Over the last few years, I’ve been contributing to a group called Physics in Medicine. It focuses on how physics contributes to, and indeed is essential to, the practice of medicine. The team consists of both physicists and medical doctors collaborating to demonstrate how physics can be better taught to medical students. My interactions with this team influenced the preparation of the sixth edition of Intermediate Physics for Medicine and Biology (which you can now find listed at Amazon with a projected publication date of October of this year).
My role was to lead the effort on the chapter “The Integrated Cardiovascular-Pulmonary System: The Underlying Principles That Make It Work.” When working on it, I often used the shorthand title “Physics of the Heart.” The abstract states
The Physics in Medicine program is an attempt to improve medical education in a way consistent with the AAMC-HHMI 2009 report on the Scientific Foundations for Future Physicians. Our aim is to illustrate how the findings of this report can be applied to the cardiovascular system. We do this by examining one specific case study of an elderly man with shortness of breath, and review the physics required in his diagnosis and treatment.
The amount of physics in the medical treatment of cardiovascular disease is astounding. One of the figures from our chapter illustrates this. Many topics in physics—fluid mechanics, acoustics, optics, electricity and magnetism, and nuclear physics—play a role in the treatment of just one disorder (patent foramen ovale, or an opening between the left and right atria).
The editor of our Proceedings, Ed Szuszczewicz, is the visionary that leads Physics in Medicine. Ed is a plasma physicist who was asked by his department chairman to teach a physics-for-premeds class. That got him hooked. If you just read his Preface and Epilogue in Physics in Medicine and Medical Education you’ll get the gist of our effort.
In Chapter 4 of the Proceedings, one of my coauthors, Nancy Donaldson, describes her experience directing a Physics of Medicine undergraduate major at Rockhurst University in Kansas City. Nancy is a passionate advocate for active learning and describes several of the modules used in her classes. It kind of makes me want to retake my physics major. I especially like her analysis of the lungs, a topic that doesn’t get as much attention as it should have in IPMB. Nancy is also one of the founders the Living Physics Portal, where you can find high-quality materials for teaching physics to life science students at the college level. The other two coauthors on my chapter, Chad Miller and Andrew Olson, are MDs who helped keep the story focused
on medicine. I have a tendency to stress the physics too much, and they
helped counterbalance that.
Another contributor to Physics in Medicine and Medical Education was the late Joe Redish. He was a central figure in our effort until he passed away at age of 82 in 2024. I made sure to cite his helpful “Using Math in Physics” articles published in The Physics Teacher, and I featured his wonderful “warp and weft” figure connecting subareas of physics to learning techniques in our Physics of the Heart chapter. I miss Joe.
What do the lens and the heart have in common? Both tissues are made up of cells that are coupled together by gap junctions: small channels that connect the inside of one cell to the inside of its neighboring cells. To get from one cell to another, current does not have to cross the cell membrane and enter the extracellular space. Instead, it can just pass through the junctions, always remaining inside the cell (such a tissue is called a syncytium). This key feature underlies the bidomain concept, which treats the tissue as a two-phase medium, intracellular and extracellular, coupled by the membrane.
“Electrical Properties of Spherical Syncytia,” by Eisenberg, Barcilon, and Mathias.
Today I introduce a new homework problem for readers of IPMB, motivated by two papers from the group at Rush:
Both articles imagine that a microelectrode injects a current pulse into the intracellular space of a spherical lens. The general problem is too complicated for an undergraduate homework exercise, so I’ve simplified it considerably. First, I assume the current pulse has been on long enough that the system has reached steady state. Second, I assume the microelectrode injects current into the center of a lens of radius a (at the origin of a spherical coordinate system). Third, I ignore anisotropy, and assume the lens is an isotropic tissue. Fourth, and finally, the boundary conditions at the lens surface r = a complicate the analysis, so I avoid them by considering a very large lens (essentially, an unbounded tissue). With these assumptions, the homework problem is still difficult, but not prohibitively so.
Section 7.9
Problem 31 ½. Consider a tissue represented using the bidomain model, with intracellular conductivity σi and extracellular conductivity σe. The cell membrane has a conductance per unit area Gm, and the surface area of cell membrane divided by tissue volume (the surface-to-volume ratio) is β. A current I0 is injected into the intracellular space at the origin (r = 0).
