ3JOOJsNMAEJc23A3A4XdhgYvZxrsjaifkWum59h_3CID/w320-h136/Gradient%20Coil%203.jpg" title="A rotated Golay coil." width="320" /></a></div><p style="text-align: left;">So, to perform magnetic resonance imaging you need a nested set of three coils as shown below. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNW96nqa5PCJFGR_dFQoaNE4n23RDuh8qghVbYInz5sN5RNwHhGuqJIfadPcpXbTz4P-WWdhEaiZ8y4roHZ7m0W7dFt4NMUGyiOTtXfpugS1mY_z4-2nKPfClWjtOnrbVUOeupwSKsoO-DhqfxI1YNo4_iPzaLC8e6cNHMd8uwzK3HZKWJM0dCAuqs7Tln/s906/Gradient%20Coil%204.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A set of three gradient coils used in MRI." border="0" data-original-height="235" data-original-width="906" height="83" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNW96nqa5PCJFGR_dFQoaNE4n23RDuh8qghVbYInz5sN5RNwHhGuqJIfadPcpXbTz4P-WWdhEaiZ8y4roHZ7m0W7dFt4NMUGyiOTtXfpugS1mY_z4-2nKPfClWjtOnrbVUOeupwSKsoO-DhqfxI1YNo4_iPzaLC8e6cNHMd8uwzK3HZKWJM0dCAuqs7Tln/w320-h83/Gradient%20Coil%204.jpg" title="A set of three gradient coils used in MRI." width="320" /></a></div><p>The picture gets confusing with all the hidden lines. Here is how the set looks with the hidden parts of the coils truly hidden.
<br /></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_HACXH3bY5vnY5ExQ4ZSFgd1p3SzskIEP_e1sy1XRITC9Ex0mrbW5L3OZVHBEthlx3IBSHXgxMalczMBRyn-9iQrs7qPCH9DTWP44sEFB4NhM-RKyf62AAp_pZxPa3RbnboSwhDNPKwpAbl-oae6rTmAfBOudQZchlmAgB3PfK0S9YYan5W6COBzoNI6E/s903/Gradient%20Coil%205.jpg" style="margin-left: 1em; margin-right: 1em;"><img alt="A set of three gradient coils used in MRI (hidden lines removed)." border="0" data-original-height="237" data-original-width="903" height="85" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_HACXH3bY5vnY5ExQ4ZSFgd1p3SzskIEP_e1sy1XRITC9Ex0mrbW5L3OZVHBEthlx3IBSHXgxMalczMBRyn-9iQrs7qPCH9DTWP44sEFB4NhM-RKyf62AAp_pZxPa3RbnboSwhDNPKwpAbl-oae6rTmAfBOudQZchlmAgB3PfK0S9YYan5W6COBzoNI6E/w320-h85/Gradient%20Coil%205.jpg" title="A set of three gradient coils used in MRI (hidden lines removed)." width="320" /></a></div><p></p><p>
While this set of coils will produce linear magnetic field gradients in the central region, in state-of-the-art MRI scanners the coils are somewhat more complicated, with multiple loops corresponding to each loop shown above.
<br /><br />
We all know who <a href="https://en.wikipedia.org/wiki/Hermann_von_Helmholtz">Helmholtz</a> and <a href="https://en.wikipedia.org/wiki/James_Clerk_Maxwell">Maxwell</a> are, but who is Golay? <a href="https://en.wikipedia.org/wiki/Marcel_J._E._Golay">Marcel J. E. Golay</a> (1902-1989) was a Swiss scientist who came to the US to get his PhD at the <a href="https://en.wikipedia.org/wiki/University_of_Chicago">University of Chicago</a> and then stayed. He had a varied career, making fundamental advances in <a href="https://en.wikipedia.org/wiki/Chromatography">chromatography</a>, <a href="https://en.wikipedia.org/wiki/Information_theory">information theory</a>, and the detection of <a href="https://en.wikipedia.org/wiki/Infrared">infrared light</a>. He studied the process of <a href="https://en.wikipedia.org/wiki/Shim_(magnetism)">shimming</a>: making small adjustments to the magnetic field of a MRI scanner to make the static field more homogeneous. This work ultimately led to the design of gradient coils.
<br /><br />
In Chapter 18 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss magnetic resonance imaging and the need for magnetic field gradients. In a nutshell, MRI converts magnetic field strength to spin <a href="https://en.wikipedia.org/wiki/Precession">precession</a> frequency. By measuring this frequency, you can obtain information about magnetic field strength. A magnetic field gradient lets you map frequency to position, an idea which is at the heart of imaging using magnetic resonance.
</p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-53236878354961660442023-10-27T05:00:00.198-04:002023-10-27T05:00:00.148-04:00The Helmholtz Coil and the Maxwell Coil<div>To do <a href="https://en.wikipedia.org/wiki/Magnetic_resonance_imaging">magnetic resonance imaging</a>, you need a static magnetic field that is uniform and a switchable magnetic field that has a uniform gradient. How do you produce such fields? In this post, I explain one of the simplest ways: using a <a href="https://en.wikipedia.org/wiki/Helmholtz_coil">Helmholtz coil</a> and a <a href="https://en.wikipedia.org/wiki/Maxwell_coil">Maxwell coil</a>.
<br /><br />
Both of these are created using circular coils. The magnetic field <i>B<sub>z</sub></i> produced by a circular coil can be calculated using the <a href="https://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law">law of Biot and Savart </a>(see Chapter 8 of <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>)<br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjkKkGbv0zoluL9TZ7q-0xEzrcPJjTDcGtys6WJgCY3-pn-_tHtnSMTKwzjJZYHLq_hF4YdxRDH1DCx99LWWrFImIOBwHpdHOs-5hy8vuIxRQbpx8Paij8XtY8Bt1shH7Zus2nPekXjLxAnAOFePT-gnd-g-qXlJuj4-ft1naewJgR9F7QzUWzjRq3rlZP/s222/Eq1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="58" data-original-width="222" height="58" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgjkKkGbv0zoluL9TZ7q-0xEzrcPJjTDcGtys6WJgCY3-pn-_tHtnSMTKwzjJZYHLq_hF4YdxRDH1DCx99LWWrFImIOBwHpdHOs-5hy8vuIxRQbpx8Paij8XtY8Bt1shH7Zus2nPekXjLxAnAOFePT-gnd-g-qXlJuj4-ft1naewJgR9F7QzUWzjRq3rlZP/s1600/Eq1.jpg" width="222" /></a></div><br />
where μ<sub>0</sub> is the <a href="https://en.wikipedia.org/wiki/Vacuum_permeability">permeability of free space</a> (the basic constant of <a href="https://en.wikipedia.org/wiki/Magnetostatics">magnetostatics</a>), <i>I</i> is the coil current, <i>N</i> is the number of turns, <i>R</i> is the coil radius, and <i>z</i> is the distance along the axis from the coil center.
