Friday, February 22, 2019

Francis Crick, Biological Physicist

I'm fascinated by scientists who straddle physics and biology. In particular, I'm curious how a scientist trained in one field switches to another. The quintessential physicist-turned-biologist is Francis Crick. Yes, I mean Crick of “Watson and Crick," the team who discovered the structure of DNA.

Asimov's Biographical Encyclopedia of Science and Technology, superimposed on the cover of Intermediate Physics for Medicine and Biology.
Asimov's Biographical
Encyclopedia of Science
and Technology
To start learning about the education of Francis Crick, consider his entry in Asimov’s Biographical Encyclopedia of Science and Technology.
CRICK, Francis Harry Compton
English biochemist
Born: Northampton, June 8, 1916

Crick was educated at University College in London and went on to obtain his Ph.D. at Cambridge University in 1953. He was a physicist to begin with and worked in the field during World War II, when he was involved in radar research and in magnetic mine development…

At the time, under the leadership of [Max] Perutz, a veritable galaxy of physics-minded scientists was turning to biochemistry at Cambridge and their refined probings established the science of molecular biology, as fusion of biology, chemistry, and physics…

Crick was one of the physicists who turned to biochemistry or, rather, to molecular biology, and with him was a young American, James Dewey Watson
The Eighth Day of Creation, superimposed on the cover of Intermediate Physics for Medicine and Biology.
The Eighth Day of Creation,
by Horace Freeland Judson.
To explore in more detail how Crick changed from physics to biology, let’s turn to the definitive history of modern biology: Horace Freeland Judson’s masterpiece The Eighth Day of Creation.
Crick is to an unusual extent self-educated in biology. He went to a minor English public school, Mill Hill, in northern London; his interest in science was already so single-minded that his family thought him odd. At University College, London, he read physics and had nearly finished his doctorate when the war broke out and a German bomb destroyed his laboratory and gear. When Crick left the Admiralty and physics in 1947, he set out to master the literature of biology, reading with an appetite that has slackened, if at all, only in the last few years [Judson published The Eighth Day of Creation in 1979]. His peers concede without question his astonishing reach. Perutz, whose knowledge is encyclopedic in scope and order: “Francis of course reads more widely than the rest of us.” Jacques Monod, the science’s other great theorist: “No one man discovered or created molecular biology. But one man dominates intellectually the whole field, because he knows the most and understands the most. Francis Crick.”
This idea that you have to read the literature resonates with me. I spent the first months of graduate school at Vanderbilt reading research articles about how nerves worked. I took no classes in neurobiology. I didn’t have a biological mentor (my PhD advisor, John Wikswo, was a physicist). I just read. That's the way many physicists learn biology.

Judson humorously tells of Crick's introduction to Perutz's laboratory:
"The first thing Francis did was to read everything we had done," Perutz said. "Then he started criticizing."
Why did Crick change to biology? Judson explains
“An important reason Crick changed to biology, he said to me, was that he is an atheist, and was impatient to throw light into the remaining shadowy sanctuaries of vitalistic illusions. ‘I had read [Erwin] Schrodinger’s little book [What is Life?], too [According to Judson, "everyone read Schrodinger."]. Essentially, if you read that book critically, the main import is very peculiar; for one thing, it’s a book written by a physicist who doesn’t know any chemistry! But the impact—there’s no doubt that Schrodinger wrote it in a compelling style, not like the junk that most people write, and it was imaginative. It suggested that biological problems could be thought about, in physical terms—and thus gave the impression that exciting things in this field were not far off. My own motives I never had any doubt about; I was very clear in my mind. Because when I decided to leave the Admiralty, when I was about thirty, then on the grounds that I knew so little anyway I might just as well go into anything I liked, I looked around for fields which would illuminate this particular point of view, against vitalism. And the two fields I chose were what we would now call molecular biology, though the term wasn’t common then, certainly I didn’t know it—but I would have said the borderline between the living and nonliving. That was the phrase I had in my mind, on the one hand. And on the other, the higher nervous system and this problem of consciousness...”
What Mad Pursuit: A Personal View of Scientific Discovery, by Francis Crick, superimposed on the cover of Intermediate Physics for Medicine and Biology.
What Mad Pursuit:
A Personal View
of Scientific Discovery,
by Francis Crick.
Crick reminisces about his shift from physics to biology in his autobiography What Mad Pursuit.
"By the time most scientists have reached age thirty they are trapped by their own expertise. They have invested so much effort in one particular field that it is often extremely difficult, at that time in their careers, to make a radical change. I, on the other hand, knew nothing, except for a basic training in somewhat old-fashioned physics and mathematics and an ability to turn my hand to new things. I was sure in my mind that I wanted to do fundamental research rather than going into applied research...