(a) Write the bidomain equations for the intracellular and extracellular potentials Vi and Ve (Eq. 7.32) in spherical coordinates (use Appendix L). Assume that the electrical potential varies only with the radial distance r, and not with angular variables θ and φ.
(b) The solutions to these equations are
Substitute these solutions into the equations from part (a) and find an expression for the tissue length constant λ in terms of σi, σe, Gm, and β.
(c) For r << λ, find approximations for Vi and Ve. Determine how each behaves as r goes to zero.
(d) For r >> λ, find approximations for Vi and Ve. They should both be the same. Find an expression for the “effective conductivity” of the tissue based on these expressions.
(e) Derive an expression for the transmembrane potential, Vm = Vi - Ve.
My advice: stop reading and solve the problem…
OK, for those who absolutely don’t have time to solve this yourself, let me outline the solution.
(a) The bidomain equations become
The delta function source term only appears in the intracellular equation because the current is injected into the intracellular space. Notice that the sign of the term corresponding to the membrane current (the one containing β) is different in the two equations. Current coming out of the intracellular space is current going into the extracellular space.
(b) When you substitute the solutions into the differential equations, you should find that they work if
(c) When r << λ, Vi is proportional to 1/r, while Ve is constant. Therefore, Vi goes to infinity as r goes to zero, but Ve remains finite.
(d) When r >> λ, both Vi and Ve are equal. They each fall off as 1/r and the conductivity factor that appears is σi + σe. This is the parallel combination of the intracellular and extracellular resistances, and can be thought of as the “effective” conductivity of the tissue.
(e) The first terms in the expressions for Vi and Ve, which contain the factor 1/r, cancel out when you take the difference to get Vm. Therefore, Vm falls off as e-r/λ/r. If you are more than a few length constants from the stimulating electrode, Vm is much smaller than either Vi or Ve. If you want to determine Vm by measuring Vi and Ve and taking their difference, you must record them very accurately, as you will be subtracting two big numbers to get a much smaller one, which is always susceptible to noise.
If you look at the derivations by Eisenberg et al. or Peskoff, you’ll find more complicated expressions than those given above, because they include time dependence, they don’t require the electrode to be at the center of the lens, and they consider a lens of finite radius rather than an unbounded tissue. I hope that this homework problem at least gives you a feel for their results.
Both Eisenberg et al.’s and Perkoff’s papers were published in 1979, just one year after Les Tung’s PhD dissertation and Walter Miller and David Geselowitz’s Circulation Research paper, two founding documents of the bidomain model. Moreover, Eisenberg, Mathias, and their collaborators had been publishing related studies for several years before the 1979 papers. They truly have a claim as critical contributors to the development of the bidomain model. To survey this body of work, see Eisenberg’s 2023 review in Modeling and Artificial Intelligence in Ophthalmology.
Robert Eisenberg is an emeritus faculty member at Rush University Medical Center in Chicago. He has a long history of using mathematical modeling and computer simulation to address issues in bioelectricity. His graduate study was at the University College London, where he studied under Andrew Huxley (of the Hodgkin and Huxley model) among others. Richard Mathias worked with Eisenberg at Rush during the era when the bidomain model was developed, and later was on the faculty at Stony Brook University. He not only looked at the lens electrical properties, but more importantly examined its fluid flow behavior using a model analogous to the electrical bidomain model. Because the lens is transparent, it cannot contain any blood vessels, so fluid flow in the intracellular and extracellular spaces is crucial for keeping the tissue perfused. Victor Barcilon (1939–2020) was an applied mathematician who worked for many years at the University of Chicago. Arthur Peskoff is with the UCLA School of Medicine.
A firefly flash contains roughly 108–1011photons—far fewer than the 1013–1014 photons implied by Coblentz’s 1912 report of 1/50–1/400 candlepower for Photinus pyralis. We trace this discrepancy to selective citation of the upper end of Coblentz’s range and to systematic biases in early visual photometry. We derive a theoretical bound from luciferase abundance and quantum yield. We also measure flash brightness directly with a lux meter and reanalyze two historical datasets. These independent lines of evidence all fall well below the historical candlepower values. The error persisted because modern bioluminescence research often reports quantum yields and relative intensities; reconstructing absolute photons per flash also requires in vivo substrate turnover or measurement geometry, so the comparison with early photometry was rarely made directly.
What did I like about this paper?
