Scholarpedia

Scholarpedia: The Bidomain Model.

Anyone who teaches college students or has teenage children knows that the first place they go to for information is Wikipedia, the free online encyclopedia that anyone can edit. I, too, find Wikipedia useful. It’s extraodinarily simple to search for information, and surprisingly accurate. But sometimes, for technical information, you may prefer a more authoritative source. Now you have it: Scholarpedia. Like Wikipedia, Scholarpedia is online, free, and simple to use. The main difference with Wikipedia is that in Scholarpedia articles are authored and maintained by experts and undergo peer review. Anyone can edit Scholarpedia, but all changes must be approved by the “curator” (often the author) of the article, who’s responsible for its content.

Scholarpedia is just getting started, so it’s incomplete. But one of the first categories added to Scholarpedia was Cardiac Dynamics. Dr. Vadim Biktashev of the Department of Mathematical Sciences at the University of Liverpool is the editor for this category, and has organized many fascinating articles related to this topic. Anyone studying Chapters 7–10 of the 4th edition of Intermediate Physics for Medicine and Biology will find these Scholarpedia articles on cardiac dynamics to be a convenient online source of additional information. I’m the author of an article on the Bidomain Model that describes the electrical properties of cardiac tissue (introduced on page 191 in our book). Other particularly good articles are Cardiac Arrhythmia by Flavio Fenton, Elizabeth Cherry and Leon Glass; Models of Cardiac Cell by Fenton and Cherry; and FitzHugh-Nagumo Model by Eugene Izhikevich and Richard FitzHugh. Another category of interest to readers of Intermediate Physics for Medicine and Biology is Models of Neurons, with an article about Neuronal Cable Theory and a planned article about the Hodgkin-Huxley Model. Also, there are excellent articles on Magnetic Resonance Imaging, Transcranial Magnetic Stimulation, and many more topics. Take advantage of this excellent source to find more in-depth information on specific topics than Russ Hobbie and I could fit into our book.

Even More on "Medical Physics: the Perfect Intermediate Level Physics Class"

In 2001, Nelson Christensen of Carleton College published an article in the European Journal of Physics (Volume 22, Pages 421–427) titled “Medical Physics: The Perfect Intermediate Level Physics Class.” (See the Jan 25, 2008 and the Oct 5, 2007 blog entries for my earlier discussions about this paper.) The primary textbook for the class was the 3rd edition of Intermediate Physics for Medicine and Biology. Below is the introduction to his paper.

Physics is changing the way medicine is practised. While a doctor will still use a stethoscope, a diagnosis now often requires devices that make use of sophisticated physics and engineering. The importance of physics in medicine may be best displayed when a physicist needs to visit their doctor: we seem to be the only people who can intimidate doctors as we are the ones who actually know how their devices work. As a consequence of the technological evolution of the discipline, medical schools are admitting more and more students who major in physics or engineering.

Almost all major engineering schools will now have a department of biomedical engineering. There are numerous opportunities in academia in medical physics and biomedical engineering. Students interested in becoming an academic physicist now have a fast-growing field to aim for, a field that is providing more and more opportunities. The industrial sector in biomedical engineering is also advancing and evolving quickly. Physicists and engineers can find numerous and lucrative opportunities with companies.

With all of these opportunities it is no wonder that undergraduates are very interested in knowing more about medical physics. Partly due to student interest, and partly due to the faculty’s desire to provide interesting physics classes, Carleton College offered an intermediate level course in medical physics. This was a course open to students who have completed the first year physics courses. We deliberately designed the medical physics course so that the curriculum would be advanced, thereby negating the possibility that this course alone would satisfy a pre-medical school requirement. At this level we then attracted physics majors and pre-medical students who had a genuine interest in studying more physics.

Medical Physcis in the News

Teachers and students using the 4th edition of Intermediate Physics for Medicine and Biology might want a simple, enjoyable way to learn about the latest breakthroughs in medical physics. I suggest viewing some of the stories and videos at the website Medical Physics in the News. This site, sponsored by the American Association of Physicists in Medicine, contains 90 second videos about recent medical physics developments. The videos are produced by Discoveries and Breakthroughs Inside Science, a syndicated science and engineering news service for local television newscasts.

