Terminal Speed of Microorganisms

A Paramecium aurelia seen through an optical microscope.
Source: Wikipedia (http://en.wikipedia.org/wiki/Image:Paramecium.jpg)

Homework Problem 28 at the end of Chapter 2 in Intermediate Physics for Medicine and Biology asks the reader to calculate the terminal speed of an animal falling in air. Although this problem provides insight, it includes a questionable assumption. Russ and I tell the student to “assume that the frictional force is proportional to the surface area of the animal.” If, however, the animal falls at low Reynolds number, this assumption is not valid. Instead, the drag force is given by Stokes’ law, which is proportional to the radius, not the surface area (radius squared). The new homework problem given below asks the reader to calculate the terminal speed for a microorganism falling through water at low Reynolds number.

Section 2.8

Problem 28 ½. Calculate the terminal speed, V, of a paramecium sinking in water. Assume that the organism is spherical with radius R, and that the Reynolds number is small so that the drag force is given by Stokes’ law. Include the effect of buoyancy. Let the paramecium’s radius be 100 microns and its specific gravity be 1.05. Verify that its Reynolds number is small.

The reader will first need to get the density ρ and viscosity η of water, which are ρ = 1000 kg/m³ and η = 0.001 kg/(m s). The specific gravity is not defined in IPMB, but it’s the density divided by the density of water, implying that the density of the paramecium is 1050 kg/m³. Finally, Stokes’ law is given in IPMB as Eq. 4.17, F_drag = –6πRηV.

I’ll let you do your own calculation. I calculate the terminal speed to be about 1 mm/s, so it takes about a fifth of a second to sink one body diameter. The Reynolds number is 0.1, which is small, but not exceptionally small.

You should find that the terminal speed increases as the radius squared, in contrast to a drag force proportional to the surface area for which the terminal speed increases in proportion to the radius. Bigger organisms sink faster. The dependence of terminal speed on size is even more dramatic for aquatic microorganisms than for mammals falling in air. To paraphrase Haldane’s quip, “a bacterium is killed, a diatom is broken, a paramecium splashes,” except the speeds are small enough that none of the “wee little beasties” are really killed (the terminal speed is not terminal...get it?) and splashing is a high Reynolds number phenomenon.

Buoyancy is not negligible for aquatic animals. The effective density of a paramecium in air would be about 1000 kg/m³, but in water its effective density drops to a mere 50 kg/m³. Microorganisms are made mostly of water, so they are almost neutrally buoyant. In this homework problem, the effect of gravity is reduced to only five percent of what it would be if buoyancy were ignored.

A paramecium is a good enough swimmer that it can swim upward against gravity if it wants to. Its surface is covered with cilia that beat together like a Roman galley to produce the swimming motion (ramming speed!).

Whenever discussing terminal speed, one should remember that we assume the fluid is initially at rest. In fact, almost any volume of water will have currents moving at speeds greater than 1 mm/s, caused by tides, gravity, thermal convection, wind driven waves, or the wake of a fish swimming by. A paramecium would drift along with these currents. To observe the motion described in this new homework problem, one must be careful to avoid any bulk movement of water.

If you watched a paramecium sink in still water, would you notice any Brownian motion? You can calculate the root-mean-squared thermal speed with Eq. 4.12 in IPMB, using the mass of the paramecium as four micrograms and a temperature of 20° C. You get approximately 0.002 mm/s. That is less than 1% of the terminal speed, so you wouldn’t notice any random Brownian motion unless you measured extraordinarily carefully.

Breathless

Breathless,
by David Quammen.

Whenever David Quammen has a new book, I put it on my “to read” list. Recently I finished his latest: Breathless: The Scientific Race to Defeat a Deadly Virus. Here’s the opening paragraph:

To some people it wasn’t surprising, the advent of this pandemic, merely shocking in the way a grim inevitability can shock. Those unsurprised people were infectious disease scientists. They had for decades seen such an event coming, like a small, dark dot on the horizon of western Nebraska, rumbling toward us at indeterminable speed and with indeterminable force, like a runaway chicken truck or an eighteen-wheeler loaded with rolled steel. The agent of the next catastrophe, they knew, would almost certainly be a virus. Not a bacterium as with bubonic plague, not some brain-eating fungus, not an elaborate protozoan of the sort that cause malaria. No, a virus—and, more specifically, it would be a “novel” virus, meaning not new to the world but newly recognized as infecting humans.

