Rounding Off the Cow

In the October 2012 issue of the American Journal of Physics, Dawn Meredith and Jessica Bolker published an article about “Rounding Off the Cow: Challenges and Successes in an Interdisciplinary Physics Course for Life Science Students” (Volume 80, Pages 913–922). The article is interesting, and much of the motivation for their work is nearly identical to that of Russ Hobbie and I in writing the 4th edition of Intermediate Physics for Medicine and Biology. They focus on an introductory physics class, whereas Russ and I wrote an intermediate level textbook. Nevertheless, many of the ideas and challenges are the same. Here, I want to focus on their Table 1, in which they list topics that are emphasized and deemphasized compared to standard introductory classes.

Table I. Changes in topic emphasis compared to standard course

	Semester 1	Semester 2
Included/stressed	Kinematics	Heat transfer
	Dynamics	Kinetic theory of gases
	Static torque	Entropy
	Energy	Diffusion, convection, conduction
	Stress/strain and fracture	Simple harmonic motion
	Fluids (far more)	Waves (sound, optics)
Omitted/de-emphasized	Projectile motion	Heat engines
	Relative motion	Magnetism (less)
	Rotational motion	Induction (qualitatively)
	Statics	Atomic physics (instrumentation)
	Collisions	Relativity
	Newton’s law of gravitation
	Kepler’s laws

How does this list compare with the content of IPMB? We don’t stress kinematics and dynamics much. In fact, most of our mechanics discussion centers on static equilibrium. Interestingly, Meredith and Bolker emphasize static torque, which is absolutely central to our analysis of biomechanics in Chapter 1. Rotational equilibrium and torque is what explains why bones, muscles and tendons often experience forces far larger than the weight of the body. It also underlies our rather extensive discussion of the role of a cane. We discuss mechanical energy in Chapter 1, but energy doesn’t become an essential topic until our Chapter 3 on thermodynamics. We agree completely with Meredith and Bolker’s listing of “stress/strain and fracture” and “Fluids (far more)”, and I second the “far more”. Our Chapter 1 contains a lot of fluid dynamics, including the biologically-important concept of buoyancy, the idea of high and low Reynolds number, and applications of fluid dynamics to the circulatory system.

The time allotted to an introductory physics class is limited, so something must get deemphasized to free up time for topics like fluids. Meredith and Bolker mention projectile motion (we agree, it is nowhere in IPMB), relative motion (not crucial if not covering relativity), and rotational motion (we don’t emphasize this either, except when analyzing the centrifuge). I don’t really understand the omission of statics, because as I said earlier static mechanical equilibrium is crucial for biomechanics. They deemphasize collisions, and so do we, although we do discuss the collision of an electron with a photon when analyzing Compton Scattering in Chapter 15. Newton’s law of gravity and Kepler’s laws of planetary motion are absent from both our book and their class.

In the second semester, Meredith and Bolker stress heat transfer (convection and conduction), the kinetic theory of gases, and entropy. Russ and I discuss all these topics in our Chapter 3. Diffusion is a topic they emphasize, and rightly so. It is a topic that is typically absent from an introductory physics class, but is crucial for biology. We discuss it in detail in Chapter 4 of IPMB. Meredith and Bolker list simple harmonic motion among the topics they stress. We talk about harmonic motion in Chapter 10, but mainly as a springboard for the study of nonlinear dynamics. Much of the analysis of linear harmonic motion is found in IPMB in an appendix. Finally, they stress waves (sound and optics). We do too, mainly in our Chapter 13 about sound and ultrasound; a new chapter in the 4th edition.

