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.

Term Papers

My friend and the senior author of Intermediate Physics for Medicine and Biology, Russ Hobbie, sent me this blog entry to share with you all:

One of the motivations for developing the course that led to this book is the huge gap between a general physics course and the research literature. Often when I was teaching this course, I had students write a term paper instead of a final exam. The term paper was to take a paper from the research literature and fill in the missing steps. Students selected a candidate research paper early in the term and gave it too me for approval. They could come to me as often as necessary for help understanding the research. The last week of the term they turned in both the research paper and term paper and scheduled a half-hour “oral exam” with me a couple of days later. They knew that I would ask them questions about anything I suspected they did not really understand. I had a grading algorithm that assigned points for the difficulty of the research paper, the clarity of the term paper, and my assessment of how well they understood the research based on the oral exam. I had a lot of informal visits by students the week before the term paper was due. Students seemed to learn a lot, and some of these papers became paragraphs or problems in later editions of our book.

Point/Counterpont

When teaching Medical Physics at Oakland University, I have found an excellent way to expose students to current issues in the field: discuss “Point/Counterpoint” articles from the journal Medical Physics, published by the American Association of Physicists in Medicine. Each issue of Medical Physics contains one 3- or 4-page article discussing a fascinating but controversial claim. The format of each Point/Counterpoint article is a debate between two leading medical physicists (something like the old 60 Minutes TV show segment with the same title, parodied so hilariously on Saturday Night Live.) For instance, the January 2008 issue of Medical Physics debates if “Exposure Limits for Emergency Responders Should be the Same as the Prevailing Limits for Occupational Radiation Workers.” My students seem to enjoy the lively style of these articles, and they have to learn enough medical physics to understand the science and vocabulary underlying the debate. I typically spend 15 minutes discussing one article every Friday afternoon. The Point/Counterpoint articles are a great way to augment our textbook, Intermediate Physics for Medicine and Biology, in a Medical Physics class.

Note added March 2, 2008: You can now download a publication titled Controversies in Medical Physics from http://www.aapm.org/ that contains ten years of Point/Counterpoint articles.

More from the Preface

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

This book... is intended to serve as a text for an intermediate course taught in a physics department and taken by a variety of majors. Since its primary content is physics, I hope that physics faculty who might shy away from teaching a conventional biophysics course will consider teaching it. I also hope that research workers in biology and medicine will find it a useful reference to brush up on the physics they need or to find a few pointers to the current literature in a number of areas of biophysics. (The bibliography in each chapter is by no means exhaustive; however, the references should lead you quickly into a field.) The course offered at the University of Minnesota is taken by undergraduates in a number of majors who want to see more physics with biological applications and by graduate students in physics, biophysical sciences, biomedical engineering, physiology, and cell biology.

Top Ten Biological Physics Books

Each year at this time, we are bombarded by top ten lists, such as “Top Ten News Stories of 2007” or “Top Ten Movies of the Year.” Russ Hobbie and I cite many excellent books in the 4th edition of Intermediate Physics for Medicine and Biology. Below I list ten of my favorites. Other good books are cited in the November 23 entry of my blog.

Random Walks in Biology Howard Berg, 1983, Princeton University Press. This book is simply the best introduction to the role that diffusion plays in biology.

Air and Water Mark Denny, 1993, Princeton University Press. A wonderful book that covers some of the same topics we discuss in our first 10 chapters. It approaches the material from the point of view of a physiologist with some knowledge of physics, compared to our approach as physicists with some knowledge of physiology.

Machines in Our Hearts: The Cardiac Pacemaker, the Implantable Defibrillator, and American Health Care Kirk Jeffrey, 2001, Johns Hopkins University Press. More of a history book than an engineering book, it tells the fascinating story of how pacemakers and defibrillators were developed.

 Electric Fields of the Brain: The Neurophysics of EEG Paul Nunez and Ramesh Srinivasan, 2005, Oxford University Press. The electroencephalogram from a physicists point of view.

