Friday, December 25, 2015

The Royal Institution's 2015 Christmas Lecutres: How to Survive in Space

A picture of Michael Faraday lecturing at the Royal Institution.
Michael Faraday lecturing
at the Royal Institution.
190 years ago at the Royal Institution in London, Michael Faraday presented the first Christmas Lectures. These lectures about science have continued annually except during the worst years of World War II, and are now broadcast on television and online. Each year is a different topic, and this year the topic is How to Survive in Space.
In December 2015, Tim Peake will become the first Briton in space for more than 20 years and a new member of the European Astronaut Corps. As Tim adjusts to life on board the International Space Station (ISS), Kevin Fong’s CHRISTMAS LECTURES will take us on a journey from planet Earth into Low Earth Orbit and beyond. This is the story of human survival against all the odds; the story of how science, medicine and engineering come together to help answer our biggest questions about Life, the Earth, the Universe and our place in it.

From artificial gravity and greenhouses in space to plasma drives and zero-G surgical suits, the Lectures will reveal how what once was the stuff of science fiction is fast becoming today’s science fact.

Throughout the three-part series, Kevin will be accompanied by special guest appearances from ISS astronauts who will reveal what daily life is like 400 kilometres above the Earth, demonstrate the technology and techniques that help them stay safe and healthy, and explain the scientific experiments they are part of that are helping to stretch the limits of our understanding of human physiology and survival in a way that no experiment back on Earth could.
Intermediate Physics for Medicine and Biology does not address space medicine specifically, but many of the topics examined in these Christmas Lectures require a deep understanding of how physics and medicine interact. I plan to watch. The lectures will be first broadcast by the BBC on December 28, 29, and 30. I won’t be able to view them until they are posted afterward (hopefully, soon afterward) on the Ri Channel.

A Christmas Carol, by Charles Dickens, superimposed on Intermediate Physics for Medicine and Biology.
A Christmas Carol,
by Charles Dickens.
Because this year I’m posting on Christmas Day, I’ll conclude with a Christmas present—the final lines of my all-time favorite book (yes, even better that IPMB): A Christmas Carol, by Charles Dickens. I reread it every December.
Scrooge was better than his word. He did it all, and infinitely more; and to Tiny Tim, who did not die, he was a second father. He became as good a friend, as good a master, and as good a man, as the good old city knew, or any other good old city, town, or borough, in the good old world. Some people laughed to see the alteration in him, but he let them laugh, and little heeded them; for he was wise enough to know that nothing ever happened on this globe, for good, at which some people did not have their fill of laughter in the outset; and knowing that such as these would be blind anyway, he thought it quite as well that they should wrinkle up their eyes in grins, as have the malady in less attractive forms. His own heart laughed: and that was quite enough for him.

He had no further intercourse with Spirits, but lived upon the Total Abstinence Principle, ever afterwards; and it was always said of him, that he knew how to keep Christmas well, if any man alive possessed the knowledge. May that be truly said of us, and all of us! And so, as Tiny Tim observed, God bless Us, Every One!

Friday, December 18, 2015

Star Wars

With The Force Awakens opening in theaters, now is the perfect time to answer your questions about how Intermediate Physics for Medicine and Biology relates to Star Wars. (Warning: This post is spoiler laden for Episodes I - VI, but not for Episode VII which I haven’t seen yet.)

Luke and Vadar in a lightsaber duel, from Star Wars
1. With so many light saber duels, why is there so little blood? Even blasters kill without gore or carnage. In Section 14.11 of IPMB, Russ Hobbie and I discuss tissue ablation. According to Wookieepedia, ablation cauterizes wounds, preventing bleeding. This is the same reason we use lasers in surgery.

A storm trooper, from Star Wars.

2. Why do blaster shots not propagate at the speed of light? Chapter 14 of IPMB gives the speed of light as 3 × 108 m/s. In Star Wars, shots travel not much faster than a hard-thrown fastball, maybe 100 m/s. Apparently this far-away galaxy has a large permeability of free space, μo. Next time you view these films, watch for exaggerated magnetic effects.

