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.

Teaching Medical Physics

In the journal Physics Education (Volume 41, Pages 301–306, 2006) is an article by Gibson, Cook, and Newing about “Teaching Medical Physics.” They write

Medical Physics provides immediate and accessible examples that can assist in the teaching of a range of science subjects. To help teachers, we have produced a teaching pack that will be sent to all UK secondary schools in June 2006 and will be available from www.teachingmedicalphysics.org.uk. Here we discuss the advantages of teaching using applications drawn from Medical Physics, careers in Medical Physics, and some sources of other Medical Physics-related teaching resources.

Their website contains many excellent color pictures and videos that could be used to augment our static, black and white 4th edition of Intermediate Physics for Medicine and Biology. They aim for a lower level and younger audience and than we do in our book, but their power-point presentations might be useful supplementary aids when introducing some of the topics covered in our text.

The American Journal of Physics

What is my favorite physics journal? Undoubtedly it is the American Journal of Physics. Russ Hobbie and I cite many AJP papers in the 4th edition of Intermediate Physics for Medicine and Biology. In fact, Russ has published over a dozen items in that most wonderful of journals. (I’m still looking for an opportunity to publish something there.) What is my favorite AJP paper of all time? That would be Edward Purcell’s “Life at Low Reynolds Number” (Volume 45, Pages 3–11, 1977). I hand out copies of this paper to my students whenever I teach Chapter 1 of our book, where we discuss the Reynolds number and its role in biology and medicine.

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

Nelson Christensen's article “Medical Physics: the Perfect Intermediate Level Physics Class” (European Journal of Physics, Volume 22, Pages 421–427, 2001) contains a section devoted to textbooks (see my October 5 blog entry for more on Christensen’s paper). He writes

There are numerable good sources and books that one may draw upon for a course like this, however we found no text that covered all of the topics we wanted. Our class primarily used Intermediate Physics for Medicine and Biology (3rd edn) by Hobbie [1]. This book covers a wide array of topics, and has a large number of problems to draw from. The level of the text was, at times, too advanced for undergraduates, and more suitable to graduate students in biomedical engineering. The book also lacks detailed examinations of imaging techniques, especially ultrasound.

Well, the 4th edition contains a new chapter on Sound and Ultrasound. If Christensen liked the “large number of problems,” he’s going to love having 44% more problems in the latest edition. Is the book at times too advanced for undergraduates? The level didn’t change much between the 3rd and 4th editions. We tried to aim the text toward upper level undergraduates. You’ll have to decide for yourself if we hit the mark.