Titan: The Life of John D. Rockefeller

Titan: The Life of John D. Rockefeller, Sr.,
by Ron Chernow.

Recently I listened to an audio recording of Titan: The Life of John D. Rockefeller, Sr. by Ron Chernow. Rockefeller reminds me of Bill Gates: corporate corruption, fantastic fortune, and phenomenal philanthropy. Chernow says that Rockefeller’s “good side was every bit as good as his bad side was bad. Seldom has history produced such a contradictory figure.”

Rockefeller intersects with Intermediate Physics for Medicine and Biology through the Rockefeller Foundation and The Rockefeller Institute for Medical Research, now known as the Rockefeller University. Russ Hobbie and I mention the name “Rockefeller” once in IPMB, a Chapter 6 reference to a report written by neuroscientist Rafael Lorente de Nó, who worked at Rockefeller University for decades.

Davis L Jr, Lorente de Nó R (1947) Contribution to the mathematical theory of the electrotonus. Stud Rockefeller Inst Med Res Repr 131(Part 1):442–496.

Lady Luck, by Warren Weaver.

In Chapter 3 we cite Lady Luck by Warren Weaver, the director of the Division of Natural Sciences at the Rockefeller Foundation. Their website states that in 1932

Warren Weaver comes to the Foundation and during his 27-year association becomes the principal architect of programs in the natural sciences. He sees his task as being “to encourage the application of the whole range of scientific tools and techniques, and specially those which had been so superbly developed in the physical sciences, to the problems of living matter.”

He sounds like an IPMB kind of guy.

Ion Channels of Excitable Membranes,
by Bertil Hille.

In Chapter 9, Russ and I discuss Roderick MacKinnon, who first determined the structure of the potassium channel. MacKinnon leads a laboratory at Rockefeller University, located in Manhattan along the East River about a mile north of the United Nations headquarters. Nowadays students earn graduate degrees from Rockefeller University. Bertil Hille, author of Ion Channels of Excitable Membranes, is an alum.

Rockefeller University hosts the Center for Studies in Physics and Biology, whose website states

The Center for Studies in Physics and Biology was conceived by physicists and biologists to increase communication between their disciplines, with the goal of developing innovative solutions to biological questions. Much of the work at the center aims to understand how physical laws govern the operation of biochemical machinery and the processing of information inside cells. To this end, researchers study both the basic physical properties of biological systems (such as elasticity of DNA and DNA-protein interactions) and the application of physical techniques to the modeling of neural, genetic, and metabolic networks.

Although the research is more microscopic that you would typically find in our book, the Center epitomizes the goal of Intermediate Physics for Medicine and Biology: apply physics and mathematics to research in medicine and biology. I sometimes see the Center advertising for fellows, and suspect it would be an interesting place to work.

John D. Rockefeller,
from Wikipedia.

John D. Rockefeller was one of the greatest philanthropists of all time. Besides Rockefeller University and the Rockefeller Foundation, he helped found both the University of Chicago and Spelman College. His family has carried on his philanthropic tradition. Three years ago, Rockefeller’s grandson David Rockefeller passed away. The university website said

The entire Rockefeller University community deeply mourns the loss of David Rockefeller, our beloved friend and benefactor, Honorary Chairman, and Life Trustee. During its long and storied history, no single individual had a more profound influence on the University than David. His inspired leadership, extraordinary vision, and immense generosity have been essential factors in the University’s success. His integrity, strength, wisdom, and judgment—and especially his unequivocal commitment to excellence—shaped the University and made it the powerhouse of biomedical discovery it is today.

One of the greatest philanthropists of our time, as well as one of the world’s foremost leaders in the spheres of finance, international relations, and public service, David Rockefeller dedicated his life to improving the world and the lives of all who share our planet. David was born in New York City in 1915, the youngest of Abby Aldrich Rockefeller and John D. Rockefeller, Jr.’s six children and a grandson of John D. Rockefeller.

One of my favorite parts of Titan is the story about Rockefeller’s dad, William Rockefeller, a bigamist, con artist, and snake oil salesman. Chernow isn’t fond of Ida Tarbell, the muckraking journalist who wrote influential articles in McClure’s Magazine condemning Standard Oil, the company founded by Rockefeller. Tarbell’s articles led the trust buster Teddy Roosevelt to brake up the monopoly.

Ron Chernow is an excellent writer who’s written fine books about Grant and Washington. He’s best known for his wonderful biography of Alexander Hamilton, which inspired Lin Manuel-Miranda’s musical masterpiece Hamilton.

Listen to Ron Chernow talk about John D. Rockefeller.

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

My favorite song from Hamilton: “It’s Quiet Uptown.”

https://www.youtube.com/watch?v=vjEoOeXId1k

Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential

Roth BJ, “Influence of a Perfusing Bath on the
Foot of the Cardiac Action Potential,”
Circ. Res., 86:e19-e22, 2000.

Twenty years ago this week, I published a Research Commentary in Circulation Research about the “Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential” (Volume 86, Pages e19-e22, 2000). I like this article for several reasons: it’s short and to the point; it’s a theoretical paper closely tied to data; it’s well written; and it challenges a widely-accepted interpretation of an experiment by a major figure in cardiac electrophysiology.

Back in my more pugnacious days, I wouldn’t hesitate to take on senior scientists when I disagreed with them. In this case, I critiqued the work of Madison Spach, a Professor at Duke University and a towering figure in the field. In 1981, Spach led an all-star team that measured cardiac action potentials propagating either parallel to or perpendicular to the myocardial fibers.

Spach MS, Miller WT III, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. “The Discontinuous Nature of Propagation in Normal Canine Cardiac Muscle: Evidence for Recurrent Discontinuities of Intracellular Resistance that Affect the Membrane Currents.” Circulation Research, Volume 48, Pages 39–45, 1981.