Since I essentially knew nothing, I had an almost completely free choice...Working in the Admiralty, I had several friends among the naval officers. They were interested in science but knew even less about it than I did. One day I noticed that I was telling them, with some enthusiasm, about recent advances in antibiotics—penicillin and such. Only that evening did it occur to me that I myself really knew almost nothing about these topics...It came to me that I was not really telling them about science. I was gossiping about it.

This insight was a revelation to me. I had discovered the gossip test—what you are really interested in is what you gossip about. Without hesitation, I applied it to my recent conversations. Quickly I narrowed down my interests to two main areas: the borderline between the living and nonliving, and the workings of the brain..."
I'm not sure Crick's reflections can be generalized. To me, they imply that the choice of a research topic can be haphazard and personal.

Four good books: What Mad Pursuit. The Eighth Day of Creation, Asimov's Biographical Encyclopedia of Science and Technology, and Intermeidate Physics for Medicine and Biology.
Four good books.
Perhaps more useful is Crick's thoughts about theory in biology, which appear in the conclusion of What Mad Pursuit.
"Physicists are all too apt to look for the wrong sorts of generalizations, to concoct theoretical models that are too neat, too powerful, and too clean. Not surprisingly, these seldom fit well with the data. To produce a really good biological theory one must try to see through the clutter produced by evolution to the basic mechanisms lying beneath them, realizing that they are likely to be overlaid by other, secondary mechanisms. What seems to physicists to be a hopelessly complicated process may have been what nature found simplest, because nature could only build on what was already there...

The job of theorists, especially in biology, is to suggest new experiments. A good theory makes not only predictions, but surprising predictions that then turn out to be true. (If its predictions appear obvious to experimentalists, why would they need a theorist?) ... If this book helps anyone to produce good biological theories, it will have performed one of its main functions."
Crick is a case study into how and why a physicist switches to studying biology. Readers of Intermediate Physics for Medicine and Biology who are contemplating such a switch may benefit from his story.

Want to learn more? Listen to Crick himself discuss how he became interested in science.

 Listen to Francis Crick talking about how he became interested in science.

