Bill Catterall (1946–2024)

William Catterall, known as “the father of ion channels,” died on February 28 at the age of 77. Russ Hobbie and I cite Catterall’s article on the structure of sodium ion channels in Chapter 9 of Intermediate Physics for Medicine and Biology.

Payandeh J, Scheuer T, Zheng N, Catterall WA (2011) The crystal structure of a voltage-gated sodium channel. Nature 475:353–358.

Catterall worked in the intramural program at the National Institutes of Health in the laboratory of Marshall Nirenberg. He then moved to the University of Washington, where he was a professor of Pharmacology for over 40 years. There he was a collaborator with Bertil Hille, the author of the landmark textbook Ion Channels of Excitable Membranes. An obituary published by the University of Washington website states

First and foremost, Bill was an exceptional scientist. He pioneered the biochemical investigation of calcium and sodium ion channels; molecular portals that allow the controlled passage of ions across cell membranes. The proper passage of ions into the cell is essential for healthy brain, heart, and muscle function. Early work from Catterall elucidated the molecular basis of ion channel gating whereas later studies with UW Pharmacology colleague Dr. Ning Zheng revealed details of how these clinically relevant macromolecular machines operate at the atomic level. With this latter information, Catterall was able to ascertain how a variety of toxins as well as local anesthetics and antiarrhythmic drugs act to “lock the gate” on these ion channels. Bill was recognized for these pivotal discoveries by election to the National Academy of Sciences USA and the Royal Society London. He also received prestigious awards including the Gairdner Award from Canada, the Robert R. Ruffolo Career Achievement Award in Pharmacology from the American Society of Pharmacology and Therapeutics, and a Lifetime Achievement Award from the International Union of Pharmacologists.

To learn more, listen to Catterall discuss his work in a three-part series of lectures for iBiology. 

William Catterall (U. Washington) Part 1: Electrical Signaling: Life in the Fast Lane  

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

 

William Catterall (U. Washington) Part 2: Voltage-gated Na+ Channels at Atomic Resolution

 https://www.youtube.com/watch?v=hfXGsJCOC9A

 

William Catterall (U. Washington) Part 3: Voltage-gated Calcium Channels

https://www.youtube.com/watch?v=bUE8gzMqqb8

Happy Birthday, Erwin Neher!

German biophysicist Erwin Neher turned 80 last week. Neher and Bert Sakmann received the 1991 Nobel Prize in Physiology or Medicine for their development of patch clamping: a method to record the current through individual ion channels. Russ Hobbie and I discuss Neher and Sakmann’s work in Chapter 9 of Intermediate Physics for Medicine and Biology.

I will turn over the rest of this post to Neher. In the two-minute video below, he offers advice to young scientists.

 

Erwin Neher's Advice to Young People: From a Nobel Prize Winner 

https://www.youtube.com/watch?v=vB3MNPuMFCI

 

In a ten-minute video, listen to Erwin Neher discuss advances in modern medicine.

Erwin Neher, Nobel Laureate for Medicine | Journal Interview 

https://www.youtube.com/watch?v=Rm3gHuxouZo

Finally, in this longer lecture, Neher describes the development of patch clamping. 

Lecture by Erwin Neher at the University of Hyderabad. The talk begins at approximately minute 18, after a rather long introduction.

https://www.youtube.com/watch?v=okB2coPEJJk

Happy Birthday, Erwin Neher!

A New Version of Figure 10.13 in the Sixth Edition of IPMB

Gene Surdotovich and I are hard at work preparing the 6^th edition of Intermediate Physics for Medicine and Biology. One change compared to the 5^th edition is that we are redrawing most of the figures using Mathematica. It’s a lot of work, but the revised figures look great and many are in color.

One advantage of redrawing the figures is that it forces us to rethink what the figure is all about and if it makes sense. This brings me to Figure 10.13 in the chapter about feedback. Specifically, it is from Section 10.6 about a negative feedback loop with two time constants. Without going into detail, let me outline what this figure is describing.