Topics they omit or deemphasize in the second semester include heat engines. We barely mention heat engines at the end of Chapter 3, and the well-known Carnot heat engine is never analyzed in our book. Meredith and Bolker deemphasize magnetism and magnetic induction. As a researcher in biomagnetism, I would hate to see these topics go. Russ and I analyze biomagnetism in Chapter 8. However, I could see how one might be tempted to deemphasize these topics; biomagnetic fields are very weak and do not play a large role in either biology or medicine. I personally would keep them in, and they remain an important part of IPMB. They do not stress “Atomic Physics (Instrumentation)” and I am not sure exactly what they mean, especially with their parenthetical comment about instruments. We talk a lot about atomic physics in Chapter 14 on Atoms and Light. Finally, Meredith and Bolker omit relativity, and so do Russ and I, except as needed to understand photons. We never discuss the more traditional phenomena of relativity, such as the Lorentz contraction, time dilation, or simultaneity.

Some topics should get about the same amount of attention as in a traditional class, but with slight changes in emphasis. For instance, I would cover geometrical optics, including lenses (when discussing the eye and eyeglasses) but I would skip mirrors. I would cover nuclear physics, but I would skip fission and fusion, and focus on radioactive decay, including positron decay (positron emission tomography).

I think that Meredith and Bolker provide some useful guidance on how to construct an introductory physics class for students interested in the life sciences. Russ and I aim at an intermediate class for students who have taken a traditional introductory class and want to explore applications to biology and medicine in more detail. Our book is clearly at a higher mathematical level: we use calculus while most introductory physics classes for life science majors are algebra based. But for the most part, we agree with Meredith and Bolker about what physics topics are central for biology majors and pre-med students.

Eleanor Adair (1926-2013)

Eleanor Adair, who studied the health risks of microwave radiation, died on April 20 in Hamden, Connecticut at the age of 86. A 2001 interview with Adair, published in the New York Times, began

Eleanor R. Adair wants to tell the world what she sees as the truth about microwave radiation.

New widely reported studies have failed to find that cellular phones, which use microwaves to transmit signals, cause cancer. And most academic scientists say the microwave radiation that people are exposed to with devices like cell phones is harmless. But still, Dr. Adair knows that many people deeply fear these invisible rays.

She knows that many people hear the word “radiation” and assume that all radiation is dangerous, equating microwaves to the very different X-rays.

Microwaves, she points out, are at the other end of the electromagnetic spectrum from high energy radiation like X-rays and gamma rays. And unlike gamma rays and X-rays, which can break chemical bonds and injure cells, even causing cancer, microwaves, she says, can only heat cells. Of course, if cells get hot enough, they can die, but the heat level has to be closer to that in an oven than the extremely low level from cell phones.

The interview ends with this exchange:

Q. If I were to say to people, “Hey there’s this really cool idea: Why heat your whole house when you could use microwaves to heat yourself?” they would say: “You’ve got to be kidding. Don’t you know that microwaves are dangerous? They can even cause cancer.” What do you say to people who respond like that?

A. I try to educate them in exactly what these fields are. That they are part of the full electromagnetic spectrum that goes all the way from the radio frequency and microwave bands, through infrared, ultraviolet, the gamma rays and all that.

And the difference between the ionizing X-ray, gamma ray region and the microwave frequency is in the quantum energy. The lower you get in frequency the lower you get in quantum energy and the less it can do to the cells in your body.

If you have a really high quantum energy such as your X-rays and ionizing-radiation region of the spectrum, this energy is high enough that it can bump electrons out of the orbit in your cells and it can create serious changes in the cells of your body such that they can turn into cancers and various other things that are not good for you.

But down where we are working, in the microwave band, you are millions of times lower in frequency and there the quantum energy is so low that they can’t do any damage to the cells whatsoever. And most people don’t realize this.

Somehow, something is missing in their basic science education, which is something I keep trying to push. Learn the spectrum. Learn that you’re in far worse shape if you lie out on the beach in the middle of summer and you soak up that ultraviolet radiation than you are if you use your cell phone.

Q. Some people say that with the ever-increasing exposure of the population to microwaves—cell phones have really taken off in the past few years—we need to redouble our research efforts to look for dangerous effects of microwaves on cells and human tissues. Do you agree?

