John Moulder (1945–2022)

John Moulder,
from Khurana et al. (2008) Med. Phys.,
35:5203, with permission from Wiley.

John Moulder, a leading expert in radiation biology, died about a year ago (on July 17, 2022; I wasn’t aware of his death until last week). When Russ Hobbie and I discuss the possible health risks of weak electric and magnetic fields in Intermediate Physics for Medicine and Biology, we cite a website about powerlines and cancer “that unfortunately no longer exists.” (However, in a previous blog post I found that is does still exist.) We also cite several papers that Moulder wrote with his collaborator Ken Foster about potential electromagnetic field hazards, including

Moulder JE, Foster KR (1995) Biological Effects of Power-Frequency Fields as they Relate to Carcinogenesis. Proceedings of the Society for Experimental Biology and Medicine Volume 209, Pages 309–324.

Moulder JE, Foster KR (1999) Is There a Link Between Exposure to Power-Frequency Electric Fields and Cancer? IEEE Engineering in Medicine and Biology Magazine, Volume 18, Pages 109–116.

Moulder JE, Foster KR, Erdreich LS, McNamee JP (2005) Mobile Phones, Mobile Phone Base Stations and Cancer: A Review. International Journal of Radiation Biology, Volume 81, Pages 189–203.

Foster KR, Moulder JE (2013) Wi-Fi and Health: Review of Current Status and Research. Health Physics, Volume 105, Pages 561–575.

Perhaps my favorite of Moulder’s publications is his Point/Counterpoint article in the journal Medical Physics.

Khurana VG, Moulder JE, Orton CG (2008) There is Currently Enough Evidence and Technology Available to Warrant Taking Immediate Steps to Reduce Exposure of Consumers to Cell-Phone-Related Electromagnetic Radiation. Medical Physics, Volume 35, Pages 5203–5206.

Here is how Moulder is introduced in that paper.

Dr. Moulder obtained his Ph.D. in Biology in 1972 from Yale University. Since 1978, he has served on the faculty of the Medical College of Wisconsin, where he directs the NIH-funded Center for Medical Countermeasures Against Radiological Terrorism. His major research interests include the biological basis for carcinogenesis and cancer therapy, biological aspects of human exposure to non-ionizing radiation, and the prevention and treatment of radiation-induced normal tissue injuries. He has served on a number of national advisory groups concerned with environmental health, non-ionizing radiation, and radiological terrorism; and he currently serves as a radiation biology consultant to NASA.

Are Electromagnetic Fields
Making Me Ill?

In my book Are Electromagnetic Fields Making Me Ill? I wrote:

Radiation biologist John Moulder, of the Medical College of Wisconsin, began maintaining a website titled “Power Lines and Cancer FAQs [frequently asked questions],” which exhaustively summarized the evidence pro and con. Although this website is no longer available online, an archived pdf of it is [13]. In a 1996 article published by IEEE Engineering in Medicine and Biology, Moulder reviewed dozens of studies, and concluded that:

Given the relative weakness of the epidemiology, combined with the extensive and unsupportive laboratory studies, and the biophysical implausibility of interactions at relevant field strengths, it is often difficult to see why there is still any scientific controversy over the issue of power-frequency fields and cancer. [14]

13. large.stanford.edu/publications/crime/references/moulder/moulder.pdf. Access date: January 12, 2022. 

14. Moulder JE (1996) Biological Studies of Power-Frequency Fields and Carcinogenesis. IEEE Engineering in Medicine and Biology Magazine, Volume 15, Pages 31–49.

In a special issue of the International Journal of Radiation Biology dedicated to Moulder, Andrea DiCarlo and her colleagues discussed his work on radiological terrorism.

Through his awarded research grant and cooperative agreements from the NIH and beyond, John leaves behind a legacy of excellent, rigorous, and robust scientific findings, research collaborators who benefited from his expertise and dedication, and a cadre of well-trained students. Although it is impossible to list here all the lives that were touched, and the careers that were impacted by John’s influence, the authors can state with certainty that the field of medical preparedness for a radiation public health emergency would not be where it is now without the steadying hand and role played by Dr. Moulder, both in the early days in the program and during his final years as an active researcher. We are grateful for his years of research and join the entire radiation community in mourning the loss of a great investigator and person.

John Moulder, you were a voice of reason in a crazy world. We’ll miss you.

