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.