For instance, a video from December 2007 titled “Baby Thinking” describes a technique using diffuse optical tomography to study brain activity in children. Diffuse optical tomography is based on the diffusion of infrared and visible light through biological tissue, a topic examined in Chapter 14 of Intermediate Physics for Medicine and Biology. The November 2007 video titled “Safer MRI Scans for Heart Patients” explains how magnetic resonance images can be obtained safely in patients with implanted pacemakers and defibrillators. Pacemakers are described in Chapter 7, and MRI is explained in Chapter 18, of our textbook.

For those teachers who spend a lecture on the technical aspects of, say, optical diffusion may want to end the class with a 90 second video describing a potential application to modern medicine. It could help make the the basic science learned from Intermediate Physics for Medicine and Biology more relevant to the students.

If You Can Solve Only One Differential Equation...

If you can solve only one differential equation, let it be

 dy/dt = k y . 

This equation states that the rate of increase of a quantity y is proportional to the present amount of y. The solution is the exponential function

y = e^kt . 

Exponential growth is extremely important in medicine and biology, and in the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I devote the entire Chapter 2 to this topic.

The exponential function is one of the most important and widely occurring functions in physics and biology. In biology, it may describe the growth of bacteria or animal populations, the decrease of the number of bacteria in response to a sterilization procedure, the growth of a tumor, or the absorption or excretion of a drug... In physics, the exponential function describes the decay of radioactive nuclei, the emission of light by atoms, the absorption of light as it passes through matter, the change in voltage or current in some electrical circuits, the variation of temperature with time as a warm object cools, and the rate of some chemical reactions.

The Essential Exponential!
For the Future of Our Planet,
by Albert Bartlett.

Albert Bartlett has written a fascinating collection of essays about the exponential function: The Essential Exponential! For the Future of Our Planet. He claims that “the greatest shortcoming of the human race is our inability to understand the exponential function.” You can see Bartlett talking about the exponential and its implications for population growth on Youtube.

e: The Story of a Number,
by Eli Maor.

The exponential function is often written using the number e = 2.718... (If you want better precision, go to Google and search for "e"). This may be the most famous number, besides π, that’s not an integer. If you would like to read about the history of e, try Eli Maor’s delightful book  e: The Story of a Number.

 Arithmetic, Population, and Energy, by Albert Bartlett.
https://www.youtube.com/embed/O133ppiVnWY

Magnetic Therapy

I’m a skeptic when it comes to “alternative medicine.” Often the claims of alternative medicine conflict with the basic laws of physics—and in the end, physics always wins. In particular, there are many dubious health claims about the biological effects of electric and magnetic fields. For instance, I don’t know of any research supporting the idea that magnets in your shoes or jewelry have health benefits, nor can I think of any plausible mechanism underlying such an effect. Are there companies that really promote such silliness? Go to Google and search for “magnetic therapy” and you’ll find that, indeed, there are.

Voodoo Science:
The Road from Foolishness to Fraud,
by Robert Park.

Bob Park is a prominent debunker of bogus alternative medicine claims. He discusses magnetic therapy in his book Voodoo Science: The Road from Foolishness to Fraud.

“Natural” remedies [such as magnetic therapy] are presumed by their proponents to be somehow both safer and more powerful than science-based medicine. Fortunately, most natural medicine is in itself relatively harmless, aside from the financial damage done by paying eighty-nine dollars for a refrigerator magnet... It can, however, become dangerous if it leads people to forego needed medical treatment. Worse, alternative medicine reinforces a sort of upside-down view of how the world works, leaving people vulnerable to predatory quacks.

Another source of useful information is the magazine Skeptical Inquirer. In particular, see the article “Magnet Therapy, A Billion-dollar Boondoggle” by Bruce Flamm (July 2006), where he claims that there exists “a worldwide epidemic of useless magnet therapy.” Also, see Stephen Barrett’s article “Magnet Therapy: A Skeptical View” published by Quackwatch, Inc., a nonprofit corporation whose purpose is to combat health-related frauds, myths, fads, fallacies, and misconduct. Barrett’s bottom line is that “there is no scientific basis to conclude that small, static magnets can relieve pain or influence the course of any disease. In fact, many of today’s products produce no significant magnetic field at or beneath the skin’s surface.”
 