Spach et al., “The Discontinuous Nature of
Propagation in Normal Canine Cardiac Muscle:
Evidence for Recurrent Discontinuities of
Intracellular Resistance that Affect the
Membrane Currents,” Circ. Res., 48:39-45, 1981.

They found that the rate-of-rise of the action potential and the time constant of the action potential foot depend on the direction of propagation. Continuous cable theory predicts that the rate-of-rise and time constant should be the same, regardless of direction. Therefore, they concluded, cardiac tissue is not continuous. Instead, they claimed that their experiment revealed the tissue’s discrete structure.

To be sure, cardiac tissue is discrete in a sense. It’s made of individual cells, coupled by intercellular junctions to form a “syncytium.” Often, however, you can average over the cellular structure and treat the tissue as a continuum, just as you can often treat a material as a continuum even through it’s made from discrete atoms. For example, the bidomain model is a continuous description of the electrical properties of a microscopically heterogeneous tissue (See Section 7.9 of Intermediate Physics for Medicine and Biology for more about the bidomain model).

I’m skeptical of Spach’s interpretation of his data, and I’m not convinced that his observations imply the tissue’s discrete nature. I didn’t waste any time making this point in my article; I mention Spach by name in the first sentence of the Introduction. (In all quotes, I don’t include the references.)

In 1981, Spach et al observed a smaller maximum rate of rise of the action potential, V̇_max, and a larger time constant of the action potential foot, τ_foot, during propagation parallel to the myocardiac [sic] fibers (longitudinal) than during propagation perpendicular to the fibers (transverse). They attributed these differences to the discrete cellular structure of the myocardium. Their research has been cited widely and is often taken as evidence for discontinuous propagation in cardiac tissue.

Several researchers have suggested that the observations of Spach et al may be caused by the bath perfusing the tissue rather than the discrete nature of the tissue itself... The purpose of this commentary is to model the experiment of Spach et al using a numerical simulation and to show that the perfusing bath plays an important role in determining the time course of the action potential foot.

I performed a computer simulation of wave fronts propagating through a slab of cardiac tissue that is perfused by a tissue bath. The tissue is represented as a bidomain, so its discrete nature was not incorporated into the model. I found that the rate-of-rise of the action potential is slower when propagation is parallel to the fibers compared to perpendicular to the fibers, just as Spach et al. observed. However, when I eliminated the purfusing bath this effect disappeared and the rate-of-rise was the same in both directions.

My favorite part of the article is in the Discussion, where I summarize my conclusion using a syllogism.

The data of Spach et al are cited widely as evidence for discontinuous propagation in cardiac tissue. Their hypothesis of discontinuous propagation is supported by the following logic: (1) During 1-dimensional propagation in a tissue with continuous electrical properties, the time course of the action potential (including V̇_max and τ_foot) does not depend on the intracellular and interstitial conductivities; (2) experiments indicate that in cardiac tissue V̇_max and τ_foot differ with the direction of propagation and therefore with conductivity; and (3) therefore, the conductivity of cardiac tissue is not continuous. A flaw exists in this line of reasoning: when a conductive bath perfuses the tissue, the propagation is not 1-dimensional. The extracellular conductivity is higher for the tissue near the surface (adjacent to the bath) than it is for the tissue far from the surface (deep within the bulk). Therefore, gradients in V_m exist not only in the direction of propagation, but also in the direction perpendicular to the tissue surface. Reasoning based on the 1-dimensional cable model (such as used in the first premise of the syllogism above) is not applicable.

In biology and medicine, the main purpose of computer simulations is to suggest new experiments, so I proposed one.

One way to distinguish between the 2 mechanisms ([the discrete structure] versus perfusing bath) would be to repeat the experiments of Spach et al with and without a perfusing bath present. The tissue would have to be kept alive when the perfusing bath was absent, perhaps by arterial perfusion. The results … indicate that when the bath is eliminated, the action potential foot should become exponential, with no differences between longitudinal and transverse propagation. Furthermore, the maximum rate of rise of the action potential should increase and become independent of propagation direction. Although this experiment is easy to conceive, it would be susceptible to several sources of error. If V_m were measured optically, the data would represent an average over a depth of a few hundred microns. Because the model predicts that V_m changes dramatically over such distances, the data would be difficult to interpret. Microelectrode measurements, on the other hand, are sensitive to capacitative [sic] coupling to the perfusing bath, and the degree of such coupling depends on the bath depth. The rapid depolarization phase of the action potential is particularly sensitive to electrode capacitance. Although it is possible to correct the data for the influence of electrode capacitance, these corrections would be crucial when comparing data measured at different bath depths.

A later paper by Oleg Sharifov and Vladimir Fast (Heart Rhythm, Volume 3, Pages 1063-1073, 2006) suggests a better way to perform this experiment: use optical mapping but with the membrane dye introduced through the perfusing bath so it stains only the surface tissue. In this case, there is no capacitive coupling (no microelectrode) and little averaging over depth (the optical signal arises from only surface tissue). This would be an important experiment, but it hasn’t been performed yet. Until it is, we can’t resolve the debate over discrete versus continuous behavior. 

The last paragraph in the paper sums it all up. I particularly like the final sentence.

We cannot conclude from our study that [discrete structures] are not important during action potential propagation. Nor can we conclude that discontinuous propagation does not occur (particularly in diseased tissue). These factors may well play a role in propagation. We can conclude, however, that the influence of a perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction... Therefore, differences in action potential shape with direction cannot be taken as definitive evidence supporting discontinuous propagation... if a perfusing bath is present. Finally, without additional experiments, we cannot exclude the possibility that in healthy tissue the difference in the shape of the action potential upstroke with propagation direction is simply an artifact of the way the tissue was perfused.

