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.

Is Cell Phone Electromagnetic Radiation Dangerous?

Is electromagnetic radiation from cell phones dangerous? This point is debated in a point/counterpoint article in the December, 2008 issue of the journal Medical Physics. (See my January 11, 2008 entry to this blog for more about point/counterpoint articles). This readable, if somewhat testy, exchange between scientists highlights many of the crucial issues in this debate.

Arguing for the proposition that cell phones are dangerous is Dr. Vini Khurana, a neurosurgeon at the Canberra Hospital in Australia. Khurana appeared on Larry King Live (May 27, 2008) and claimed that cell phones could cause cancer. He writes that “there is a statistically significant elevated odds (about twofold) of developing a glioma or acoustic neuroma on the same side of the head preferred for cell phone use over a duration of exposure [greater than or equal to] 10 years.” He cites the BioInitiative Report: A Rationale for a Biologically-based Public Exposure Standard for Electromagnetic Fields to support his claim.

Arguing against the proposition is Dr. John Moulder of the Medical College of Wisconsin. Moulder, an expert on the biological effects of exposure to non-ionizing radiation, contends that “the current evidence for a causal association between cancer and exposure to radiofrequency (RF) energy is weak and unconvincing.” He cites a study published in the New England Journal of Medicine titled “Cellular-Telephone Use and Brain Tumors” (Volume 344, Pages 79–86, 2001) to support his claim.

Readers of the 4th edition of Intermediate Physics for Medicine and Biology will be familiar with this topic from Chapter 9, Section 10: Possible Effects of Weak External Electric and Magnetic Fields. Our discussion there was centered on the question of 60 Hz power line fields and health hazards, but these considerations also apply to cell phone frequencies.

Where do I stand on this issue? I am skeptical of these claims of cell-phone-induced brain cancer. The key point is that these fields are non-ionizing. Cell phones operate at a frequency of about 850 MHz. The energy of a photon of that frequency is 3.5 millionths of an electron volt (0.0000035 eV). Energies of an electron volt or more are needed to break most chemical bonds. X-ray photons, and even ultraviolet photons, have that much energy, but photons at cell phone frequencies do not have nearly enough energy to break bonds, and most cancers are caused by the breaking of bonds in a DNA molecule. Moreover, the thermal energy of particles at body temperature is about 0.03 electron volts, which is roughly ten thousand times more energy than an 850 MHz photon has. In other words, all the molecules in your body are bouncing around and colliding with your DNA molecules with energies vastly larger than the energy of a cell phone photon. Perhaps there are a whole lot of photons, what then? That is another way of saying that the electromagnetic radiation heats the tissue (like in a microwave oven). Strong electric fields in the MHz and GHz range can heat tissue, that is the main way they can interact with your body, but slight heating doesn’t cause cancer.

Physicist Bob Park, author of the weekly newsletter What’s New, makes a similar case against the danger of biological effects of nonionizing radiation in an editorial published by the Journal of the National Cancer Institute. Khurana’s response to these arguments is that “no known mechanism does not equate to no mechanism.” Perhaps. But without a plausible mechanism, one expects the epidemiological evidence to be compelling and unambiguous. I suggest you read the point/counterpoint article and cited references, and then decide for yourself. One point I am certain about: you need a good understanding of basic physics and its application to medicine and biology in order to sort out complex issues such as these. The 4th edition of Intermediate Physics for Medicine and Biology is one place to gain that knowledge.

Adrian Kantrowitz (1918-2008)

Last week heart surgeon and pacemaker pioneer Andrian Kantrowitz died in Ann Arbor, Michigan. Among his many roles, Kantrowitz was an Adjunct Professor in the Department of Physics here at Oakland University where I work. Soon after I arrived at OU in 1998, Emeritus Professor Norm Tepley and I visited Kantrowitz’s company L.VAD Technology in Detroit, which makes a left ventricular assist device that helps the heart pump blood. In February 2005 I invited Kantrowitz to give our weekly physics colloquium. At the time his health was already fragile and he gave his lecture sitting down. But it was an excellent talk to one of the largest crowds we ever had at our colloquium series.

Machines in Our Hearts: The Cardiac Pacemaker,
the Implantable Defibrillator, and American Health Care,
by Kirk Jeffrey.