Quammen—a national treasure—is writing about covid (or, to use its official name, SARS-CoV-2). The coronavirus pandemic did not startle him; he almost predicted it in his earlier book Spillover. Quammen’s book Breathless is to tracing the origins and variants of covid as Walter Isaacson’s book The Code Breaker is to developing a vaccine for covid: required reading to understand what we’ve all been through the last three years. (And what I went through last month with my first case of covid, but I’m healthy now and feeling fine.)

Breathless describes the scientists who developed amazing software to analyze the virus’s genome, such as Áine O’Toole’s genomic pipeline PANGOLIN. Intermediate Physics for Medicine and Biology doesn’t discuss computational genomics, but at the heart of IPMB is the idea that you can combine a hard science like computer programming with a biological science like genomics to gain more information about, and insight into, biology and medicine. Quammen interviewed O’Toole about her experience writing the PANGOLIN program (“O’Toole stayed up late one night, and the next morning, there it was.”). But he didn’t interview just her. He talked to 96 heroic scientists and medical doctors who sought to understand covid, from those I’ve never heard of such as O’Toole to those we all are familiar with such as the brilliant Anthony Fauci. These interviews give the book credibility, especially given all the covid conspiracy theories and anti-vaccine nonsense that floats around the internet these days.

For anyone who may doubt the reality of evolution, I challenge you to try making sense of covid variants without it. Quammen takes us through the list: Alpha, Beta, Gamma, and the frightening Delta.

And after Delta, we knew, would come something else. The Greek alphabet contains twenty-four letters; at that point, the WHO [World Health Organization] list of variants only went up to mu. A virus will always and continually mutate, as I’ve noted, and the more individuals it infects, the more mutations it will produce. The more mutations, the more chances to improve its Darwinian success. Natural selection will act on it, eliminating waste, eliminating ineptitude, carving variation like a block of Carrara marble at the hands of Michelangelo, finding beautiful shapes, preserving the fittest. Evolution will happen. That’s not a variable, it’s a constant.

The latest variant, Omicron, seems to have appeared just as Quammen was finishing his book.

Omicron’s panoply of mutations reflects a period of active, extensive evolution—because the mutations not only occurred but they were preserved, within the lineage, suggesting they offered adaptive value.

One of the most interesting questions addressed in Breathless is the source of covid. Was it a lab accident, a spillover from an animal host (called a zoonotic event), or a malevolent attempt at biological warfare? Quammen doesn’t provide a definitive answer, but he favors the conclusions reached in a review article written by a group of prominent virologists led by Eddie Holmes.

Yes, Holmes and his coauthors agreed, the possibility of a lab accident can’t be entirely dismissed. Furthermore, that hypothesis may be nearly impossible to disprove. But it’s “highly unlikely,” they judged, “relative to the numerous and repeated human-animal contacts that occur routinely in the wildlife trade.” Failure to investigate that zoonotic dimension, with collaborative studies, crossing borders between countries and boundaries between species, would leave this pandemic festering and the world still very vulnerable to the next one.

Run, do not walk, to your library or bookstore and get Breathless. You need to read this book. Take special heed of Quammen’s alarming, disturbing, terrifying last sentence.

There are many more fearsome viruses where SARS-CoV-2 came from, wherever that was.

 A conversation with author and journalist David Quammen.

https://www.youtube.com/watch?v=jsREp6XI0nY

The Unscientific King: Charles III’s History Promoting Homeopathy

King Charles III of England was crowned this week. What’s that got to do with Intermediate Physics for Medicine and Biology? Well, the king is a big supporter of alternative medicine and one goal of IPMB is to highlight science-based medicine. If you believe in science, you don’t believe in alternative medicine. If science shows that some treatment works, it becomes part of medicine; there is nothing “alternative” about it. If science doesn’t show that some treatment works, then advocating for that treatment as “alternative medicine” is silly and foolish. In the realm of medicine, the king is a snake oil salesman.

Voodoo Science
by Robert Park.