Han Solo frozen in carbonite, from Star Wars
 3. How did Han Solo freeze so quickly (and reversibly!) in carbonite? The bioheat equation  developed in Chapter 14 of IPMB implies that heat diffuses into tissue, and over long distances diffusion is slow. My guess is that carbonite freezing makes use of the blood flow term in the bioheat equation, perhaps by rapidly injecting cold carbonite intravenously. However, I don’t see any IV tubes coming out of Han. Do you? Carbonite freezing has to be dangerous. But no matter; had Han died during freezing, Chewbacca would have saved Princess Leia.

Luke Skywalker's robotic hand, from Star Wars.
4. How does Luke Skywalker’s artificial hand work? Chapter 7 of IPMB discusses electrical stimulation of nerves, which is crucial for developing neural prostheses. Luke had such a prosthesis after he lost his hand during his epic duel with Darth Vader (Luke’s FATHER!). Functional neural stimulation is becoming so sophisticated that artificial hands may arrive sooner than you think.

Darth Vadar, from Star Wars.
5. How does Darth Vader control his breathing? Chapter 10 in IPMB analyzes feedback loops, and our main example describes how we control the carbon dioxide in our blood by adjusting our ventilation rate. I wonder, does Vader’s mask break that feedback loop? Perhaps a carbon dioxide sensor in the mask adjusts the rate of his slow, heavy breathing. I suspect something is horribly wrong with his physiological control mechanism, because once the mask comes off Vader dies.

Jabba the Hut, from Star Wars.
6. What determines the anatomy of all those alien life forms? In Chapter 2 of IPMB, Russ and I describe how size impacts the structure of animals: scaling. One famous result involves the strength of bones. Body mass scales as length cubed, but the strength of a bone scales as its radius squared, meaning that bones must get thicker relative to their length in larger animals. This is why Jabba the Hutt has no legs. Yoda lied when he said “size matters not.”

Luke Skywalker riding his tauntaun on Hoth, from Star Wars.
7. How did Luke avoid freezing to death on Hoth? When an animal dies, it loses heat according to Newton’s law of cooling (Chapter 3 in IPMB). After Han killed the tauntaun and shoved Luke into its belly, its temperature began to fall exponentially. Luke must have gotten really cold. What saved him was immersion into a bacta tank, which speeds rewarming by taking advantage of convection as well as conduction. I suspect bacta may also contain suspended stem cells, but who knows? Whatever the mechanism, Luke survived. During his recuperation is the most disturbing event in the entire Star Wars saga: the incestuous kiss. Ewwwwww!

Admiral Ackbar, from Star Wars.
8. What did leaders of the Rebel Alliance say when they realized that Vader knew about their plans to attack the Death Star? One way to measure radiation dose is to use thermoluminescent phosphors, which Russ and I describe in Chapter 16 of IPMB as a “dielectric material that has been doped with impurities or has missing atoms in the crystal lattice to form metastable energy levels or traps.” So, Admiral Ackbar must have just discovered the mechanism of thermoluminescence when he exclaimed “It’s a trap!” 

Jar Jar Binks, from Star Wars.
If you want answers to all of your Star Wars questions, keep a copy of Intermediate Physics for Medicine and Biology handy. Before watching the new film, find time for a Star Wars marathon (with episodes in machete order, thereby avoiding Jar Jar Binks). Finally, don’t miss my favorite version of the Star Wars theme song, performed in the video below by lounge singer Nick Winters. Now, off to the movies. And, May The Force Be With You.

Friday, December 11, 2015

The Art of Insight in Science and Engineering

The Art of Insight in Science and Engineering, by Sanjoy Mahajan, superimposed on Intermediate Physics for Medicine and Biology.
The Art of Insight
in Science and Engineering,
by Sanjoy Mahajan.
I recently read The Art of Insight in Science and Engineering, by Sanjoy Mahajan (MIT Press, 2014). The Preface begins:
Science and engineering, our modern ways of understanding and altering the world, are said to be about accuracy and precision. Yet we best master the complexity of our world by cultivating insight rather than precision.

We need insight because our minds are but a small part of the world. An insight unifies fragments of knowledge into a compact picture that fits in our minds. But precision can overflow our mental registers, washing away the understanding brought by insight. This book shows you how to build insight and understanding first, so that you do not drown in complexity.
I think that Mahajan makes a good point. I’ve noticed that many of my students can use complicated algorithms to calculate numbers correctly, but often lack the ability to estimate a solution. This leads students to make mistakes in their homework that result in ridiculously wrong results. When this happens, I often print “THINK BEFORE YOU CALCULATE” in big red letters on their paper, and take off more than my normal number of points. On the other hand, when a homework question requires an intricate calculation that the student skips but instead writes down a reasonable estimate for the solution, I take off a few points but give them most of the credit because they actually thought about what they were doing.

