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!

This and That

Most of my blog posts are about a single topic related to Intermediate Physics for Medicine and Biology, but today’s post consists of a dozen brief notes. Read to the end for your Christmas gift.

1. Previously in this blog, I’ve mentioned the website medicalphysicsweb.com. That site no longer exists, but was replaced by a page dedicated to medical physics on the Physics World website. Former medicalphysicsweb editor Tami Freeman is still in charge, and the new site is useful for instructors and students using IPMB. I get updates by email.
2. I taught my Biological Physics class (PHY 3250) this fall at Oakland University, and videos of the class meetings are posted on Youtube. The quality is poor; often the blackboard is difficult to read. But if you want to see how I teach the first half of IPMB, take a look.
3. On the Wednesday before Thanksgiving, my class played Trivial Pursuit IPMB. The students had fun and earned extra credit. Earlier this year my wife and I bought two Trivial Pursuit games—complete with game boards and pieces—at a garage sale for a couple dollars, so I was able to accommodate twelve students. You can download the questions at the IPMB homepage. 
4. In 2012 I wrote about the website iBioMagazine. I no longer can find it, but I believe the website iBiology is related to it. I recommend iBiology for physics students trying to improve their knowledge of biology.
5. Today The Rise of Skywalker opens. It’s the final episode in the Star Wars trilogy of trilogies. I remember watching the first Star Wars movie as a teenager in 1977; I can’t wait to see the latest.
6. From the Oakland University campus you can see the Headquarters and Tech Center of Fiat Chrysler Automobiles. This fall the folks at Chrysler introduced a new advertising blitz called the Dodge Horsepower Challenge. Each week they presented a new physics problem about cars, and those who answered correctly were entered in a drawing for a 2019 Dodge Challenger SRT Hellcat Redeye. They needed a physicist to review their problems and solutions, and somehow I got the job. You can find the problems on Youtube, presented by a colorful wrestler named Goldberg.
7. Lately I’ve been republishing these blog posts on medium.com. Oddly, among my most popular stories on Medium is the one about the Fourier series of the cotangent. It has over 160 reads while others that I think are better have just a handful.
8. The Blogger software keeps its own statistics, and claims that my most popular post is about Frank Netter, with over 6000 page views. I think its popularity has to do with Search Engine Optimization.
9. The IPMB Facebook page now has over 200 members. Thanks everyone, and let’s try to finish 2020 with 220.
10. Regular readers know that my two favorite authors are Isaac Asimov and Charles Dickens. Recently I’ve discovered another: P. G. Wodehouse. His books about Bertie Wooster and Jeeves are hilarious, and a joy to read.
11. If you want to know what books I’m reading, you can follow my Goodreads account. Often books in the category Read More Science become subjects of blog posts.
12. Finally, here’s your Christmas present. Last year Oakland University Professor Andrea Eis organized an event—called Encountering the Rare Book—to highlight the OU Kresge Library’s special collections. I was one of the faculty members Andrea asked to select a book from the collection and write a brief essay about it. I chose A Christmas Carol and my essay is below. A Merry Christmas to you all.

I read A Christmas Carol every December, so I was delighted to find a first edition of Charles Dickens’ classic novella in the Rare Book Collection of Kresge Library. I never tire of Dickens’ “ghostly little book.” I love his language, humor, and wonderfully drawn characters.

I enjoy the Ghosts of Christmas Past and Present best; the Ghost of Christmas Yet to Come frightens me. One of my favorite scenes is when Scrooge’s nephew Fred and the Ghost of Christmas Present collude with Topper to catch Fred’s sister-in-law (the plump one with the lace tucker) during a game of blind man’s bluff. I’m a cheapskate focused on my work, so I have a certain sympathy for Ebenezer. I read the book each year as a reminder to not become a “tight-fisted hand at the grindstone.”

All of us in higher education ought to recall the words of the Ghost of Christmas Present at the end of Stave 3, as he revealed two wretched children hidden in his robes: “This boy is Ignorance. This girl is Want. Beware them both…but most of all beware this boy.”