Particularly worrisome is the king’s support for homeopathy. For those not familiar with homeopathic medicine, it works like this: a drug is repeatedly diluted, first by a 10:1 ratio of water to active ingredient (1X), then again a 10:1 dilution so the total dilution is by a factor of 100 (2X), then again a 10:1 dilution (3X), and so on. In Voodo Science, Bob Park described it this way:

The dilution limit is reached when a single molecule of the medicine remains. Beyond that point, there is nothing left to dilute. In over-the-counter homeopathic remedies, for example, a dilution of 30X is fairly standard. The notation 30X means the substance was diluted one part in ten and shaken, and then this was repeated sequentially thirty times. The final dilution would be one part medicine to 1,000,000,000,000,000,000,000,000,000,000 parts of water. That would be far beyond the dilution limit. To be precise, at a dilution of 30X you would have to drink 7,874 gallons of the solution to expect to get just one molecule of the medicine.

The supporters of homeopathy would have us believe that the water “remembers” the presence of the active ingredient.

King Charles’s support of alternative medicine was discussed in a recent article in The Scientist by Sophie Fessl, titled “The Unscientific King: Charles III’s History Promoting Homeopathy.” The first paragraph is reproduced below.

King Charles III has been conferred many new titles following the recent death of his mother, Queen Elizabeth II, but one existing title that remains is “Royal Patron of the Faculty of Homeopathy,” an organization of healthcare practitioners who also practice the pseudoscientific form of medicine. And the new king’s ties with alternative medicine go beyond this patronship and a dalliance with alternative medicine: In several instances, then-Prince Charles appears to have lobbied for homeopathy and other fields of alternative medicine. As King Charles ascends the throne, experts are reflecting on his influence on medical science in the UK as Prince of Wales, and how he might affect alternative medicine in the UK going forward as monarch. 

One book I have not read yet but is on my to-read list is Charles, The Alternative King, by Edzard Ernst, an advocate for evidence-based medicine and one of my heroes. In his preface, Ernst writes

This book chronicles Charles’s track record in promoting pseudo- and anti-science in the realm of alternative medicine. The new edition includes an additional final chapter with a summary of some of the scientific evidence that has emerged since this biography [originally titled Charles, The Alternative Prince] was first published. It demonstrates that the concerns about the safety and efficacy of the treatments in question are becoming even more disquieting. Whether such data will tame the alternative bee under the royal bonnet seems, however, doubtful.

This is the man who now sits on the thrown of England. We Americans owe George Washington so much.

Plans for a 6th Edition of Intermediate Physics for Medicine and Biology

Thank you for your interest in the 5th edition of Intermediate Physics for Medicine and Biology. We’re considering a 6th edition and we would like to get your opinions and input. Some of you may have heard that about a year ago the senior author Russ Hobbie passed away. He was a joy to work with and will be missed. The 6th edition will have three authors: Hobbie, me, and a new coauthor Gene Surdutovich.

Gene and I would appreciate any feedback you have about our plans for the 6th edition. If you have time, please answer the questions below and email your responses to me at roth@oakland.edu. It would help us a lot to hear from you. I know that I listed many questions. Don’t worry if you have answers to only a few (or even just one). 

Thank you. 

1. Was there any topic in the textbook that you think could be removed? 
2. Was there any topic NOT in the textbook that you would like to see added in the 6th edition? 
3. Regarding the homework problems, were they too easy? Too difficult? Too many? Too few? 
4. How useful was the list of symbols at the end of each chapter? 
5. Regarding the references, were there too many? Too few?
   
6. Were the figures useful? Not useful? Easy to understand? Difficult to understand? 
7. A few chapters had computer code. Was it useful? Was it unnecessary? 
8. Are the Appendices useful? Unnecessary? Too many? Too few? 
9. Do you have any general input or advice? 
10. Do you have any specific issues with the 5th edition that you would like us to address?

Biomagnetism: The First Sixty Years

Roth, B. J., 2023,
Biomagnetism: The first sixty years.
Sensors, 23:4218.

The last two blog posts have dealt with biomagnetism: the magnetic fields produced by our bodies. Some of you might have noticed hints about how these posts originated in “another publication.” That other publication is now published! This week, my review article “Biomagnetism: The First Sixty Years” appeared in the journal Sensors. The abstract is given below.

Biomagnetism is the measurement of the weak magnetic fields produced by nerves and muscle. The magnetic field of the heart—the magnetocardiogram (MCG)—is the largest biomagnetic signal generated by the body and was the first measured. Magnetic fields have been detected from isolated tissue, such as a peripheral nerve or cardiac muscle, and these studies have provided insights into the fundamental properties of biomagnetism. The magnetic field of the brain—the magnetoencephalogram (MEG)—has generated much interest and has potential clinical applications to epilepsy, migraine, and psychiatric disorders. The biomagnetic inverse problem, calculating the electrical sources inside the brain from magnetic field recordings made outside the head, is difficult, but several techniques have been introduced to solve it. Traditionally biomagnetic fields are recorded using superconducting quantum interference device (SQUID) magnetometers, but recently new sensors have been developed that allow magnetic measurements without the cryogenic technology required for SQUIDs.