Kantrowitz had an inspirational life story. As a young man, he served as a battalion surgeon in World War Two. He later performed the first heart transplant in the United States. He also played a role in the early development of the pacemaker, a topic discussed in Chapter 7 of the 4th edition of Intermediate Physics for Medicine and Biology. Kirk Jeffrey, in his book  Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care, wrote

GE [General Electric] had developed an implantable pacemaker in its electronics laboratory in cooperation with heart surgeon Adrian Kantrowitz of Maimonides Hospital in Brooklyn. This project began in 1960, apparently in response to the announcement of the Chardack-Greatbatch pacemaker. The initial model was implanted in May 1961 and, as was common with these early devices, the designers made improvements based on the experience of the early patients.

The GE pacemakers had one remarkable technological feature—an external control unit that communicated with the implanted generator by magnetic induction. When taped to the skin on the patient's abdomen, the controller enabled the physician to set the pacing rate anywhere between 64 and 120 beats per minute. Kantrowitz viewed rate control as a means to safeguard the elderly patient.

You can learn more about Adrian Kantrowitz from obituaries in the New York Times, the Washington Post and the Los Angeles Times.

Howard Hughes Medical Institute Holiday Lectures on Science

Each year in early December the Howard Hughes Medical Institute presents their Holiday Lectures on Science. Not sure you can make it to Chevy Chase, Maryland for this year’s lectures? Don’t worry, all the lectures are webcast live, and then are available as on-demand webcasts and on DVD.

This year the live webcast is December 4 and 5, starting at 10:00 A.M. each day. The topic is “Making Your Mind: Molecules, Motion, and Memory,” presented by Eric Kandel and Thomas Jessell.

Eric R. Kandel, M.D. and Thomas M. Jessell, Ph.D. of Columbia University will help us understand how the nervous system turns an idea into action—from the complex processing that takes place in the brain to the direct marching orders the spinal cord gives to the muscles. Modern neuroscience equates mind with the organ we call the brain, an astounding network more than 100 billion neurons connected in a vast complicated web. The presenters will help us puzzle out how the brain is organized and identify the seat of human memory. The question of understanding how the brain functions is rivaled by the question of how such a complex network of cells develops in the first place.

I have watched these Holiday Lectures the last couple years, and they are extremely well done. They are aimed at high school students interested in careers in science or medicine. I think that readers of the 4th edition of Intermediate Physics for Medicine and Biology will find them very informative and inspirational.

Topics from previous years (all available as free on-demand webcasts) are

• 2007 AIDS: Evolution of an Epidemic
• 2006 Potent Biology: Stem Cells, Cloning, and Regeneration
• 2005 Evolution: Constant Change and Common Threads

plus many others. Also at the HHMI website are other lectures, animations, videos, virtual labs, and a virtual museum. It is all cool science. The website is ideal for someone trying to get up-to-date on hot topics in medicine and biology. Enjoy.

Virtual Journal of Biological Physics Research

Looking for a way to keep up with the scientific literature in biological physics? Make a habit of perusing the Virtual Journal of Biological Physics Research. The journal’s website states that

this semi-monthly virtual journal contains articles that have appeared in one of the participating source journals and that fall within a number of contemporary topical areas in biological physics research. The articles are primarily those that have been published in the previous month; however, at the discretion of the editors older articles may also appear, particularly review articles. Links to other useful Web resources on biological physics are also provided.

The virtual journal is free and the abstracts are free, but sometimes in order to download a pdf of the full article you need a subscription to the participating source journal. Examples of participating journals are the Biophysical Journal, Physical Review E, and the Proceedings of the National Academy of Sciences. You can sign up to have the virtual journal delivered by email if you prefer. The virtual journal is published by the American Institute of Physics and the American Physical Society.

The fourth edition of Intermediate Physics for Medicine and Biology provides a great introduction to biological physics research up to the year 2005. You can keep abreast of the current literature using the Virtual Journal of Biological Physics Research.

Physics for Future Presidents

Physics for Future Presidents:
The Science Behind the Headlines,
by Richard Muller.

This blog has remained free of politics throughout the fall’s presidential election. Having no intention of injecting partisanship now that the voting is over, I nevertheless would like to find a way to celebrate the election with you all. My solution: write a post about Richard Muller’s recently published book Physics for Future Presidents: The Science Behind the Headlines. I checked out a copy from the Rochester Hills Public Library and started reading it. Those of you familiar with the 4th edition of Intermediate Physics for Medicine and Biology won’t be surprised that I focused on the aspects of Physics for Future Presidents that have biomedical relevance.