I’m fascinated by how errors propagate through the scientific literature. Not little mistakes, but orders-of-magnitude blunders in determining the value of physical parameters. In this case, there seems to be a thousand-fold difference between the commonly reported value for the number of photons emitted by a firefly flash and the actual number of photons. How can researchers get something that wrong? It reminds me of the motto I repeatedly urged my undergraduate physics students to adopt: “Think before you calculate!” Scientists need to make order-of-magnitude estimates, like those in this article, before doing more detailed calculations and even before making extensive measurements.
My wife and I are native plant gardeners. Our goal is to attract and support pollinators, but one side benefit is that we encourage fireflies. Back when I was growing up in Morrison, Illinois, we called them lightning bugs. During summer nights their flashing lights filled our back yard. We used to catch some, put them in a glass jar, and bring them with us to our bedroom to serve as a nightlight. Nowadays there are far fewer lightning bugs, at least in the subdivision where I live in Michigan. Any physics article about lightning bugs is going to interest me.
The article uses both radiometry and photometry units. Intermediate Physics for Medicine and Biology has a long section about these different units. Radiometric quantities are in traditional metric units. For example, the radiant flux (power emitted) is in watts. Photometric quantities weight the light emitted by the sensitivity of the eye. For green light, one watt corresponds to 683 lumens, where the lumen is the photometric unit. The same one watt emitted in the infrared or ultraviolet would have zero lumens.
I learned a new unit! First, let me describe a photometric unit I was already familiar with, the candela. One lumen per steradian (solid angle) is one candela. The luminance, or luminance intensity, is the number of candelas per square meter. The unit that I had never heard of is the lambert. The lambert is one over π candelas per square meter. Why the 1/π? I expect it has something to do with the solid angle, but I’m not sure.
It is often useful to translate these units into number of photons. The lumen measures the number of photons emitted per second. The candela is the number of photons per steradian. The lambert is the number of photons per steradian per square meter (with that pesky 1/π thrown in). If you’re interested in the total number of photons per steradian per square meter recorded by a single flash of the firefly at some distance from the bug, the lambert is the unit you want. If you can assume the light is emitted isotropically, the solid angle is just a factor of 4π. The per m2 accounts for the 1/r2 fall off of the intensity.
So who is Lambert? Johann Heinrich Lambert (1728–1777) was a Swiss mathematician, physicist, and astronomer. This is the same Lambert of Lambert’s cosine law discussed in Section 14.12 of IPMB. This is also the same guy as in the Beer-Lambert law introduced in Section 14.5. Asinov’s Biographical Encyclopedia of Science & Technology states: “In 1760 he [Lambert] published his investigations of light reflection. His book was in Latin and his word for the fraction of light reflected diffusely by a body was albedo (“whiteness”). The term is still commonly used in astronomy to represent the reflectivity of planetary bodies. He was the first to devise methods for measuring light intensities accurately, and the unit of brightness is the lambert, in his honor.”
Asimov's Biographical Encyclopedia of Science & Technology.
Blood flows through
a branching network of vessels (Sect. 1.19), the smallest
of which are capillaries. Each capillary has a diameter of
about 8 μm, meaning that the red blood cells can barely pass
through it single-file.
Eight microns is pretty small; too small to see with your naked eye. So how did we learn about capillaries? The first person to observe capillaries was the Italian microbiologist Marcello Malpighi (1628–1694). He was one of the early users of a microscope.
Malpighi received a medical degree from the University of Bologna, and eventually became the private physician for Pope Innocent XII. He favored rational medicine, based on empirical evidence, during a time when much medicine was still based on ancient authorities with little experimental support.
English physician William Harvey had previously discovered the circulation of blood, showing that the heart pumped blood to the body through the arteries and then returned it to the heart through the veins. Harvey’s theory implied there must be some connection between the arteries and veins so blood could flow in a continuous circuit, but he never identified that connection. Even the great anatomist Andreas Vesalius had wrong ideas about this issue. Malpighi’s greatest discovery was using the microscope to observe capillaries, the tiny blood vessels joining an artery to a vein. He was one of the first scientists to observe red blood cells, and also studied the clotting of blood. He described this research in his book De Polypo Cordis, published in 1666.
In addition, he examined the structure of small insects, such as the silkworm, and discovered that they do not use lungs to breathe but instead small holes in their skin called tracheae (Homework Problem 42 in Chapter 4 of IPMB discusses this issue further). He also observed the microstructure of plants and the development of chick embryos.