<br /><h4 style="text-align: left;">
The Helmholtz Coil
</h4>
The Helmholtz coil consists of two circular coils in parallel planes, having the same axis and the same current in the same direction, that are separated by a distance <i>d</i>. Our goal will be to find the value of <i>d</i> that gives the most uniform magnetic field. By superposition, the magnetic field is </div><div><br /></div><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-V5jZacUPcRN0cLXhGBjWnAID3-WpfeEUpUxWIvU33PQHzQu_IyyqRFyQKT_2fylGaqlh7M9SjUGUrhYynrMh_KrmsXDmi4xus9uJVnWSAbFdPIwfVRjH1VCpGhOLyUqh8GOXPsIQ4l81Ec_yynOVX7_efVB9IGSGWF_9krVLP8DatkbJ-aCSl8dnbc-/s538/Eq2.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="103" data-original-width="538" height="76" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN-V5jZacUPcRN0cLXhGBjWnAID3-WpfeEUpUxWIvU33PQHzQu_IyyqRFyQKT_2fylGaqlh7M9SjUGUrhYynrMh_KrmsXDmi4xus9uJVnWSAbFdPIwfVRjH1VCpGhOLyUqh8GOXPsIQ4l81Ec_yynOVX7_efVB9IGSGWF_9krVLP8DatkbJ-aCSl8dnbc-/w400-h76/Eq2.jpg" width="400" /></a><br /></div><div> </div><div>To create a uniform magnetic field, we will perform a <a href="https://en.wikipedia.org/wiki/Taylor_series">Taylor expansion</a> of the magnetic field about the origin (<i>z</i> = 0). We will need derivatives of the magnetic field. The first derivative is
<br /><br /></div><div style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5dknOiSJBoi9lQCFM3TrWcf3trQBftJvmNZiukbxb7jAiadpE6j3KhYTpkUnyyYXnBVX2gRwu1FZG6eu-hdLhbkNkzE8CBqWEsZvBDecu6_VuSHvh3DTJMD9vdNM6Ai2dNIyzyy-WczGLk7AwFfVPGT_V-4TD4UxXC17hLEF48N8TckSB42z4PNinY74z/s568/Eq3.jpg"><img border="0" data-original-height="101" data-original-width="568" height="71" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5dknOiSJBoi9lQCFM3TrWcf3trQBftJvmNZiukbxb7jAiadpE6j3KhYTpkUnyyYXnBVX2gRwu1FZG6eu-hdLhbkNkzE8CBqWEsZvBDecu6_VuSHvh3DTJMD9vdNM6Ai2dNIyzyy-WczGLk7AwFfVPGT_V-4TD4UxXC17hLEF48N8TckSB42z4PNinY74z/w400-h71/Eq3.jpg" width="400" /></a></div><br /><div>(The reader will have to fill in the missing steps when calculating these derivatives.) At <i>z</i> = 0, this derivative will go to zero. In fact, because the magnetic field is even about the <i>z</i> axis, all odd derivatives will be zero, regardless of the value of <i>d</i>.
<br /><br />
The second derivative is
<br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSJpv99-6fj7ixwjOpSaFoT0CA2wc0AHKcOTtYUJ4t1GQ5F0Qugq1CcV7fL5h4OnPeIRJVP0iqBoIliKyIlVDiyE9SmMcGyoojKvx0p6qJwhWCd25IWglfzPntuZOea_imNqcuTNwAS7a_OfoDSiu9EBmuZ6_VhAjfhKoDAya80nTLWzcK3AdJruqNQldp/s578/Eq4.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="578" height="69" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSJpv99-6fj7ixwjOpSaFoT0CA2wc0AHKcOTtYUJ4t1GQ5F0Qugq1CcV7fL5h4OnPeIRJVP0iqBoIliKyIlVDiyE9SmMcGyoojKvx0p6qJwhWCd25IWglfzPntuZOea_imNqcuTNwAS7a_OfoDSiu9EBmuZ6_VhAjfhKoDAya80nTLWzcK3AdJruqNQldp/w400-h69/Eq4.jpg" width="400" /></a></div><br /><div>At <i>z</i> = 0, the two terms in the brackets are the same. Our goal is to have this term be zero, implying that the second order term in the Taylor series vanishes. This will happen if
<br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie9PUID1DUfC6DKsBWHtpHanPfRDhy8vJSmDIGqLOwbrGdIP83jnj7xzPe9thyQZvgS7C2RondmP1XZ_ais_jp4HsiWWOLEQZvIYZt42N6Vm-voXn9qMoFIV3barV1GE63X7xEj3bbhfOEr7pGvKb75_SWj7N5Mwgb8B4Ddh_XMGCuLhGrCbO5sO25DVn_/s145/Eq5.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="56" data-original-width="145" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie9PUID1DUfC6DKsBWHtpHanPfRDhy8vJSmDIGqLOwbrGdIP83jnj7xzPe9thyQZvgS7C2RondmP1XZ_ais_jp4HsiWWOLEQZvIYZt42N6Vm-voXn9qMoFIV3barV1GE63X7xEj3bbhfOEr7pGvKb75_SWj7N5Mwgb8B4Ddh_XMGCuLhGrCbO5sO25DVn_/s1600/Eq5.jpg" width="145" /></a></div><div>or, in other words, <i>d</i> = <i>R</i>. This famous result says that for a Helmholtz pair the coil separation should equal the coil radius.
<br /><br />
A Helmholtz coil produces a remarkably uniform field near the origin. However, it is not uniform enough for use in most magnetic resonance imaging machines, which typically have a more complex set of coils to create an even more homogeneous field. If you need a larger region that is homogeneous, you could always just use a larger Helmholtz coil, but then you would need more current to achieve the desired magnetic field at the center. A Helmholtz pair isn’t bad if you want to use only two reasonably sized coils.
<br /><h4 style="text-align: left;">
The Maxwell Coil
</h4>
The Helmholtz coil produces a uniform magnetic field, whereas the Maxwell coil produces a uniform magnetic field gradient. It consists of two circular coils, in parallel planes having the same axis, that are separated by a distance <i>d</i>, but which have current in the <i>opposite</i> directions. Again, our goal will be to find the value of <i>d</i> that gives the most uniform magnetic field gradient. The magnetic field is
<br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixTHCsT1f3JqlToVhKA_YICvDzO5ev44BT1dmPqfkQHKrd4yEvpFi7SE3nfWiStIsQbMm4NYsYqbUSwfzeZ9u2yl7wgA1qapZ5tzmFEBJpjWvxcXdVZSh6kn0m1pw8QDjm1JNqx3HBSA9MGrGc9GdAs5b_4XL87iTpKUvUlNSh_5h4v8Wsl-f3clG0OtKl/s520/Eq6.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="101" data-original-width="520" height="78" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixTHCsT1f3JqlToVhKA_YICvDzO5ev44BT1dmPqfkQHKrd4yEvpFi7SE3nfWiStIsQbMm4NYsYqbUSwfzeZ9u2yl7wgA1qapZ5tzmFEBJpjWvxcXdVZSh6kn0m1pw8QDjm1JNqx3HBSA9MGrGc9GdAs5b_4XL87iTpKUvUlNSh_5h4v8Wsl-f3clG0OtKl/w400-h78/Eq6.jpg" width="400" /></a></div><div><br />
The only difference between this case and that for the Helmholtz coil is the change in sign of the second term in the bracket. If <i>z</i> = 0, the magnetic field is zero. Moreover, the magnetic field is an odd function of <i>z</i>, so all even derivatives also vanish. The first derivative is
<br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwyaXHlsQTOnbb6wUIV6XgrNvyfWjIT-mHT_KGbnY80zxUh7f82H9W0ai3YxiPVGDPEzoReqK1NHO2XAjyiRn48H4YcnzwgfVe6foQUza3Q3Ke8Gwfg-K2IRMCSz0tW0cajiYLnF1Fg7ggE5DZuZhN89wRMckQh8yHstTgPUJYrNBWWjAcyt_EmgQKCCjC/s554/Eq7.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="554" height="71" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwyaXHlsQTOnbb6wUIV6XgrNvyfWjIT-mHT_KGbnY80zxUh7f82H9W0ai3YxiPVGDPEzoReqK1NHO2XAjyiRn48H4YcnzwgfVe6foQUza3Q3Ke8Gwfg-K2IRMCSz0tW0cajiYLnF1Fg7ggE5DZuZhN89wRMckQh8yHstTgPUJYrNBWWjAcyt_EmgQKCCjC/w400-h71/Eq7.jpg" width="400" /></a></div><div><br />
This expression gives us the magnitude of the gradient at the origin, but it doesn’t help us create a more uniform gradient. The second derivative is
<br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQERbgzjmPZzAUl9RcXvM3JxzSQ-eBvKhBeEC6cOZ5GlcPr25NbMzrdjY8bNZvU-JG7eGjuXHa54w7ggIL2006-vLSSNAfZ3isLl6ntit7T820cZ-DJc9_V8OGcI1wcTBKAQs-1_T5c-6B1kVAH0IsW_6SB92ueHgZxF_7CulkiEx9GRe7sAV8nj9MapMw/s563/Eq8.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="101" data-original-width="563" height="71" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQERbgzjmPZzAUl9RcXvM3JxzSQ-eBvKhBeEC6cOZ5GlcPr25NbMzrdjY8bNZvU-JG7eGjuXHa54w7ggIL2006-vLSSNAfZ3isLl6ntit7T820cZ-DJc9_V8OGcI1wcTBKAQs-1_T5c-6B1kVAH0IsW_6SB92ueHgZxF_7CulkiEx9GRe7sAV8nj9MapMw/w400-h71/Eq8.jpg" width="400" /></a></div><div><br />
This derivative is zero at the origin, regardless of the value of <i>d</i>. So, we have to look at the third derivative.
