Image Gently

The December 7, 2007 entry of this blog addressed a controversy over the safety of computed tomography scans, particularly for children. In response to these concerns, the Society for Pediatric Radiology, the American Association of Physicists in Medicine, the American College of Radiology, and the American Society of Radiologic Technologists have banded together to establish the Alliance for Radiation Safety in Pediatric Imaging. Its “image gently” website states that

The Alliance for Radiation Safety in Pediatric Imaging—the Image Gently Alliance—is a coalition of health care organizations dedicated to providing safe, high quality pediatric imaging nationwide. The primary objective of the Alliance is to raise awareness in the imaging community of the need to adjust radiation dose when imaging children.

The ultimate goal of the Alliance is to change practice.

The Alliance has chosen to focus first on computed tomography (CT) scans. The dramatic increase in the number of pediatric CT scans performed in the United States in the past five years and the rapid evolution, change and availability of CT technology and equipment well justify this Alliance strategy.

Image Gently offers reasonable recommendations to parents, pediatricians, radiologic technologists, and medical physicists about the risks and benefits of CT scans. While asserting that “there’s no question: CT helps us save kids’ lives!,” it nevertheless provides specific suggestions for reducing radiation dose, such as: “child size the kVp and mA”; “one scan (single phase) is often enough”; and “scan only the indicated area”. Image gently offers such calm, science-based advice on a subject often dominated by emotion and a misunderstanding of risk assessment. You won’t find much physics at the image gently website, but you will benefit from a case study in how to use physics to help patients without scaring them (or hurting them) in the process.

After exploring the image gently website, if you want to know more about how computed tomography works, or about the biological effects of radiation, see Chapter 16 in the 4th edition of Intermediate Physics for Medicine and Biology.

Darwin Day

The Origin of Species,
by Charles Darwin.

Thursday, Feb 12, is Darwin Day: the 200th anniversary of Charles Darwin’s birth. This year is special because it also marks the sesquicentennial of Darwin’s masterpiece The Origin Of Species.

Although Darwin Day is primarily a time to celebrate biology, physics plays two important roles in Darwin’s theory of evolution. First, physics constrains evolution. Natural selection has produced an amazing variety and diversity of organisms, but each and every one obeys the laws of physics. You can dream up all sorts of organisms in your imagination, but some just won't work. Readers of the 4th edition of Intermediate Physics for Medicine and Biology will learn about several of these constraints. For instance, in Chapter 2 Russ Hobbie and I discuss scaling (see my blog entry from August 8, 2008 for an earlier discussion of scaling). One can imagine a giant spider a hundred feet high with thin spider legs, but physics won’t allow this: the spider would be crushed under its own weight (weight scales as the volume, but the strength of the legs scale as the cross-sectional area, so the larger the spider the more difficult it would be to support the weight). In Chapter 4 we show that diffusion is an effective way to transport molecules over short distances, but is a poor method over long distances. One can envision a three-story high single cell—a giant amoeba—but if that cell depends on diffusion to obtain oxygen and get rid of carbon dioxide, it will not survive. So, physics limits biological evolution, and these limitations provide important insights into why animals are designed the way they are.

The second role of physics in the study of evolution comes from the interplay between evolution and astronomy. A famous example is the idea proposed by physicist Luis Alverez that an asteroid slammed into the earth 65 million years ago, leading to the death of the dinosaurs and many other species. I’d like to highlight a different example, in part because it’s new and less familiar, and in part because it’s been developed by researchers in the Department of Physics at the University of Kansas, my undergraduate alma mater (go jayhawks!). Professor Adrian Melott and his colleagues have proposed that gamma-ray bursts may have caused other mass extinctions. In the January 2004 issue of the International Journal of Astrobiology (Volume 3, Pages 55–61), Melott et al. write

Gamma-ray bursts (GRBs) produce a flux of radiation detectable across the observable universe. A GRB within our own galaxy could do considerable damage to the Earth’s biosphere; rate estimates suggest that a dangerously near GRB should occur on average two or more times per billion years. At least five times in the history of life, the Earth has experienced mass extinctions that eliminated a large percentage of the biota. Many possible causes have been documented, and GRBs may also have contributed. The late Ordovician mass extinction approximately 440 million years ago may be at least partly the result of a GRB. A special feature of GRBs in terms of terrestrial effects is a nearly impulsive energy input of the order of 10 s. Due to expected severe depletion of the ozone layer, intense solar ultraviolet radiation would result from a nearby GRB, and some of the patterns of extinction and survivorship at this time may be attributable to elevated levels of UV radiation reaching the Earth. In addition, a GRB could trigger the global cooling which occurs at the end of the Ordovician period that follows an interval of relatively warm climate. Intense rapid cooling and glaciation at that time, previously identified as the probable cause of this mass extinction, may have resulted from a GRB.