The “First Sixty Years” refers to this year (2023) being six decades since the original biomagnetism publication in 1963, when Baule and McFee first measured the magnetocardiogram. 

My article completes a series of six reviews I’ve published in the last few years. 

• Roth, B. J., 2021, Bidomain modeling of electrical and mechanical properties of cardiac tissue. Biophysics Reviews, 2:041301. 
• Roth, B. J., 2022, The development of transcranial magnetic stimulation. BOHR International Journal of Neurology and Neuroscience, 1:8–20. 
• Roth, B. J., 2023, Can MRI be used as a sensor to record neural activity? Sensors, 23:1337. 
• Roth, B. J., 2023, A mathematical model of mechanotransduction. Academia Biology, 1. 
• Roth, B. J., 2023, Magneto-acoustic imaging in biology. Applied Sciences, 13:3877. 
• Roth, B. J., 2023, Biomagnetism: The first sixty years. Sensors, 23:4218.

Get the whole set! All are open access except the first. If you need a copy of that one, just email me at roth@oakland.edu and I’ll send you a pdf.

I’m not preparing any other reviews, so this will probably be the last one. But, you never know. 

You can learn more about biomagnetism in Chapter 8 of Intermediate Physics for Medicine and Biology.

Enjoy! 

 

The Magnetic Field Associated with a Plane Wave Front Propagating Through Cardiac Tissue

When I was on the faculty at Vanderbilt University, my student Marcella Woods and I examined the magnetic field produced by electrical activity in a sheet of cardiac muscle. I really like this analysis, because it provides a different view of the mechanism producing the magnetic field compared to that used by other researchers studying the magnetocardiogram. In another publication, here is how I describe our research. I hope you find it useful.

Roth and Marcella Woods examined an action potential propagating through a two-dimensional sheet of cardiac muscle [58]. In Fig. 6, a wave front is propagating to the right, so the myocardium on the left is fully depolarized and on the right is at rest. Cardiac muscle is anisotropic, meaning it has a different electrical conductivity parallel to the myocardial fibers than perpendicular to them. In Fig. 6, the fibers are oriented at an angle to the direction of propagation. The intracellular voltage gradient is in the propagation direction (horizontal in Fig. 6), but the anisotropy rotates the intracellular current toward the fiber axis. The same thing happens to the extracellular current, except that in cardiac muscle the intracellular conductivity is more anisotropic than the extracellular conductivity, so the extracellular current is not rotated as far. Continuity requires that the components of the intra- and extracellular current densities in the propagation direction are equal and opposite. Their sum therefore points perpendicular to the direction of propagation, creating a magnetic field that comes out of the plane of the tissue on the left and into the plane on the right (Fig. 6) [58–60].

Figure 6. The current and magnetic field produced by a planar wave front propagating in a two-dimensional sheet of cardiac muscle. The muscle is anisotropic with a higher conductivity along the myocardial fibers.

This perspective of the current and magnetic field in cardiac muscle is unlike that ordinarily adopted when analyzing the magnetocardiogram, where the impressed current is typically taken as in the same direction as propagation. Nonetheless, experiments by Jenny Holzer in Wikswo’s lab confirmed the behavior shown in Fig. 6 [61].

The main references are:

58. Roth, B.J.; Woods, M.C. The magnetic field associated with a plane wave front propagating through cardiac tissue. IEEE Trans. Biomed. Eng. 1999, 46, 1288–1292.

61. Holzer, J.R.; Fong, L.E.; Sidorov, V.Y.; Wikswo, J.P.; Baudenbacher, F. High resolution magnetic images of planar wave fronts reveal bidomain properties of cardiac tissue. Biophys. J. 2004, 87, 4326–4332. 

You can learn more about how magnetic fields are generated by cardiac muscle by reading about what happens at the apex of the heart. Or, solve homework problem 19 in Chapter 8 of Intermediate Physics for Medicine and Biology.