<br /><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOKcLEFjhdunBaLQTZXLaVJIl4dwFizcHl1P0EmqJZTlhU6433ZRoxKIosdRwBgLwLTdE1u7zniHP8jMTTVQG5GhalnvVjeWutnWXPwmMrWzXzCUny_rnFAe7YWSn263OrRuNWrucCoFhyphenhyphenq8jYbk80kS9YmWzkEDx-l25XABktHNVphX72JILsD6fQA_0k/s636/Eq9.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="99" data-original-width="636" height="63" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOKcLEFjhdunBaLQTZXLaVJIl4dwFizcHl1P0EmqJZTlhU6433ZRoxKIosdRwBgLwLTdE1u7zniHP8jMTTVQG5GhalnvVjeWutnWXPwmMrWzXzCUny_rnFAe7YWSn263OrRuNWrucCoFhyphenhyphenq8jYbk80kS9YmWzkEDx-l25XABktHNVphX72JILsD6fQA_0k/w400-h63/Eq9.jpg" width="400" /></a></div><div><br />
At <i>z</i> = 0, this will vanish if
<br /></div><div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjwFQZ7oEaWtmZgweXWiPjktjKTJ5Wm0xp2o01S0cWTVOVOBBX_HatK6qpRiTyB2s-Y3mfyCUsAWeYLkeL-Mg7ltnKc_zkgIaF-N0hi0TCiAA6JTItND683xdHGAONC79S2EpGXezWL6lh29eQYEWFzIb9hWcRJl2xJvm1Snk-pbMj6PEXIF9qt21-OaIA/s185/Eq10.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="58" data-original-width="185" height="58" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjwFQZ7oEaWtmZgweXWiPjktjKTJ5Wm0xp2o01S0cWTVOVOBBX_HatK6qpRiTyB2s-Y3mfyCUsAWeYLkeL-Mg7ltnKc_zkgIaF-N0hi0TCiAA6JTItND683xdHGAONC79S2EpGXezWL6lh29eQYEWFzIb9hWcRJl2xJvm1Snk-pbMj6PEXIF9qt21-OaIA/s1600/Eq10.jpg" width="185" /></a></div><div>or, in other words, <i>d</i> = √3 <i>R = </i>1.73<i> R</i>. Thus, the two coils have a greater separation for a Maxwell coil than for a Helmholtz coil. The Maxwell coil would be useful for producing the slice selection gradient during MRI (for more about the need for gradient fields in MRI, see Chapter 18 of <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i>).
<br /><h4 style="text-align: left;">
Conclusion
</h4>
Below is a plot of the normalized magnetic field as a function of <i>z</i> for the Helmholtz coil (blue) and the Maxwell coil (yellow). As you can see, the region with a uniform field or gradient is small. It depends on what level of accuracy you need, but if you are more than half a radius from the origin you will see significant deviations from homogeneity. <br /> </div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioPd8L0eHhMALgDbh1cd0-De7VgexfpzLCGZd72EU-RMM1MGtXf-Q0ppXCojd77c8jTFfoe_5ugjsujUYlWnN0wLnQtlAt_6szWNwtwqZRi9w9roLCdB4SsaHjb6gB515YhxFbHT8NU2ZQOyZF6xIWAW3LfEF2fdJgW0Dzjh-YE2ovJLcByrlFHjbZ52j3/s1250/HelmholtzMaxwellFigure.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="864" data-original-width="1250" height="221" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEioPd8L0eHhMALgDbh1cd0-De7VgexfpzLCGZd72EU-RMM1MGtXf-Q0ppXCojd77c8jTFfoe_5ugjsujUYlWnN0wLnQtlAt_6szWNwtwqZRi9w9roLCdB4SsaHjb6gB515YhxFbHT8NU2ZQOyZF6xIWAW3LfEF2fdJgW0Dzjh-YE2ovJLcByrlFHjbZ52j3/s320/HelmholtzMaxwellFigure.jpg" width="320" /></a></div><br /><div><a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I never discuss the Helmholtz coil in <i>Intermediate Physics for Medicine and Biology</i>. We don’t mention the Maxwell coil by name, but Problem 33 of Chapter 18 analyzed a Maxwell pair even if we don’t call it that.
<br /><br />
The Maxwell coil is great for producing the magnetic field gradient <i>dB<sub>z</sub>/dz</i> needed for slice selection in MRI, but how do you produce the gradients <i>dB<sub>z</sub>/dx</i> and <i>dB<sub>z</sub>/dy</i> needed during MRI readout and phase encoding? That, my friends, is a story for another post.
<br /></div>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-6869811740045064022023-10-20T05:00:00.116-04:002023-10-20T05:00:00.156-04:00Mr. Clough<p style="text-align: center;">
<i>A teacher affects eternity; he can never tell where his influence stops. </i></p><p style="text-align: center;">Henry Adams
<br /></p><table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu9GN1Fjx4i994oNgpBCTi0EdMHh1kBWBteGVpVz6HLQ1Pk-eU5IxhCViZiYa5PWm4qiGvMHjq2ul9WF1qUhMtByRP1Ov161k3SGzvfWSVDlnsHNd2xQmV7pvbcXJr4joqbdgDoHZL7Eu-dz_wFOpskO6-5VRxGyN0yA_Obx5Er4xlLRZkIFKbKbkUX04-/s218/Clough.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="173" data-original-width="218" height="173" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiu9GN1Fjx4i994oNgpBCTi0EdMHh1kBWBteGVpVz6HLQ1Pk-eU5IxhCViZiYa5PWm4qiGvMHjq2ul9WF1qUhMtByRP1Ov161k3SGzvfWSVDlnsHNd2xQmV7pvbcXJr4joqbdgDoHZL7Eu-dz_wFOpskO6-5VRxGyN0yA_Obx5Er4xlLRZkIFKbKbkUX04-/s1600/Clough.jpg" width="218" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Stephen Clough, from the 1975<br />Homestead Jr.-Sr. High School Yearbook.<br /></td></tr></tbody></table>How does someone end up being coauthor on a textbook like <i><a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8">Intermediate Physics for Medicine and Biology</a></i>? It takes a lot of friends, teachers, and role models who help you along the way. I had many excellent teachers when I was young. One of the best was Stephen Clough.
<br /><br />
I attended grades 7–10 at <a href="https://en.wikipedia.org/wiki/Homestead_High_School_(Indiana)">Homestead Junior-Senior High School</a>. Usually a junior high and senior high are in separate buildings, but the suburb of <a href="https://en.wikipedia.org/wiki/Fort_Wayne,_Indiana">Fort Wayne</a> where I lived at the time was new and growing, and had the two combined. For two years (I think grades 9 and 10) I had English with Mr. Clough. He was one of the younger teachers and had longish hair and a mustache, and I thought he was little bit of a <a href="https://en.wikipedia.org/wiki/Hippie">hippie</a>. That’s OK, because in the mid 70s hippies were still groovy (although they would go out of fashion soon).
