William Hendee (1938–2026)

Medical Imaging Physics,
by William Hendee and E. Russell Ritenour.

I recently learned that William Hendee died on March 14, 2026 at the age of 88. The book Medical Imaging Physics, by Hendee and E. Russell Ritenour, had a big impact on Intermediate Physics for Medicine and Biology. Russ Hobbie and I cite Medical Imaging Physics in IPMB several times in the chapters on ultrasound and on medical x-rays. In fact, we even reproduce some of the figures from their book.

Another way Hendee influenced IPMB is by developing the “Point/Counterpoint” series in the journal Medical Physics. He was the first editor of point/counterpoint articles, in charge of them from 1998 to 2005. Russ and I cite several of these articles, which are wonderful tools to teach students about current controversies in medical physics. We only cite point/counterpoint articles that were moderated by Hendee’s successor, Colin Orton, but when I taught medical physics at Oakland University, every Friday we would end class with a discussion of one pint/counterpoint article, many of them moderated by Hendee. They’re such an important contribution to medical physics education. Hendee was editor-in-chief of the entire journal Medical Physics from 1985–2004. 

Often in this blog I discuss how physicists make the transition from physics to biology or medicine. Hendee tells his story in an interview with the American Society for Radiation Oncology. He grew up near Jackson, Mississippi and became interested in physics because of an inspiring high school physics teacher. He obtained a bachelors degree in physics from Millsaps College, and then went to Vanderbilt (where I got my PhD) on an Atomic Energy Commission fellowship. He worked with with Robert Lagemann in acoustics (from 1995–1998 I was the Robert T. Lagemann Assistant Professor of Living State Physics). When his wife became pregnant, his meager fellowship salary could not support a family. At a conference, he saw a advertisement for a medical physics fellowship with more pay at the University of Texas. He talked to the person who had posted the ad and his first question was “what is medical physics?” The rest is history, as he accepted the position, went to Texas, and got his PhD in 1962. I guess sometimes the transition from physics to medicine is motivated in part by financial considerations.

Other interesting facts about Hendee: 

• He was in the Marine Corps Reserves from 1956 to 1963.
• After his PhD, he returned to Millsaps College on the faculty, in part to participate in the civil rights movement in Mississippi. He eventually left Millsaps because of a disagreement about the dean’s efforts to identify homosexuals on the faculty. 
• He was at the University of Colorado for 20 years, and then was a dean at the Medical College of Wisconsin.  
• He received many awards, including from the American Association of Physicists in Medicine (Coolidge Award), the American Roentgen Ray Society (Gold Medal), the Radiological Society of North America (Gold Medal), the International Organization for Medical Physics (Harald Johns Medal), and the Health Physics Society (Elda Anderson Award).
• After he retired, be bought a lake house in Wisconsin, and enjoyed fishing and being close to nature.
• His obituary says that “Bill is most remembered by people who knew him as inspiring, passionate about learning, kind-hearted, charming, devoted to his family, and a friend you could count on.”

Russ Hobbie and I owe a great debt to Hendee, because Medical Imaging Physics had such an influence on the last half of Intermediate Physics for Medicine and Biology. His passing is sad for us all, and especially for us medical physics textbook writers. He had a long, productive life. Rest in peace, William Hendee. 

The History of Medical College of Wisconsin: Our Voices, Our Legacies featuring William Hendee

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

 

Radiological Society of North America Luminaries Series: William Hendee

https://www.youtube.com/watch?v=Me06HwRQNvc

Advice for Young Scientists

I’m so worried about the state of American science. The layoffs in government research centers, the budget cutbacks, the difficulty of getting grants, the demonization of scientists, and the denial of entire branches of knowledge such as climate change and vaccines... it’s just terrible. I’m especially concerned about young scientists. The ones just starting out, trying to establish a career. It must be devastating for many.

Today I want to share some stories about another difficult time for young scientists, the mid 1990s. President Clinton was cutting federal funding for scientific research to try and balance the budget, scientists and engineers from the former Soviet Union and Eastern Europe were flooding the US job market, and former industry scientists were looking for jobs as centers like Bell Labs were cutting basic research. I don’t want to imply that 1995 was as bad as 2026, but there were some parallels.