I came to the book a skeptic, as I imagined it would be a very elementary, watered down presentation of physics. But after reading it, I came away with a positive impression of the work. It really does capture much of the physics that world leaders will need to know in the 21st century. The introduction begins

Are you intimidated by physics? Are you mystified by global warming, spy satellites, ICBMs, ABMs, fission, and fusion? Do you think all nukes, those in bombs and those in power plants, are basically the same? Are you perplexed by claims that we are running out of fossil fuels when there are counterclaims that we are not? Are you confused by the ongoing debate over global warming, when some prestigious scientists say that the debate is over? Are you baffled, bewildered, and befuddled by physics and high technology?

If so, then you are not ready to be a world leader. World leaders must understand these issues. The moment when you are being told that a terrorist left a dirty bomb hidden in midtown Manhattan is not a good time to have to telephone your local science advisor to find out how bad that situation really is. Nor is it a good time simply to assume the worst, to decide that all government resources must now be pulled off other projects to address this new emergency. You have to know enough to act wisely, quickly, proportionately.

About one-fourth of the book deals with issues related to nuclear physics (in section III, titled “Nukes”). Particularly relevant to readers of Intermediate Physics for Medicine and Biology is the chapter “Radioactivity and Death.” It discusses the biological effects of radiation (using the old fashioned unit of rem instead of the more modern Sievert). I particularly liked its discussion of the “linear hypothesis,” which states that there is no threshold for biological effects of low-dose radiation, a topic Hobbie and I discuss in our Chapter 16. Muller writes

The government asked the National Academy of Sciences to review the question [of the threshold for radiation effects], and they published a report in 2006. They examined all the papers that argued for a threshold effect and concluded that the evidence was not sufficiently compelling to change the policy [of assuming no threshold]. So the US government continues to derive its laws according to the linear hypothesis.

Future presidents should note that that was a policy decision, not a scientific one. Many people have argued that the effects of the policy are not just health, but other central aspects of national policy. Much of the fear of nuclear power, for example, comes from the projections of the number of people who will die of cancer from low levels of radiation. If the policy results in consequences that hurt people in other ways (everything from evacuating their homes to fighting in a war), then the linear hypothesis is no longer the conservative choice. This is policy, not science—at least not yet.

Other medical physics topics the book addresses with this clear, if qualitative, tone are the risk posed by environmental radioactivity, the safety of storing nuclear waste, anthrax attacks (“It turns out that the spread of the spores, and their failure to kill more people, is more related to physics than biology”), and the danger of microwave radiation produced by cell phones (“Much of the fear of microwaves undoubtedly comes from the fact that they share the name radiation with the other, far more dangerous forms, such as gamma radiation. The fear that some people have shown toward such cell phone radiation finds its origin not in physics, but in linguistics”). I would say that much of the book deals with risk analysis, and the impact physics has on estimating risk.

Muller teaches a class based on the book at Berkeley. Videos of his lectures are posted on his class website. The San Francisco Chronicle has an article about his book and lectures, and says that “self-starting students in 35 states and 43 countries have been watching the 90-minute Physics for Future Presidents talks he gives every Tuesday and Thursday morning to a packed lecture hall of 300 undergrads on campus.”
 
I believe that readers of Intermediate Physics for Medicine and Biology—future scientists and engineers—must be able to express many concepts that Muller explores quantitatively through mathematics. Yet, I see his point that future presidents require a qualitative, rather than quantitative, understanding of physics. In any event, I welcome our new president by suggesting that one of the first book he reads (after the 4th edition of Intermediate Physics for Medicine and Biology, of course!) is Physics for Future Presidents. 

 Richard Muller talks about Physics for Future Presidents.
https://www.youtube.com/embed/ocwxNvM6uLU 

The Impact of Physics on Biology and Medicine

For the last few years that I worked at the National Institutes of Health, Harold Varmus was the NIH director. Varmus was a Nobel Prize winner who often rode his bike to work. He began his academic career studying poetry at Amherst College and ended up being awarded the National Medal of Science. He is currently the president of the Memorial Sloan-Kettering Cancer Center.

On March 22, 1999, Varmus gave a Plenary Talk titled “The Impact of Physics on Biology and Medicine” at the Centennial Meeting of the American Physical Society in Atlanta, Georgia. Readers of the 4th edition of Intermediate Physics for Medicine and Biology will find this speech fascinating and inspirational. He began

The organizers of your hundredth birthday party have asked me to describe the impact of your field, physics, on the two fields, biology and medicine, that are most obviously identified with the agency I lead, the National Institutes of Health. They have done me this honor not to recognize any knowledge I might have retained from college course work in your field, but to allow me to discuss one of my convictions about medical research, namely, the opinion that the NIH can wage an effective war on disease only if we—as a nation and a scientific community, not just as a single agency—harness the energies of many disciplines, not just biology and medicine. These allied disciplines range from mathematics, engineering, and computer sciences to sociology, anthropology, and behavioral sciences. But the weight of historical evidence and the prospects for the future place physics and chemistry most prominently among them.