Has my commentary had much impact? Nope. Compared to other papers I’ve written, this one is a citation dud. It has been cited only 27 times (22 if you remove self-citations); barely once a year. Spach’s 1981 paper has over 800 citations; over 20 per year. Even a response by Spach and Barr (Circ. Res., Volume 86, Pages e23-e28, 2000) to my commentary has almost twice as many citations as my original commentary. Does this difference in citation rate arise because I’m wrong and Spach’s right? Maybe. The only way to know is to do the experiment.

The Future of Low Dose Radiation Research in the United States

In Section 16.12 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the risk of radiation. In recent posts I’ve considered the risk of low-frequency electromagnetic radiation (such as microwaves), but today I’m talking about ionizing radiation (x-rays, gamma rays, and charged particles). A central concept for assessing risk is the linear no-threshold model.

In dealing with radiation to the population at large, or to populations of radiation workers, the policy of the various regulatory agencies has been to adopt the linear no-threshold (LNT) model to extrapolate from what is known about the excess risk of cancer at moderately high doses and high dose rates, to low doses, including those below natural background.

The National Academies Press website
where you can download The Future of Low
Dose Radiation Research in the United States.

Recently, the National Academies Press published the proceedings of a symposium about The Future of Low Dose Radiation Research in the United States. You can download a pdf copy for free, or purchase a paper copy. It begins

Exposures at low doses of radiation, generally taken to mean doses below 100 millisieverts, are of primary interest for setting standards for protecting individuals against the adverse effects of ionizing radiation. However, there are considerable uncertainties associated with current best estimates of risks and gaps in knowledge on critical scientific issues that relate to low dose radiation. Nevertheless, in the United States there is no program that is dedicated to advancing knowledge on low dose radiation exposures. Starting in 1999, the Department of Energy’s (DOE’s) Low Dose Radiation Research Program funded experimental research on cellular and molecular responses to low dose radiation but was terminated in 2016 after ramping down funding over several years. Since then, Congress attempted to re-establish a low dose radiation research program in the United States but negotiations within the government have not yet resulted in its establishment.

The Nuclear and Radiation Studies Board of the National Academies hosted the symposium on The Future of Low Dose Radiation Research in the United States on May 8 and 9, 2019. The goal of the symposium was to provide an open forum for a national discussion on the need for a long-term strategy to guide a low dose radiation research program in the United States.

My favorite part of the symposium was a talk by David Brenner, Director of the Columbia University Center for Radiological Research. His remarks emphasize why the risk of low doses of radiation is an important question. He cites seven specific instances where the validity of the linear no-threshold model impacts public health decisions.

Dr. Brenner argued that there are significant health, social, and economic consequences for both under- and overprotecting against radiation. He and others provided examples of how uncertainties regarding the appropriate level of protection are affecting decisions of national and global significance:

1. Protective action guidelines during the 2011 Fukushima nuclear power plant accident were based on incomplete knowledge about radiation risks at low doses. The differing recommendations for evacuation during the accident issued by the United States and Japanese governments caused confusion and stress, and a number of people died because of the evacuation process. Also, many evacuees still remain displaced or have chosen not to return to areas that have been declared safe for habitation, citing radiation fears.

2. The true health effects of the Fukushima nuclear power plant accident have not been assessed due to incomplete information about radiation risks at low doses. Dr. Brenner said that various attempts to quantify health risks from the accident have reached different conclusions, ranging from no predicted future cancer deaths to hundreds of deaths attributed to the releases from the accident.

3. Cleanup activities at sites that were utilized for nuclear weapons production and testing in the United States are estimated to cost more than $377 billion and take longer than 50 years to complete. DOE has committed to cleaning these sites to below background radiation levels and this commitment is based on incomplete scientific understanding of risks at those levels.

4. Planning for high-level radioactive waste disposal and constructing a deep geological repository is impeded by current requirements for protecting future generations from low dose radiation risks.

5. A global move toward phasing out nuclear power is the result of concerns about the environmental and health consequences of nuclear power plant accidents and the lack of planning for long-term storage of high-level radioactive waste.

6. Risks from radon exposure in homes are uncertain, and better estimates could provide support (or not) for reducing radon exposure by mitigation strategies.

7. Risks associated with medical procedures such as CT scans are not fully understood and therefore a balanced consideration of probable benefits and probable risks is not always possible.

I can think of other examples:

8. I often hear about plans for a manned mission to Mars. Any months-long space mission would expose astronauts to radiation. Are such missions justified given the risks?

9. Health care providers receive small radiation exposures when administering nuclear medicine procedures such as positron emission tomography or single-photon computed emission tomography. At what point does the risk to the doctor or nurse outweigh the benefit to the patient?

10. How much should we worry about, and defend against, terrorist attacks involving wide-spread, low-dose radiation; for instance contamination of a municipal water supply?

11. What is the risk to distant neutral countries during a small-scale nuclear war (for example, the risk to the United States resulting from wind-blown radioactive fallout following a limited nuclear war between India and Pakistan)?

12. The lingering risks of the Chernobyl accident are unclear. First responders at the site received lethal doses of radiation during and immediately following the accident, but people living far away, or working near the site long after the accident, suffer from low-dose exposure, and governments must decide how much effort and expense are justified to mitigate these risks.

Assessing the effect of low doses of radiation is a critical issue. You can’t weigh the benefits against the risks if you don’t know the risks. Intermediate Physics for Medicine and Biology introduces readers to this topic, and the National Academies symposium adds more depth. I know it is a cliché to always whine that “we need more research,” but in this case we really do.