I worked at the National Institutes of Health in Bethesda, Maryland in the late 1980s and early 1990s. I loved NIH, and believed that it was the greatest biomedical research institution anywhere, ever. I was in the Biomedical Engineering and Instrumentation Program (BEIP), which hired physicists, engineers, and mathematicians to collaborate with NIH biologists and medical doctors. BEIP wasn’t funded directly from Congress, but instead was a service organization that was supported by a “tax” on the other institutes.

When the cutbacks began in the mid 1990s, I was just about ready to be put up for a permanent position. BEIP didn’t hire “tenure-track” faculty like the institutes did. It did, however, have a tradition of deciding after six years if a staff fellow like me would be promoted into a permanent position, in a process similar to a tenure decision at at a university. Suddenly around 1994, we in BEIP who had been expecting to go up for a permanent spot started being called “postdocs” and were told we needed more “mentoring.” A month or two later we were told there was a hiring freeze and no BEIP staff fellows would be moved into permanent positions. I started looking for another job.

I applied to colleges and universities throughout the country. I searched for industrial positions too, and as time went by I even began looking for jobs at community colleges. I had no luck for months. Between April 1994 and September 1995 I received over one hundred rejection letters, and many more potential employers didn’t even bother to respond at all to my application. I began to worry how I was going to feed my two children. I had seven job interviews, but only two offers. One was verbal and informal (“we can make this happen if you are interested”) and the other (which I accepted) was for a non-tenure track Assistant Professorship at Vanderbilt University, where I had been a graduate student seven years earlier.

I wasn’t the only one in this situation. BEIP had four young researchers coming up for a decision about a permanent position, and we all were in the same boat. Let me tell you about the four of us. Perhaps our stories will provide hope to young people today facing the current job market. 

 

Akram Aldroubi

Akram Aldroubi (PhD, Carnegie Mellon 1987) was a mathematician who worked with the BEIP director, Murray Eden. He, Eden and Michael Unser published a series of highly cited papers about signal processing, investigating topics like b-splines and wavelets. In 1997 Akram moved to the Department of Mathematics at Vanderbilt University (he and I were reunited at Vanderbilt for a year until I left in 1998). He was coauthor with Peter Basser (more on Basser later) on a landmark paper about using MRI diffusion tensor imaging to do fiber tractography. Akram is still at Vanderbilt today, and in 2014 he was inducted as a fellow in the American Mathematical Society for his “contributions to modern harmonic analysis and its applications, and for building bridges between mathematics and other areas of science and engineering.” 

Akram Aldroubi 

https://www.youtube.com/watch?v=sn4GNGnFovY

 

Cynthia Sung

Cynthia Sung (PhD, Harvard-MIT, 1988) was in the Chemical Engineering Section of BEIP. There she worked with Robert Dedrick and Paul Morrison to study pharmacokinetics. After she left NIH she held a variety of positions, such as with the Gates Medical Research Institute and with the Food and Drug Administration. Cynthia went to Singapore and established her own consulting firm, Rainbow Pharma Consulting, and worked with the Singapore Health Sciences Authority. She’s now an Adjunct Associate Professor in the Centre of Regulatory Excellence at Duke-National University of Singapore Medical School. In 2023 she won the Titan Award for Community Collaboration to recognize her collaborative spirit in helping fellow community members reach their goals. 

Cynthia Sung 

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

 

Joe Schmitt

Joe Schmitt (PhD, Stanford, 1986) worked in the Electrical Engineering Section of BEIP with Robert Bonner, studying how light propagates through tissue. After leaving NIH he was an Associate Professor in the Department of Electrical and Electronic Engineering at the Hong Kong University of Science and Technology. There he wrote a highly cited review about Optical Coherence Tomography (a topic discussed in Chapter 14 of Intermediate Physics for Medicine and Biology). He then entered industry and is now the Chief Technology Officer of LightLab Imaging. 