Chapter 10 centers around one particular feedback loop, relating the amount of carbon dioxide in your lungs (which we call x) to your breathing rate (y). The faster you breath, the more CO₂ you blow out of your lungs, so an increase in y causes a decrease in x. But your body detects when CO₂ is building up and reacts by increasing your breathing rate, so an increase in x causes an increase in y. There is one additional parameter, your metabolic rate, p. If your metabolic rate increases, so does the amount of CO₂ in your lungs.

Our book emphasizes mathematical modeling, so we develop a toy model of how x and y behave. We assume that initially x and y are in steady state for some p, and call these values x₀, y₀, and p₀. At time t = 0, p increases from  p₀ to p₀ + Δp, which could represent you starting to exercise. How do x and y change with time? We define two new variables, ξ and η, that represent the deviation of x and y from their steady state values, so x = x₀ + ξ and y = y₀ + η. We then develop two differential equations for ξ and η,

The variables ξ and η have different time constants, τ₁ and τ₂. The parameters G₁ and G₂ are the “gains” of the system, determining how much ξ changes in response to η, and how much η changes in response to ξ. In our model, G₁ is negative (an increase in breathing rate causes the amount of CO₂ in the lungs to decrease) and G₂ is positive (an increase in CO₂ causes the rate of breathing to increase). The “open loop gain” of the feedback loop is the product G₁G₂. Finally, the constant a is simply a factor to get the units right.

All is good so far. But now let’s look at the 5^th edition’s version of Fig. 10.13. 

What’s wrong with it? First, the calculation uses a positive value of G₁ and a negative value of G₂, so it doesn’t correspond correctly to our model, which has negative G₁ and positive G₂. Second, the calculation uses Δp = 0, so the steady state values of x and y don’t change and ξ and η both approach zero. That’s odd. I thought the whole point of the model was to look at how the system responds to changes in p. Finally, the initial values of ξ and η are not zero. What’s up with that? We know their values are zero for t < 0, when x = x₀ and y = y₀. How could they suddenly change at t = 0?

In the 6^th edition, the new version of Figure 10.13 is going to look something like this: 

The figure has color and switches from landscape to portrait orientation. Those changes are trivial. Here are the important differences:

1. I made G₁ negative and G₂ positive, like in our breathing model. Now an increase in CO₂ causes the body to increase the breathing rate, rather than decrease it as in the 5^th edition figure.
2. The parameter Δp is no longer zero. To be simple, I set aΔp = 1. The person starts exercising at t = 0.
3. Because there is a change in metabolic rate, the new steady state values of ξ and η are not zero. In fact, they are equal to ξ = aΔp/(1-G₁G₂) and η = G₂aΔp/(1-G₁G₂). Notice how the factor of 1-G₁G₂ plays a big role. Since the product G₁G₂ is negative, this means that 1-G₁G₂ is a positive number greater than one. It’s in the denominator, so it makes ξ smaller. That’s the whole point. The feedback loop is designed to keep ξ from changing much. It’s a control system to suppress changes in ξ. To make life simple, I set G₁ = −5 and G₂ = 5 (the same values from the 5^th edition except for the signs), so the open loop gain is 25 and the steady state value of ξ is only 1/26 of what it would be if no feedback were present (in which case, ξ would rise monotonically to one while η would remain zero).
4. The initial values of ξ and η are now zero, so there is no instantaneous jump of these variables at t = 0.

When revising the 5^th edition of IPMB, I began wondering why Russ Hobbie and I never worried about the units for the time constants, the gains, a, or Δp. This motivated me to write a new homework problem for the 6^th edition, in which the student is asked to rewrite the model equations in nondimensional variables Ξ, Η, and T instead of ξ, η, and t. Interestingly, such a switch results in a pair of differential equations for Ξ and Η that depend on only two nondimensional parameters: the ratio of time constants and the open loop gain. So, our plot in the 5^th edition has the qualitative behavior correct (except for the signs of G₁ and G₂). The system oscillates because the open loop gain is so high. The correct units for the various parameters would only rescale the horizontal and vertical axes. 

Is the new version of Figure 10.13 in this blog post what you’ll see in the 6^th edition of IPMB? I don’t know. I haven’t passed the figure by Gene yet, and he’s my Mathematica guru. He might make it even better.