I propose to consider the effects of physics on the medical sciences from three perspectives. First, I will briefly catalog some of the consequences of a simple and obvious connection between physics and medicine, namely, that the human body and its components are physical objects that can be viewed and measured and altered in ways that resemble what a physicist might do with any physical object. Second, I will remind you of an enormously important phase in the history of biology in which physicists transformed the study of living things by helping to discover the principles of heredity. Third, I will describe some contemporary problems in the biomedical sciences that I believe should be inviting challenges to physicists, young and old. In the context of doing this, I will also allude to ways in which the NIH is attempting to ease the path from a formal training in physics to an active investigative role in biomedical sciences.

If you want to read more by Varmus, you can preorder his new book The Art and Politics of Science due out in February. 

Harold Varmus describes how he became a scientist.
https://www.youtube.com/watch?v=ct3bDM6YBEw

Sound and Ultrasound

When Russ Hobbie and I started to prepare the 4th edition of Intermediate Physics for Medicine and Biology, we discussed if we should add any new chapters. After reviewing comments from users of the 3rd edition, we concluded that there was one essential topic not covered in previous editions: medical ultrasound. So, Chapter 13 of the 4th edition is our attempt to describe the physics of sound and ultrasound, as applied to biology and medicine.

Sound (or acoustics) plays two important roles in our study of physics in medicine and biology. First, animals hear sound and thereby sense what is happening in their environment. Second, physicians use high-frequency sound waves (ultrasound) to image structures inside the body. This chapter provides a brief introduction to the physics of sound and the medical uses of ultrasonic imaging. A classic textbook by Morse and Ingard (1968) provides a more thorough coverage of theoretical acoustics, and books such as Hendee and Ritenour (2002) describe the medical uses of ultrasound in more detail.

In Sec. 13.1 we derive the fundamental equation governing the propagation of sound: the wave equation. Section 13.2 discusses some properties of the wave equation, including the relationship between frequency, wavelength, and the speed of sound. The acoustic impedance and its relevance to the reflection of sound waves are introduced in Sec. 13.3. Section 13.4 describes the intensity of a sound wave and develops the decibel intensity scale. The ear and hearing are described in Sec. 13.5. Section 13.6 discusses attenuation of sound waves. Physicians use ultrasound imaging for medical diagnosis, as described in Section 13.7. Ultrasonic imaging can provide information about the flow of blood in the body by using the Doppler effect, as shown in Sec. 13.8.

At 16 pages, this chapter on sound is the shortest in our book. Throughout the 4th edition, we moved many interesting applications into the homework problems, and nowhere is this more evident than in Chapter 13. Many aspects of ultrasonic imaging are only addressed in the problems, so you really need to work them in order to get a full understanding of ultrasound techniques.

Air and Water,
by Mark Denny.

Chapter 13 has the fewest references (only six) of any chapter in our book. To provide some additional guidance, let me comment on some these references. Theoretical Acoustics by Morse and Ingard is excellent but quite mathematical. Don’t look there for a gentle introduction. I always recommend Denny’s Air and Water for insight into biological physics, in this case his Chapter 10, Sound in Air and Water: Listening to the Environment. Hendee and Ritenour's Medical Imaging Physics (4th Edition) has several excellent chapters on medical ultrasound.

Where can you get additional information? First, there is always Wikipedia. Another online source can be found at How Stuff Works. The American Institute of Ultrasound in Medicine has a useful website, and publishes the Journal of Ultrasound in Medicine. Hendee and Ritenour repeatedly cite Zagzebski’s Essentials of Ultrasound Physics. Although I haven’t read it, my understanding is that it is aimed at students who are preparing to take the ARDMS exam. The American Registry for Diagnostic Medical Sonography (ARDMS) administers accreditation examinations in the area of diagnostic medical sonography, and publishes a list of topics covered on the Ultrasound Physics and Instrumentation exam. Another book that I haven’t read but have heard good things about is Diagnostic Ultrasound, by Rumack, Wilson, and Charboneau. At $325, the third edition of this two-volume tome is a bit pricey, but perhaps your library will have a copy. Finally, Russ and I always like to point out good American Journal of Physics articles, such as Mark Denny’s “The physics of bat echolocation” (Volume 72, Pages 1465–1477, 2004). Those brave souls who are teaching medical or biological physics with a lab incorporated into the class may find the paper “Undergraduate experiment to measure the speed of sound in liquid by diffraction of light” (Luna et al., American Journal of Physics, Volume 70, Pages 874–875, 2002) useful.