Joe Schmitt

https://www.youtube.com/watch?v=HqEuxXHW7Cs

 

Brad Roth

My PhD was from Vanderbilt in 1987. At NIH I worked for Seth Goldstein in the Mechanical Engineering Section of BEIP, the same section where my friend Peter Basser (the inventor of MRI diffusion tensor imaging) also worked. Basser was a year ahead of me, and he obtained a permanent position at NIH just before the hiring freeze took effect. After leaving NIH, I went back to Vanderbilt for three years, and then took a tenure-track faculty position at Oakland University in Rochester, Michigan, where I taught and did research for over two decades. One of my main accomplishments at OU was to become coauthor with Russell Hobbie on the textbook Intermediate Physics for Medicine and Biology. Though I was never again quite as productive as during those wonderful years at NIH, I nevertheless had a happy and successful career at Oakland. 

 Brad Roth

https://www.youtube.com/watch?v=IKjab7_unRA

Those are the stories of four young researchers who faced a rough patch in their careers just a little over 30 years ago. Fortunately, we all survived—and eventually thrived—in our lives after NIH, whether in academia, industry, or government. I know what young scientists face now is so much worse than what we encountered, and I don’t want to minimize their challenges. But we four friends did overcome our obstacles and managed to remain in science, making a living and contributing to knowledge. Our paths were sometimes tortuous, but with perseverance and patience—and a resurgence of science funding in the late 1990s—we managed to stay in the game. I hope you young scientists facing obstacles now (obstacles that are unfair and no fault of your own) can likewise find a way to stay in science and keep contributing. One thing I know for sure: our country needs you now more than ever.

Good luck. Have courage. Have hope.

The Page Proofs are Here!!!

The page proofs for the sixth edition of Intermediate Physics for Medicine and Biology have arrived, and they’ve taken over my life. I’ve got no time for much of anything else, including writing blog posts. My coauthor Gene Surdutovich and I are trying hard to fix all the errors, but man oh man is there a lot to check. The pdf of the proofs has about 580 pages, whereas the 5th edition had more like 650 (from title page to end of the index). So the book is down about 7% in number of pages. That’s good, because we cut out a lot of what we rarely teach in our classes. That decrease is even more impressive when you consider that we added a chapter on surface tension, we added a chapter on damage from ionizing radiation, and we split the chapter on feedback and nonlinear dynamics into two. In addition, readers now have over 1000 homework problems to test their understanding. So, really, we cut at least 10% from the chapter text present in the fifth edition.

That’s all for now, but just let me add a big thank you to all the readers of Intermediate Physics for Medicine and Biology. And let me assure you traditionalists out there that there’s still a lot of Russ Hobbie here in the sixth edition. It’s still his book, and he’s still first author.

Leon Glass and the Wandering Thoughts Podcast

From Clocks to Chaos,
by Glass and Mackey.

Chapter 10 of Intermediate Physics for Medicine and Biology talks about nonlinear dynamics, and in particular how simple sets of nonlinear differential equations can lead to chaotic behavior. One researcher who Russ Hobbie and I mention often is Leon Glass. We cite his book with Michael Mackey, From Clocks to Chaos, which influenced me as a young scientist, and his textbook with Daniel Kaplan, Understanding Nonlinear Dynamics.

Recently I discovered a wonderful interview with Glass where he describes his life and work. It’s part of a podcast series titled Wandering Thoughts, and you can listen to it below. It’s over two hours long, but Glass talks slowly and I could understand it at 2× speed or even faster. It’s well worth the time.

Several topics covered in the interview will be interesting to readers of IPMB and of this blog. I’ve always been interested in how physicists end up learning and studying biology, and conversely how biologists learn physics. Right at the start of the interview Glass outlines his own circuitous path toward biological physics. Everyone has their own unique path, but Glass’s highlights one feature I find common in many: it isn’t part of a grand master plan, but just sort of happens, and is catalyzed by interactions with other scientists. Glass describes his work on the periodic electrical stimulation of chick heart cells, which Russ and I illustrate using a figure from one of his papers (in IPMB, it’s Fig. 10.36). Stimulation can simply drive the system in a 1:1 behavior, or give a more complicated periodic behavior at a lower frequency, or produce deterministic chaos. This is lovely work and Glass was one of the pioneers. He also talks about the modeling of spiral waves as an example of a heart arrhythmia, a concept studied by his friend and collegue Art Winfree. (In 2013 Glass won the Arthur T. Winfree Prize awarded by the Society of Mathematical Biology.) When asked what traits were most valuable to him in his career, Glass mentioned curiosity and tenacity. Those two traits would be useful to anyone wanting to learn biological physics from IPMB.  