What’s the moral of this story? THINK BEFORE YOU CALCULATE! That’s the motto I often would tell my students, but it applies just as well to textbook authors. The plot should not only be correct but also make physical sense. You should be able to explain what’s happening in words as well as pictures. If you can’t tell the story of what’s taking place by looking at the figure, something’s wrong.

Finally, is there really no physical problem that the original version of Fig. 10.13 describes? Actually, there is. Imagine you are resting throughout this “event”; you sit in your chair and don’t change your metabolic rate, so Δp = 0 meaning p is the same before and after t = 0. However, at time t = 0, your “friend” sneaks up on you, shoves a fire extinguisher in front of your face, and gives you a quick, powerful blast of CO₂. Except for the sign issue on G₁ and G₂, the original figure shows how your body would respond.

Stirling's Approximation

I've always been fascinated by Stirling’s approximation,

ln(n!) = n ln(n) − n,

where n! is the factorial. Russ Hobbie and I mention Stirling’s approximation in Appendix I of Intermediate Physics for Medicine and Biology. In the homework problems for that appendix (yes, IPMB does has homework problems in its appendices), a more accurate version of Stirling’s approximation is given as

ln(n!) = n ln(n) − n + ½ ln(2π n) .

There is one thing that’s always bothered me about Stirling’s approximation: it’s for the logarithm of the factorial, not the factorial itself. So today, I’ll derive an approximation for the factorial. 

The first step is easy; just apply the exponential function to the entire expression. Because the exponential is the inverse of the natural logarithm, you get

n! = e^{n ln(n) − n + ½ ln(2π n)}

Now, we just use some properties of exponents

n! = e^{n ln(n)} e⁻ⁿ e^{½ln(2π n)}

n! = (e^ln(n))ⁿ e⁻ⁿ √(e^{ln(2π n)})

n! = nⁿ e⁻ⁿ √(2π n) 

And there we have it. It’s a strange formula, with a really huge factor (nⁿ) multiplied by a tiny factor (e⁻ⁿ) times a plain old modestly sized factor (√(2π n)). It contains both e = 2.7183 and π = 3.1416.

Let's see how it works.

n	n!	nn e−n √(2π n)	fractional error (%)
1	1	0.92214	7.8
2	2	1.9190	4.1
5	120	118.02	1.7
10	3.6288 × 106	3.5987 × 106	0.83
20	2.4329 × 1018	2.4228 × 1018	0.42
50	3.0414 × 1064	3.0363 × 1064	0.17
100	9.3326 × 10157	9.3249 × 10157	0.083

For the last entry (n = 100), my calculator couldn’t calculate 100¹⁰⁰ or 100!. To get the first one I wrote

100¹⁰⁰ = (10²)¹⁰⁰ = 10^{2 × 100} = 10²⁰⁰.

The calculator was able to compute e⁻¹⁰⁰ = 3.7201 × 10⁻⁴⁴, and of course the square root of 200π was not a problem. To obtain the actual value of 100!, I just asked Google.

Why in the world does anyone need a way to calculate such big factorials? Russ and I use them in Chapter 3 about statistical dynamics. There you have to count the number of states, which often requires using factorials. The beauty of statistical mechanics is that you usually apply it to macroscopic systems with a large number of particles. And by large, I mean something like Avogadro’s number of particles (6 × 10²³). The interesting thing is that in statistical mechanics you often need not the factorial, but the logarithm of the factorial, so Stirling's approximation is exactly what you want. But it’s good to know that you can also approximate the factorial itself. 

Finally, one last fact from Mr. Google. 1,000,000! = 8.2639 × 10^5,565,708. Wow!

Stirling’s Approximation

https://www.youtube.com/watch?v=IJ5N28-Ujno

A Text-Book on Medical Physics

Intermediate Physics for Medicine and Biology provides, for the first time, a textbook about the role that physics plays in medicine.

Well… no.

I recently found a textbook that preceded IPMB by over a century. Below is its preface.