How can you distinguish the legitimate from nonsense? I suspect the layman will have a hard time telling the difference between “magnetic therapy” (bogus) and “magnetic stimulation” (a well-understood technique to excite nerves in the brain). The only way I know to sort out the good from the bad is to educate yourself on the underlying physics as it applies to biology and medicine. One place to start is the 4th edition of Intermediate Physics for Medicine and Biology. Whether you consult our book or another source of information, beware of suspicious claims about the benefits of electric and magnetic fields. Bioelectricity and biomagnetism are vibrant and important fields of study (see Chapters 6–9 of our book), but there’s a lot of baloney out there too.

The World is Flat

The World is Flat,
by Thomas Friedman.

I recently finished reading The World Is Flat by Thomas Friedman. This fascinating book is an “account of the great changes taking place in our time, as lightning-swift advances in technology and communications put people all over the globe in touch as never before.” I recommend it highly.

Is the world of medical physics flat? That I can write this blog about the 4th edition of the textbook Intermediate Physics for Medicine and Biology and have it read immediately, anywhere, by anyone in the world is amazing, and suggests how our world is flattening.

One example that Friedman presents is the outsourcing of reading x-rays and MRIs to India and other countries. On pages 15–16, Friedman quotes an email from Bill Brody, president of Johns Hopkins University:

Dear Tom, I am speaking at a Hopkins continuing education medical meeting for radiologists (I used to be a radiologist)... I have just learned that in many small and some medium-sized hospitals in the US, radiologists are outsourcing reading of CAT scans to doctors in India and Australia!!! Most of this evidently occurs at night (and maybe weekends) when the radiologists do not have sufficient staffing to provide in-hospital coverage... Since CAT (AND MRI) images are already in digital format and available on a network with standardized protocol, it is no problem to view the images anywhere in the world... Best, Bill

A 2006 New York Times article by David Leonhardt, “Political Clout in the Age of Outsourcing,” states that

For now, the practical effect on radiology is small. At its highest levels, the United States health care system may be the best the world has ever known. India doesn’t even have many radiologists today, let alone a large number who measure up to American standards. But that’s going to change. Eventually, Indian doctors will be able to do the preliminary diagnoses that are a big part of radiology.

In his editorial “American Radiology and Outsourcing,” published in the journal Radiology (Volume 242, Pages 654–657, 2007), William Reinus writes

...to one degree or another, health care experiences the same market forces as do other industries. Whether in manufacturing, accounting, law, research science, or medicine, ultimately efficient markets will carry business activity to the lowest-cost and highest-quality supplier. At the current time, radiology is particularly vulnerable to outsourcing because of recent technologic developments. Other specialties, such as pathology, may soon follow suit. As the level of education rises in other countries, it is likely that medical tourism will also grow. If nothing else, American medicine should expect some major changes in its way of doing business in the coming years.

Outsourcing can be good or bad, depending on your perspective. Take a look at the website of the company Outsource2India to get the Indian view on outsourcing.

What is the bottom line? Outsourcing in radiology is a complex issue that I cannot resolve here. Generally I favor free trade, so I don’t view these developments with fear. One thing I can say with reasonable certainty is that, like it or not, the world of medical physics is becoming flatter.

Happy Birthday!

Happy birthday to the 4th edition of Intermediate Physics for Medicine and Biology! Determining the precise date to celebrate is difficult, but one year ago this week (March 2) I received an email from my coauthor Russ Hobbie saying that an advance copy of our textbook had arrived at his house. This first anniversary is an appropriate time to thank all our readers for their support and encouragement. Without our dear readers, writing our book would have been a pointless exercise. Russ and I have heard from several instructors who are using our text for a class on biological or medical physics. We are grateful that you chose our book for your class. To the students in those classes, we hope we’ve not caused you too much grief. To all of you who have offered your kind words and compliments, they are greatly appreciated. And a special thank you to those who have pointed out and helped us correct mistakes. You can find a list of known mistakes, and other information, at the book’s website.