The Magnetoencephalogram is Not Sensitive to a Radial Dipole

One of the key limitations of the magnetoencephalogram (MEG) is that it’s not sensitive to a radial dipole. What does this mean? The MEG is the magnetic field outside the head produced by the electrical activity of neurons in the brain. Often the source of this activity can be described by a current dipole, p, representing the intracellular current in the neurons. Because current flows in continuous loops, a dipole is surrounded by extracellular “return currents” flowing throughout the brain. Often the brain can be approximated as a sphere.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I explain the lack of a magnetic signal from a radial dipole this way:

One can see from the symmetry argument in the caption of Fig. 8.19 that in a spherically symmetric conducting medium the radial component of p and its return currents do not generate any magnetic field outside the sphere. Therefore the MEG is most sensitive to detecting activity in the fissures of the cortex, where the trunk of the postsynaptic dendrite is perpendicular to the surface of the fissure. A tangential component of p does produce a magnetic field outside a spherically symmetric conductor.

Figure 8.19 from IPMB is shown below.

While this text and figure do explain why a radial dipole has zero magnetic field, the explanation is a bit cryptic. Here is an alternative explanation that I wrote for another publication, and a better (or at least more colorful) figure.

A radial dipole produces no magnetic field (Fig. 8). This result is best proved using Ampere’s law: the magnetic field integrated along a closed loop is proportional to the net current threading the loop. The symmetry is sufficient that the integral over the path (dashed circle in Fig. 8) equals the path length times the magnetic field. The current produced by a dipole, including the return current, must be contained within the sphere because the region outside is not conducting. Hence, the net current threading the loop (the dipole plus the return current) is zero, so the magnetic field of a radial dipole vanishes.

Figure 8. The magnetic field of a radial dipole is zero outside a spherical conductor.

I hope this description is clearer!

I’ve Got Covid

For three years I’ve dodged the bullet, but no more; I have covid. I’m doing fine, thank you. For me the symptoms were similar to a moderate cold. My doctor put me on a five-day regimen of the antiviral drug Paxlovid plus some supplements to support my immune system (vitamin C, vitamin D3, and zinc). I’ve been isolating in our spare bedroom, which is boring but otherwise comfortable. I think I’m over the hump.

During the last few days I’ve taken several of those at-home covid rapid antigen tests. There’s some interesting physics at work in them. The figure below illustrates how they’re constructed. 

A covid rapid antigen test. From: Gupta et al. (2020) Nanotechnology-Based Approaches for the Detection of SARS-CoV-2. Frontiers in Nanotechnology, Volume 2, Article 589832.

To perform a test, you typically swab your nose, dip the swab in saline, stir, and then place a few drops of the solution onto the sample pad (A). You’re not detecting the virus itself, but instead the SARS-Cov 2 antibody. To explain what that means, I need to delve into a bit of immunology.

Our immune system produces a Y-shaped protein called an antibody, or immunoglobulin, that can selectively bind to an antigen, which is typically a protein that’s part of the coronavirus. The beauty of the antibody-antigen reaction is that it’s so specific: it lets the immune system attack a particular virus, bacteria, or other pathogen, ignoring everything else. When you get covid, your body launches an immune attack by producing SARS-Cov 2 antibodies. In the illustration above, the yellow Y is the antibody you are trying to detect. See David Goodsell’s marvelous painting of a virus being attacked by antibodies at the bottom of this post.

In the above figure, the conjugate pad (B) is where much of the physics lives. The pad contains gold nanoparticles (AuNP) that are coated with anti-human antibodies. An “anti-human antibody” is a molecule that binds selectively to a human antibody. In the figure, a red dot with a blue Y sticking out is a gold nanoparticle with an anti-human antibody bound to it.

A nitrocellulose membrane (NC membrane) is made from a mesh of nitrocellulose fibers (C). The mesh is porus and acts something like a wick, pulling the fluid from left to right by capillary action. This is why a device like that in the figure above is sometimes called a lateral flow test. The mesh also provides protected space for the nanoparticles and molecules to move around and interact in. The absorbent pad (D) acts like a sponge, soaking up the fluid as it reaches the right end of the detector, contributing to the capillary action and preventing any back flow.

As any SARS-Cov 2 antibody passes by a gold nanoparticle/anti-human antibody, it binds and the entire complex flows to the right together (in the figure, a combined red dot/blue Y/yellow Y).