Friday, February 15, 2019

The Electric Field Induced During Magnetic Stimulation

Chapter 8 of Intermediate Physics for Medicine and Biology discusses electromagnetic induction and magnetic stimulation of nerves. It doesn't, however, explain how to calculate the electric field. You can learn how to do this from my article “The Electric Field Induced During Magnetic Stimulation” (Electroencephalography and Clinical Neurophysiology, Supplement 43, Pages 268-278, 1991). It begins:
A photograph of the first page of The Electric Field Induced During Magnetic Stimulation by Roth, Cohen ad Hallett (EEG Suppl 43:268-278, 1991), superimposed on the cover of Intermediate Physics for Medicine and Biology.
“The Electric Field Induced
During Magnetic Stimulation.”
Magnetic stimulation has been studied widely since its use in 1982 for stimulation of peripheral nerves (Polson et al. 1982), and in 1985 for stimulation of the cortex (Barker et al. 1985). The technique consists of inducing current in the body by Faraday’s law of induction: a time-dependent magnetic field produces an electric field. The transient magnetic field is created by discharging a capacitor through a coil held near the target neuron. Magnetic stimulation has potential clinical applications for the diagnosis of central nervous system disorders such as multiple sclerosis, and for monitoring the corticospinal tract during spinal cord surgery (for review, see Hallett and Cohen 1989). When activating the cortex transcranially, magnetic stimulation is less painful than electrical stimulation.
Appendix 1 in the paper The Electric Field Induced During Magnetic Stimulation by Roth, Cohen ad Hallett (Electroencephalography and Clinical Neurophysiology, Suppl 43: 268-278, 1991), superimposed on the cover of Intermediate Physics for Medicine and Biology.
Appendix 1.
Although there have been many clinical studies of magnetic stimulation, until recently there have been few attempts to measure or calculate the electric field distribution induced in tissue. However, knowledge of the electric field is important for determining where stimulation occurs, how localized the stimulated region is, and what the relative efficacy of different coil designs is. In this paper, the electric field induced in tissue during magnetic stimulation is calculated, and results are presented for stimulation of both the peripheral and central nervous systems.
In Appendix 1 of this article, I derived an expression for the electric field E at position r, starting from
An equation for the electric field induced during magnetic stimulation.
where N is the number of turns in the coil, μ0 is the permeability of free space (4π × 10-7 H/m), I is the coil current, r' is the position along the coil, and the integral of dl' is over the coil path. For all but the simplest of coil shapes this integral can't be evaluated analytically, so I used a trick: approximate the coil as a polygon. A twelve-sided polygon looks a lot like a circular coil. You can make the approximation even better by using more sides.
A circular coil approximated by a 12-sided polygon.
A circular coil (black) approximated by
a 12-sided polygon (red).
With this method I needed to calculate the electric field only from line segments. The calculation for one line segment is summarized in Figure 6 of the paper.
Figure 6 from The Electric Field Induced During Magnetic Stimulation, showing the polygon approximation to the coil geometry.
Figure 6 from “The Electric Field
Induced During Magnetic Stimulation.”
I will present the calculation as a new homework problem for IPMB. (Warning: t has two meanings in this problem: it denotes time and is also a dimensionless parameter specifying location along the line segment.)
Section 8.7

Problem 32 ½. Calculate the integral
The integral needed to calculate the electric field induced during magnetic stimulation.
for a line segment extending from x2 to x1. Define δ = x1 - x2 and R = r - ½(x1 + x2).
(a) Interpret δ and R physically.
(b) Define t as a dimensionless parameter ranging from -½ to ½. Show that r' equals rRtδ.
(c) Show that the integral becomes
An intermediate step in the calculation of the electric field induced during magnetic stimulation.
(d) Evaluate this integral. You may need a table of integrals.
(e) Express the integral in terms of δ, R, and φ (the angle between R and δ).

The resulting expression for the electric field is Equation 15 in the article
Equation (15) in The Electric Field During Magnetic Stimulation by Roth, Cohen ad Hallett (Electroencephalography and Clinical Neurophysiology, Suppl 43: 268-278, 1991).
Equation (15) in “The Electric Field Induced During Magnetic Stimulation.”
The photograph below shows the preliminary result in my research notebook from when I worked at the National Institutes of Health. I didn't save the reams of scrap paper needed to derive this result.

The November 10, 1988 entry in my research notebook, where I derive the equation for the electric field induced during magnetic stimulation.
The November 10, 1988 entry
in my research notebook.
To determine the ends of the line segments, I took an x-ray of a coil and digitized points on it. Below are coordinates for a figure-of-eight coil, often used during magnetic stimulation. The method was low-tech and imprecise, but it worked.