The fact that a knowledge of Physics is indispensable to a thorough understanding of Medicine has not yet been as fully realized in this country as in Europe, where the admirable works of Desplats and Gariel, of Robertson, and of numerous German writers, constitute a branch of educational literature to which we can show no parallel. A full appreciation of this, the author trusts, will be sufficient justification for placing in book form the substance of his lectures on this department of science, delivered during many years at the University of the City of New York.

Broadly speaking, this work aims to impart a knowledge of the relations existing between Physics and Medicine in their latest state of development, and to embody in the pursuit of this object whatever experience the author has gained during a long period of teaching this special branch of applied science. In certain cases topics not strictly embraced in the title have been included in the text—for example, the directions for section-cutting and staining; and in other instances exceptionally full descriptions of apparatus have been given, notably of the microscope; but in view of the importance of these subjects, the course pursued will doubtless be approved. Attention may be called to the paragraph headings and italicized words, which suggest a system of questions facilitating a review of the text.

In conclusion, the author will feel that his labor has not been in vain if the work should serve to call deserved attention to a subject hitherto slighted in the curriculum of medical education.

Readers of IPMB might be interested in a brief table of contents for this earlier book.

I. Matter

      1. Properties of matter

      2. Solid matter

      3. Liquid matter

      4. Gaseous matter

      5. Ultragaseous and radiant matter

II. Energy

               1. Potential energy 

               2. Kinetic energy 

               3. Machines and instruments 

               4. Translatory molecular motion 

               5. Acoustics 

               6. Optics 

               7. Heat 

               8. Electricity 

               9. Dynamic electricity 

             10. Magnetism 

             11. Electrobiology

Many of these topics are familiar to readers of IPMB. Yet, the list and the language seem quaint and just a little old-fashioned.

A Text-Book on Medical Physics,
by John C. Draper.

This should not be surprising. The book was titled A Text-Book on Medical Physics, written by John C. Draper, and published in 1885. Russ Hobbie and I are following a long tradition of applying physics to medicine and biology. In nearly 140 years much has changed, but also much has stayed the same. The last sentence of the preface could serve as our call to arms, and the subtitle of Draper’s book could be our own: “For the Use of Students and Practitioners of Medicine.” 

Below I post the definition of medical physics in the Text-Book. I love it. Draper should have written a blog!

 

The Rest of the Story 4

Allan was born in Johannesburg, the youngest of three children. He spent his teenage years in Cape Town, and was interested in debating, tennis, and acting. He also loved astronomy, which triggered an interest in physics and mathematics.

At the University of Cape Town he studied electrical engineering, following in the footsteps of his father and brother. But he soon abandoned engineering to learn physics and to engage in mountaineering. After he obtained his undergraduate degree, he went to England and studied physics at the Cavendish Laboratory in Cambridge. 

He didn’t finish his PhD, however, because in Paul Dirac’s quantum mechanics class he fell in love with one of his classmates, an American physics student named Barbara Seavey. He wanted to marry her but he had no money. As fortune would have it, there was a teaching position available back in Cape Town. He married Barbara and returned home to South Africa. There he was happy, but isolated from cutting edge research. He didn’t seem posed for success in the high-power and competitive world of physics.

Page 2

At Cape Town Allan eventually qualified for a sabbatical, which Barbara wanted to spend in the United States. So they traveled to the Harvard cyclotron, where he worked on nucleon-nucleon scattering with Norman Ramsey and Richard Wilson. While on sabbatical leave, he was offered a position at Tufts University.

Allan became interested in a computer imaging problem: how to make a 2-d image of the inside of an object based on projections taken at different angles. He published the results of this work, but it didn’t make a splash. No one seemed to care about his algorithm. So he went back to his research on high energy physics.

Several years latter, researchers suddenly began to pay attention to Allan’s imaging work. Medical doctors were interested in forming two- or even three-dimensional images of the body using X-rays applied from different directions. Allan’s algorithm was exactly what they needed.

These studies became fundamental to the emerging field of medical imaging. It was so important, that in 1979 he—Allan MacLeod Cormack—and Godfrey Hounsfield shared the Nobel Prize in Physiology or Medicine for the invention of computed tomography.

And now you know the rest of the story.

Good day!

***************************

Imagining the Elephant:
A Biography of Allan MacLeod Cormack.
by Christopher Vaughan.