On Darwin Day, as you celebrate Charles Darwin and his theory of evolution by natural selection, remember that a knowledge of physics as well as biology is crucial to understanding this important idea. The 4th edition of Intermediate Physics in Medicine and Biology is a good place to obtain the necessary physics background.

Lady Luck

Lady Luck, by Warren Weaver.

At the bottom of page 50 in the 4th edition of Intermediate Physics for Medicine and Biology is a short footnote: “A good book on probability is Weaver (1963).” The reference given at the end of the chapter is to Lady Luck, by Warren Weaver. This book is one of my favorites, and reflects my interest in probability. I particularly enjoyed Weaver’s description (in Chapter 6) of a game that at first glance is counter-intuitive:

Take three identical cards. Make a red mark on both sides of one, a black mark on both side of the second, and mark the third black on one side and red on the other. Mix them up in a hat, pick out a card at random, and put it down on the table without disclosing to yourself or anyone else what color is marked on the concealed side.

Suppose the upper side of the card is marked red. You say to your opponent, “Obviously we are not dealing with the black-black card. That one is clearly eliminated. We definitely have either the red-black card or the red-red card. We shuffled fairly and drew at random, so it is just as likely to be one of these as the other. I will therefore bet you even money that the other side is red.”

It isn’t too hard to find takers, although ... the odds in favor of your bet are not even, but are actually two to one! The catch, of course, is the clause “so it is just as likely to be one as the other.” It is twice as likely that it is the red-red card! Forty years ago, when graduate students had to work for their living, the author used to teach this particular problem, at reasonable rates and using the experimental method, to his college friends.

Weaver is an interesting figure in 20th century mathematics and science, and fits in well with our theme of applying physics to medicine and biology. He was director of the Division of Natural Sciences at the Rockefeller Foundation from 1932 to 1955. According to Wikipedia,

Weaver early understood how greatly the tools and techniques of physics and chemistry could advance knowledge of biological processes, and used his position in the Rockefeller Foundation to identify, support, and encourage the young scientists who years later earned Nobel Prizes and other honors for their contributions to genetics or molecular biology.

When I teach probability (often in the first week of a class on statistical mechanics or quantum mechanics), I like to use the example of playing craps. Weaver analyzes craps in chapter 15 of Lady Luck.

The game of craps furnishes a good example of probability calculations in a gambling game; for craps is sufficiently more complicated than “heads and tails” to raise some nice little problems, but not so complicated (as is bridge, for example) that the calculations are tedious.

It is also interesting for the students, who have visited the casinos and played craps more than I have. (Anyone who understands probability will find gambling at casinos to be financially unwise).

In Intermediate Physics for Medicine and Biology, probability is particularly important in Chapter 3, when Hobbie and I discuss statistical mechanics. Probabilistic ideas also appear throughout the book in the form of the Poisson probability distribution, which we analyze in detail in our Appendix J.

Citation Classic Commentaries

From 1977 to 1993, thousands of Citation Classic Commentaries appeared in Current Contents, a database of journal tables of contents originally published by the Institute of Scientific Information. The full texts of these mostly one-page articles are now available at http://garfield.library.upenn.edu/classics.html. In each article, the author of a highly-cited paper tells the story behind the research and describes how the paper came to be published. I find that these commentaries provide a glimpse into the human side of science. They offer insight into what an author thinks about his own work years after it is completed. I always enjoyed reading them, and wish they were still being written.

Many of these commentaries are related to medical and biological physics. Below I list a dozen that readers of the 4th edition of Intermediate Physics for Medicine and Biology might enjoy. Each link will download a pdf of the commentary.

N Bloembergen, EM Purcell, and RV Pound (1948) “Relaxation Effects in Nuclear Magnetic Resonance Absorption,” Physical Review, Volume 73, Pages 679–712.