 David Brenner talking about “Living with Uncertainty About Low Dose Radiation Risks” in 2013.

https://www.youtube.com/watch?v=fMDPHj9Pvpg

Takuo Aoyagi and the Discovery of Pulse Oximetry

A pulse oximeter.
Photograph by Rama,
Wikimedia Commons, Cc-by-sa-2.0-fr

The pulse oximeter is among the most significant applications of physics and engineering to medical and biology. In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I describe oximetry.

Near-infrared light in the range 600-1000 nm is used to measure the oxygenation of the blood as a function of time by determining the absorption at two different wavelengths…

Pulse oximeters that fit over a finger are widely used… The basic feature is that arterial blood flow is pulsatile, not continuous. Therefore, measuring the time-varying (AC) signal selectively monitors arterial blood and eliminates the contribution from venous blood and tissue.

Takuo Aoyagi,
From the Engineering and Technology History Wiki.

The pulse oximeter has a long history, but an important milestone was reached by Takuo Aoyagi, a Japanese engineer. He tells his story in “Pulse Oximetry: It’s Invention, Theory, and Future” (Journal of Anesthesia, Volume 17, Pages 259-266, 2003). Below I present excerpts from the article. As you read, notice how Aoyagi transforms an annoying artifact into a breakthrough.

In 1958, I graduated from Niigata University and was employed by Shimadzu Corporation at Kyoto. There, I became interested in patient monitoring. In 1969, I attended the summer school of physiology and measurement organized by H.A. Hoff and L.A. Geddes held at Baylor University, Houston, TX, USA. This was a very valuable experience for me. After that, I visited several institutions to see patient monitoring systems in the USA. Based on these experiences I came to have a belief that the final goal of patient monitoring must be the automatic control of patient treatment…

Just after I was employed by Shimadzu Corporation, I read a report on an interview with Dr. Yoshio Ogino, founder of Nihon Kohden Corporation, in a newspaper. I was deeply impressed by his words: “A skilled physician can treat only a limited number of patients. But an excellent medical instrument can treat countless patients in the world…”

The first order made by our Research and Development division manager, Mr. S. Ouchi, was “Develop something unique.” And he made me leader of a group of several members newly assigned to the division. In those days, research on automatic control of artificial ventilation was being carried out at Tokyo University in the Department of Anesthesiology by Professor H. Yamamura. I was very interested in this project and visited Professor Yamamura’s group. Assistant Professor M. Kamiyama explained the system and told me that, “To make this system a practical product, a reliable continuous measurement of arterial O₂ (Sa_O2 ) and CO₂ is indispensable…”

As a theme of our research group I decided to develop a high-accuracy noninvasive dye densitometer for cardiac output measurement. My new idea was to adopt the principle of Wood’s earpiece oximeter to improve the accuracy of previous earpiece dye densitometers... In Wood’s oximeter, the blood in the ear is expelled pneumatically before the measurement, and light transmitted through the blood is measured and the value is stored as a reference. Next, the blood is readmitted to the ear. After that, the optical density of the blood is calculated continuously against the reference value. Two light wavelengths, red and infrared, are used. The ratio of the optical densities at the two wavelengths is calculated and converted to Sa_O2 by using an empirical calibration curve…

I appointed Mr. K. Yamaguchi chief of this project. An experimental model was constructed. For animal experiments, secondhand monitors and instruments were brought into an old hut… Just after starting the experiments, we noticed a pulsatile variation in the tissue optical density caused by arterial pulsation. This phenomenon made us anxious…

At this point… I thought as follows:

(1) If the optical density of the pulsating portion is measured at two appropriate wavelengths and the ratio of the optical densities is obtained, the result must be equivalent to Wood’s ratio.

(2) In this method, the arterial blood is selectively measured, and the venous blood does not affect the measurement. Therefore, the probe site is not restricted to the ear.

(3) In this method, the reference for optical density calculation is set for each pulse. Therefore, an accidental shift of probe location introduces a short artifact and quick return to normal measurements.

This was my conception of the pulse oximeter principle... It was December 1972.

In the 2007 article “Takuo Aoyagi: Discovery of Pulse Oximetry” (Anesthesia and Analgesia, Volume 105, Pages S1-S4), John Severinghaus writes

Greatness in science often, as here, comes from the well-prepared mind turning a chance observation into a major discovery. “One man’s noise is another man’s signal” commented the respiratory physiologist Jere Mead half a century ago.

Severinghaus concludes

Introduction of pulse oximetry coincided with a 90% reduction in anesthesia-related fatalities. Takuo Aoyagi’s invention was serendipitous. Although he could use the infrared signal to cancel pulsatile “noise” in the dye decay optical signal, hypoxic desaturation spoiled the smooth dye curve. In that noise, he recognized a useful signal—oximetry—because his mind was well prepared to understand what he saw happen. The process of turning his insight into more accurate, convenient and inexpensive saturation monitors still continues in dozens of laboratories and firms, while he continues to innovate.

Intermediate Physics for Medicine and Biology can’t teach readers how to make creative leaps leading to innovations and discoveries. But perhaps it can prepare the mind, so when you encounter a chance observation you can recognize it as an opportunity.

Leonardo Da Vinci, Biological Physicist

Leonardo da Vinci,
by Walter Isaacson.

Leonardo da Vinci (1452 – 1519) is never mentioned in Intermediate Physics for Medicine and Biology, but his presence can be felt throughout. Over the Christmas break I listened to Walter Isaacson’s biography of da Vinci. He’s best known for his famous paintings such as The Last Supper and Mona Lisa. Yet, his accomplishments as a scientist are what tie him to IPMB.

I’m a big fan of Isaacson, and I enjoyed his biographies of Einstein and Jobs (his book about Franklin is on my to-read list). In his introduction, Isaacson describes why he chose to write about da Vinci.