Early microscopists like Malpighi, as well as Robert Hooke and Antonie van Leeuwenhoek, demonstrate why Russ and I encourage readers to think about distances and sizes in the very first section of IPMB. Having an intuitive feel for distance scales—what can be seen with the naked eye, what requires a light microscope, and what is too small to see even with a microscope—is so important for understanding biology as well as the history of biology. Early microscopists explored with world of life at a scale from one to one hundred microns; the realm of protozoans, cells, and bacteria. Below that scale, diffraction blurs images, and studies of viruses and macromolecules had to await more advanced technologies such as the electron microscope.
Malpighi died in 1694, at the age of 66, from a stroke. He is often considered the father of histology and embryology.
Recently several research groups have used sub-millimeter sized microcoils to perform magnetic stimulation of nerves. This review assesses the magnitude of the electric field induced by these microcoils. In some cases magnetic stimulation is a plausible mechanism for neural excitation, but in other cases the induced electric field is far too small to excite a neuron. These results indicate that microcoil magnetic stimulation may not occur via magnetic stimulation, but by some other mechanism. One alternative mechanism is capacitive coupling.
Basically, this paper reviews the entire field of microcoil stimulation, and finds that in some cases the idea is plausible, but in other cases it is not. One thing I like about the article is that I develop a toy model for calculating the electric field produced by the coil. While the model is an approximation, it should determine the electric field correct to at least an order of magnitude. The strengths of the model are that it provides great insight, it is so simple computationally that anyone can reproduce the calculation, and it supplies a common way to analyze a host of different publications. One goal of Intermediate Physics for Medicine and Biology is to train students in forming and analyzing such toy models. I think that the field of microcoil stimulation illustrates what happens when researchers skip the simple model and go straight to complicated numerical calculations using code that is treated as a black box. These computations often produce numbers but little intuition or understanding. The user cannot tell if something goes wrong. Back when I was teaching, I would urge my students to “think before you calculate!” This review shows why.
The conclusion of the review states
Magnetic stimulation by microcoils is an active and growing field in neural stimulation. It may have promise for the development of neural prostheses. This review, however, suggests there are many unanswered questions in this area of research… Frankly, the field appears prone to errors. One must analyze the articles carefully to separate the wheat from the chaff.
Transcranial magnetic stimulation works by magnetic induction. Stimulation using a millimeter-sized, multi-turn coil placed close to the target neuron and carrying several amps of current may work by magnetic induction, but the electric field it generates is sometimes slightly below the threshold value you expect is required to excite neurons. Nevertheless, magnetic induction in these cases seems plausible. On the other hand, when milliamps of current are passed through a single-turn wire, magnetic induction does not seem to be a plausible mechanism for excitation; the electric field appears to be too weak. One alternative mechanism is capacitive coupling. An important goal of future microcoil magnetic stimulation research is to resolve what exactly is the underlying mechanism.
The article is open access, so anyone can read it online without a subscription. Enjoy!
Micro-magnetic stimulation (μMS) through micro-scale coils is a rapidly
advancing form of neuromodulation that possesses qualities that give it the potential to be
used as an alternative to electrical stimulation in cases where it cannot be used. However,
reliability of the technique is inconsistent as reported in the peer reviewed literature,
suggesting that there is not a strong understanding of the basis of the technique. In this
thesis, we provide empirical evidence of the efficacy of μMS in dissociated cortical
cultures and a review of μMS’ consistency across early pioneering works. We then simulate
the electric fields generated by μMS using COMSOL and couple the fields to neuron
models in Python to study their response across a range of parameters in neural stimulation.
This is followed by an aim to measure the electric fields of these micro-scale coils to
determine whether they surpass stimulus thresholds reported in literature. Our key findings
suggest that μMS should not be feasible. Finally, we investigate confounding factors during
μMS stimulation that may have effects being mis-attributed to μMS.
I’m delighted that it’s not just my former graduate student Mohammed Alzahrani and me who are skeptical of microcoil magnetic stimulation. We are no longer alone!
Russ Hobbie wrote a review of a revised edition of Physics with Illustrative Examples from Medicine and Biology for the magazine Physics Today (July, 2001). Here are some excerpts.