EL Hahn (1950 “Spin Echoes,” Physical Review, Volume 80, Pages 580–594.

B Lown, R Amarasingham, and I Neumann (1962) “A New Method for Terminating Cardiac Arrhythmias,” Journal of the American Medical Association, Volume 182, Pages 548–555.

S Meiboom and D Gill (1958) “Modified Spin-Echo Method for Measuring Nuclear Relaxation Times,” Review of Scientific Instruments, Volume 29, Pages 688–691.

AL Hodgkin and AF Huxley (1952) “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve,” Journal of Physiology, Volume 117, Pages 500–544.

JH Hubbell (1969) “Photon Cross Sections, Attenuation Coefficients, and Energy Absorption Coefficients From 10 keV to 100 GeV,” Washington, DC: US Government Printing Office, August 1969. National Standard Reference Data Series Report No. NSRDS-NBS 29. 8Op.

ME Phelps, EJ Hoffman, S-C Huang and DE Kuhl (1978) “ECAT: A New Computerized Tomographic Imaging System for Positron-Emitting Radiopharmaceuticals,” Journal of Nuclear Medicine, Volume 19, Pages 635–647.

FJ Bonte, RW Parkey, KD Graham, J Moore and EM Stokely (1974) “A New Method for Radionuclide Imaging of Myocardial Infarcts,” Radiology, Volume 110, Pages 473– 474.

IR Young, DR Bailes, M Burl, AG Collins, DT Smith, MJ McDonnell, JS Orr, LM Banks, GM Bydder, RH Greenspan and RE Steiner (1982) “Initial Clinical Evaluation of a Whole Body Nuclear Magnetic Resonance (NMR) Tomograph,” Journal of Computer Assisted Tomography, Volume 6, Pages 1–18.

JH Hubbell (1982) “Photon Mass Attenuation and Energy-Absorption Coefficients from 1 keV to 20 MeV,” Internatonal Journal of Applied Radiation and Isotopes, Volume 33, Pages 1269–1290.

PA Bottomley and ER Andrew (1978) “Magnetic Field Penetration, Phase Shift and Power Dissipation in Biological Tissue: Implications for NMR Imaging,” Physics in Medicine and Biology, Volume 23, Pages 630–643.

JW Cooley and JW Tukey (1965) “An Algorithm for the Machine Calculation of Complex Fourier Series,” Mathematics of Computation, Volume 19, Pages 297–301.

Cardiac Bioelectric Therapy

Cardiac Bioelectric Therapy:
Mechanisms and Practical Implications,
Edited by Efimov, Kroll, and Tchou.

In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce some fundamental concepts about the electrical properties of the heart (see, for example, Chapters 7 and 10). A new multi-author book, Cardiac Bioelectric Therapy: Mechanisms and Practical Implications, provides an in depth examination of this topic. In a foreword to the book, Ray Ideker writes

Since pacemakers and defibrillators were developed a little more than 50 years ago, their usage has grown rapidly, so that over 900,000 pacemakers and 200,000 defibrillators are implanted every year throughout the world. During this half century there have been astonishing advances in the efficacy and sophistication of these devices. Yet the devices still have major limitations...

Although there are many books that deal with the practical aspects of pacing and defibrillation, there is a pressing need for a single source that presents current knowledge about the basic mechanisms of cardiac bioelectric theory. This book, edited by Efimov, Kroll, and Tchou [admirably] fulfills this need. The chapters thoroughly and masterfully cover all aspects of this subject and are written by experts in the field... I predict this book will be the standard source that will be consulted both by experienced workers in this area as well as by students and others who wish to learn more about this subject.

I have two chapters in this book: “The Bidomain Theory of Pacing” written with my former graduate student Debbie Janks, now at the University of Vermont College of Medicine, and “Virtual Electrode Theory of Pacing” coauthored with John Wikswo of Vanderbilt University, a long-time collaborator and my PhD dissertation advisor. Other chapters that I find particularly useful are “Bidomain Model of Defibrillation” by Natalia Trayanova and Gernot Plank, “The Generalized Activating Function” by Leslie Tung (who invented the bidomain model of cardiac tissue in his PhD dissertation), “Critical Points and the Upper Limit of Vulnerability for Defibrillation” by Raymond Ideker and Derek Dosdall, and “The Virtual Electrode Hypothesis of Defibrillation” by Crystal Ripplinger and Igor Efimov. This is only a partial list; other excellent chapters are written by a Who’s Who of leaders in the field, such as Craig Henriquez, Steve Knisley, Vladimir Fast, Hrayr Karagueuzian, Niels Otani, Alain Karma, Shiien-Fong Lin, and Wanda Krassowska, among others.