<br /><br />
Before I had Mr. Clough, I didn’t read much. I was obsessed with baseball and would read an occasional sports biography, but not much else. I did well in school, but I don’t remember our classes being too challenging or having much homework. Life was about hanging around with friends, playing ping pong, riding bikes, listening to music, and watching television. But Mr. Clough had us reading modern fiction, like <i><a href="https://en.wikipedia.org/wiki/Animal_Farm">Animal Farm</a></i> and <i><a href="https://en.wikipedia.org/wiki/Lord_of_the_Flies">Lord of the Flies</a></i>. For me, this was an intellectual awakening. Before Mr. Clough I rarely read books; after Mr. Clough I read all the time (and still do).
<br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgLECH4CFH_X7uyV-FB26X8gG7VAWJeKQPcdAofaUCNorjGGaJ4cbi3BGLN2DDH-pLOZWxm5SUA4ZbZQKYsaGcwrIPEOCJ7zJgzWEWprQxaMvT9JfrtU3nNHmVmHDq_QKRBgJird82WjU5jXwAjv4z5wD2dKoPo1XIq44b24koeKj-FwDqtaPutUJH1Koe/s133/RothInHS.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="133" data-original-width="103" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjgLECH4CFH_X7uyV-FB26X8gG7VAWJeKQPcdAofaUCNorjGGaJ4cbi3BGLN2DDH-pLOZWxm5SUA4ZbZQKYsaGcwrIPEOCJ7zJgzWEWprQxaMvT9JfrtU3nNHmVmHDq_QKRBgJird82WjU5jXwAjv4z5wD2dKoPo1XIq44b24koeKj-FwDqtaPutUJH1Koe/w155-h200/RothInHS.jpg" width="155" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Me (age 15) from the 1975 <br />Homestead Jr.-Sr. High School Yearbook.<br /></td></tr></tbody></table><p>I remember how, on Fridays, Mr. Clough would bring his guitar to school
and play for us and sing. I thought this was the coolest thing I’d ever
seen. None of my other teachers related to us like that. He played a lot
of <a href="https://en.wikipedia.org/wiki/Bob_Dylan">Dylan</a>. I’ll never forget the day he explained what the words meant in the song <i><a href="https://en.wikipedia.org/wiki/American_Pie_(song)">American Pie</a></i>. </p><p>Mr. Clough had a huge influence on my academic development. Reading books led to reading the scientific writing of <a href="https://en.wikipedia.org/wiki/Isaac_Asimov">Isaac Asimov</a>, which led to majoring in physics in college, which led to a PhD, which ultimately led to becoming a coauthor of <i><a href="https://link.springer.com/book/10.1007/978-0-387-49885-0">Intermediate Physics for Medicine and Biology</a></i>. I owe him much.
<br /><br />As <a href="https://en.wikipedia.org/wiki/Henry_Adams">Henry Adams</a> said, a teacher affects eternity. I hope everyone teaching a class using <i>IPMB</i> keeps that in mind. You can never tell where your influence stops. <br /></p><p>I last saw Mr. Clough at my 30<sup>th</sup> high school reunion. My friend from high school, <a href="https://longy.edu/team/david-small/">Dave Small</a>, became an opera singer, and he sang several songs for us at the gathering. Guess who accompanied him on the guitar? Stephen Clough. </p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/PRpiBpDy7MQ" width="320" youtube-src-id="PRpiBpDy7MQ"></iframe></div><p></p><p style="text-align: center;"><i>American Pie</i>, by <a href="https://en.wikipedia.org/wiki/Don_McLean">Don McLean</a>. <br /></p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=PRpiBpDy7MQ">https://www.youtube.com/watch?v=PRpiBpDy7MQ</a></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-22347352036047092232023-10-13T05:00:00.243-04:002023-10-13T05:00:00.141-04:00 J. Robert Oppenheimer, Biological Physicist<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9LFhrKvEWLnUCCVwdjliNkB4qZ__gXRyjeT_6x8QOm7FID35RIAbkz4EjXaBZ8kzew1-GIi8uMJHrE3qJkjxcUBd_EbqD8XZ-41DxDd2AMG2CmjZPq6l-SdTe2vLR358MEEMfWF9K4nroOFyl4gbpzjQWzwOyBGzjCMZ1ErDs7zED9esPDkjmpkV0TQ_d/s2277/Oppenheimer.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="J. Robert Oppenheimer." border="0" data-original-height="2261" data-original-width="2277" height="199" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9LFhrKvEWLnUCCVwdjliNkB4qZ__gXRyjeT_6x8QOm7FID35RIAbkz4EjXaBZ8kzew1-GIi8uMJHrE3qJkjxcUBd_EbqD8XZ-41DxDd2AMG2CmjZPq6l-SdTe2vLR358MEEMfWF9K4nroOFyl4gbpzjQWzwOyBGzjCMZ1ErDs7zED9esPDkjmpkV0TQ_d/w200-h199/Oppenheimer.jpg" title="J. Robert Oppenheimer." width="200" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">J. Robert Oppenheimer.<br /></td></tr></tbody></table>Did you watch <i><a href="https://en.wikipedia.org/wiki/Oppenheimer_(film)">Oppenheimer</a></i> in the theater this summer? I did. The movie told how <a href="https://en.wikipedia.org/wiki/J._Robert_Oppenheimer">J. Robert Oppenheimer</a> led the <a href="https://en.wikipedia.org/wiki/Manhattan_Project">Manhattan Project</a> that built the first <a href="https://en.wikipedia.org/wiki/Nuclear_weapon">atomic bomb</a> during <a href="https://en.wikipedia.org/wiki/World_War_II">World War II</a>. But the movie skipped <a href="https://www.amazon.com/American-Prometheus-Triumph-Tragedy-Oppenheimer/dp/0375726268">Oppenheimer</a>’s research in <a href="https://en.wikipedia.org/wiki/Biophysics">biological physics</a> related to <a href="https://en.wikipedia.org/wiki/Photosynthesis">photosynthesis</a>.
<br /><br />
<a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I only make a passing mention of <a href="https://education.nationalgeographic.org/resource/photosynthesis/">photosynthesis</a> in Chapter 3 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>.
<br /><blockquote>
The creation of <a href="https://en.wikipedia.org/wiki/Glucose">glucose</a> or other sugars is the reverse of the <a href="https://en.wikipedia.org/wiki/Cellular_respiration">respiration</a>
process and is called <a href="https://www.livescience.com/51720-photosynthesis.html"><i>photosynthesis</i></a>. The <a href="https://en.wikipedia.org/wiki/Gibbs_free_energy">free energy</a>
required to run the reaction the other direction is supplied by
<a href="https://en.wikipedia.org/wiki/Light">light</a> energy.