Russ Hobbie and I stress estimation in the very first section of Intermediate Physics for Medicine and Biology: “One valuable skill in physics is the ability to make order of-magnitude estimates, meaning to calculate something approximately right.”. We provide several “back-of-the-envelope” homework problems in our book, such as “Estimate the number of hemoglobin molecules in a red blood cell,” “Estimate the size of a box containing one air molecule”, and “Estimate the density of water”. In fact, if you search through our book for the word “estimate” you will find many such questions. Students often object to these problems. When I explore why they are having difficulty, I find that many are reluctant to guess some number. For instance, a homework problem in Chapter 6 says “Suppose that an action potential in a 1-μm diameter unmyelinated fiber has a speed of 1.3 m s−1. Estimate how long it takes a signal to propagate from the brain to a finger.” Some students grind to a halt because the length of the arm is not given (or they use 1 μm for the length, getting a ridiculous result). When I tell them that the word “estimate” means “make a reasonable guess,” they’re not any happier; they think that guessing the length of the arm is cheating. But I’m just asking them to estimate the time to send a signal from the brain to the hand, and then THINK about the result. That’s why the last sentence in the problem says “Speculate on the significance of these results for playing the piano.”

In The Art of Insight, Mahajan also talks about units. In homework assignments, I often ask my students to algebraically solve for some expression; for example a relationship involving a distance x, time t, and speed v. A student will sometimes hand in a result like “v + x t”. Yikes! The units don’t work! (I use a lot of exclamation points when grading assignments.) I am stingy with partial credit when the derived equation is dimensionally incorrect, not because I want to punish a minor error, but because the student didn’t take the time to look at their equation and ask “do the units make sense?”

Another skill Mahajan stresses is proportional reasoning. Russ and I emphasize this in Chapter 2, when we discuss scaling. For instance, here is a question from an exam I gave earlier this semester in my Biological Physics class:
Assume the specific metabolic rate R* scales with mass M as R* = C M1/4 , where C is a constant. If an 81 kg person has a specific metabolic rate of 1.5 W/kg, what is the specific metabolic rate of a 1 kg guinea pig?
Some students get stuck because I didn’t give them a value for C. The point is, R* times M1/4 is a constant, so R*person Mperson1/4 = R*guinea pig Mguinea pig1/4. You don’t need C. (You don't even need your calculator if you recall that 81 = 34.)

Mahajan talks about examining “easy cases,” which is similar to our emphasis on taking limits of equations. Consider the analysis of Eq. 2.25 in IPMB: dy/dt = a – by. The solution (Eq. 2.26) is y = a/b (1 – e−bt). When I derive this equation in class, I always stop and ask the students what is the limit when t goes to inifinity? The answer is clearly y = (a/b), which they usually get right. Then I ask what is the limit when t goes to zero? This case requires more thought. A student will often say “zero,” but then I respond “yes, but HOW does it go to zero?” Using the Taylor series ex = 1 + x gives a limit of y = at. This skill is even more important for more complicated expressions. For instance, Section 4.12 in IPMB compares drift and diffusion. Equation 4.63 gives the concentration of a material that drifts with fluid speed v and diffuses with diffusion constant D through a tube of length x1. The student gains much insight by taking the limits when x1v/D is much greater than one and much less than one. If the student doesn’t take these limits, then this example is just a mathematical exercise that provides no insight.

Finally, Mahajan discusses briefly the value of log-log plots when analyzing scaling laws. This is a topic Russ and I emphasize in Chapter 2 of IPMB. It’s amazing how much information you can get from a log-log plot. One little fact I never realized until I read Mahajan’s book is that the geometric mean, √ab, of two numbers a and b is just the half-way point between the two numbers on a logarithmic scale.