The book covers two topics in detail: the bidomain, a mathematical model of the heart’s electrical properties that I have worked on much in my career, and optical mapping of transmembrane potential. This second topic is an experimental technique that involves a fluorescent dye that is bound to the cell membrane. This amount the dye fluoresces depends on the transmembrane potential, which allows researchers to record an electrical quantity using optical methods.

I can think of only one problem with the book: at $199 it’s expensive (you could get two copies of the 4th edition of Intermediate Physics for Medicine and Biology for that price and still have money left over). But for students and researchers serious about understanding pacemakers and defibrillators, this book is worth the money. For students interested in browsing the book to expand their knowledge, all I can say is try your library, and there’s always interlibrary loan.

The National Institutes of Health

The National Institutes of Health.

About now, you undergraduate students studying from the 4th edition of Intermediate Physics for Medicine and Biology are probably starting to wonder what you’ll be doing this summer. I suggest you consider an internship to do biomedical research at the National Institutes of Health (application deadline: March 1). I can’t think of a better first step toward a career applying physics to medicine and biology.

For seven years (1988–1995), I had the privilege of working at the National Institutes of Health in Bethesda, Maryland. According to Wikipedia:

The National Institutes of Health (NIH) is an agency of the United States Department of Health and Human Services and is the primary agency of the United States government responsible for biomedical and health-related research. The Institutes are responsible for 28%—about $28 billion—of the total biomedical research funding spent annually in the U.S., with most of the rest coming from industry. The NIH is divided into two parts: the “Extramural” parts of NIH are responsible for the funding of biomedical research outside of NIH, while the “Intramural” parts of NIH conduct research. Intramural research is primarily conducted at the main campus in Bethesda.

I was part of the intramural Biomedical Engineering and Instrumentation Program, which no longer exists. (Now Bioengineering has an entire institute, the National Institute of Biomedical Imaging and Bioengineering.) The mission of our group was to provide expertise in physics, engineering, and mathematics, and to collaborate with NIH’s biologists and medical doctors. I learned much during my stay at NIH about how physics is applied to biomedicine. It was the ideal preparation for working on a book like Intermediate Physics for Medicine and Biology.

Doing research at NIH was a joy and an honor, and I highly recommend it to any physicist (or physics student) interested in biomedical applications. Apply for an internship today.

Isaac Asimov

I, Robot, by Isaac Asimov.

Isaac Asimov (1920–1992) was born 89 years ago today. He is best known as a science fiction writer, and is considered one of the “big three” of science fiction (along with Robert Heinlein and Arthur C. Clarke). He was also a great author of science popularizations, and wrote or edited over 500 books.

I started reading Asimov’s nonfiction when in high school, and it had a big influence on me. One of the main reasons I decided to study science in college was because of his books. I particularly enjoyed his collections of essays originally published in The Magazine of Fantasy and Science Fiction. Asimov’s writing covered all areas of science: biology, chemistry, physics, geology, astronomy, and medicine. My personal intellectual journey—from physics to biological physics to coauthor of the 4th edition of Intermediate Physics for Medicine and Biology—began with the scientific liberal education he provided. When I was young, my goal was to read every book Asimov had ever written. I read scores of them, but soon I realized that he was writing them faster than I could read them.

The Foundation Trilogy,
by Isaac Asimov.

Which of Asimov’s books do I recommend? Among his fiction, I suggest  I, Robot and the The Foundation Trilogy. Unfortunately, his science popularizations are a bit dated now, but you might still enjoy many of his books, including his three-volume Understanding Physics, The Genetic Code, The Wellsprings of Life, The Human Body, and The Human Brain. For those wanting an Asimov sampler, try Opus 100, Opus 200, or Opus 300. Asimov aficionados will enjoy his two-volume autobiography In Memory Yet Green and In Joy Still Felt. The Isaac Asimov Home Page has much information including a complete list of his books. One obsessive Asimov fan provides summaries and reviews of all his work.