I embarked on this book because Leonardo da Vinci is the ultimate example of the main theme of my previous biographies: how the ability to make connections across disciplines—arts and sciences, humanities and technology—is a key to innovation, imagination, and genius. Benjamin Franklin, a previous subject of mine, was a Leonardo of his era: with no formal education, he taught himself to become an imaginative polymath who was Enlightenment America’s best scientist, inventor, diplomat, writer, and business strategist… Albert Einstein, when he was stymied in his pursuit of his theory of relativity, would pull out his violin and play Mozart… Ada Lovelace, whom I profiled in a book on innovators, combined the poetic sensibility of her father, Lord Byron, with her mother’s love of the beauty of math to envision a general-purpose computer. And Steve Jobs climaxed his product launches with an image of street signs showing the intersection of the liberal arts and technology. Leonardo was his hero.

Drawings of blood vessels,
by Leonardo da Vinci.
Credit: Wellcome Collection,
CC BY.

In Chapter 14 of IPMB, Russ Hobbie and I describe the many different medical imaging techniques used to study atherosclerosis: the narrowing of an artery. I learned from Isaacson that da Vinci was the first to understand this deadly disease. He figured it out during his autopsy of a man who claimed, just before died, that he was over one hundred years old.

In his quest to figure out how the centenarian died, Leonardo made a significant scientific discovery: he documented the process that leads to arteriosclerosis, in which the walls of arteries are thickened and stiffened by the accumulation of plaque-like substances. “I made an autopsy in order to ascertain the cause of so peaceful a death, and found that it proceeded from weakness through the failure of blood and of the artery that feeds the heart and the other lower members, which I found to be very dry, shrunken, and withered,” he wrote. Next to a drawing of the veins in the right arm, he compared the centenarian’s blood vessels to those of a two-year-old boy who also died at the hospital. He found those of the boy to be supple and unconstricted, “contrary to what I found in the old man.” Using his skill of thinking and describing through analogies, he concluded, “The network of vessels behaves in man as in oranges, in which the peel becomes tougher and the pulp diminishes the older they become.”

I’m standing in front of The American Horse,
inspired by da Vinci’s unfinished Horse sculpture,
at Meijer Gardens in Grand Rapids, Michigan.

One aspect of da Vinci’s career that I hadn’t appreciated before was how many of his projects were unfinished, including paintings such as the Adoration of the Magi and the Battle of Anghiari, as well as his Horse sculpture. Much of his scientific work was incomplete, or at least unpublished. An example was his collaborative research with Marcantonio della Torre, an anatomy professor at the University of Pavia.

Marcantonio died in 1511 of the plague that was devastating Italy that year. It is enticing to imagine what he and Leonardo could have accomplished. One of the things that could have most benefited Leonardo in his career was a partner who would help him follow through and publish his brilliant work. Together he and Marcantonio could have produced a groundbreaking illustrated treatise on anatomy that would have transformed a field still dominated by scholars who mainly regurgitated the notions of the second-century Greek physician Galen. Instead, Leonardo’s anatomy studies became another example of how he was disadvantaged by having few rigorous and disciplined collaborators along the lines of Luca Pacioli, whose text on geometric proportions Leonardo had illustrated. With Marcantonio dead, Leonardo retreated to the country villa of Francesco Melzi’s family to ride out the plague.

I think Isaacson lets da Vinci off the hook too easily. Leonardo needed some of Michael Faraday’s discipline to “Work, Finish, Publish.”

A drawing of the heart, by
Leonardo da Vinci.

Much of Chapter 7 in IPMB is about the heart. da Vinci contributed much to our understanding the heart’s anatomy.

Leonardo’s studies of the human heart, conducted as part of his overall anatomical and dissection work, were the most sustained and successful of his scientific endeavors. Informed by his love of hydraulic engineering and his fascination with the flow of liquids, he made discoveries that were not fully appreciated for centuries…

Leonardo was among the first to fully appreciate that the heart, not the liver, was the center of the blood system. “All the veins and arteries arise from the heart,” he wrote on the page that includes the drawings comparing the branches and roots of a seed with the veins and arteries emanating from the heart. He proved this by showing, in both words and a detailed drawing, “that the largest veins and arteries are found where they join with the heart, and the further they are removed from the heart, the finer they become, dividing into very small branches.” He became the first to analyze how the size of the branches diminish with each split, and he traced them down to tiny capillaries that were almost invisible. To those who would respond that the veins are rooted in the liver the way a plant is rooted in the soil, he pointed out that a plant’s roots and branches emanate from a central seed, which is analogous to the heart.

Leonardo was also able to show, contrary to Galen, that the heart is simply a muscle rather than some form of special vital tissue. Like all the muscles, the heart has its own blood supply and nerves. “It is nourished by an artery and veins, as are other muscles,” he found.

Self portrait,
by Leonardo da Vinci.

One of the greatest contributions of physics and engineering to medicine is artificial heart valves. Again, this work builds on da Vinci’s discoveries, including his research on biomechanics and hydrodynamics.

Leonardo’s greatest achievement in his heart studies, and indeed in all of his anatomical work, was his discovery of the way the aortic valve works, a triumph that was confirmed only in modern times. It was birthed by his understanding, indeed love, of spiral flows. For his entire career, Leonardo was fascinated by the swirls of water eddies, wind currents, and hair curls cascading down a neck. He applied this knowledge to determining how the spiral flow of blood through a part of the aorta known as the sinus of Valsalva creates eddies and swirls that serve to close the valve of a beating heart…

Leonardo’s breakthroughs on heart valves were followed, however, by a failure: not discovering that the blood in the body circulates. His understanding of one-way valves should have made him realize the flaw in the Galenic theory, universally accepted during his time, that the blood is pulsed back and forth by the heart, moving to-and-fro. But Leonardo, somewhat unusually, was blinded by book learning. The “unlettered” man who disdained those who relied on received wisdom and vowed to make experiment his mistress failed to do so in this case. His genius and creativity had always come from proceeding without preconceptions. His study of blood flow, however, was one of the rare cases where he had acquired enough textbooks and expert tutors that he failed to think differently. A full explanation of blood circulation in the human body would have to wait for William Harvey a century later.