</blockquote>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiwn3ebLTa__n5wTnI0P44SKQFEYwECX_-C0S9oKd2dFVQ-RlaWR3yQq6aKKLmzpbLRgBCLnh7wTshdtPh7T9JzMcwOmmdtGQPkHdvY0g1M6IbJFu-OQU6sHxar5yDY5qe2ctT-x2zroH0el-dkliZNMw4j_9HUf_C0RgdwDYPsrmFA0JiHAi0jDyUsehI/s4032/FromPhotonToNeuron.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="From Photon to Neuron: Light, Imaging, Vision, by Philip Nelson, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="4032" data-original-width="3024" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiiwn3ebLTa__n5wTnI0P44SKQFEYwECX_-C0S9oKd2dFVQ-RlaWR3yQq6aKKLmzpbLRgBCLnh7wTshdtPh7T9JzMcwOmmdtGQPkHdvY0g1M6IbJFu-OQU6sHxar5yDY5qe2ctT-x2zroH0el-dkliZNMw4j_9HUf_C0RgdwDYPsrmFA0JiHAi0jDyUsehI/w150-h200/FromPhotonToNeuron.jpg" title="From Photon to Neuron: Light, Imaging, Vision, by Philip Nelson." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><a href="https://press.princeton.edu/books/paperback/9780691175195/from-photon-to-neuron"><i>From Photon to Neuron</i></a>,<br />by <a href="https://twitter.com/PhilNel46870034?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor">Philip Nelson</a>.<br /></td></tr></tbody></table>To learn more about Oppie and photosynthesis, I turn to <a href="https://www.physics.upenn.edu/~pcn/">Philip Nelson</a>’s <a href="https://hobbieroth.blogspot.com/2018/01/from-photon-to-neuron-light-imaging.html">wonderful textbook</a> <i><a href="https://www.amazon.com/Photon-Neuron-Light-Imaging-Vision/dp/0691175195/ref=sr_1_1?keywords=From+Photon+to+Neuron&qid=1695761780&s=books&sr=1-1">From Photon to Neuron: Light, Imaging, Vision</a></i>. His discussion of photosynthesis begins
<br /><div><div><blockquote>
Photosynthetic organisms convert around 10<sup>14</sup> kg of <a href="https://en.wikipedia.org/wiki/Carbon">carbon</a> from <a href="https://en.wikipedia.org/wiki/Carbon_dioxide">carbon dioxide</a> into <a href="https://en.wikipedia.org/wiki/Biomass_(ecology)">biomass</a> each year. In addition to generating the food that we enjoy eating, photosynthetic organisms emit a waste product, free <a href="https://en.wikipedia.org/wiki/Oxygen">oxygen</a>, that we enjoy breathing. They also stabilize Earth’s climate by removing atmospheric CO<sub>2</sub>.
</blockquote><a href="https://scholar.google.com/citations?user=hgGCUoUAAAAJ&hl=en">Nelson</a> begins the story by introducing <a href="https://link.springer.com/article/10.1007/s11120-014-0013-9">William Arnold</a>, Oppenheimer’s future collaborator.<br /><blockquote>
W. Arnold was an undergraduate student interested in a career in astronomy. In 1930, he was finding it difficult to schedule all the required courses he needed for graduation. His advisor proposed that, in place of Elementary Biology, he could substitute a course on Plant Physiology organized by <a href="https://en.wikipedia.org/wiki/Robert_Emerson_(scientist)">[Robert] Emerson</a>. Arnold enjoyed the class, though he still preferred astronomy. But unable to find a place to continue his studies in that field after graduation, he accepted an offer from Emerson to stay on as his assistant.
</blockquote>
Emerson and Arnold went on to perform critical experiments on photosynthesis. Then Emerson performed another experiment with [<a href="https://www.jstor.org/stable/2437236">Charlton] Lewis</a>, in which they found that <a href="https://en.wikipedia.org/wiki/Chlorophyll">chlorophyll</a> does not absorb light with a wavelength of 480 nm (blue), but an accessory pigment called <a href="https://en.wikipedia.org/wiki/Phycocyanin">phycocyanin</a> does. Emerson and Lewis concluded that “the energy absorbed by phycocyanin must be available for photosynthesis.”
<br /><br />
Here is where <a href="https://www.atomicarchive.com/resources/biographies/oppenheimer.html">Oppenheimer</a> comes into the story. I will let Nelson tell it.
<br /><blockquote>
Could phycocyanin absorb light energy and somehow <i>transfer</i> it to the chlorophyll system?...
<br /><br />
Arnold eventually left Emerson’s lab to study elsewhere, but they stayed in contact. Emerson told him about the results with Lewis, and suggested that he think about the energy-transfer problem. Arnold had once audited a course on <a href="https://en.wikipedia.org/wiki/Quantum_mechanics">quantum physics</a>, so he visited the professor for that course to pose the puzzle. The professor was J. R. Oppenheimer, and he did have an idea. Oppenheimer realized that a similar energy transfer process was known in <a href="https://en.wikipedia.org/wiki/Nuclear_physics">nuclear physics</a>; from this he created a complete theory of <a href="https://en.wikipedia.org/wiki/F%C3%B6rster_resonance_energy_transfer">fluorescence resonance energy transfer</a>. Oppenheimer and Arnold also made quantitative estimates indicating that phycocyanin and chlorophyll could play the roles of donor and acceptor, and that this mechanism could give the high transfer efficiency needed to explain the data.
</blockquote>
So, what nuclear energy transfer process was Oppenheimer talking about? In <a href="https://rupress.org/jgp/article/33/4/423/12269/INTERNAL-CONVERSION-IN-THE-PHOTOSYNTHETIC">Arnold and Oppenheimer’s paper</a>, they wrote
<br /><blockquote>
It is the purpose of the present paper to point out a mechanism
of energy transfer from phycocyanin to chlorophyll, the efficiency of
which seems to be high enough to account for the results of Emerson and
Lewis. This new process is, except for the scale, identical with the process of
<a href="https://en.wikipedia.org/wiki/Internal_conversion">internal conversion</a> that we have in the study of <a href="https://en.wikipedia.org/wiki/Radioactive_decay">radioactivity</a>.
</blockquote>
Internal conversion is a topic <a href="http://hobbieroth.blogspot.com/2021/12/russell-hobbie-19342021.html">Russ</a> and I address in <i><a href="https://link.springer.com/book/10.1007/978-3-319-12682-1">IPMB</a></i>. We said
<br /><blockquote>
Whenever a nucleus loses energy by γ decay, there is a
competing process called <i>internal conversion</i>. The energy to
be lost in the transition, <i>E<sub>γ</sub></i>, is transferred directly to a bound
electron, which is then ejected.
</blockquote>
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVC5yYNRxJCAMq-qwzk3XUH0pNCybOb_CeyQVKXXgerEa-hqO16facSpqItPuR7PCQxSjEXNvEns2VYR1K7qNK194gqLoX5oABF4v7ej1MbZM1gm_z__CTQXXK_iEhoeUcI6-2WJMI5EdSfAv5beZOCQz7KMhyYMm5-A42ZfqAnENJxqYOgR3DNXPhw9KN/s2016/IntroductoryNuclearPhysics.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Introductory Nuclear Physics by Kenneth Krane, superimposed on Intermediate Physics for Medicine and Biology." border="0" data-original-height="2016" data-original-width="1512" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVC5yYNRxJCAMq-qwzk3XUH0pNCybOb_CeyQVKXXgerEa-hqO16facSpqItPuR7PCQxSjEXNvEns2VYR1K7qNK194gqLoX5oABF4v7ej1MbZM1gm_z__CTQXXK_iEhoeUcI6-2WJMI5EdSfAv5beZOCQz7KMhyYMm5-A42ZfqAnENJxqYOgR3DNXPhw9KN/w150-h200/IntroductoryNuclearPhysics.jpg" title="Introductory Nuclear Physics by Kenneth Krane." width="150" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><i>Introductory Nuclear Physics</i>,<br />by Kenneth Krane.<br /></td></tr></tbody></table>More detail can be found in <a href="https://www.amazon.com/Introductory-Nuclear-Physics-Kenneth-Krane/dp/047180553X/ref=sr_1_1?keywords=Introductory+Nuclear+Physics&qid=1695769995&s=books&sr=1-1&ufe=app_do%3Aamzn1.fos.f5122f16-c3e8-4386-bf32-63e904010ad0"><i>Introductory Nuclear Physics</i></a> by <a href="https://physics.oregonstate.edu/directory/kenneth-krane">Kenneth Krane</a>.