The Physics Department of the Massachusetts Institute of Technology began about 30 years ago to offer a special calculus-based introductory course for freshmen and sophomores interested in biology. This led to the first edition of George B. Benedek and Felix M. H. Villars’s Physics with Illustrative Examples from Medicine and Biology. The book was issued by Addison-Wesley in 1979 as three paperback typescript volumes. The book fascinated many physicists with the applications of physics in biochemistry and physiology, but they have been out of print since 1990. Now that the AIP Press and Springer-Verlag have issued a second edition, as printed volumes, a new generation of physicists can learn from them…
These are classic books, and anyone planning to include biophysical examples in a calculus-level course should study them carefully. The authors are to be congratulated for their work, and I commend AIP Press and Springer-Verlag for making the books available again.
In his review, Russ lists the book as published in 1979, but I think there must have been earlier editions, because the first edition of Intermediate Physics for Medicine and Biology, published in 1978, cites Physics with Illustrative Examples from Medicine and Biology several times, and lists the publication date as 1973 (Volume 1) and 1974 (Volume 2). Clearly Benedek and Villars influenced the first edition of IPMB and all subsequent editions. You can learn more about Physics with Illustrative Examples from Medicine and Biologyhere, here, and here.
Benedek wasn’t just a textbook author. He invented quasi-elastic light scattering spectroscopy and became a fellow of the American Physical Society in 1962. He received the Association for Research in Vision and Ophthalmology’s Proctor Medal in 1997 for “outstanding research in basic or clinical sciences as applied to ophthalmology.” He was a true biological physicist. He’ll be missed.
MKUltra (pronouced M-K-ultra) was a covert Central Intelligence Agency research program carried out between 1953 and 1973 to investigate mind control. It used techniques such as high doses of the psychedelic drug LSD, hypnosis, sensory isolation, and electroshock therapy to influence a subject’s brain, and in particular to obtain secrets from unwilling people. This program is notorious for torturing studying subjects without their consent, which is considered a grave sin in research today.
One subproject of MKUltra (#119) was to use very low frequencyelectromagnetic fields to influence the brain. This project comes disturbingly close to techniques I’ve worked on over the years, such as transcranial magnetic stimulation. It got me to wondering: is mind control using electromagnetic fields possible?
I guess I have thought about this before, because in the August 14, 2015 post in this blog I suggested that the “psychic probe” described in Isaac Asimov’s famous Foundation Trilogy might be made by combining transcranial magnetic stimulation (TMS) and magnetoencephalography (MEG), which are both described in Chapter 8 of Intermediate Physics for Medicine and Biology. In that post I wrote “a combo TMS/MEG unit could therefore both detect and alter brain function.” Of course, I was writing tongue-in-cheek, joking about how a science fiction device might have worked within the constraints of real science. On the other hand, perhaps I was actually an MKUltra agent sending a secret message to my underground accomplices?
That last sentence mocks the recent conspiracy theories surrounding MKUltra. Last week the House Task Force on the Declassification of Federal Secrets held a hearing about the research program. It didn’t focus on the historical record (which is sparse because most of the MKUltra documents were destroyed) but instead went off on weird tangents, talking about things like mind control related to the assassination of President Kennedy. The purpose of this hearing seemed to be aimed primarily at blaming science in general for past errors. Some issues that were brought up, like MKUltra itself, were serious mistakes that should be, and have been, investigated. Others, like bogus lab leak theories related to the origin of Covid, were just crazy talk with no scientific justification. One researcher, Elizabeth Ginexi, a respected former program official at the National Institutes of Health, was invited by the Democrats to talk about the horrendous anti-science policies currently imposed on NIH by anti-vax zealot Robert F. Kennedy, Jr. Ginexi (a hero in my view) tried to discuss these vital issues, but was constantly cut off by Republican members of the committee who were focused on the bizarre and engaged in an attempt to demonize scientists and public health workers.
But back to my question: could electromagnetic fields be used for brain control? Well, transcranial magnetic stimulation is currently used to treat depression, so you can’t rule out the possibility. However, the technique is very nonspecific. I spent seven years at NIH trying to improve the focality and spatial resolution of transcranial magnetic stimulation. Generating a localized stimulus is extraordinarily difficult, especially for activating deep brain structures. You can use transcranial magnetic stimulation to make individual fingers move, but only because the hand has a widespread representation in the motor cortex. The idea that transcranial magnetic stimulation could control individual thoughts or suggest specific actions seems like science fiction to me. Other techniques that have been suggested as potentially useful for mind control are brain-computer interfaces and deep brain stimulation. Both of these have important medical uses. For example, deep brain stimulation can help reduce or control tremors caused by Parkinson’s disease. Perhaps these techniques could potentially be used for controlling behavior, but they are highly invasive (requiring surgery to implant electrodes in the brain).