The November 17, 1988 entry in my research notebook, in which I digitized points along a figure-of-eight coil used for magnetic stimulation.
The November 17, 1988 entry
in my research notebook.
Ten comments:
  • My coauthors were Leo Cohen and Mark Hallett, two neurologists at NIH. I recommend their four-page paper “Magnetism: A New Method for Stimulation of Nerve and Brain.”
  • The calculation above gives the electric field in an unbounded, homogeneous tissue. The article also analyzes the effect of tissue boundaries on the electric field.
  • The integral is dimensionless. “For distances from the coil that are similar to the coil size, this integral is approximately equal to one, so a rule of thumb for determining the order of magnitude of E is 0.1 N dI/dt, where dI/dt has units of A/μsec and E is in V/m.”
  • The inverse hyperbolic sine can be expressed in terms of logarithms: sinh-1z = ln[z + √(z2 + 1)]. If you're uncomfortable with hyperbolic functions, perhaps logarithms are more to your taste. 
  • This supplement to Electroencephalography and Clinical Neurophysiology contained papers from the International Motor Evoked Potential Symposium, held in Chicago in August 1989. This excellent meeting guided my subsequent research into magnetic stimulation. The supplement was published as a book: Magnetic Motor Stimulation: Principles and Clinical Experience, edited by Walter Levy, Roger Cracco, Tony Barker, and John Rothwell
  • Leo Cohen was first author on a clinical paper published in the same supplement: Cohen, Bandinelli, Topka, Fuhr, Roth, and Hallett (1991) “Topographic Maps of Human Motor Cortex in Normal and Pathological Conditions: Mirror Movements, Amputations and Spinal Cord Injuries.”
  • To be successful in science you must be in the right place at the right time. I was lucky to arrive at NIH as a young physicist in 1988—soon after magnetic stimulation was invented—and to have two neurologists using the new technique on their patients and looking for a collaborator to calculate electric fields.
  • A week after deriving the expression for the electric field, I found a similar expression for the magnetic field. It was never published. Let me know if you need it.
  • If you look up my article, please forgive the incorrect units for μ0 given in the Appendix. They should be Henry/meter, not Farad/meter. In my defense, I had it correct in the body of the article. 
  • Correspondence about the article was to be sent to “Bradley J. Roth, Building 13, Room 3W13, National Institutes of Health, Bethesda, MD 20892.” This was my office when I worked at the NIH intramural program between 1988 and 1995. I loved working at NIH as part of the Biomedical Engineering and Instrumentation Program, which consisted of physicists, mathematicians and engineers who collaborated with the medical doctors and biologists. Cohen and Hallett had their laboratory in the NIH Clinical Center (Building 10), and were part of the National Institute of Neurological Disorders and Stroke. Hallett once told me he began his undergraduate education as a physics major, but switched to medicine after one of his professors tried to explain how magnetic fields are related to electric fields in special relativity.
A map of the National Institutes of Health campus in Bethesda, Maryland. I worked in Building 13. Hallett and Cohen worked in Building 10 (the NIH Clinical Center).
A map of the National Institutes of Health campus
in Bethesda, Maryland.

Friday, February 8, 2019

A screenshot of the website, superimposed on the cover of Intermediate Physics for Medicine and Biology.
In this blog, I sometimes share websites related to Intermediate Physics for Medicine and Biology. Recently, I discovered
The human brain is the most complex biological structure in the known universe. Its roughly 86 billion nerve cells power all of our thoughts, perceptions, memories, emotions, and actions. It’s what inspires us to build cities and compels us to gaze at the stars.

That sense of wonder drives We are a public information initiative of The Kavli Foundation, the Gatsby Charitable Foundation, and the Society for Neuroscience – global nonprofit organizations dedicated to advancing brain research.

Powered by the global neuroscience community and overseen by an editorial board of leading neuroscientists from around the world, shares the stories of scientific discovery and the knowledge they reveal. Unraveling the mysteries of the brain has the potential to impact every aspect of human experience and civilization.