Vitruvian Man,
by Leonardo da Vinci.

I’ll let Isaacson sum up the moral of his story. It’s a lesson that is relevant for interdisciplinary scientists working at the intersection between physics and physiology, who draw connections between mathematics and medicine.

The fifteenth century of Leonardo and Columbus and Gutenberg was a time of inventions, exploration, and the spread of knowledge by new technologies. In short, it was a time like our own. That is why we have much to learn from Leonardo. His ability to combine art, science, technology, the humanities, and the imagination remains an enduring recipe for creativity. So, too, was his ease at being a bit of a misfit: illegitimate, gay, vegetarian, left-handed, easily distracted, and at times heretical. Florence flourished in the fifteenth century because it was comfortable with such people. Above all, Leonardo’s relentless curiosity and experimentation should remind us of the importance of instilling, in both ourselves and our children, not just received knowledge but a willingness to question it—to be imaginative and, like talented misfits and rebels in any era, to think different.

The Last Supper, by Leonardo da Vinci.

Mona Lisa, by Leonardo da Vinci.

Listen to Walter Isaacson talk about Leonardo da Vinci on Sunday Morning.
https://www.youtube.com/embed/KJboCFa4iVQ?feature=player_embedded%22%20width=%22320

Significant Advances in Computed Tomography

The journal Medical Physics recently published a virtual issue about “Significant Advances in Computed Tomography.” It’s accessible to all for free and is a wonderful resource for an instructor teaching a class based on Intermediate Physics for Medicine and Biology. Marc Kachelrieß, curator of the virtual issue, writes

It is now 40 years since Allan M. Cormack and Godfrey N. Hounsfield were jointly awarded the Nobel Prize in Physiology or Medicine for the development of computer assisted tomography, today known as computed tomography or simply as CT. Since its introduction in 1972 CT has become the most widespread and the most important tomographic medical imaging modality.

This inaugural virtual issue of the journal Medical Physics was created in honor of the 40^th anniversary of Cormack and Hounsfield’s 1979 Nobel Prize. It is a compilation of the most significant original scientific papers on advances in CT that have been published in our journal. These papers have been selected among the most cited CT articles published in our journal so far, with a focus on clinical relevance. CAD [coronary artery disease] papers were not considered. If there were two or more papers on a similar topic that met all selection criteria the one that was published first was chosen.

This compilation reflects many important CT developments starting with Hounsfield’s Nobel award address on “Computed Medical Imaging” [cited in IPMB]. Some of the topics that are covered include basic image reconstruction technologies, spiral CT, cardiac CT, CBCT [cone beam CT], tube current modulation, 4D respiratory CT, dual-source dual-energy CT, and new technologies such as iterative image reconstruction as well as the future technology of photon counting detector CT.

Thus, this virtual issue provides the reader with an opportunity to reflect on the historical developments of CT and also to gain insights into the hot CT topics of today and of the near future.

Table of Contents:

• “Computed Medical Imaging” by Godfrey N. Hounsfield
• “Optimal Short Scan Convolution Reconstruction for Fan Beam CT” by Dennis L. Parker 
• “Fast Calculation of the Exact Radiological Path for a Three-Dimensional CT Array” by Robert L. Siddon
• “Physical Performance Characteristics of Spiral CT Scanning” by Willi A. Kalender and Arkadiusz Polacin
• “Three‐Dimensional Computed Tomographic Reconstruction Using a C-Arm Mounted XRII: Correction of Image Intensifier Distortion” by Rebecca Fahrig, Michel Moreau, and David Wayne Holdsworth 
• “Electrocardiogram-Correlated Image Reconstruction from Subsecond Spiral Computed Tomography Scans of the Heart” by Marc Kachelriess and Willi A. Kalender 
• “Performance Evaluation of a Multi-Slice CT System” by Cynthia H. McCollough and Frank E. Zink 
• “Dose Reduction in CT by Anatomically Adapted Tube Current Modulation. II. Phantom Measurements” by Willi A. Kalender, Heiko Wolf, and Christoph Suess 
• “Cone-Beam Computed Tomography with a Flat-Panel Imager: Initial Performance Characterization” by David A. Jaffray and Jeff H. Siewerdsen 
• “Calculation of Effective Dose” by Cynthia H. McCollough and Beth A. Schueler 
• “Cone-Beam Volume CT Breast Imaging: Feasibility Study” by Biao Chen and Ruola Ning 
• “4D-CT Imaging of a Volume Influenced by Respiratory Motion on Multi-Slice CT” by Tinsu Pan, Ting-Yim Lee, Eike Rietzel, and George T. Y. Chen 
• “Volume CT with a Flat-Panel Detector on a Mobile, Isocentric C-Arm: Pre-Clinical Investigation in Guidance of Minimally Invasive Surgery” by Jeff H. Siewerdsen, Douglas J. Moseley, Shane Burch, Stuart K. Bisland, Arjan Bogaards, Brian C. Wilson, and David A. Jaffray 
• “A Three-Dimensional Statistical Approach to Improved Image Quality for Multislice Helical CT” by Jean‐Baptiste Thibault, Ken D. Sauer, Charles A. Bouman, and Jiang Hsieh 
• “Prior Image Constrained Compressed Sensing (PICCS): A Method to Accurately Reconstruct Dynamic CT Images from Highly Undersampled Projection Data Sets” by Guang‐Hong Chen, Jie Tang, and Shuai Leng 
• “Improved Dual-Energy Material Discrimination for Dual-Source CT by Means of Additional Spectral Filtration” by Andrew N. Primak, Juan C. Ramirez Giraldo, Xin Liu, Lifeng Yu, and Cynthia H. McCollough 
• “Dual-Source Spiral CT with Pitch up to 3.2 and 75 ms Temporal Resolution: Image Reconstruction and Assessment of Image Quality” by Thomas G. Flohr, Shuai Leng, Lifeng Yu, Tmas Allmendinger, Herbert Bruder, Martin Petersilka, Christian D. Eusemann, Karl Stierstorfer, Bernhard Schmidt, and Cynthia H. McCollough 
• “Vision 20/20: Single Photon Counting X-Ray Detectors in Medical Imaging” by Katsuyuki Taguchi and Jan S. Iwanczyk
• “Photon-Counting CT for Simultaneous Imaging of Multiple Contrast Agents in the Abdomen: An In Vivo Study” by Rolf Symons, Bernhard Krauss, Pooyan Sahbaee, Tyler E. Cork, Manu N. Lakshmanan, David A. Bluemke, and Amir Pourmorteza