<br /><blockquote>
Internal conversion is an <a href="https://en.wikipedia.org/wiki/Electromagnetism">electromagnetic</a> process that competes with <a href="https://en.wikipedia.org/wiki/Gamma_ray">γ emission</a>. In this case the electromagnetic multipole fields of the nucleus do not result in the emission of a <a href="https://en.wikipedia.org/wiki/Photon">photon</a>; instead, the fields interact with the atomic <a href="https://en.wikipedia.org/wiki/Electron">electrons</a> and cause one of the electrons to be emitted from the atom. In contrast to <a href="https://en.wikipedia.org/wiki/Beta_decay">β decay</a>, the electron is not created in the decay process but rather is a previously existing electron in an <a href="https://en.wikipedia.org/wiki/Atomic_orbital">atomic orbit</a>. For this reason internal conversion decay rates can be altered slightly by changing the chemical environment of the atom, thus changing somewhat the atomic orbits. Keep in mind, however, that this is <i>not</i> a two-step process in which a photon is first emitted by the nucleus and then knocks loose an orbiting electron by a process analogous to the <a href="https://en.wikipedia.org/wiki/Photoelectric_effect">photoelectric effect</a>; such a process would have a negligibly small probability to occur.
</blockquote>Nelson compares the photosynthesis process to another process widely used in biological imaging: Fluorescence resonance energy transfer (FRET). He describes FRET this way.<br /><blockquote>
We can find pairs of molecular species, called donor/acceptor pairs, with the property that physical proximity abolishes <a href="https://en.wikipedia.org/wiki/Fluorescence">fluorescence</a> from the donor. When such a pair are close, the acceptor nearly always pulls the excitation energy off the donor, before the donor has a chance to fluoresce. The acceptor may either emit a photon, or lose its excitation without fluorescence (“nonradiative” energy loss).
</blockquote>
Let’s put this all together. The donor in FRET is like the phycocyanin molecule in photosynthesis is like the nucleus in internal conversion. The acceptor in FRET is like the chlorophyll molecule in photosynthesis is like the electron cloud in internal conversion. The fluorescence of the donor/phycocyanin/nucleus is suppressed (in the nuclear case, fluorescence would be gamma decay). Instead, the electromagnetic field of the donor/phycocyanin/nucleus interacts with, and transfers energy to, the acceptor/chlorophyll/electron cloud. In the case of FRET, the acceptor then fluoresces (which is what is detected when doing FRET imaging). The chlorophyll/electron cloud does not fluoresce, but instead ejects an electron in the case of internal conversion, or energizes an electron that can ultimately perform chemical reactions in the case of photosynthesis. All three processes are exquisitely sensitive to physical proximity. For FRET imaging, this sensitivity allows one to say if two molecules are close to each other. In photosynthesis, it means the chlorophyll and phycocyanin must be near one another. In internal conversion, it means the electrode cloud must overlap the nucleus, which implies that the process usually results in emission of a <a href="https://en.wikipedia.org/wiki/Electron_shell">K-shell</a> electron since those innermost electrons have the highest probability of being near the nucleus.
<br /><br />
There’s lots of interesting stuff here: How working at the border between disciplines can result in breakthroughs; how physics concepts can contribute to biology; how addressing oddball questions arising from data can lead to new breakthroughs; how quantum mechanics can influence biological processes (<a href="https://www.amazon.com/Newton-Rules-Biology-Physical-Biological/dp/0198540213">Newton rules biology</a>, except when he doesn’t); how seemingly different phenomena—such as FRET imaging, photosynthesis, and nuclear internal conversion—can have underlying similarities.
I wish my command of quantum mechanics was strong enough that I could explain all these <a href="https://en.wikipedia.org/wiki/Resonance">resonance</a> effects to you in more detail, but alas it is not.<br /><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: right;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2ZkUZxJ9vRim9Onz6YWgx8EfSLdbtp8YzJdvLUPAT5ToV6ufz5Ik7kthIzXDNDzBNyUMxt04F_SI6PATrLFBnwWN0XHSG5jhpF14cUTMp3TwNZBU4SG94-KhWal3w5O8zz6PUpqGEgXloBMVEPNQ_ZnBFif-aOFnl5IJjryKnpkJb-9tmsTsnRIuFwF__/s1652/Oppenheimer%20and%20Groves.jpg" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img alt="Oppenheimer and General Groves at the Trinity test site." border="0" data-original-height="1652" data-original-width="1129" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2ZkUZxJ9vRim9Onz6YWgx8EfSLdbtp8YzJdvLUPAT5ToV6ufz5Ik7kthIzXDNDzBNyUMxt04F_SI6PATrLFBnwWN0XHSG5jhpF14cUTMp3TwNZBU4SG94-KhWal3w5O8zz6PUpqGEgXloBMVEPNQ_ZnBFif-aOFnl5IJjryKnpkJb-9tmsTsnRIuFwF__/w219-h320/Oppenheimer%20and%20Groves.jpg" title="Oppenheimer and General Groves at the Trinity test site." width="219" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Oppenheimer and <a href="https://en.wikipedia.org/wiki/Leslie_Groves">General Groves</a> <br />at the <a href="https://en.wikipedia.org/wiki/Trinity_(nuclear_test)">Trinity</a> test site. I love<br />Oppie’s <a href="https://discover.lanl.gov/publications/national-security-science/2023-summer/the-man-under-the-porkpie-hat/">pork pie hat</a>.<br /></td></tr></tbody></table>If you haven’t seen <a href="https://www.oppenheimermovie.com/"><i>Oppenheimer</i></a> yet, I recommend you do. Go see <a href="https://en.wikipedia.org/wiki/Barbie_(film)"><i>Barbie</i></a> too. Make it a full <a href="https://en.wikipedia.org/wiki/Barbenheimer">Barbenheimer</a>. But if you want to learn about the father of the atomic bomb’s contributions to biology, you’d better stick with <a href="https://www.physics.upenn.edu/biophys/PtN/"><i>From Photon to Neuron</i></a> or this blog. </div><div> </div><div> <div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/bK6ldnjE3Y0" width="320" youtube-src-id="bK6ldnjE3Y0"></iframe></div></div></div><p style="text-align: center;">
The official trailer to Oppenheimer.</p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=bK6ldnjE3Y0">https://www.youtube.com/watch?v=bK6ldnjE3Y0</a></p><p style="text-align: center;"> <br /></p><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/jlO8NiPbgrk" width="320" youtube-src-id="jlO8NiPbgrk"></iframe></div> <p></p><p style="text-align: center;">Photosynthesis.</p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=jlO8NiPbgrk&t=14s">https://www.youtube.com/watch?v=jlO8NiPbgrk&t=14s</a> <br /></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-50612577337751490492023-10-06T05:00:00.090-04:002023-10-06T05:00:00.141-04:00The Dobson Unit
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk4B4KaViushRNHIGt_rJGoUdfpnC21ILRmSV45MXwhV_GY99UuHdDCqVsIFlefkWREMWK6mABNpdudCOBcIeMei395kfoZVQIFbQjyzE8j9QziskOQzBpot-gaKC55D4DT3U4y2LWl1tFkOtth-dGYcMtAFkNfXYDhjh9sAwet4a-pF1nmbFK3gdn6o-Z/s517/Ozone.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Figure 14.28 from Intermediate Physics for Medicine and Biology, showing the spectral dose rate weighted for ability to damage DNA." border="0" data-original-height="517" data-original-width="472" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjk4B4KaViushRNHIGt_rJGoUdfpnC21ILRmSV45MXwhV_GY99UuHdDCqVsIFlefkWREMWK6mABNpdudCOBcIeMei395kfoZVQIFbQjyzE8j9QziskOQzBpot-gaKC55D4DT3U4y2LWl1tFkOtth-dGYcMtAFkNfXYDhjh9sAwet4a-pF1nmbFK3gdn6o-Z/w293-h320/Ozone.jpg" title="Figure 14.28 from Intermediate Physics for Medicine and Biology." width="293" /></a></div>In Chapter 14 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss the risk of <a href="https://en.wikipedia.org/wiki/DNA_damage_(naturally_occurring)">DNA damage</a>—and therefore <a href="https://en.wikipedia.org/wiki/Cancer">cancer</a>—caused by <a href="https://en.wikipedia.org/wiki/Ultraviolet">ultraviolet light</a> from the sun. Figure 14.28 in <a href="https://link.springer.com/book/10.1007/978-3-319-12682-1"><i>IPMB</i></a> presents the results of a calculation of UV dose rate, weighted for DNA damage. The caption of the figure states “the calculation assumes clear skies and an ozone layer of 300 <a href="https://en.wikipedia.org/wiki/Dobson_unit">Dobson units</a> (1 DU = 2.69 × 10<sup>20</sup> molecule m<sup>-2</sup>).”