Are Electromagnetic Fields Making Me Ill?
What about techniques growing out of subproject 119? That work was led by W. Ross Adey and Mary (“Mollie”) Brazier, two leading scientists studying how electromagnetic fields interact with, and are produced by, the brain. I mentioned Adey in my book Are Electromagnetic Fields Making Me Ill?. He claimed to find “window” effects, for which one particular applied field strength resulted in an observable effect, but stronger or weaker fields did not. Similarly, he found that certain frequencies had marked responses (“resonances”) but both higher and lower frequencies did not. These window effects are not very reproducible and are not widely accepted today. Generally, resonant effects are claimed at very low frequencies (say, 20 Hz). Ultimately subproject 119 ended in failure because no mind control methods were found. Some say that a modern offshoot of this research is microwave weapons responsible for the Havana syndrome. Again, in Are Electromagnetic Fields Making Me Ill? I discuss why electromagnetic fields are almost certainly not responsible for the Havana syndrome. My opinion is that this is another anti-science conspiracy theory.
The final question I address is: could something like MKUltra happen today? The ethics rules governing research are far more stringent now than several decades ago. About 15 years ago, I served for one year in an interim role as Oakland University’s Vice Provost for Research, which is the chief research officer at the institution. Among other things, I was in charge of overseeing research misconduct issues at OU. Any human subjects research had to go through our Institutional Review Board. If a faculty member merely wanted to give a simple survey to students, that survey had to be assessed by this board and a detailed consent form was required. Any potentially dangerous human studies were monitored particularly closely, and informed consent was essential. It’s the same at all academic institutions. MKUltra would be virtually impossible in today’s academic research environment. Could it happen in the CIA or another research center associated with the military? I don’t know. Perhaps. But the CIA and other intelligence agencies can’t compete with academia and scientific institutions like the NIH and NSF when it comes to scientific advances. (Take, for example, the recent brouhaha over the military’s claims about “ghost murmur” which are almost certainly bogus.) I don’t believe MKUltra or anything related to it is going on today, especially involving electromagnetic fields to control the brain. I believe that such a suggestion is a conspiracy theory, advanced to discredit scientists and scientific institutions. It’s part of the Republican War on Science. Please, don’t believe the anti-science crackpots. At the very least, insist that they support their claims with evidence. They rarely can.
Angela Rasmussen and Liz Ginexi discuss MKUltra and What Really Happened in the Wuhan Lab
I’m old enough to remember the bicentennial. In 1976 the USA reached the age of 200. I was 15 years old, about to start my junior year in high school, and living in Ashland, Ohio. I recall the bicentennial being a much bigger event than what we are experiencing this year. Perhaps I was simply younger and more easily impressed. Or, perhaps, Chuck Todd’s explanation is correct; I’ve always liked Chuck. Or, perhaps, the problem is that semiquincentennial is so @#%& hard to pronounce!
What was the status of Intermediate Physics for Medicine and Biology back in the summer of 1976? Russ Hobbie, then the sole author, was 43 years old. Just three years before he finished auditing all the courses medical students take in the first two years at the University of Minnesota and must have been hard at work on the first edition of IPMB, published two years later, in 1978, the year I graduated from high school. I didn’t become aware of the book until I reached graduate school at Vanderbilt University. I probably saw it first in 1982 or 1983.
Move forward 50 years and the 6th edition of IPMB should appear (assuming all goes well) just a couple months after the semiquincentennial celebration. Russ Hobbie passed away in 2021, but Gene Surdutovich will join as an author of this new edition.
I expect that during the tricentennial celebration in 2076 people will look back at 2026 as a dark and dangerous time for science, when anti-science forces came to dominate the federal government, promoting vaccine hesitancy, climate change denial, and other nonsense. I hope that by 2076 this era will have passed, and science will have become respectable again, but I’m not certain that will be the case. Will IPMB still be read and used in college courses? Who knows? I’ll be gone by then, and most likely Gene will too. But perhaps new coauthors will come along, and the tricentennial will coincide with the 11th edition of Intermediate Physics for Medicine and Biology!