Join us as we explore the universe between our ears. Because when you know your brain, you know yourself.
A screenshot of the article "To Understand the Brain, You Have to Do the Math” by Alexandre Pouget.
To Understand the Brain,
You Have to Do the Math
Browsing is an excellent way to learn about neuroscience. The articles are beautifully written, with a professional polish honed by a team of talented science writers (unlike, written by an aging amateur journalist-wannabe; a one-man-band hawking textbooks). My favorite article—one in the spirit of IPMB—is “To Understand the Brain, You Have to Do the Math” by Alexandre Pouget. He concludes
The brain is the most complex computational device we know in the universe…and unless we do the math, unless we use mathematical theories, there’s absolutely no way we’re ever going to make sense of it.
Browsing prompted me to examine how useful Intermediate Physics for Medicine and Biology is for students of neuroscience.
IPMB may not reach the cutting edge of brain science as does, but it does discuss many of the technological devices and mathematical tools needed to explore the frontier.

Intermediate Physics for Medicine and Biology plus is a winning combination.

 A video about by Editor-in-Chief John Morrison

Friday, February 1, 2019

Harry Pennes, Biological Physicist

The first page of Pennes HH (1948) Journal of Applied Physiology, Volume 1, Page 93, superimposed on the cover of Intermediate Physics for Medicine and Biology.
First page of Pennes (1948) J Appl Physiol 1:93-122.
I admire scientists who straddle the divide between physics and physiology, and who are comfortable with both mathematics and medicine. In particular, I am interested in how such interdisciplinary scientists are trained. Many, like myself, are educated in physics and subsequently shift focus to biology. But more remarkable are those (such as Helmholtz and Einthoven) who begin in biology and later contribute to physics.