<br /><br />
The Dobson Unit, what’s that?
<br /><br />
Rather than explaining it myself, let me quote the <a href="https://en.wikipedia.org/wiki/NASA">NASA</a> <a href="https://ozonewatch.gsfc.nasa.gov/facts/dobson_SH.html">website</a> about ozone.
<br /><blockquote>
What is a Dobson Unit?
<br /><br />
The Dobson Unit is the most common unit for measuring ozone concentration. One Dobson Unit is the number of molecules of ozone [O<sub>3</sub>] that would be required to create a layer of pure ozone 0.01 millimeters thick at a temperature of 0 degrees Celsius and a pressure of 1 atmosphere (the air pressure at the surface of the Earth). Expressed another way, a column of air with an ozone concentration of 1 Dobson Unit would contain about 2.69 × 10<sup>16 </sup>ozone molecules for every square centimeter of area at the base of the column. Over the Earth’s surface, the ozone layer’s average thickness is about 300 Dobson Units or a layer that is 3 millimeters thick.
</blockquote><p>
The Dobson Unit was named after British physicist and meteorologist <a href="https://en.wikipedia.org/wiki/G._M._B._Dobson">Gordon Miller Bourne Dobson</a> (1889 –1976) who did early research on <a href="https://en.wikipedia.org/wiki/Ozone_layer">ozone in the atmosphere</a>.
<br /><br />
Worried about <a href="https://en.wikipedia.org/wiki/Climate_change">climate change</a>? The ozone story may provide some hope. When man-made chemicals such as <a href="https://en.wikipedia.org/wiki/Chlorofluorocarbon">chlorofluorocarbons</a>, for example <a href="https://en.wikipedia.org/wiki/Freon">freon</a>, are released into the atmosphere, they damage the ozone layer, allowing larger amounts of ultraviolet radiation to reach the earth’s surface. In the 1970s, an ozone hole developed each year over the south pole. In 1987, countries from all over the world united to pass the <a href="https://en.wikipedia.org/wiki/Montreal_Protocol">Montreal Protocol</a>, which banned many ozone depleting substances. Since that time, the ozone hole has been getting smaller. This represents a success story demonstrating how international cooperation can address critical environmental hazards. Now, we need to do the same thing for <a href="https://en.wikipedia.org/wiki/Greenhouse_gas">greenhouse gases</a> to combat climate change. </p><p> </p><p></p><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/GS0dilngPws" width="320" youtube-src-id="GS0dilngPws"></iframe></div><p style="text-align: center;">How the ozone layer was discovered.</p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=GS0dilngPws ">https://www.youtube.com/watch?v=GS0dilngPws</a></p><p><br /></p><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" class="BLOG_video_class" height="266" src="https://www.youtube.com/embed/nCpH71npnvo" width="320" youtube-src-id="nCpH71npnvo"></iframe></div><p style="text-align: center;">Don't let this happen to your planet! <br /></p><p style="text-align: center;"><a href="https://www.youtube.com/watch?v=nCpH71npnvo">https://www.youtube.com/watch?v=nCpH71npnvo</a></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991tag:blogger.com,1999:blog-9045015217135885587.post-55729295049352848842023-09-29T05:00:00.029-04:002023-09-29T05:00:00.149-04:00Decay Plus Input at a Constant Rate Revisited<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8BbfRgarTZi-NdaV9ZcWX6Ka6gD5GZyhksfrWnab7YnfdllGeW-_gWTrEWO-hpXCkXSomlkyEeRgsyMSd8ZrhtSRe7mHf_qp6o1iRjqdTcg2KmXwl9Gs2LhQDd0W1wDk7PpPX7Y01Xl0RDeFPXEGG-jM8jSbIHyM3ZW_nBTNU8fhu7_CN0wiOoI15pNGi/s1096/IPMB.jpg" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1096" data-original-width="827" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8BbfRgarTZi-NdaV9ZcWX6Ka6gD5GZyhksfrWnab7YnfdllGeW-_gWTrEWO-hpXCkXSomlkyEeRgsyMSd8ZrhtSRe7mHf_qp6o1iRjqdTcg2KmXwl9Gs2LhQDd0W1wDk7PpPX7Y01Xl0RDeFPXEGG-jM8jSbIHyM3ZW_nBTNU8fhu7_CN0wiOoI15pNGi/w151-h200/IPMB.jpg" width="151" /></a></div>In Chapter 2 of <a href="https://www.amazon.com/Intermediate-Physics-Medicine-Biology-Russell/dp/3319126814/ref=asap_bc?ie=UTF8"><i>Intermediate Physics for Medicine and Biology</i></a>, <a href="https://cse.umn.edu/physics/news/memoriam-russell-hobbie-1934-2021">Russ Hobbie</a> and I discuss the problem of <a href="https://hobbieroth.blogspot.com/2012/02/decay-plus-input-at-constant-rate.html">decay plus input at a constant rate</a>.
<br /><blockquote>
Suppose that in addition to the removal of <i>y</i> from the system at a rate –<i>by</i>, <i>y</i> enters the system at a constant rate <i>a</i>, independent of <i>y</i> and <i>t</i>. The net rate of change of <i>y</i> is given by
</blockquote><blockquote><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG3zK_85Rkp9qEEjWMgz_X-KoUSjG2y9QZ7h9Q-aD10dWHtsJaRs8yV_DUv72sAXl9DRSTQCUPWrtA_f_Emhf0q6hhcLj08e3qTr_bjEE6AkwjU5vC8eDiMDUOUhLp9atZMi12rJHps2VpxuH5imPJrAwqHEzsM7KRKYn3u13BMOw9hmfvYYlAi9gSqYMe/s354/Eq2-25.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="51" data-original-width="354" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgG3zK_85Rkp9qEEjWMgz_X-KoUSjG2y9QZ7h9Q-aD10dWHtsJaRs8yV_DUv72sAXl9DRSTQCUPWrtA_f_Emhf0q6hhcLj08e3qTr_bjEE6AkwjU5vC8eDiMDUOUhLp9atZMi12rJHps2VpxuH5imPJrAwqHEzsM7KRKYn3u13BMOw9hmfvYYlAi9gSqYMe/s320/Eq2-25.jpg" width="320" /></a></blockquote><p>Then we go on to discuss how you can learn things about a differential equation without actually solving it.
<br /></p><p></p><blockquote>
It is often easier to write down a differential equation describing a problem than it is to solve it… However, a good deal can be learned about the solution by examining the equation itself. Suppose that <i>y</i>(0) = 0. Then the equation at <i>t</i> = 0 is <i>dy</i>/<i>dt</i> = <i>a</i>, and <i>y</i> initially grows at a constant rate <i>a</i>. As <i>y</i> builds up, the rate of growth decreases from this value because of the –<i>by</i> term. Finally when <i>a </i>–<i> by </i>= 0, <i>dy</i>/<i>dt</i> is zero and <i>y</i> stops growing. This is enough information to make the sketch in Fig. 2.13.