Some additional molecules are bound to two spots on the nitrocellulose membrane. One, the test strip, has the SARS-cov 2 antigen. If any SARS-Cov 2 antibody passes by, it will bind to the antigen, immobilizing the gold nanoparticles. The other strip is goat anti-mouse antibody. How did a goat and mouse get involved? I don’t know. As I understand it, gold nanoparticles with antibodies that bind to the goat anti-mouse antibody are included in the conjugate pad, so regardless of if you have covid or not it serves as a control. If the nanoparticles don’t collect at the control strip, something is wrong.

Why bother with the gold nanoparticles? Their role is to transduce the signal so it becomes visible. Nanoparticles have interesting optical properties. When exposed to an electromagnetic field such as light, the electric field causes electrons to accumulate on one side of the particle creating a negative surface charge, leaving the opposite side positive from a lack of electrons. Such a distribution of charge oscillates at its own natural frequency (its plasma frequency), and when this frequency matches the driving frequency of the light there is a resonance. This “localized surface plasmon resonance” is effective at absorbing or scattering light. Scattering is particularly important because Rayleigh scattering (the scattering of light by particles with a radius much smaller than the wavelength of the light) depends on the sixth power of the particle radius. The binding of nanoparticles (which typically have a diameter of tens of nanometers) with large antibodies and antigens, and the aggregation of these complexes, can increase their effective size, accentuating scattering. In addition, the high concentration of the nanoparticles at the test and control strips enhance any optical effect. The end result is that you see a dark line if the nanoparticles are present.

So swab your nose, swish it in some saline, add a few drops to the sample pad, and wait. After about 15 minutes look at the results. If there is no control line, you’ve messed up. Throw the test away and try again. If there’s a control line but no test line, you’re negative. Be happy (but not too happy, because these tests are prone to false negatives). If there’s both a control line and a test line, you’ve got covid. The tests don’t give false positives too often, so you can be fairly confident you have the disease. Isolate yourself and talk to you doctor.

Where is the physics in all this? First, in the flow, which results from the surface tension created by the mesh of fibers, leading to capillary action. Second, in the optical properties of the nanoparticles, which provide the color that you see in the test and control strips. Unfortunately, Intermediate Physics for Medicine and Biology doesn’t discuss capillary action or surface plasmons, so you can’t learn about them there. Sorry; no book can cover everything. But there is interesting physics hidden in these tests.

Stay safe, dear reader, and may all your covid tests be negative.

This painting shows a cross section through a coronavirus surrounded by blood plasma, with neutralizing antibodies in bright yellow. The painting was commissioned for the cover of a special COVID-19 issue of Nature. From: David S. Goodsell, RCSB Protein Data Bank and Springer Nature; doi: 10.2210/rcsb_pdb/goodsell-gallery-025

 

A chemist explains how at-home covid tests work. From WIRED.

https://www.youtube.com/watch?v=2B-iZGNiPA0

See how a lateral flow immunoassay works.

https://www.youtube.com/watch?v=z07CK-4JoFo

Should Exclamation Points Be Used in Scientific Writing? Yes!

Exclamation points are rare in scientific writing, but I like them. Occasionally Russ Hobbie and I use them in Intermediate Physics for Medicine and Biology. They’re fine as long as you don’t overdo it.

Let’s see what my favorite books about writing say.

The Elements of Style,
by Strunk and White.

Strunk and White (The Elements of Style): “Do not attempt to emphasize simple statements by using a mark of exclamation…The exclamation mark is to be reserved for use after true exclamations or commands.”

On Writing Well,
by William Zinsser.

Zinsser (On Writing Well): “Don’t use it unless you must to achieve a certain effect. It has a gushy aura…Resist using an exclamation point to notify the reader that you are making a joke or being ironic…Humor is best achieved by understatement, and there’s nothing subtle about an exclamation point.”

  Dreyer's English,
by Benjamin Dreyer.

Dreyer (Dreyer’s English): “Go light on the exclamation points. When overused, they’re bossy, hectoring, and, ultimately, wearying. Some writers recommend that you should use no more than a dozen exclamation points per book; others insist that you should use no more than a dozen exclamation points in a lifetime.”

Plain Words,
by Sir Ernest Gowers.

Gowers (Plain Words): His disdain for the exclamation point is so complete he doesn’t even acknowledge that it exists.

Below I list eleven places where exclamation points appear in IPMB. In each case, I indicate if we should keep the exclamation point or toss it out. Note: I don’t include any exclamation point that indicates a factorial, such as 4! = 1 × 2 × 3 × 4 = 24; that’s a mathematical symbol, not punctuation.