Readers of Intermediate Physics for Medicine and Biology may sometimes wonder how they will ever obtain the prerequisite background in physics, chemistry, biology and medicine necessary for such an interdisciplinary field of study. My solution was to start by reading Isaac Asimov. I don’t know of any single author who could provide a better introduction to these topics.

Happy Birthday, Dr. Asimov. You left us too soon.

Asimov’s Autobiographies.

Part of my Asimov collection.

 Listen to an interview with Isaac Asimov.
https://www.youtube.com/embed/4gn3MyTE80A 

A Gift For the Readers of Intermediate Physics for Medicine and Biology

The holiday season is a time when we often exchange gifts. My gift to the readers of the 4th edition of Intermediate Physics for Medicine and Biology is a new homework problem. It belongs to the chapter on magnetic resonance imaging, and specifically to Section 18.12 (this section about functional MRI has no homework problems associated with it, so the new one fills the gap), but it also draws heavily on Section 8.1 about the magnetic force on a current, sometimes called the Lorentz force. The purpose of the problem is to determine if you can use MRI and the Lorentz force to detect nerve activation.

Section 18.12

Problem 37 1/2 Suppose your median nerve, having a radius of 2 mm, carries a current density of 10 Amps per square meter over a length of 10 millimeters. (Assume all the axons are simultaneously active, so the current density is uniformly distributed throughout the nerve).

a) You are having a magnetic resonance image taken, and the steady uniform magnetic field has a strength of 4 Tesla and is directed perpendicular to the nerve. Calculate the magnitude and direction of the magnetic force on the nerve.

b) Assume the nerve is held in position by an elastic force equal to the product of k and s, where k is the spring constant of 400 Newtons per meter and s is the distance the nerve is displaced from its equilibrium position. Calculate the displacement of the nerve experiencing the force found in part a.

c) Finally, assume that a magnetic field gradient of 36 milliTesla per meter is present, so that when the nerve moves the distance calculated in part b, it enters a region of different magnetic field strength. Calculate the change in magnetic field that the nerve experiences because of its motion. Calculate the change in resonance angular frequency (assuming you are imaging protons). If the gradient and current last for 15 milliseconds, what is the change in phase of the MRI signal?

Where did I come up with this problem? It is based on a paper that Peter Basser and I recently published, titled “Mechanical Model of Neural Tissue Displacement During Lortenz Effect Imaging,” which appeared in the January 2009 issue of the journal Magnetic Resonance in Medicine (Volume 61, Pages 59–64). The mechanical problem is somewhat more complicated than described in part b of the above problem, but the calculated displacement is similar to what Basser and I find for the more accurate calculation. If you solve the new homework problem correctly, you should obtain a very small displacement, implying a phase shift too small to measure with current technology. The conclusion is that nerve action currents are unlikely to be measurable using this method.

Do you want the solution to the problem? Send me an email (roth@oakland.edu) and I will be happy to supply it.

Happy Holidays!

Benjamin Franklin, Biological Physicist

The First American:
The Life and Times of
Benjamin Franklin,
by Henry Brands.

I recently finished reading H. W. Brands’ biography The First American: The Life and Times of Benjamin Franklin. (Actually, I listened to the book on tape while walking my dog Suki each evening.) I enjoy history and biography, but was not expecting to find any biological physics in the book.

Wrong. Late in Franklin’s life, during his years in France, he played a role in a bizarre episode related to biomagnetism. Brands writes

“Friedrich Anton Mesmer had studied medicine at Vienna during the period when Franklin’s electrical experiments were becoming known on the European continent. Like many of Franklin’s readers from the Poor Richard days, Mesmer believed in astrology; having learned from Franklin how lightning carried celestial energy to earth, he easily concluded that electricity provided an invisible but pervasive fluid that linked the stars to human lives. Unfortunately for both his scientific theory and his medical practice, electricity was unpleasant to patients, sometimes violently so. But Mesmer was resourceful, and substituting magnetism for electricity as the invisible transmitter, he developed a flourishing practice stroking patients with magnets. In time he dispensed with the magnets, replying simply on his own powers of persuasion to release the therapeutic effects of “animal magnetism”...