These papers support and expand the discussion of computed tomography in Section 16.8 of Intermediate Physics for Medicine and Biology.

To learn more about this virtual issue, and about the history of computed tomography, listen to two videos by Cynthia McCollough, the president of the American Association of Physicists in Medicine. 

Cynthia McCollough introduces the virtual issue about 

“Significant Advances in Computed Tomography,”

published by the journal Medical Physics. 

https://www.youtube.com/watch?v=b_NB-EGmzc4

A video about the history of CT technology.

https://www.youtube.com/watch?v=RSyR8BlEz60

The Isaac Winners

Yesterday was the 100^th anniversary of Isaac Asimov’s birth. Regular readers of this blog know that Asimov had a huge impact on my decision to become a scientist. Although his name never appears in Intermediate Physics for Medicine and Biology, his influence is on every page.

Adding a Dimension,
by Isaac Asimov.

From 1959 to 1992, Asimov wrote a monthly essay for The Magazine of Fantasy & Science Fiction. Of all his writings, this series of essays was his favorite (and mine too). Each time he completed seventeen essays he would collect them in a book. One of these collections, Adding a Dimension, ended with an essay about his list of the ten greatest scientists.

The only scientist who, it seemed to me, indubitably belonged to the list and who would, without a doubt, be on such a list prepared by anyone but a consummate idiot, was Isaac Newton.

But how to choose the other nine?

Asimov needed a name for these awards.

I would be false to current American culture if I did not give the ten winners a named award… To go along with the Oscar, Emmy, Edgar, and Hugo, let us have the Isaac.

In a footnote, he added

If anyone has some wild theory that the choice of the name derives from any source other than Newton, let him try to prove it.

Below I list the Isaac winners in alphabetical order, and note which appear in Intermediate Physics for Medicine and Biology.

• Archimedes is not in IPMB. I suppose Russ Hobbie and I could have mentioned him in Chapter 1 in our section on buoyancy.
• Charles Darwin does not appear in IPMB. In my blog post about Darwin Day, I note that many of the physics principles we discuss—diffusion, fluid dynamics, thermodynamics—constrain how animals evolve, so topics in IPMB impact Darwin’s theory of evolution.
• Albert Einstein is in IPMB by name: once as the unit of a mole of photons, and again for his diffusion-viscosity relationship. As I noted in my blog post “Where’s Albert?,” his influence is felt in our analysis of special relativity and in the quantum theory of light.
• Michael Faraday is one of the leading characters in Chapter 8 of IPMB because of his discovery of electromagnetic induction, which plays the key role in transcranial magnetic stimulation. The unit of capacitance (the farad) and a mole of charge (the Faraday constant) are named after him.
• Galileo is never mentioned in IPMB. In my blog post about the book Galileo’s Daughter, I noted that Galileo analyzed the bones of differently sized animals. He would’ve fit well in the section of Chapter 2 about scaling.
• Antoine Lavoisier is absent. We don’t do much chemistry in IPMB.
• James Maxwell, one of my heroes, is mentioned by name once, in a homework problem in Chapter 8 about Maxwell’s equations.
• Isaac Newton; where do I begin? Russ and I use Newton’s calculus without apology. Newton’s 2^nd law of motion is discussed in several places, but primarily in Chapter 13 on sound and ultrasound. Newton’s law of cooling appears in the homework problems of Chapter 3, his ideas on the nature of light are in Chapter 14, and the unit of force is the newton.
• Louis Pasteur was a great scientist, but isn’t in IPMB.
• Ernest Rutherford was added to the 5th edition of IPMB in a homework problem about his alpha particle scattering experiment. Russ and I discuss the different types of nuclear radiation in Chapter 17, but there we don’t mention Rutherford by name.

Half of the Isaac Award winners appear in Intermediate Physics for Medicine and Biology. Not bad.

I, Robot, by Isaac Asimov.

In honor of Asimov’s centenary, yesterday I reread I, Robot, one of his best science fiction books. Delightful. I’ve read The Foundation Trilogy several times, and I’ve enjoyed his many short stories such as the classic “Nightfall.” I’m not sure how many Asimov books I’ve read, but probably on the order of a hundred.

If you want to learn more about Asimov, read the essay “Asimov at 100: From Epic Space Operas to Rules for Robots, the Prolific Author's Literary Legacy Endures,” by James Gunn. When I was an undergraduate at the University of Kansas, I took a science fiction class taught by Gunn; the topic of my term paper was Asimov’s future history.