Page 29: Homework Problem 43 in Chapter 1 says “Suppose a student asked you, ‘How can blood be moving more slowly in a capillary than in the aorta? … The capillary has a much smaller cross-sectional area than the aorta. Therefore, the blood should move faster in the capillary than in the aorta!” The exclamation point belongs to the hypothetical student, not to Russ and me. If you don’t like it, take it up with the student (and beware, those students tend to be gushy). Keep.

Page 44: In Chapter 2, Russ and I write “Moreover, commercial graphing software does not impose this constraint on log–log plots, so it is becoming less and less likely that you can determine the exponent by glancing at the plot. Be careful!” The exclamation point is a warning. Keep.

Page 51: In the references at the end of Chapter 2, we cite Albert Bartlett’s delightful book “The Essential Exponential!” The exponential point is Bartlett’s, and is part of the title (like Oklahoma!). Keep.

Page 53: In the introduction to Chapter 3, Russ and I explain why statistical methods are so useful in thermodynamics. We estimate how long is required to simulate all the particles in a cubic millimeter of blood. We conclude “If a computer can do 10¹² operations/s, then the complete calculation for a single time interval will require 10⁸ s or 3 years!” In other words, a really long time. My feelings on this one are mixed. Toss.

Page 270: In a footnote in Chapter 10, we write “Strictly speaking, (dV/dt)_alveoli is not the derivative of a function V. (It always has a positive value, and the lungs are not expanding without limit!) We use the notation to remind ourselves that it is the rate of air exchange in the alveoli.” If I could delete only one exclamation point from IPMB, this would it. The thought of those lungs getting bigger and bigger is just disturbing. Toss.

Page 308: In Chapter 11, Russ and I compare two methods for doing a least squares fit of an exponentially decaying function. Method 1: take the logarithm of the data and then do a linear fit. Method 2: do a nonlinear fit to the original data. We end the analysis with a moral: “Use nonlinear least squares, Method 2!” Keep.

Page 388: A section in Chapter 14 has tricky units. We remind the reader to “Be careful with units!” Exclamation points are legitimate when issuing a command or warning. Perhaps, however, we shouldn’t have used both bold and an exclamation point. Keep.

Page 484: When explaining the linear-quadratic model for radiation damage, Russ and I concoct an illustrative but unrealistic example. We then warn the reader “(This is not realistic!).” I wonder if we should’ve made a more realistic example and avoided the exclamation point. Toss.

Page 497: In Homework Problem 8 of Chapter 16, Russ and I discuss x-ray imaging devices used to fit kids’ shoes, common in the 1940s. “These marvelous units were operated by people who had no concept of radiation safety and aimed a beam of x-rays upward through the feet and right at the reproductive organs of the children!” My vote is to keep this exclamation point at all costs! Let’s even keep the sarcasm. Keep.

Page 587: In Appendix H, we use an exclamation point when trying to make a joke. We had already developed the binomial probability distribution using p for the probability of success and q for the probability of failure. Then we write “Suppose that we do N independent tests, and suppose that in healthy people, the probability that each test is abnormal is p. (In our vocabulary, having an abnormal test is ‘success’!).” Lame. Toss.

Page 593: Appendix I has a footnote containing my favorite exclamation point in Intermediate Physics for Medicine and Biology. It appears when we introduce Stirling’s formula: ln n! ≈ n ln n - n. “For more about Stirling’s formula, see N. D. Mermin (1994) Stirling’s formula! Am J Phys 52: 362–365.” The exclamation point is a pun. Keep!

Three New Reviews

Over the last couple years, I’ve been writing lots of review articles. In the last few weeks three have been published. All of them are open access, so you can read them without a subscription.

Can MRI be Used as a Sensor to Record Neural Activity?

“Can MRI be Used as a Sensor
to Record Neural Activity?”

This review asks the question “Can MRI be Used as a Sensor to Record Neural Activity?” The article is published in the journal Sensors (Volume 23, Article Number 1337). The abstract is reproduced below.

Magnetic resonance provides exquisite anatomical images and functional MRI monitors physiological activity by recording blood oxygenation. This review attempts to answer the following question: Can MRI be used as a sensor to directly record neural behavior? It considers MRI sensing of electrical activity in the heart and in peripheral nerves before turning to the central topic: recording of brain activity. The primary hypothesis is that bioelectric current produced by a nerve or muscle creates a magnetic field that influences the magnetic resonance signal, although other mechanisms for detection are also considered. Recent studies have provided evidence that using MRI to sense neural activity is possible under ideal conditions. Whether it can be used routinely to provide functional information about brain processes in people remains an open question. The review concludes with a survey of artificial intelligence techniques that have been applied to functional MRI and may be appropriate for MRI sensing of neural activity.