This podcast provides insight into what a career in biological physics is like. Enjoy! 

Chaos in Biological Systems, with Leon Glass, on The Wandering Thoughts podcast.

https://music.youtube.com/watch?v=aDx9t2vA9s0  

The Good Friday Meeting and mRNA

Messenger ribonucleic acid (mRNA) is in the news these days because of mRNA vaccines. But how was mRNA discovered? One reason I'm interested in this question is because mRNA (at least, our knowledge of mRNA) is almost the same age as I am: we were both born in 1960.

First, what role does mRNA play in biology? The central dogma of molecular biology is that DNA with its genetic code is stored in the cell nucleus. Transcription—where the base pairs in double stranded DNA are transcribed into bases in single-stranded mRNA—occurs in the nucleus, catalyzed by enzymes like RNA polymerase. Then, the mRNA leaves the nucleus and enters the cytoplasm. There, the mRNA attaches to the cell organelle called a ribosome (itself made from another type of RNA, rRNA) where the genetic code of base-pairs is translated into a string of amino acids in a protein. Yet another kind of RNA, tRNA, aids in this translation. In short:

DNA > transcription > mRNA > translation > Protein

Clearly mRNA plays a crucial role in all protein synthesis and is essential to life.

The Eighth Day of Creation,
by Horace Freeland Judson.

Russ Hobbie and I talk a little about DNA and proteins in Intermediate Physics for Medicine and Biology, but not much about mRNA. If you want to learn how mRNA was discovered, I suggest reading The Eighth Day of Creation: The Makers of the Revolution in Biology, by Horace Freeland Judson. It’s a long and complicated story, but a key moment was an informal meeting on April 15, 1960 (Good Friday), attended by biologists Francis Crick, Sydney Brenner, François Jacob, and others (Jacques Monod, a collaborator of Jacob, was not present) in Brenner’s rooms at Cambridge University. At that time, the structure of DNA and its role in creating proteins was already known, but the details of how that occurred was uncertain. Out of that meeting came the idea that mRNA was the messenger between DNA and Protein.

Judson writes

That fall, Jacob and Monod christened the unstable, information-bearing intermediate between gene and protein “messenger RNA.” Out of the amorphous biochemistry of RNA, three distinct anatomies had now been differentiated: rRNA, tRNA, mRNA. Two had begun their scientific careers as purely intellectual creations, function postulating structure. .Jacob and Monod wrote the idea of the messenger, and the term, into a theoretical summation they were preparing. Meanwhile, Brenner had written up the experimental work… At the end [of Jacob and Monod's article] they came to the function of the ribosome.

The property attributed to the structural messenger of being an unstable intermediate is one of the most specific and novel implications of this scheme… This leads to a new concept of the mechanism of information transfer, where the protein synthesizing centers (ribosomes) play the role of non-specific constituents which can synthesize different proteins, according to specific instructions which they receive from the genes through M-RNA.

There, in a sentence, was the first published statement of the pivotal realization that had come to Crick, Brenner, and Jacob in their conversation on Good Friday, eight months earlier….

Jacob and Monod titled their paper “Genetic Regulatory Mechanisms in the Synthesis of Proteins.” It reached The Journal of Molecular Biology on 28 December 1960.

So, next time you hear someone arguing about mRNA and vaccines and you aren’t sure what it is all about, go get a copy of The Eighth Day of Creation. At least you'll learn what mRNA is. Judson's book is one of the best about the history of science, and the absolute best I know of about the history of modern biology.

Physics in Medicine and Medical Education

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).

Physics in Medicine
and Medical Education.

Recently, we published a proceedings titled Physics in Medicine and Medical Education. You can purchase a hard copy of this book on Amazon, or view it for free as a flip-book. Here is the table of contents.