In March 1784 King Louis appointed a committee of the Paris faculty of medicine to investigate; the distinguished members included Joseph Ignace Guillotin, who would add a word to several languages by his advocacy of the use of a swift and thereby comparatively humane decapitation machine. The doctors decided they needed help from the Academy of Sciences, whereupon Louis added five members, including the great chemist Lavoisier—who would meet his end at the device endorsed by Dr. Guillotin—and the eminent American, Dr. Franklin...

Franklin and the commissioners filed their report [on Mesmer’s activities], with his name heading the list of signatures. A public version was hurried into print, and twenty thousand copies were snatched up. The report declared the claims of animal magnetism unproven; such mitigation of symptoms as appeared were due to the customary causes of self-delusion and ordinary remission.

Voodoo Science,
by Robert Park.

I am not too surprised that Mesmer was able to fool so many for so long in the 1700s, long before Faraday, Maxwell, and others provided a complete understanding of electricity and magnetism, and well before the importance of well controlled, double-blind medical studies was appreciated. What’s disturbing about this tale is that similar hoaxes go on today, at a time when we know so much more about bioelectricity and biomagnetism, and put much more effort into conducting careful clinical trials (for specific examples, see Bob Park’s book Voodoo Science). Such non-scientific activities have a striking similarity to Mesmer’s claims.

How do we combat such nonsense? Knowledge and education is the only way I know. Hopefully readers of the 4th edition of Intermediate Physics for Medicine and Biology will be in position to more effectively detect and expose non-scientific claims. Like Franklin, we must encourage educational and civic measures designed to separate exciting and important scientific developments from unfortunate and unsupportable scientific frauds.

The FDA Approves Transcranial Magnetic Stimulation for Treatment of Depression

In Chapter 8 of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I describe transcranial magnetic stimulation. This technique is a classic example of how fundamental physics can be applied to solve a medical problem. A pulse of current is passed through a coil held near the head. The changing magnetic field produced by this current induces an electric field that excites neurons, thus allowing noninvasive, painless stimulation of the brain. Magnetic simulation was invented in the 1980s by Tony Barker and his colleagues in Great Britain. One of my projects when I worked at the National Institutes of Health in the late 1980s and early 1990s was to calculate the electric field induced in the head by different coil geometries. I had the pleasure of working with leading neurologists like Mark Hallett, Leo Cohen, and others in the intramural program of the National Institute of Neurological Disorders and Stroke, and with engineer Peter Basser (my May 30, 2008 entry to this blog tells the story of how Basser subsequently developed magnetic resonance diffusion tensor imaging).

For many years the main use of magnetic stimulation was as a diagnostic tool to assess diseases of the central nervous system, or as a research method to study how the brain changes over time. But another less well understood use of this technique is for therapy. Transcranial magnetic stimulation made news this fall when the Food and Drug Administration approved its use for treating depression (for more information about this decision, see the brain stimulant: stimulation blog or an article in IEEE Spectrum Online). Magnetic stimulation was first applied as a psychiatric treatment with the goal of improving on or replacing electroconvulsive therapy. The gist of both methods is to stimulate neurons in the brain, and thereby affect brain function. One major difference between electroconvulsive therapy and transcranial magnetic stimulation is that magnetic stimulation does not require a siezure. Electroconvulsive therapy is performed under sedation because in that case the brain must undergo a siezure in order to benefit the patient. The method is effective, but has severe side effects. Magnetic stimulation, on the other hand, is safe but less effective.

On October 8 of this year Neuronetics, a medical device company in Malvern, Pennsylvania, obtained FDA clearance for its Neurostar TMS Therapy for the Treatment of Depression. A recent double blind multisite study, whose results were published in the journal Biological Psychiatry (Volume 62, Pages 1208–1216, 2007), showed a statistically significant improvement in symptoms in patients treated with transcranial magnetic stimulation who had not responded to more traditional treatments for depression, compared to a control group. Despite these promising results, I think the effectiveness of magnetic stimulation as a psychiatric therapy is still an open question. I hope it proves successful, because it would be gratifying to me personally to have worked on a technique that could benefit so many people, but I’ll need to see some confirmation of the initial success before I consider it as a proven treatment. Nevertheless, it certainly makes an interesting case study in the application of physics to medicine and biology.