Parts of the review may be familiar to readers of this blog. For instance, in June of 2016 I wrote about Yoshio Okada’s experiment to measure neural activation in a brain cerebellum of a turtle, in August 2019 I described Allen Song’s use of spin-lock methods to record brain activity, and in April 2020 I discussed J. H. Nagel’s 1984 abstract that may have been the first to report using MRI to image action currents. All these topics are featured in my review article. In addition, I analyzed my calculation, performed with graduate student Dan Xu, of the magnetic field produced inside the heart, and I reviewed my work with friend and colleague Ranjith Wijesinghe, from Ball State University, on MRI detection of bioelectrical activity in the brain and peripheral nerves. At the end of the review, I examined the use of artificial intelligence to interpret this type of MRI data. I don’t really know much about artificial intelligence, but the journal wanted me to address this topic so I did. With AI making so much news these days (ChatGPT was recently on the cover of TIME magazine!), I’m glad I included it.

Readers of Intermediate Physics for Medicine and Biology will find this review to be a useful extension of Section 18.12 (“Functional MRI”), especially the last paragraph of that section beginning with “Much recent research has focused on using MRI to image neural activity directly, rather than through changes in blood flow...”

Magneto-Acoustic Imaging in Biology

“Magneto-Acoustic Imaging in Biology”

Next is “Magneto-Acoustic Imaging in Biology,” published in the journal Applied Sciences (Volume 13, Article Number 3877). The abstract states

This review examines the use of magneto-acoustic methods to measure electrical conductivity. It focuses on two techniques developed in the last two decades: Magneto-Acoustic Tomography with Magnetic Induction (MAT-MI) and Magneto-Acousto-Electrical Tomography (MAET). These developments have the potential to change the way medical doctors image biological tissue.

The only place in IPMB where Russ Hobbie and I talked about these topics is in Homework Problem 31 in Chapter 8, which analyzes a simple example of MAT-MI.

A Mathematical Model of Mechanotransduction

“A Mathematical Model of Mechanotransduction”

Finally comes “A Mathematical Model of Mechanotransduction” in the new journal Academia Biology (Volume 1; I can’t figure out what the article number is?!).

This article reviews the mechanical bidomain model, a mathematical description of how the extracellular matrix and intracellular cytoskeleton of cardiac tissue are coupled by integrin membrane proteins. The fundamental hypothesis is that the difference between the intracellular and extracellular displacements drives mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two or three dimensions. In a few cases, the bidomain equations can be solved analytically, demonstrating how tissue motion can be divided into two parts: monodomain displacements that are the same in both spaces and therefore do not contribute to mechanotransduction, and bidomain displacements that cause mechanotransduction. The model contains a length constant that depends on the intracellular and extracellular shear moduli and the integrin spring constant. Bidomain effects often occur within a few length constants of the tissue edge. Unequal anisotropy ratios in the intra- and extracellular spaces can modulate mechanotransduction. Insight into model predictions is supplied by simple analytical examples, such as the shearing of a slab of cardiac tissue or the contraction of a tissue sheet. Computational methods for solving the model equations are described, and precursors to the model are reviewed. Potential applications are discussed, such as predicting growth and remodeling in the diseased heart, analyzing stretch-induced arrhythmias, modeling shear forces in a vessel caused by blood flow, examining the role of mechanical forces in engineered sheets of tissue, studying differentiation in colonies of stem cells, and characterizing the response to localized forces applied to nanoparticles.

This review is similar to my article that I discussed in a blog post about a year ago, but better. I originally published it as a manuscript on the bioRxiv, the preprint server for biology, but it received little attention. I hope this version does better. If you want to read this article, download the pdf instead of reading it online. The equations are all messed up on the journal website, but they look fine in the file.

If you put these three reviews together with my previous ones about magnetic stimulation and the bidomain model of cardiac electrophysiology, you have a pretty good summary of the topics I’ve worked on throughout my career. Are there more reviews coming? I’m working feverishly to finish one more. For now, I’ll let you guess the topic. I hope it’ll come out later this year.