I sometimes wonder if I should have been born a Victorian. I love their physics—Faraday, Maxwell, and Kelvin are my heroes—as well as their literature. A Christmas Carol was published in 1843, the same year that James Joule measured the mechanical equivalent of heat, George Stokes analyzed incompressible fluids, and Ada Lovelace wrote the first computer program. Holding a first edition in your hands connects you to that time; as if Dickens, like Marley’s Ghost, “sat invisible beside you.” The library’s copy has lovely illustrations, which at that time had to be painstakingly hand-colored.

I intend to continue reading A Christmas Carol each year, with the hope that I, like Scrooge, can “become as good a friend, as good a master, and as good a man, as the good old city knew.”

Encountering the Rare Book, an exhibition celebrating
the Special Collections in Kresge Library at
Oakland University, organized by Andrea Eis.

How Russ Hobbie Came to Write Intermediate Physics for Medicine and Biology

In the preface of Intermediate Physics for Medicine and Biology, Russ Hobbie writes

Between 1971 and 1973 I audited all the courses medical students take in their first 2 years at the University of Minnesota.

I was amazed at the amount of physics I found in these courses and how little of it is discussed in the general physics course. I found a great discrepancy between the physics in some papers in the biological research literature and what I knew to be the level of understanding of most biology majors or premed students who have taken a year of physics. It was clear that an intermediate level physics course would help these students. It would provide the physics they need and would relate it directly to the biological problems where it is useful.

This book is the result of my having taught such a course since 1973…

Want to hear more about how Russ came to write IPMB? You can! Russ was interviewed for the University of Minnesota Oral History Project. Below is an excerpt about the origin of the book.

Interview with Russell Hobbie

Interviewed by Professor Clarke A. Chambers. University of Minnesota

Interviewed on September 29, 1994. University of Minnesota Campus

…I wrote Al Sullivan who was the assistant dean of the Medical School asking if it was possible to snoop around over there. Al asked me to have lunch with him one day—it was in October—and said, “What you really ought to do is to attend Medical School.” I said, “I can’t. I’m director of undergraduate studies in Physics. I’m teaching a full load, which is a course each quarter. There’s just no time to do that.” He said, “You could just audit things and skip the labs.” So, for two years, I did that….

I sat through the remainder of the year in embryology, and biochemistry, and anatomy, and pathology, and physiology, and then, in the second year, the organ systems, the neuro psych, the cardiovascular, the pulmonary, the renal, the dermatology, the bones, the GI [gastrointestinal] ….

I really got a fairly good knowledge there and found that there was just too much physics ever to fit it into the pre-med physics course. I also found that there was a tremendous gap between what we teach the pre-meds, who will take one year of physics and that’s it, and what you found in the physiology and biophysics research literature. I convinced the Physics Department that I ought to try teaching a course to try to fill that gap, a 5000 level course that has a year of general physics and a year of calculus as a prereq[uisite] that would appeal to the physiologists and so on. Probably around 1972 or 1973, I started teaching that course, developing it as I went. That turned into a book [Intermediate Physics for Medicine and Biology] that was published by Wiley in 1978 with a second edition about 1988. I’m trying, without much success, to do a third edition right now….

…after I started teaching the course, I can remember Professor Jack Johnson from Physiology wanted to come and sit it in; and I was quite nervous about this because I was afraid I might get some of the physiology wrong. He reminded me, in no uncertain terms, that I’d been sitting through his course and turnabout really was fair play…

I think that, as I look back at my own career, the thing that I think that was most important, that has certainly given me the greatest intellectual satisfaction is the book.

If you can’t get enough of Russ, watch him in this video about his computer program MacDose.

Russell Hobbie demonstrates MacDose, part 1.

https://www.youtube.com/watch?v=eZGfHBYMuHg&t=8s

Russell Hobbie demonstrates MacDose, part 2.

https://www.youtube.com/watch?v=Rwp8eeKFycQ

Russell Hobbie demonstrates MacDose, part 3.

https://www.youtube.com/watch?v=hB4U7T0gH6M