A Mind for Numbers: How to Excel at Math and Science (Even if You Flunked Algebra), by Barb Oakley, superimposed on Intermediate Physics for Medicine and Biology.
A Mind for Numbers,
by Barb Oakley.
I had a chance to offer my views on insight and learning when my Oakland University colleague and friend Barb Oakley published her book A Mind for Numbers: How to Excel at Math and Science (Even if You Flunked Algebra). Barb asked several people, including me, for short “sidebars” to include in her book. Here is mine:
Insights on Learning from Physics Professor Brad Roth, A Fellow of the American Physical Society and Co-Author of Intermediate Physics for Medicine and Biology

One thing I stress in my classes is to think before you calculate. I really hate the ‘plug and chug’ approach that many students use. Also, I find myself constantly reminding students that equations are NOT merely expressions you plug numbers into to get other numbers. Equations tell a story about how the physical world works. For me, the key to understanding an equation in physics is to see the underlying story. A qualitative understanding of an equation is more important than getting quantitatively correct numbers out of it.

Here are a few more tips:

1. Often, it takes way less time to check your work than to solve a problem. It is a pity to spend twenty minutes solving a problem and then get it wrong because you did not spend two minutes checking it.

2. Units of measurement are your friend. If the units don’t match on each side of an equation, your equation is not correct. You can’t add something with units of seconds to something with units of meters. It’s like adding apples and rocks—nothing edible comes of it. You can look back at your work, and if you find the place where the units stop matching, you probably will find your mistake. I have been asked to review research papers that are submitted to professional journals that contain similar errors.

3. You need to think about what the equations means, so that your math result and your intuition match. If they don’t match, then you have either a mistake in your math or a mistake in your intuition. Either way, you win by figuring out why the two don’t match.

4. (Somewhat more advanced) For a complicated expression, take limiting cases where one variable or another goes to zero or infinity, and see if that helps you understand what the equation is saying.
Books like The Art of Insight and A Mind for Numbers reinforce fundamental yet critical skills. I hope IPMB reinforces these skills too.

Friday, December 4, 2015

A Mathematical Model of Make and Break Electrical Stimulation of Cardiac Tissue by a Unipolar Anode or Cathode

The first page of A Mathematical Model of Make and Break Electrical Stimulation of Cardiac Tissue by a Unipolar Anode or Cathode (IEEE Transactions on Biomedical Engineering, 42:1174–1184. 1995).
“A Mathematical Model of Make and Break
Electrical Stimulation of Cardiac Tissue
by a Unipolar Anode or Cathode.”
Suppose I was going to die tomorrow and I could choose only one paper to cite on my tombstone. Which would I pick? I’d select
B. J. Roth, 1995, “A Mathematical Model of Make and Break Electrical Stimulation of Cardiac Tissue by a Unipolar Anode or Cathode,” IEEE Transactions on Biomedical Engineering, Volume 42, Pages 1174–1184.
Below is the introduction, with references removed. I like the way it starts with a question.
What is the mechanism by which an electrical current, passed through a unipolar electrode, excites cardiac tissue? This simple question appears to have a straightforward answer: The stimulus current depolarizes the tissue under the electrode until the transmembrane potential reaches threshold, triggering an action potential wave front. Excitation of cardiac tissue, however, is more complicated than one might initially expect. Stimulation with a cathode might be explained by depolarization of the tissue under the electrode, but how does one explain stimulation with an anode? Even more intriguing, excitation is elicited by turning a stimulus off (break) as well as by turning it on (make). Why should turning off the stimulus excite the tissue? Indeed, four distinct mechanisms are responsible for stimulation of cardiac tissue—cathode make, anode make, cathode break, and anode break—and only cathode-make stimulation can be explained by depolarization under the electrode. To understand the other three mechanisms, we make detailed calculations of the transmembrane potential distribution induced by current through a unipolar electrode. We have three goals: to explain the mechanisms of excitation qualitatively; to predict stimulation thresholds quantitatively; and to determine how the threshold varies with electrode size and with stimulus pulse duration and frequency.