This blog post was written in the style of Paul Harvey’s “The Rest of the Story” radio program. You can find three other of my “The Rest of the Story” blog posts here, here, and here.

The content is based on Cormack’s biography on the Nobel Prize website. You can read about tomographic reconstruction techniques in Chapter 12 of Intermediate Physics for Medicine and Biology.

Allan MacLeod Cormack was born on February 23, 1924, exactly 100 years ago today. 

Happy birthday Allan!

Forman Acton (1920 – 2014)

Numerical Methods That Work,
by Forman Acton.

The American computer scientist Forman Acton died ten years ago this Sunday. In Intermediate Physics for Medicine and Biology, Russ Hobbie and I cite Acton’s Numerical Methods That Work. For readers interested in using computers to model biological processes, I recommend this well written and engaging book.

Before he died, Acton donated funds to establish the Forman Acton Foundation. Here is how their website describes his life:

Forman Sinnickson Acton was born in Salem City, and he went on to change the world.

Born on August 10, 1920, he began his education in the Salem City school system before attending private boarding school at Phillips Exeter Academy and college at Princeton University. He graduated with two degrees in engineering toward the end of World War II, during which he served in the Army Corps of Engineers and worked on a team involved in the Manhattan Project.

After his service, he earned his doctorate in mathematics from Carnegie Institute of Technology, helped the Army develop the world’s first anti-aircraft missiles and became a pioneer in the evolving field of computer science.

Acton conducted research and taught at Princeton from 1952 to 1990, during which time he wrote textbooks on mathematics at his cabin on Woodmere Lake in Quinton Township, Salem County. When he turned 80, he joined the Lower Alloways Creek pool to stay in shape, swimming six days a week for 14 years.

He died on February 18, 2014, in Woodstown, New Jersey, but not before he anonymously donated thousands of dollars toward scholarships for Salem City School District students, some of whom were just then graduating from college. Before he passed, he made it clear to friends and confidants that he wanted these students to have access to the incredible educational experiences he enjoyed.

Eight months after his passing, the Forman S. Acton Educational Foundation was officially incorporated to ensure that all of Salem’s youth also have a chance to change the world.

Sometimes I will read a passage and say to myself “That’s exactly what students studying from IPMB need to hear.” I feel this way about Acton’s preface to Numerical Methods That Work. Russ and I include many homework problems in IPMB so the student can gain experience with the art of mathematical modeling. Below, in Acton’s words, is why we do that. Just replace phrases like “solving equations numerically” with “building models mathematically” and his words apply equally well to IPMB.

Numerical equation solving is still largely an art, and like most arts it is learned by practice. Principles are there, but even they remain unreal until you actually apply them. To study numerical equation solving by watching someone else do it is rather like studying portrait painting by the same method. It just won’t work. The principle reason lies in the tremendous variety within the subject…

The art of solving problems numerically arises in two places: in choosing the proper method and in circumventing the main road-blocks that always seem to appear. So throughout the book I shall be urging you to go try the problems—mine or yours.

I have tried to make my explanations clear, but sad experience has shown that you will not really understand what I am talking about until you have made some of the same mistakes I have made. I hesitate to close a preface with a ringing exhortation for you to go forth to make fruitful mistakes; somehow it doesn’t seem quite the right note to strike! Yet, the truth it contains is real. Guided, often laborious, experience is the best teacher for an art.

 

Robert Kemp Adair (1924–2020)—Notes on a Friendship

Robert Adair.
Photo credit: Michael Marsland/Yale University.

I try to write obituaries of scientists who appear in Intermediate Physics for Medicine and Biology, but for some reason I didn’t write about Robert Adair’s death in 2020. Perhaps the covid pandemic over-shadowed his demise. In Chapter 9 of IPMB, Russ Hobbie and I cite seven of his publications. He was a leader in studying the health effects (or, lack of heath effects) from electric and magnetic fields.

Recently, I read a charming article subtitled “Notes on a Friendship” about Adair, written by Geoffrey Kabat, the author of Getting Risk Right: Understanding the Science of Elusive Health Risks. I have Getting Risk Right on my to-read list. It sounds like my kind of book.