A. No. All the emphasis that we need more research on power line fields, cell phones, police radar—this involves billions of dollars that could be much better spent on other health problems. Because there is really nothing there.

We don’t cite Adair’s research in the 4th edition of Intermediate Physics for Medicine and Biology, but we do cover the interaction of electromagnetic fields with tissue in Chapter 9. Much of our discussion is about powerline (60 Hz) fields, but many of the same considerations apply to microwaves. In our discussion, we do cite Robert Adair, Eleanor’s husband and an emeritus professor of physics at Yale, who shares his wife’s interest in the health effect of microwave radiation.

Adair won the d’Arsonval Award, presented by the Bioelectromagnetics Society, to recognize her accomplishments in the field of bioelectromagnetics. In an editorial announcing the award, Ben Greenebaum writes (Bioelectromagnetics, Volume 29, Page 585, 2008)

It gives me great pleasure to introduce Dr. Eleanor R. Adair, the recipient of the Bioelectromagnetics Society’s 2007 D’Arsonval Award, as she presents her Award Lecture (Fig. 1). Dr. Adair is being honored by the Society for her body of work investigating physiological thermoregulatory responses to radio frequency and microwave fields. Her bioelectromagnetic career began with extensive experimental studies of electromagnetic radiation-induced thermophysiological responses in monkeys and concluded with experiments that accomplished the critical extrapolation of the earlier findings to humans. I believe that this body of work constitutes a majority of the literature on the latter topic.

She spent most of her career as a research scientist at the John B. Pierce Foundation Laboratory at Yale University, but finished it as a scientist at the US Air Force’s Brooks City Base in San Antonio, Texas. As she notes in her D’Arsonval address [Adair, 2008], she took her undergraduate degree at Mount Holyoke College in 1948 and her doctorate in psychology at the University of Wisconsin-Madison in 1955. Interspersed among her academic accomplishments in Madison were others—marriage to Robert Adair and children. We should not forget that combining a research career and family at that time was much rarer and required overcoming greater difficulties than those still encountered today. Those of us who have interacted with Dr. Adair over the years know that she has determination in plenty.

Dr. Adair was a charter member of the Society and was its Secretary-Treasurer (1983–1986) during a difficult time, when the Society decided to replace its first Executive Director with Bill Wisecup. She has also been active outside the Society, both with groups concerned with research into bioelectromagnetic effects and with groups concerned with the implications of these results.

However, it is for her overall scientific contributions to bioelectromagnetics that she is being presented the D’Arsonval Award. The criteria for the Award state that “. . . the D’Arsonval Medal is to recognize outstanding achievement in research in the field of Bioelectromagnetics.” And that is the topic that she will address today in her presentation entitled, “Reminiscences of a Journeyman Scientist.”

For those who want to read Adair's own words, you can find her presentation at:

Adair. E. R. (2008) “Reminiscences of a journeyman scientist: Studies of thermoregulation in non-human primates and humans,”  Bioelectromagnetics  Volume 29, Pages 586–597.

The Lorenz equations and chaos

Fifty years ago, Edward Lorenz (1917–2008) published an analysis of Rayleigh-Benard convection that began the study of a field of mathematics called chaos theory. In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I introduce chaos by analyzing the logistic map, which

is an example of chaotic behavior or deterministic chaos. Deterministic chaos has four important characteristics: 1. The system is deterministic, governed by a set of equations that define the evolution of the system. 2. The behavior is bounded. It does not go off to infinity. 3. The behavior of the variables is aperiodic in the chaotic regime. The values never repeat. 4. The behavior depends very sensitively on the initial conditions.

The sensitivity to initial conditions is sometimes called the “butterfly effect,” a term coined by Lorenz. His model is a simplified description of the atmosphere, and has implications for weather prediction.