For you scientists and science-lovers celebrating the 4th of July, I recommend a series of events sponsored by the American Philosophical Society about science during the founding of the United States, called America’s Scientific Revolutionaries. I particularly like the lecture in the video below, about Benjamin Rush—an American Founding Father who was also a medical doctor—and his role in early American medicine. The video is also about the war on vaccines today, and features vaccine scientist Paul Offit. It’s an interesting analysis of how much progress medicine has been made in the last 250 years, how much ground we have lost recently, and the work ahead of us during the next half century.
Communicating Disease: Assessing Benjamin Rush's Public Health Legacies at America's 250th.
“Methodological Guidelines for Circadian Modeling of Daylight Saving Time: Application to the United States”
Most mornings I get an email from arXiv, an archive of preprints in the sciences, especially physics. (Here at the start of this post I should warn you: Preprints on arXiv are not peer reviewed. They are preliminary, and are meant to get results out quickly, avoiding the delays associated with publishing in a scientific journal. But peer review is not just slow, it is also valuable. Almost all preprints contain some mistakes and some are garbage. So, reader beware!)
In my daily email from arXiv, I get a list of new preprint titles and abstracts submitted under the category of biological physics. Most days, I scan the titles and don’t find anything that interests me. But last week (Thursday, June 18), I saw this:
arXiv:2606.19541 (*cross-listing*)
Date: Wed, 17 Jun 2026 19:33:48 GMT (587kb)
Title: Methodological guidelines for circadian modeling of Daylight Saving Time: application to the United States
Modeling the circadian impact of seasonal clock changing requires precise
synchronization between solar and social time. This report critiques a recent
study that associated disease prevalence in the United States with seasonal
clock exposure. We identify a fundamental computational error in which a sign
reversal of the longitudinal offset effectively inverted the US East-West axis,
cross-correlating local health data with the circadian burden of hypothetical
locations on the opposite side of a time zone. We outline the methodology for a
correct modelization [note: I hate the word “modelization”] of the circadian process in the context of US geography.
This preprint, which I downloaded and read as a pdf, illustrates science in action. It critiques a previously published paper and claims to show there is a fundamental flaw in its analysis. (Another disclaimer: I am not an expert in circadian rhythms, and I cannot say from my own research who is right: the original authors Lara Weed and Jamie Zeitzer from Stanford University, or the Spanish physicists Jose Martin-Olalla and Jorge Mirab.)
Weed and Zeitzer’s original paper looked at the health hazards caused by daylight saving time. It’s fairly well known that changing the clocks twice a year at the beginning and end of daylight saving time can be associated with health problems. But how significant are those problems? And, more specifically, if we eliminate the time change, should we replace it with permanent standard time or permanent daylight saving time? Weed and Zeitzer used mathematical modeling to analyze the degree of “circadian burden” on health. Circadian burden is the physiological strain on your body’s biological clock when your daily schedule in not in sync with the sun’s natural rhythms. Weed and Zeitzer concluded that
As compared to current time policy [switching back and forth between standard time and daylight saving time], permanent SDT [standard time] and [permanent] DST [daylight saving time] reduce circadian burden and are anticipated to reduce the prevalence of obesity and stroke with SDT having a more positive impact than DST.
The preprint by Martin-Olalla and Mirab claims to have found a bug in Weed and Zeitzer’s computer program.
We identify a fundamental computational error in which a sign reversal of the longitudinal offset effectively inverted the US East-West axis, cross-correlating local health data with the
circadian burden of hypothetical locations on the opposite side of a time zone.
They conclude that
Consequently, the original study’s conclusions currently lack empirical support.
Who’s right? I can’t say for sure, and I would like to read Weed and Zeitzer’s response to this preprint before I draw any definite conclusion. But the physicists make a convincing case for a fundamental flaw. They quote Weed and Zeitzer’s computer code line by line, highlighting where the bug occurs. It seems to be a sign error in how the burden shifts with position in the time zone, inverting east and west.
Martin-Olalla and Mirab include a “manuscript timeline” in their preprint that may not survive peer review and journal policy, but is interesting nonetheless.
The curiosity bug bit us. We decided to pull down and run the original code ourselves to compute and observe the yearly burden… all of a sudden, we uncovered the inversion error. It... was sitting right there in plain sight, but we had initially trusted the comments embedded within the script rather than checking the raw mechanics. We checked that the light diets were inverted: Western locations had brighter mornings and darker evenings in their clock time analysis.