I admire Adair’s service in an infantry rifle platoon during World War II. I loved his book about baseball. I respect his independent assessment of the seriousness of climate change, although I don’t agree with all his conclusions. He certainly was a voice of reason in the debate about health risks of electric and magnetic fields. He led a long and useful life. We need more like him.

I will give Kabat the final word, quoting the last paragraph of his article.

In early October 2020, Bob’s daughter Margaret called me to tell me that Bob had died. I looked for an obituary in the New York Times, and was shocked when none appeared, likely due to the increased deaths from the pandemic. I wrote to an epidemiologist colleague and friend, who knew Bob’s work on ELF-EMF [extremely low frequency electromagnetic fields] and microwave energy, and who had served on a committee to assess possible health effects of the Pave Paws radar array on Cape Cod. My friend Bob Tarone wrote back, “Very sad to hear that. Adair was not directly involved in the Pave Paws study, but we relied heavily on his superb published papers on the biological effects of radio-frequency energy in our report. He and his wife were superb scientists. Losing too many who don’t seem to have competent replacements. Too bad honesty and truth are in such short supply in science today.” He concurred that there should have been an obituary in the Times.

“Havana Syndrome”: A post mortem

“Havana Syndrome”: A Post Mortem,
by Bartholomew and Baloh.

Remember the Havana Syndrome? You don’t hear much about it anymore. Recently I read an article titled “‘Havana Syndrome’: A Post Mortem,” by Robert Bartholomew and Robert Baloh. These two researchers are long-time skeptics who don’t believe that the Havana Syndrome was caused by a physical attack on US and Canadian diplomats. They are also critical of the National Academies report that suggested microwave weapons might be responsible for the Havana Syndrome. I came to a similar conclusion in my book Are Electromagnetic Fields Making Me Ill?, where I wrote

At this time, we have no conclusive explanation for the Havana syndrome. We need more evidence. Measuring intense beams of microwaves should be easy to do and would not be prohibitively expensive. Until someone observes microwaves associated with the onset of this illness, I will remain skeptical of the National Academies’conclusion.

Bartholomew and Baloh believe that the Havana Syndrome is psychogenic. In my book, I make an analogy to post traumatic stress syndrome: it’s a real disease, but not one with a simple physical cause. Below I quote the abstract from Bartholomew and Baloh’s paper.

Background: Since 2016, an array of claims and public discourse have circulated in the medical community over the origin and nature of a mysterious condition dubbed “Havana Syndrome,” so named as it was first identified in Cuba. In March 2023, the United States intelligence community concluded that the condition was a socially constructed catch-all category for an array of health conditions and stress reactions that were lumped under a single label.

Aims: To examine the history of “Havana Syndrome” and the many factors that led to its erroneous categorization as a novel clinical entity.

Method: A review of the literature.

Results/Conclusions: Several factors led to the erroneous classification of “Havana Syndrome” as a novel entity including the failure to stay within the limitations of the data; the withholding of information by intelligence agencies, the prevalence of popular misconceptions about psychogenic illness, the inability to identify historical parallels; the role of the media, and the mixing of politics with science.

In Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the health effects of electromagnetic fields. It’s crucial to understand the physics that underlies tissue-field interactions before postulating a nefarious role for electromagnetic fields in human health. If you suggest an idea that is not consistent with physics, prepare to be proved wrong.

A final note: Baloh and Bartholomew write

In September 2021, the head of a U.S. Government panel investigating “Havana Syndrome,” Pamela Spratlen, was forced to resign after refusing to rule out [mass psychogenic illness] as a possible cause... A former senior C.I.A. operative wrote that Spratlen’s position was “insulting to victims and automatically disqualifying.”

I think we all owe Pamela Spratlen an apology. Thank you for your service.

 Was “Havana Syndrome” a case of mass hysteria? DW News.

https://www.youtube.com/embed/ljf1TVWTSlQ

 

Havana Syndrome: Tilting at Windmills?

https://www.youtube.com/watch?v=4IWnhmqVsPc
 

 The Havana Syndrome: A Disorder of Neuropolitics?