An Obituary of Harry H. Pennes, published in the April 1964 issue of the American Journal of Psychiatry (Volume 120, Page 1030), superimposed on the cover of Intermediate Physics for Medicine and Biology.
Obituary of Harry H. Pennes.
Which brings me to Harry Pennes. Below I reproduce his obituary published in the April 1964 issue of the American Journal of Psychiatry (Volume 120, Page 1030).
Dr. Harry H. Pennes.—Dr. Harry H. Pennes [born 1918], who had been active in clinical work and research in psychiatry and neurology died in November, 1963, at his home in New York City at the age of 45. Dr. Pennes had worked with Dr. Paul H. Hoch and Dr. James Cattell at the Psychiatric Institute of New York Columbia-Presbyterian Medical Center on new techniques of research and medical experimentation.
Dr. Pennes was born in Philadelphia and studied medicine at the University of Pennsylvania where he received a degree in 1942. In 1944 he came to New York to do research at the Neurological Institute. Soon afterward he took a two-year residency at the New York State Psychiatric Institute, and he later joined the staff as Senior Research Psychiatrist. He was also the Research Associate in Psychiatry at Columbia University. At Morris Plains, N. J., Dr. Pennes participated in intensive studies in the Columbia-Greystone Brain Research Project. He did research into chemical warfare from 1953 to 1955 at the Army Chemical Center in Maryland. Later, in Philadelphia, he was Director of Clinical Research for the Eastern Pennsylvania Psychiatric Institute for several years. He subsequently returned to New York a few years ago and resumed private practice.
The first page of Wissler EH (1998) J Appl Physiol 85:35-41, superimposed on the cover of Intermediate Physics for Medicine and Biology.
First page of Wissler (1998).
Before we discuss what’s in his obituary, consider what’s not in it: physics, mathematics, or engineering. Yet, today Pennes is remembered primarily for his landmark contribution to biological physics: the bioheat equation. Russ Hobbie and I analyze this equation in Section 14.11 of Intermediate Physics for Medicine and Biology. In an article titled “Pennes’ 1948 Paper Revisited” (Journal of Applied Physiology, Volume 85, Pages 35-41, 1998), Eugene Wissler wrote:
It can be argued that one of the most influential articles ever published in the Journal of Applied Physiology is the “Analysis of tissue and arterial blood temperatures in the resting human forearm” by Harry H. Pennes, which appeared in Volume 1, No. 2, published in August, 1948. Pennes measured the radial temperature distribution in the forearm by pulling fine thermocouples through the arms of nine recumbent subjects. He also conducted an extensive survey of forearm skin temperature and measured rectal and brachial arterial temperatures. The purpose of Pennes’ study was “to evaluate the applicability of heat flow theory to the forearm in basic terms of the local rate of tissue heat production and volume flow of blood.” An important feature of Pennes’ approach is that his microscopic thermal energy balance for perfused tissue is linear, which means that the equation is amenable to analysis by various methods commonly used to solve the heat-conduction equation. Consequently, it has been adopted by many authors who have developed mathematical models of heat transfer in the human. For example, I used the Pennes equation to analyze digital cooling in 1958 and developed a whole body human thermal model in 1961. The equation proposed by Pennes is now generally known either as the bioheat equation or as the Pennes equation.
So, how did a psychiatrist make a fundamental contribution to physics? I don’t know. Indeed, I have many questions about this fascinating man.
  1. Did he work together with a mathematician? No. Pennes was the sole author on the paper. There was no acknowledgment thanking a physicist friend or an engineer buddy. The evidence suggests the work was done by Pennes alone.
  2. Did he merely apply an existing model? No. He was the first to include a term in the heat equation to account for convection by flowing blood. He cited a previous study by Gagge et al., but their model was far simpler than his. He didn’t just adopt an existing equation, but rather developed a new and powerful mathematical model. 
  3. Was the mathematics elementary? No. He solved the heat equation in cylindrical coordinates. The solution of this partial differential equation included Bessel functions with imaginary arguments (aka modified Bessel functions). He didn’t cite a reference about these functions, but introduced them as if they were obvious.
  4. Was his paper entirely theoretical? No. The paper was primarily experimental and the math appeared late in the article when interpreting the results. 
  5. Were the experiments easy? No, but they were a little gross. They required threading thermocouples through the arm with no anesthesia. Pennes claimed the “phlegmatic subjects occasionally reported no unusual pain.” I wonder what the nonplegmatic subjects reported?
  6. Was Pennes’s undergraduate degree in physics? I don’t know.
  7. Did Pennes’s interest in math arise late in his career? No. His famous 1948 paper was submitted a few weeks before his 30th birthday.
  8. Did Pennes work at an institution out of the mainstream that might promote unusual or quirky career paths? No. Pennes worked at Columbia University’s College of Physicians and Surgeons, one of the oldest and most respected medical schools in the country.
  9. Did Pennes pick up new skills while in the military? Probably not. He was 23 years old when the Japanese attacked Pearl Harbor, but I can’t find any evidence he served in the military during World War II. He earned his medical degree in 1942 and arrived at Columbia in 1944.  
  10. Do other papers published by Pennes suggest an expertise in math? I doubt it. I haven’t read them all, but most study how drugs affect the brain. In fact, his derivation of the bioheat equation seems so out-of-place that I’ve entertained the notion there were two researchers named Harry H. Pennes at Columbia University.
  11. Did Pennes’ subsequent career take advantage of his math skills? Again, I am not sure but my guess is no. The Columbia-Greystone Brain Project is famous for demonstrating that lobotomies are not an effective treatment of brain disorders. Research on chemical warfare should require expertise in toxicology. 
  12. How did Pennes die? According to Wikipedia he committed suicide. What a tragic loss of a still-young scientist!
I fear my analysis of Harry Pennes provides little insight into how biologists or medical doctors can contribute to physics, mathematics, or engineering. If you know more about Pennes’s life and career, please contact me (

Even though Harry Pennes’s legacy is the bioheat equation, my guess is that he would’ve been shocked that we now think of him as a biological physicist.