Before I go on, I should confess to you some of my biases. First, I’m a physicist, so I naturally suspect that the physicists will be more skilled at mathematical and computer modeling. Second, I live in Michigan, just north of Detroit, which is pretty far north and is near the western edge of the Eastern Time Zone. In the winter, it doesn’t get light until about 8 am. If we were on permanent daylight time, it wouldn’t get light until 9. I’m a morning person, and this would annoy me. My circadian clock would suffer from a whole lotta burden. So I’m passionately against the idea of permanent daylight time, and would rather keep switching twice a year if we can’t get permanent standard time.
And now back to the story. What lessons can be learned from this scientific debate?
Science is difficult. Sometimes you’re wrong. Wrong doesn’t mean evil, and wrong doesn’t mean stupid. Although I don’t know who is wrong in this case, I’m pretty sure one pair of authors is right and one is wrong (I don’t see how both pairs could each be a little right and a little wrong). That’s why science has peer review. In this case, peer review by the journal doesn’t seem to have spotted the problem. But peer review also occurs when other scientists get bit by the curiosity bug. It may take a long time, but the truth is usually uncovered by the peer review process. It can be painful on a personal level, but is vital for science as a whole.
Mathematical modeling is difficult. I should know, because I did mathematical modeling and computer simulation for a living for nearly 40 years. It’s easy for a bug to creep into a computer program. That’s why you have to test, test, test each part of the code. Toy models with analytical solutions of special cases can help verify your program. They can’t prove the code is correct, but they can uncover flaws. In general, I always tried to analyze special cases and examine intermediate results “by hand” to make sure they make sense. It’s slow, painstaking work, but minimizes the chances of being wrong.
Sharing computer code is good. I rarely shared my code early in my career; it just wasn’t a thing people did back then (and was difficult to do before the internet). But the trend now is to share code openly. Some journals insist on it. This can be embarrassing if your program is wrong, and even if it’s right but written in an ugly, complicated way. But sharing is essential. Share you code, and write your code in a way so you aren’t embarrassed to share it.
Sign up for arXiv. It’s one of the best ways I know of to keep up with the current literature. Nowadays the scientific literature sprays out like from a fire hose, so we need all the help we can get.
This is a story about science, not antiscience. Over the last couple years, the forces of antiscience are everywhere (consider vaccine hesitancy and climate change denial for starters). Antiscience advocates demonize scientists and ignore evidence. The authors I’m talking about today—Weed, Martin-Olalla, Mirab, and Zeitzer—have nothing to do with antiscience. They are merely engaged in a scientific debate. They are showing us how science should be done. Compared to advocates of antiscience, both pairs of authors in this debate are heroes. I love them all, no matter who turns out to be right in the end.
If the Week and Zeitzer article is flawed, then is permanent standard time really better than permanent daylight time? Frustratingly, Martin-Olalla and Mirab don’t say. They don’t reproduce Week and Zeitzer’s analysis using a corrected program. So, after all this debate, we still don’t know what is best. I’ll hope for permanent standard time, but policy should depend on scientifically-established, country-wide analysis and not on Brad Roth’s personal preferences. I’m not convinced we have the answer to this issue right now. Stay tuned.
Ed was born in Taylorville, a small town in central Illinois, in 1912. Some of his earliest memories were of scavenging electronic equipment like transformers, capacitors, and generators from old telephones.
He went to college at Purdue University and graduated in 1933 with a degree in electrical engineering. These were the years of the Great Depression, and many of his classmates, who had trouble affording college, would live in the basement of one of the research labs. After graduation, Ed obtained an exchange fellowship to spend a year in Germany. On the ship traveling across the Atlantic, he met Beth Busser, another exchange student from Bryn Mawr College who was studying German literature. Ed eventually attended Harvard University for graduate school. In 1937 he married Beth, and in 1938 he earned a PhD in Physics.
When World War II ended, Ed returned to Harvard on the faculty, and had to figure out what his research topic would be. Rabi had been studying nuclear magnetic moments in molecular beams, and Ed wondered if similar effects could be observed in a solid. By Christmas 1945, Ed and his coworkers had measured resonance absorption of an oscillating magnetic field by nuclear magnetic moments in paraffin wax.
I am an emeritus professor of physics at Oakland University, and coauthor of the textbook Intermediate Physics for Medicine and Biology. The purpose of this blog is specifically to support and promote my textbook, and in general to illustrate applications of physics to medicine and biology.