I’ll close with the description of Asimov’s birth from In Memory Yet Green: The Autobiography of Isaac Asimov (his 200^th book).

In Memory Yet Green:
The Autobiography of Isaac Asimov.

When my mother went into labor, there was no one to help her, therefore, but a midwife, and the process took three days and two nights, during much of which she walked the floor, leaning on my father. The result of all that was myself, and I was named Isaac after my mother’s dead father. (A Jewish child is, by tradition, named after a dead relative.)

The date of my birth, as I celebrate it, was January 2, 1920. It could not have been later than that. It might, however, have been earlier. Allowing for the uncertainties of the times, of the lack of records, of the Jewish and Julian calendars, it might have been as early as October 4, 1919. There is, however, no way of finding out. My parents were always uncertain and it really doesn’t matter.

I celebrate January 2, 1920, so let it be.

 Happy birthday, Isaac Asimov.

Listen to “Nightfall,” a short story by Isaac Asimov.

https://www.youtube.com/watch?v=aRJO4dYZ4NQ

The Magnetic Field of an Axon: Ampere versus Biot-Savart

In Homework Problem 14 of Chapter 8 in Intermediate Physics for Medicine and Biology, Russ Hobbie and I ask the reader to calculate the magnetic field produced by the action current in a nerve axon using the law of Biot and Savart, and to compare it with the result found using Ampere’s law. This is a useful exercise, but I’ve always been uncomfortable with one aspect of the calculation. I’ll explain what I mean in today’s post.

In the homework problem you assume the intracellular current is uniform along one section of the axon, and is zero elsewhere (this is a big assumption, but it lets you derive an analytical solution). When you calculate the magnetic field using the law of Biot and Savart, you get a smooth, continuous function valid for any position along the axon. However, when you use Ampere’s law the result seems like it should be discontinuous. For some positions the intracellular current contributes to the current enclosed by the Amperian loop, but for other positions the intracellular current is zero and contributes nothing. How can the magnetic field be smooth and continuous if the intracellular current is discontinuous?

Below I’ll show you an elegant way to resolve this paradox. The bottom line is that the magnetic field you calculate using Ampere’s law is the same continuous function that you’d get using the law of Biot and Savart. I’ll change the details so that you don’t solve the homework problem in the book exactly, but the fundamental idea works for the book’s problem too.

Let the intracellular current be I₀ for −b < x < b, and zero elsewhere, where x is the position along the axon (see the figure above). The axon is surrounded by saline with conductivity σ. The calculation consists of four steps: First calculate the extracellular voltage V_e in the saline, then differentiate V_e to find the x-component of the extracellular current density J_x, next integrate the current density across the area of the Amperian loop to get the return current I_ret (that part of the extracellular current that passes through the loop), and finally determine the net current enclosed by the loop and calculate the magnetic field B.

Case 1: x > b

Begin by calculating the magnetic field at point (x,y) where x > b, so you’re in the region where there is no intracellular current threading the Amperian loop (the green circle in the figure above, having radius r). To determine the extracellular voltage, realize that current crosses the membrane at only two locations: x = b (a positive point source when viewed from the extracellular space) and x = −b (a negative point source). The voltage produced by a point source is inversely proportional to the distance, so

(If you don’t follow how I derived this expression, see Section 7.1 in IPMB.)

To find the x-component of the current density, differentiate V_e with respect to x, multiple by σ, and add a minus sign.

The most difficult part of the calculation is integrating the current density over the area enclosed by the loop to find the return current. This is a two-dimensional integral, with an area element of 2πy dy and limits of the integration from 0 to r (see the figure on the right).

You can look up the needed integral in an integral table, evaluate it at the limits, and fill in any missing steps. The result is

The second term in the brackets is equal to minus one and the fourth term is equal to plus one, which cancel. There is no intracellular current for x > b, so the current enclosed by the loop is just the return current. The magnetic field is

(I switched the order of the two surviving terms and brought the minus sign inside the bracket.) This is exactly the solution you get using the law of Biot and Savart; if you don’t believe me, calculate it yourself.

Case 2: −b < x < b

The calculation for the extracellular potential, current density, and return current in the region −b < x < b is exactly as before

Now comes the interesting part. The second term in the brackets is not equal to minus one as it was earlier. Because x < b the numerator is negative, but the denominator is squared inside the square root so it is positive; the term becomes plus one. Because x > −b the fourth term is also equal to plus one, as before (both the numerator and denominator are positive). These two terms no longer cancel, so the return current becomes

This is different than we found for x > b. Don’t panic; remember that the total current enclosed by the loop is the return current plus the intracellular current. In this case, the intracellular current I₀ exactly cancels the +2 term inside the brackets in the expression for I_ret (remember, there is a minus one half in front of the brackets), so the enclosed current is just what we had for the x > b case, and the magnetic field is again

The equation for the magnetic field is the same for any value of x (you can check the x < −b case yourself; you’ll get the same equation). The “magic” comes from the term (x−b)/√(x−b)² switching from negative to positive, which is exactly what it had to do to cancel the intracellular current. The enclosed current is continuous even though the intracellular and return currents are not. The magnetic field calculated using Ampere’s law is a smooth function for all x, and is equivalent to the result obtained using the law of Biot and Savart (as it must be). Nice!

One limitation of this calculation is that the action potential has intracellular current only in one direction; a dipole. For an action potential propagating down an axon, the intracellular current first goes in one direction and then in another as the membrane depolarizes and then repolarizes; a quadrupole.

I’ll leave the calculation for this more complicated current distribution as an exercise for you. I suggest you do the calculation using both the Biot-Savart law and Ampere’s law. Enjoy!