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

Craig Henriquez (1959–2023)

I just learned that my friend Craig Henriquez passed away last summer. Craig earned his PhD at Duke University in their Department of Biomedical Engineering under the guidance of the renowned bioelectricity expert Robert Plonsey. His 1988 dissertation, titled “Structure and Volume Conductor Effects on Propagation in Cardiac Tissue,” was closely related to work I was doing at that time. Craig sent me a copy of his dissertation after he graduated. I really wanted to read it, but I was swamped with my my new job at the National Institutes of Health and helping care for my newborn daughter Stephanie. There wasn’t time to read it at work, and when I got home it was my turn to watch the baby, as my wife had been with her all day. The solution was to read Craig’s dissertation out loud to Stephanie as she crawled around in her play pen. She seemed to like the attention and I got to learn about Craig’s work.

Craig and I are nearly the same age. He was born in 1959 and I in 1960. Our careers progressed along parallel lines. After he graduated he stayed at Duke and joined the faculty. I recall he told me at the time that he didn’t know if he would make a career in academia, but he certainly did. He was on the Duke faculty for 35 years. In the early 1990s three young researchers at Duke—Craig, Natalia Trayanova, and Wanda Krassowska—were all from my generation. They were my friends, collaborators, and sometimes competitors as we worked to establish the bidomain model as the state-of-the-art representation of the electrical properties of cardiac tissue.

In my recent review about bidomain modeling (Biophysics Reviews, Volume 2, Article 041301, 2021) , I wrote (referring to myself in third person, as required by the journal; in the quotes below references are removed):

Roth’s calculation was not the first attempt to solve the active bidomain model using a numerical method. In 1984, Barr and Plonsey had developed a preliminary algorithm to calculate action potential propagation in a sheet of cardiac tissue. Simultaneous with Roth’s work, Henriquez and Plonsey were examining propagation in a perfused strand of cardiac tissue. For the next several years, Henriquez continued to improve bidomain computational methods with his collaborators and students at Duke. His 1993 article published in Critical Reviews of Biomedical Engineering remains the definitive summary of the bidomain model.

I’ve cited his 1993 review article (Crit. Rev. Biomed. Eng., Volume 21, Pages 1–77) many times, including in Intermediate Physics for Medicine and Biology. It’s a classic.

Craig and I were both interested in determining if Madison Spach’s electrical potential data from cardiac tissue samples should be interpreted as evidence of discontinuous propagation (Spach’s hypothesis) or a bath effect.

The original calculations of action potential propagation in a continuous bidomain strand perfused by a bath hinted at different interpretations of Spach’s data. As discussed earlier, the wave front is not one-dimensional because its profile varies with depth below the strand surface. The same effect occurs during propagation through a perfused planar slab, more closely resembling Spach’s experiment. The conductivity of the bath is higher than the conductivity of the interstitial space, so the wave front propagates ahead on the surface of the tissue and drags along the wave front deeper below the surface, resulting in a curved front. The extra electrotonic load experienced at the surface slows the rate of rise and the time constant of the action potential foot. Plonsey, Henriquez, and Trayanova analyzed this effect, and subsequently so did Henriquez and his collaborators and Roth.

Craig became an associate editor of the IEEE Transactions on Biomedical Engineering, and he would often send me papers to review. He was a big college basketball fan. We would email each other around March, when our alma maters—my Kansas Jayhawks and his Duke Blue Devils—would face off in the NCAA tournament. His research interests turned to nerves and the brain, and he co-directed a Center of Neuroengineering at Duke. He eventually chaired Duke’s biomedical engineering department, and at the time of his death he was an Associate Vice Provost.

I found out about Craig’s death when I was submitting a paper to a journal. This publication asks authors to suggest potential reviewers, and I was about to put Craig’s name down as a person who would give an honest and constructive assessment. I googled him to get his current email address, and discovered the horrible news. What a pity. I will miss him. 

Short bio published in the IEEE Transactions on Biomedical Engineering in January, 1990.

 Craig Henriquez talking about cardiac tissue and the bidomain model.

https://www.youtube.com/watch?v=OiSiLwP1ZPo