<br /><br />
The equation is solved in Appendix F. The solution is
<br /></blockquote><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiogFG2quS2nSz5p9l2lsX0ntrmMtA4EyeLMzE9YBL1NqimlPnNcpkRcj9WR-cMIjw2IbyyBn3lT-liOCYtSY2uLuNbDniKE6Dh333pQMkMBSNjxw-3-4uTjigAGQ4IXFB6JJFbwKZiZJKlNlJZv594_Q_38P_tz5B391mNNWw22AzmrJr6sQxb-ph9QRCZ/s348/Eq2-26.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="49" data-original-width="348" height="45" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiogFG2quS2nSz5p9l2lsX0ntrmMtA4EyeLMzE9YBL1NqimlPnNcpkRcj9WR-cMIjw2IbyyBn3lT-liOCYtSY2uLuNbDniKE6Dh333pQMkMBSNjxw-3-4uTjigAGQ4IXFB6JJFbwKZiZJKlNlJZv594_Q_38P_tz5B391mNNWw22AzmrJr6sQxb-ph9QRCZ/s320/Eq2-26.jpg" width="320" /></a></div><blockquote>
… The solution does have the properties sketched in Fig. 2.13, as you can see from Fig. 2.14.
</blockquote>
Figure 2.13 looks similar to this figure
<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj15ktNs7SJkVQG5AO3lM_gZj3uqndYOp4U36KpffZLOrOUO8W_N0Hn4Ti6gk8gwznYjNEN5CVXCf2e5UI0EP5eA_oyUwLu5YLMjWOL-7l2CbmKjy-dJdm72H_KBvm4BVhFpjdEdoAqw0tiyggwqCmq-zo0CsBvE62uuUFYfssD5B2_J2DP1wpzqiztV3Zb/s1250/SketchPlot.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="847" data-original-width="1250" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj15ktNs7SJkVQG5AO3lM_gZj3uqndYOp4U36KpffZLOrOUO8W_N0Hn4Ti6gk8gwznYjNEN5CVXCf2e5UI0EP5eA_oyUwLu5YLMjWOL-7l2CbmKjy-dJdm72H_KBvm4BVhFpjdEdoAqw0tiyggwqCmq-zo0CsBvE62uuUFYfssD5B2_J2DP1wpzqiztV3Zb/s320/SketchPlot.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Sketch of the initial slope <i>a</i> and final value <i>a/b</i> of <i>y</i> when <i>y</i>(0) = 0. In this figure, <i>a</i>=<i>b</i>=1.<br /></td></tr></tbody></table><p> And Fig. 2.14 looks like this
<br /></p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyjkFeVQDPvtfOqgRDsa10YWUpmlwtjzX8cUn2Y7QoHJ1lO6lERvGXBT9FDzD0-yxsaSy8Ld1-eKF0FQyDPP7eb7j53hTywfQN0VaxPbQt4J_XLmrorCZe7fG03AYzle5ANnyyn25464q77dXgUJgJjBWmJmZHdvXleq-GfZZxGoV-_cFaZTlfps9H6VLD/s1250/PlotOne.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="847" data-original-width="1250" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiyjkFeVQDPvtfOqgRDsa10YWUpmlwtjzX8cUn2Y7QoHJ1lO6lERvGXBT9FDzD0-yxsaSy8Ld1-eKF0FQyDPP7eb7j53hTywfQN0VaxPbQt4J_XLmrorCZe7fG03AYzle5ANnyyn25464q77dXgUJgJjBWmJmZHdvXleq-GfZZxGoV-_cFaZTlfps9H6VLD/s320/PlotOne.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A plot of <i>y</i>(<i>t</i>) using Eq. 2.26, with <i>a</i>=<i>b</i>=1.<br /></td></tr></tbody></table><p>However, Eq. 2.26 is not the only solution that is consistent with the sketch in Fig. 2.13. Today I want to present another function that is consistent with Fig. 2.13, but does not obey the differential equation in Eq. 2.25. </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwpiThEXyUtCwkGiNO9HztLFSh00QnxA8_gMGAhWEy3XoDdVVmSjsVr_mvauw1yvL3LWS0kCrrAlue0Sw-g9qq087Kd8n6W3IPEFFpuyDSTzA1gsyCvscTFAMAQTey9spFe2aYRO58tu9EuYyDaNCFnSB1fjmQl7RSTSbUvEdAQzxIc-I4ZRrpjgPs69LI/s361/Eq2-26prime.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="63" data-original-width="361" height="56" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwpiThEXyUtCwkGiNO9HztLFSh00QnxA8_gMGAhWEy3XoDdVVmSjsVr_mvauw1yvL3LWS0kCrrAlue0Sw-g9qq087Kd8n6W3IPEFFpuyDSTzA1gsyCvscTFAMAQTey9spFe2aYRO58tu9EuYyDaNCFnSB1fjmQl7RSTSbUvEdAQzxIc-I4ZRrpjgPs69LI/s320/Eq2-26prime.jpg" width="320" /></a></div><p>Let’s examine how this function behaves. When <i>bt</i> is much less than one, the function becomes <i>y</i> = <i>at</i>, so it’s initial growth rate is <i>a</i>. When <i>bt</i> is much greater than one, the function approaches <i>a</i>/<i>b</i>. The sketch in Fig. 2.13 is consistent with this behavior.</p><p>Below I show both Eqs. 2.26 and 2.26’ in the same plot.</p><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU6ZNUAyGWcWFlHAKuTCZOzBCIF7_xb-TknycmorzRauesLLXA-EZ8-XTmGV-sP0lDKivI20SMgY-3nGP4J5xzoGdTtfgn8wX1yEdlMeTGmw7OlQiFvp0u8Qg5vuhORa2shNJeu7T7b_kVi7posY9xt2erzss99A7YTFgUu9estzB45XuYW-g5p5I6uwSq/s1250/PlotBoth.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="847" data-original-width="1250" height="217" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjU6ZNUAyGWcWFlHAKuTCZOzBCIF7_xb-TknycmorzRauesLLXA-EZ8-XTmGV-sP0lDKivI20SMgY-3nGP4J5xzoGdTtfgn8wX1yEdlMeTGmw7OlQiFvp0u8Qg5vuhORa2shNJeu7T7b_kVi7posY9xt2erzss99A7YTFgUu9estzB45XuYW-g5p5I6uwSq/s320/PlotBoth.jpg" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A plot of <i>y</i>(<i>t</i>) using Eq. 2.26 (blue) and Eq. 2.26' (yellow), with <i>a</i>=<i>b</i>=1.</td></tr></tbody></table><p>The function in Eq. 2.26 (blue) approaches its asymptotic value at large <i>t</i> more quickly than the function in Eq. 2.26’ (yellow).
<br /><br />
The moral of the story is that you can learn a lot about the behavior of a solution by just inspecting the differential equation, but you can’t learn <i>everything</i> (or, at least, I can’t). To learn everything, you need to solve the differential equation. </p><p>By the way, if Eq. 2.26’ doesn’t solve the differential equation in Eq. 2.25, then what differential equation does it solve? The answer is</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6QC7akBC2KwhguFgH7yQnHeTNXXmzfAlIOJR3-_I1NFVaozAHmLJ192l00tZDJGEnrgEA85mo_tIuMkmmjV5nd-BJ0Rm2Z3RF4jl-sjpFzLw5n1cydqn8DlwTCdDrjqFISDQE6FG4BEyU05e4rLV0z_dUcapq28YH8eqZwakwj6QdefNmKE2GiBn82yZ8/s199/DifferentialEquation.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="55" data-original-width="199" height="55" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6QC7akBC2KwhguFgH7yQnHeTNXXmzfAlIOJR3-_I1NFVaozAHmLJ192l00tZDJGEnrgEA85mo_tIuMkmmjV5nd-BJ0Rm2Z3RF4jl-sjpFzLw5n1cydqn8DlwTCdDrjqFISDQE6FG4BEyU05e4rLV0z_dUcapq28YH8eqZwakwj6QdefNmKE2GiBn82yZ8/s1600/DifferentialEquation.jpg" width="199" /></a></div> How did I figure that out? Trial and error.<br /><p></p>Intermediate Physics for Medicine and Biologyhttp://www.blogger.com/profile/11077661160486900345noreply@blogger.com0Hannah Hall, Oakland University, Rochester, Michigan42.6678782 -83.20823469999999114.357644363821152 -118.36448469999999 70.978112036178842 -48.051984699999991