The mathematical model that Lorenz analyzed consists of three first-order coupled nonlinear ordinary differential equations. Because of their historical importance, I have written a new homework problem that introduces Lorenz’s equations. These particular equations don’t have any biological applications, but the general idea of chaos and nonlinear dynamics certainly does (see, for example, Glass and Mackey’s book From Clock’s to Chaos.

Section 10.7

Problem 33 1/2. Edward Lorenz (1963) published a simple, three-variable (x, y, z) model of Rayleigh-Benard convection

dx/dt = σ (y – x)

dy/dt = x (ρ – z) – y

dz/dt = xy – β z

where σ=10, ρ=28, and β=8/3.

(a) Which terms are nonlinear?

(b) Find the three equilibrium points for this system of equations.

(c) Write a simple program to solve these equations on the computer (see Sec. 6.14 for some guidance on how to solve differential equations numerically). Calculate and plot x(t) as a function of t for different initial conditions. Consider two initial equations that are very similar, and compute how the solutions diverge as time goes by.

(d) Plot z(t) versus x(t), with t acting as a parameter of the curve.

Lorenz, E. N. (1963) “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, Volume 20, Pages 130–141.

If you want to examine chaos in more detail, see Steven Strogatz’s excellent book Nonlinear Dynamics and Chaos. He has an entire chapter (his Chapter 9) dedicated to the Lorenz equations.

The story of how Lorenz stumbled upon the sensitivity of initial conditions is a fascinating tale. Here is one version in a National Academy of Sciences Biographical Memoir about Lorenz written by Kerry Emanuel.

At one point, in 1961, Ed had wanted to examine one of the solutions [to a preliminary version of his model that contained 12 equations] in greater detail, so he stopped the computer and typed in the 12 numbers from a row that the computer had printed earlier in the integration. He started the machine again and stepped out for a cup of coffee. When he returned about an hour later, he found that the new solution did not agree with the original one. At first he suspected trouble with the machine, a common occurrence, but on closer examination of the output, he noticed that the new solution was the same as the original for the first few time steps, but then gradually diverged until ultimately the two solutions differed by as much as any two randomly chosen states of the system. He saw that the divergence originated in the fact that he had printed the output to three decimal places, whereas the internal numbers were accurate to six decimal places. His typed-in new initial conditions were inaccurate to less than one part in a thousand.

“At this point, I became rather excited,” Ed relates. He realized at once that if the atmosphere behaved the same way, long-range weather prediction would be impossible owing to extreme sensitivity to initial conditions. During the following months, he persuaded himself that this sensitivity to initial conditions and the nonperiodic nature of the solutions were somehow related, and was eventually able to prove this under fairly general conditions. Thus was born the modern theory of chaos.

To learn more about the life of Edward Lorenz, see his obituary here and here. I have not read Chaos: Making a New Science by James Gleick, but I understand that he tells Lorenz’s story there.

Graduation

Today, my wife Shirley and I will attend the graduation of our daughter Kathy from Vanderbilt University. She is getting her undergraduate degree, with a double major in biology and history.

Kathy spent part of her time in college working with John Wikswo in the Department of Physics. As regular readers of this blog may know, Wikswo was my PhD advisor when I was a graduate student at Vanderbilt in the 1980s. Russ Hobbie and I often cite Wikswo’s work in the 4th edition of Intermediate Physics for Medicine and Biology, for his contributions to both cardiac electrophysiology and biomagnetism. You can see a picture of Kathy and John in an article about undergraduate research in Arts and Science, the magazine of Vanderbilt University’s College of Arts and Science. Interestingly, there are now publications out there with “Roth and Wikswo” among the authors that I had nothing to do with; for example, see poster A53 at the 6th q-bio conference (Santa Fe, New Mexico, 2012). You can watch and listen to Wikswo give his TEDxNashville talk here. Kathy also worked with Todd Graham of the Department of Cell and Developmental Biology at Vanderbilt. This fall, she plans to attend graduate school studying biology at Michigan State University.