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. 

I hope you enjoy Physics in Medicine and Medical Education. Instructors who are teaching from Intermediate Physics for Medicine and Biology might want to take a look at it, to get an idea about the physics needed in modern medicine.

A New Homework Problem and Some Bidomain History

Russ Hobbie and I describe the bidomain model of cardiac tissue in Section 7.9 of Intermediate Physics for Medicine and Biology. The bidomain equations govern the intracellular and extracellular electrical potentials in the heart. As described in my unpublished paper “The Cardiac Bidomain Model in Twelve Publications,” the model was developed in the late 1970s by several researchers, including Less Tung and David Geselowitz. However, the history of the biodmain model is complex. Two other researchers working in Russia, A. Muler and V. Markin, also developed the same idea at about the same time. In addition, another group of researchers including Robert Eisenberg, Richard Mathias, and Arthur Peskoff at Rush University Medical Center, were using the bidomain model to describe the lens of the eye. 

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:

R. S. Eisenberg, V. Barcilon, and R. T. Mathias, “Electrical properties of spherical syncytia,” Biophysical Journal, Volume. 25, Pages 151–180, 1979.

A. Peskoff, “Electric potential in three-dimensional electrically syncytial tissues,” Bulletin of Mathematical Biology, Volume 41, Pages 163–181, 1979.

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 σ_i and extracellular conductivity σ_e. The cell membrane has a conductance per unit area G_m, 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 V_i and V_e (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 σ_i, σ_e, G_m, and β. 

(c) For r << λ, find approximations for V_i and V_e. Determine how each behaves as r goes to zero. 

(d) For r >> λ, find approximations for V_i and V_e. 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, V_m = V_i - V_e.

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, V_i is proportional to 1/r, while V_e is constant. Therefore, V_i goes to infinity as r goes to zero, but V_e remains finite.

(d) When r >> λ, both V_i and V_e are equal. They each fall off as 1/r and the conductivity factor that appears is σ_i + σ_e. 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 V_i and V_e, which contain the factor 1/r, cancel out when you take the difference to get V_m. Therefore, V_m falls off as e^-r/λ/r. If you are more than a few length constants from the stimulating electrode, V_m is much smaller than either V_i  or V_e. If you want to determine V_m by measuring V_i and V_e 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.

How Bright is a Firefly? Resolving a Century of Overestimation

“How Bright is a Firefly?”
by David Silver.

My favorite science journal is the American Journal of Physics. I was browsing through recent issues and found a lovely article by David Silver titled “How bright is a firefly? Resolving a century of overestimation” (Volume 94, Pages 520–524, July, 2026). The abstract is given below.

A firefly flash contains roughly 10⁸–10¹¹ photons—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?

1. 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.
2. 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.
3. 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.
4. 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.
5. 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. 
6. 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.

Marcello Malpighi and Capillaries

Marcello Malpighi.

When discussing distances and sizes in Chapter 1 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I write

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.

Under the Microscope - Objectivity 102

https://www.youtube.com/watch?v=9QcJkgDa1dk  

Magnetic Stimulation Using Microcoils: A Skeptical Review

Magnetic Stimulation Using Microcoils:
A Skeptical Review.

Over the last decade I’ve written a lot in this blog about magnetic stimulation of nerves using microcoils, which are tiny current-carrying coils generally from one millimeter down to tens of microns in size (see here, here, here, and here). My latest (and probably last) contribution to this topic was published recently in the BOHR International Journal of Neurology and Neuroscience, titled “Magnetic Stimulation Using Microcoils: A Skeptical Review.” The abstract states

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!

Note added just before this post was published

After my review article was published earlier this week, I discovered a 2025 PhD dissertation that came to a similar conclusion as my review did. Giovanni Calixte working with his graduate advisor Robert Butera at the Georgia Tech published “An Investigation into the Efficacy and Utility of Micromagnetic Stimulation as a Means of Exciting Neural Tissue.” It’s good work, and you can download it here. I reproduce the summary below. I’ve put the critical sentence near the end of the summary in italics.

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!