Two weeks ago another landmark passed unnoticed. February 21 was the 6-month anniversary of this blog. I will keep posting weekly entries as long as I have anything useful to say (and perhaps longer). I hope the blog has served as a valuable supplement to the book.

Even More from the Preface

From the preface of the 3rd edition of Intermediate Physics for Medicine and Biology, written by Russ Hobbie:

Because the book is intended primarily for students who have taken only one year of physics, I have tried to adhere to the following principles in writing it:

1. Calculus is used without apology...

2. The reader is assumed to have taken physics and to know the basic vocabulary...

3. I have not intentionally left out steps in most derivations....

4. Each subject is approached in as simple a fashion as possible...

Teaching Biological Physics

The March 2005 issue of the magazine Physics Today contains an article by Goldstein, Nelson and Powers about “Teaching Biological Physics.” Many of the ideas they champion apply to classes taught from the 4th edition of Intermediate Physics for Medicine and Biology. Goldstein et al. write

Over the past few years, people trained in physics and working in physics departments have taken an unprecedented interest in biological problems. A host of new experimental and theoretical techniques has opened up the quantitative study of systems ranging from single molecules to networks of simple agents performing complex collective tasks. Many departments have begun aggressive programs to hire faculty into the emerging field of biological physics. Engineering departments, too, are investing in the interface of the life and physical sciences, both in bioengineering and in related areas such as chemical engineering, solid mechanics, and materials.

Not surprisingly, the new faculty members, like their colleagues, are interested in teaching subjects that excite them. Meanwhile, physical-science students are beginning to demand courses relevant to the life sciences. And high-level reports such as the National Research Council's Bio2010 have emerged to stress the importance of quantitative, physics-based thinking for future life scientists...

Mathematical Handbooks

The 4th edition of Intermediate Physics for Medicine and Biology assumes mathematical knowledge through calculus. Some of our readers with a weak math background may wonder where they can look to brush up on long-forgotten facts and formulas. The obvious starting place is the textbook you learned your calculus from. (I hope you are not the type of person who sells their textbooks back to the book store at the end of the semester.) Another place is the appendices in our book, which review many mathematical topics. For those who may need a bit more help, I have the following advice.

Mathematical Handbook
for Formulas and Tables.

If you want an inexpensive, light-weight, easy-to-use reference, I suggest  Schaum's Outline: Mathematical Handbook of Formulas and Tables, 2nd Edition, by Murray Spiegel and John Liu. I use it every day, and it has most of the mathematical information you’ll ever need. The handbook has a large table of integrals, and covers trigonometric and hyperbolic functions, series expansions, Laplace transforms, Fourier analysis, Bessel functions, and Legendre polynomials. The one thing the handbook lacks is information on vector calculus in spherical and cylindrical coordinates. I recommend xeroxing Table 1 from Appendix L of our book and taping it to the inside cover of your Schuam’s Outline.

Handbook of Mathematical Functions,
by Abramowtiz and Stegun.

For those occasions when I need more extensive information, I turn to the  Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, by Abramowitz and Stegun (cited on page 201 of our book). This classic covers many of the same topics as does Schuam’s Outline, but in much more detail. [Note: after posting this blog entry, my graduate student told me that you can download Abramowitz and Stegun online. Look at http://www.math.sfu.ca/~cbm/aands/. Apparently because this book was prepared by employees of the US government, there is no copyright issue to prevent downloading.]
 

Table of Integrals, Series, and Products,
by Gradshteyn and Ryzhik.

When you really need an integral but can’t find it anywhere else, I suggest the Table of Integrals, Series, and Products, Seventh Edition by Gradshteyn and Ryzhik. If you can’t find the integral there, you probably can’t find it anywhere. I have never used the new edition with the CD ROM, but the hardback copy I consult for my most difficult integrals is invaluable. I suggest letting the library buy this one, since you will probably only need it occasionally.