Biodamage Via Shock Waves Initiated by Irradiation With Ions

Just two doors down the hall from my office in Hannah Hall of Science at Oakland University is the office of my friend Gene Surdutovich. Gene teaches physics at OU, and is an international expert on the interaction of heavy ions with biological tissue. Recently he and his collaborators have published a review describing their work, titled “Biodamage Via Shock Waves Initiated by Irradiation With Ions,” in the journal Scientific Reports (Volume 3, Article Number 1289). Their abstract states

Radiation damage following the ionising radiation of tissue has different scenarios and mechanisms depending on the projectiles or radiation modality. We investigate the radiation damage effects due to shock waves produced by ions. We analyse the strength of the shock wave capable of directly producing DNA strand breaks and, depending on the ion’s linear energy transfer, estimate the radius from the ion’s path, within which DNA damage by the shock wave mechanism is dominant. At much smaller values of linear energy transfer, the shock waves turn out to be instrumental in propagating reactive species formed close to the ion’s path to large distances, successfully competing with diffusion.

Except for the British spelling, I enjoyed reading this paper very much.

Russ Hobbie and I discuss the interaction of ions with tissue in the 4th edition of Intermediate Physics for Medicine and Biology, in the context of proton therapy.

Protons are also used to treat tumors. Their advantage is the increase of stopping power at low energies. It is possible to make them come to rest in the tissue to be destroyed, with an enhanced dose relative to intervening tissue and almost no dose distally (“downstream”) as shown by the Bragg peak in Fig. 16.51.

Surdutovich and his colleagues note that the Bragg peak occurs for heavier ions too, such as carbon. What is really fascinating about their work is one of the mechanisms they propose. They note that

while the Bragg peak location answers a question of where most of the damage occurs, we are raising a question of how the damage happens… We investigate the effects that stem from a large inhomogeneity of the dose distribution in the vicinity of the Bragg peak on biological damage.

Their hypothesis is that when a carbon ion interacts with tissue, energy is abruptly deposited

within a cylinder of about one nm radius, which is so small that the temperature within this cylinder increases by over 1000 K by 10⁻¹³ s (we will refer to it as the ‘‘hot cylinder’’). This increase of temperature brings about a rapid increase of pressure (up to 1 GPa) compared to the atmospheric pressure outside the cylinder. Such circumstances cause the onset of a cylindrical shock wave described by the strong explosion scenario. The pressure rapidly increases on the wave front and then decreases in the wake.

I find this mechanism to be fascinating. The theory is noteworthy for its multiscale approach: analyzing events spanning a wide range of time, space, and energy scales. Interestingly, their theory also spans multiple chapters in Intermediate Physics for Medicine and Biology: Chapter 1 about pressure, Chapter 3 on temperature and heat, Chapter 4 on diffusion, Chapter 13 on sound, Chapter 15 about the interaction of radiation with tissue, and Chapter 16 about the medical use of radiation. They conclude

The notion of thermomechanical effects represents a paradigm shift in our understanding of radiation damage due to ions and requires re-evaluation of relative biological effectiveness because of collective transport effects for all ions and direct covalent bond breaking by shock waves for ions heavier than argon. These effects will also have to be considered for high-density ion beams, irradiation with intensive laser fields, and other conditions prone to causing high gradients of temperature and pressure on a nanometre scale.

This paper appears in an open access online journal, so you don’t need a subscription to read it. Be sure to look at the paper’s supplementary information, especially the movie showing a molecular dynamics simulation of the shock wave distorting a DNA molecule. And if you read very closely, you will find this nugget appearing in the acknowledgments: “We are grateful to … Bradley Roth who critically read the manuscript.”

By the way, this fall Gene is scheduled to teach PHY 325, Biological Physics, using the textbook….you guessed it….Intermediate Physics for Medicine and Biology.