Our calculations are based on the bidomain model of cardiac tissue, which is useful for predicting the transmembrane potential induced by an extracellularly applied electric field. The bidomain model is a two- or three-dimensional cable model that accounts for the resistance of both the intracellular and the extracellular spaces. Many of the most interesting and nonintuitive predictions of the bidomain model occur when the ratios of the electrical conductivities parallel to and perpendicular to the myocardial fibers in the intracellular and extracellular spaces differ. For instance, current that is passed through a point extracellular electrode into a two-dimensional bidomain with unequal anisotropy ratios induces adjacent areas of depolarization and hyperpolarization. Such a region of hyperpolarization near a cathode is called a virtual anode; a region of depolarization near an anode is called a virtual cathode. The existence of virtual anodes and cathodes is predicted by the bidomain model and is essential for three of the four mechanisms of stimulation. Recently, virtual anodes and cathodes were observed experimentally in cardiac tissue.
My use of the royal “we” seemed reasonable when I wrote the paper, but now it grates on my ear. According to Google Scholar, in the twenty years since I published this article it has been cited 169 times. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I turned the prediction of break excitation of cardiac tissue into a homework problem (Chapter 7, Problem 48).

I did this research while working at the National Institutes of Health in Bethesda, Maryland. Sometimes on a slow afternoon I would sneak away from my desk and browse the stacks of the NIH library. One day I found a fascinating paper by Egbart Dekker, who measured the threshold for each of the four mechanisms of excitation (E. Dekker, 1970, “Direct Current Make and Break Thresholds for Pacemaker Electrodes on the Canine Ventricle,” Circulation Research, Volume 27, Pages 811–823.) Once I read Dekker’s article, I knew I could simulate this behavior using the then-new bidomain model and perhaps gain insight about mechanisms. At the time I was not well versed in mathematical models of the cardiac membrane kinetics with all their different ion currents, so I just used the Hodgkin-Huxley model of a nerve axon. A paper describing that study was unpublishable because who in their right mind would use a squid nerve axon model to represent a cardiac action potential? After the manuscript using the Hodgkin-Huxley model was rejected, I set to work learning about cardiac ion channel dynamics. I chose the Beeler-Reuter model, and the paper using the BR model (no, I did not choose that model because of my initials) was ultimately accepted for publication.

I sent a draft of my article to my PhD advisor, John Wikswo. He and his post doc Marc Lin immediately verified the model predictions experimentally (see their lovely paper: J. P. Wikswo, S. F. Lin, and R. A. Abbas, 1995, “Virtual Electrodes in Cardiac Tissue: A Common Mechanism for Anodal and Cathodal Stimulation,” Biophysical Journal, Volume 69, Pages 2195–2210). I remember the day Wikswo emailed me asking something like “what would you say if I told you the cathode make, cathode break, and anode make mechanisms all behave exactly as you predicted, but your anode break mechanism is totally wrong?” I began to panic, wondering how in the world I messed up, and sent Wikswo a frantic email asking for more details. His response was along the lines of “I asked ‘what would you say?’ I didn’t claim your prediction was actually wrong.” Ha, ha, ha; all four mechanisms were verified. Their paper was published the same month as mine and now has 300 citations. Your can read a layman’s account of this work in an article published in the Vanderbilt Register.

The figures in my original article were all black-and-white contour plots of action potential wave fronts propagating through the tissue. Wikswo had beautiful color figures in his paper. So, a few years later I “colorized” the figures, including them in a review article (B. J. Roth, S.-F. Lin and J. P. Wikswo, Jr., 1998, “Unipolar Stimulation of Cardiac Tissue,” Journal of Electrocardiology, Volume 31, Supplement, Pages 6–12). This always reminds me of how some of the classic old black-and-white movies have been colorized to look modern.

One reason I like publishing in the IEEE TBME is that they provide a short biographical sketch of the author. Below is my bio from 20 years ago. My how time flies.
Bradley J. Roth was raised in Morrison, Illinois. He received the B.S. degree from the University of Kansas in 1982, where he was a Summerfield Scholar and received the Stranathan Award from the Department of Physics and Astronomy. He received the Ph.D. degree in physics from Vanderbilt University.

From 1988-1995, he worked in the Biomedical Engineering and Instrumentation Program at the National Institutes of Health. One of his primary accomplishments while at NIH was the study of the bidomain model and its application to solving fundamental problems solving the interaction of applied electric fields with cardiac muscle. Using the results of numerical simulations, he has formulated mechanisms for stimulation, defibrillation, and the initiation of arrhythmias in the heart In September, 1995, he became the Robert T. Lagemann Assistant Professor of Living State Physics at Vanderbilt University.