Theory of Sound,
by Lord Rayleigh.

Before I end, let me acknowledge one physicist who contributed much to our understanding of sound, Lord Rayleigh. I am a big fan of Victorian physicists (such as Faraday, Maxwell, and Kelvin), among whom Rayleigh is one of my favorites. This Nobel Prize winner, who published the two-volume Theory of Sound, was one of the first to discover how humans localize sound. He is one more of a long list of physicists who have made fundamental contributions to biology and medicine.

Note added October 26: A friend of mine, Neb Duric of the Karmanos Cancer Institute, has developed a way to detect breast cancer using ultrasound. For more, see the video on the Medical Physics in the news website.

Nonlinear Dynamics

Nonlinear dynamics is discussed in several chapters in the 4th edition of Intermediate Physics for Medicine and Biology, and particularly in Chapter 10. Where can you go to get a more information about this topic? Several fine books are cited in our references.

Nonlinear Dynamics and Chaos,
by Steven Strogatz.

One book that Russ Hobbie cited in earlier editions of our text is Nonlinear Dynamics and Chaos, by Steven Strogatz. Even though we still cite the book in the 4th edition, I was not really familiar with it until last year, when my daughter Stephanie used it in a class on nonlinear dynamics at the University of Michigan. She loved the book, and recommended it to me. In the preface, Strogatz writes

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. It is based on a one-semester course I’ve taught for the past several years at MIT. My goal is to explain the mathematics as clearly as possible, and to show how it can be used to understand some of the wonders of the nonlinear world... A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.

When Time Breaks Down,
by Art Winfree.

For anyone who reads Intermediate Physics for Medicine and Biology and wants to learn more about nonlinear dynamics, I recommend this delightful text. Strogatz, the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University, was a collaborator and student of one of my heroes, the late Art Winfree. Art’s book When Time Breaks Down had a tremendous influence on my early career. I have not yet read Strogatz’s newest book Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life, but reading it is on my list of things to do.

From Clocks to Chaos,
by Glass and Mackey.

A book that came out when I was working at the National Institutes of Health is Leon Glass and Michael Mackey’s From Clocks to Chaos. While this book may not present the math as elegantly as Strogatz’s book, it does focus specifically on biological and medical problems. In particular, it introduces the idea of a “dynamical diseases”: diseases characterized by abnormal temporal organization.

Dynamics:
The Geometry of Behavior,
by Abraham and Shaw.

When explained well, nonlinear dynamics is a very visual subject. An older book that makes much use of pictures is Dynamics: The Geometry of Behavior by Abraham and Shaw. In fact it could be called a “picture book,” but don’t let that description fool you. The math is presented at a high level, but in a primarily visual way. It was a great help to me when I was first learning the subject.

The Visual Display of Quantitative Information

The Visual Display
of Quantitative Information,
by Edward Tufte.

Early in my graduate school career (back when I used to have time to read widely), a fascinating book was published titled The Visual Display of Quantitative Information. Its author Edward Tufte describes the book as a “celebration of data graphics.” In the introduction, he writes

Modern data graphics can do much more than simply substitute for small statistical tables. At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers—even a very large set—is to look at pictures of those numbers. Furthermore, of all methods for analyzing and communicating statistical information, well-designed graphics are usually the simplest and at the same time the most powerful.

A page from The Visual Display
of Quantitative Information,
by Edward Tufte.

Tufte suggests ways to improve data graphics. For instance, Chapter 4 concludes by summarizing these five principles: 1) Above all else show the data, 2) Maximize the data-ink ratio, 3) Erase non-data-ink, 4) Erase redundant data-ink, and 5) Revise and edit. Chapter 9 offers this recommendation: “Graphical elegance is often found in simplicity of design and complexity of data.” Perhaps Tufte’s poem at the end of Chapter 8 summarizes these ideas more succinctly:

For non-data-ink, less is more.
For data-ink, less is a bore.

Of course, words can’t convey the lessons of this book. You need to see the graphics appearing on every page to appreciate his points.

Many of the readers of the 4th edition of Intermediate Physics for Medicine and Biology will go on to become research scientists, engineers, or medical doctors, and will publish papers full of interesting data. That data will be presented more clearly, simply, and elegantly by following the principles and techniques outlined in The Visual Display of Quantitative Information and Tufte’s other books. 

Listen to Edward Tufte talk about the Art of Visualization.
https://www.youtube.com/watch?v=AdSZJzb-aX8