Electricity and Magnetism Edward Purcell, 1985, Berkeley Physics Course, Vol. 2, McGraw Hill. Other E and M books may be more comprehensive (for example Griffiths or Jackson), but when I’m looking for insight I go to Purcell.

Statistical Physics Frederick Reif, 1964, Berkeley Physics Course, Vol. 5, McGraw Hill. I admire Reif’s statistical approach to thermodynamics. Much of Chapter 3 in our book follows the same path as Reif. It is a great choice for those looking for an introduction to statistical mechanics.

Div, Grad, Curl, and All That: An Informal Text on Vector Calculus H. M. Schey, 2005, Norton. A gentle introduction to vector calculus. Much more intuitive than other math books I know of.

Scaling: Why is Animal Size so Important? Knut Schmidt-Nielsen, 1984, Cambridge University Press. A delightful discussion of how physics and physiology conspire to constrain how large animals can become. See also his book How Animals Work.




 

Life in Moving Fluids Steven Vogel, 1992, Oxford University Press. One of the best introductions to biological fluid dynamics that I know. Vogel has many other fascinating books, including Vital Circuits about the circulatory system.






 

When Time Breaks Down Arthur Winfree, 1987, Princeton University Press. A book that had a huge influence on my own research on the electrical behavior of the heart. See also his book The Geometry of Biological Time, especially the second edition that contains updated information on cardiac electrophysiology.

Should the Premed Requirements in Physics be Changed?

Nearly 30 years ago, Abraham Liboff and Michael Chopp—both faculty members at Oakland University—published an article in the American Journal of Physics titled “Should the Premed Requirements in Physics be Changed?” (Volume 47, Pages 331–336, 1979). Their conclusions are still relevant today, and eloquently confirm the purpose of Intermediate Physics for Medicine and Biology. Abe and Mike concluded

The reasons usually given for including the physics component in the premedical curriculum include its importance in a liberal arts education, and the use of physics grades as a screening yardstick for admissions committees. However, educators have ignored the wide range of applications of physics to medicine in diverse areas such as physiology, problem solving, quantitation, diagnostic techniques, etc.

Most premeds take physics too late in their undergraduate program to accommodate physics electives. In medical school there is no tradition of specialized physics, as occurs in chemistry and biology. The net result is that medical students are disadvantaged in physics, unable to cope with advances in technology requiring a stronger base than the usual ten hours of undergraduate physics.

The new MCAT examination perhaps signals a change in thinking by the medical community, in that the test goes for towards recognizing the essential role that physics plays in modern medicine. Not only is knowledge of each of the sciences required, but, equally important, problem-solving and quantitative skills are tested, reflecting the sort of techniques emphasized in physics.

To directly address the question of the poor undergraduate physics preparation of future physicians and other health care professionals, we suggest that at least one, and probably, two, semesters of additional physics be added to all premedical programs. This added work should be specialized material in the physics of medicine and should require both a year of calculus and a year of introductory physics as prerequisites.

Technetium Shortage

The shutdown of a nuclear reactor at Chalk River, Ontario has caused a shortage of an isotope of technetium (Tc-99m) used for medical imaging (see the New York Times article for details). What is technetium, and how is it produced? The following is a quote from the 4th edition of Intermediate Physics for Medicine and Biology (page 497).

The most widely used isotope [for medical imaging] is Tc-99m. As its name suggests, it does not occur naturally on earth, since it has no stable isotopes. We consider it in some detail to show how an isotope is actually used... The isotope is produced in the hospital from the decay of its parent, Mo-99 [molybdenum], which is a fission product of U-235 and can be separated from about 75 other fission products. The Mo-99 decays to Tc-99m.

Technetium is made available to hospitals through a “generator” that was developed at Brookhaven National Laboratories in 1957 and is easily shipped. Isotope Mo-99, which has a half-life of 67 h, is adsorbed on an alumina substrate... As the Mo-99 decays, it becomes pertechnetate (TcO4-). Sterile isotonic eluting solution is introduced under pressure above the alumina and passes through after filtration into an evacuated eluate container. After removal of the technetium, the continued decay of Mo-99 causes the Tc-99m concentration to build up again. A generator lasts about a week.