To hear Moulder in his own words, go to times 4:40 and 5:05 in this video about Power Line Fears.

https://www.youtube.com/watch?v=kf7KWkod3Zw

The Biological Physics Major

Today I want to talk to high school students who, when they attend college, might be majoring in biological physics. What does a biological physics major look like? Below I present my vision of a biological physics curriculum.

Foundational Courses

 Mathematics     

• Calculus 1 
• Calculus 2

Chemistry

• Chemistry 1 
• Chemistry 2 

Biology

• Biology 1 
• Biology 2 

Physics

• Physics 1 
• Physics 2
  

These are the core introductory courses that you absolutely must take. The physics class should be calculus-based. All the science classes need to have a laboratory component (whether as part of the introductory class or as a separate laboratory class to be taken concurrently with the lecture course). In a four-year undergraduate career, these classes represent one course per semester. You’ll probably take most of them in your freshman and sophomore years, because they’ll be prerequisites for more advanced courses. These foundational courses are required for just about any science or engineering major (including premed); if unsure what you want to study you can take them first and then decide your major once you know what you like best. 

Some high school students will have advanced placement credits for many of these classes, which is great, but it’s alright if you don’t. I’ll assume, however, that you’re ready to take calculus the first semester of your freshman year. The best thing you can do in high school to prepare for a biological physics major is to take enough math that you are ready for calculus on day one.

Advanced Courses

Mathematics 

• Multivariable Calculus 
• Differential Equations 

Chemistry 

• Organic Chemistry 
• Biochemistry 

Biology 

• Physiology 

Physics 

• Modern Physics 
• Thermodynamics 
• Electricity and Magnetism
  

Ideally you would take all these advanced courses, but there may be too many for that. Students coming in with advanced placement credits might be able to skip the introductory classes and take these instead. Some universities teach Biochemistry in the chemistry department, and some in the biology department. It doesn’t matter, take one. Many schools offer a two-semester sequence of Organic Chemistry. That would be okay, but it’s probably more Organic than you’ll need. In fact, if pressed for time you might skip Organic altogether, assuming you can still enroll in Biochemistry (which is essential) without needing Organic as a prerequisite. There are many biology classes you could add to this list, but I have included only the one I think is crucial: Physiology. 

If your school is like Oakland University, where I taught, you can take Modern Physics, which is basically a third semester of introductory physics with emphasis on modern topics (relativity, quantum mechanics, nuclear physics). If your school doesn’t have such a course, you could just take the physics department’s Quantum Mechanics class instead. I put E&M on my list because I think it’s the ultimate undergraduate physics course (and my favorite). I’ve noticed that other schools offering biological physics or biophysics curricula sometimes don’t include Electricity and Magnetism. I guess if you can’t cram all these advanced courses into four years and you have to skip something, consider skipping E&M.

Electives

Mathematics

• Linear Algebra 
• Probability and Statistics 

Chemistry

• Physical Chemistry 

Biology

• Genetics 
• Molecular Biology 
• Cell Biology 
• Anatomy 

Physics

• Nuclear Physics 
• Optics 
• Advanced Laboratory
  

I doubt you’ll have time for many of these electives. I believe your undergrad years are a time for getting a liberal education, so I would favor non-science electives over taking all these optional science courses. For example, be sure to take whatever classes are necessary to learn to write well. The Probability and Statistics course is higher priority than Linear Algebra. Don’t bother with Physical Chemistry unless you somehow got through all your physics courses without learning any quantum mechanics. I would load up on the elective biology classes only if you really love biology (you want to study BIOLOGICAL physics, not biological PHYSICS). The most important biology class in the list is, in my opinion, Anatomy. Nuclear Physics is useful if your interests lean toward medical physics; Optics if your interests tend toward biomedical engineering. If you plan on being an experimentalist, an Advanced Laboratory is valuable. 

For you readers who think I’m missing an essential class, or believe some of my recommendations are not needed, add your opinions to the comments section below. I’m sure readers would benefit from other points of view.

Specialty Courses

• Intermediate Physics for Medicine and Biology 1 
• Intermediate Physics for Medicine and Biology 2
  

I may have a vested interest here, but I think a two-semester sequence based on Intermediate Physics for Medicine and Biology should be mandatory. There are some topics in courses like these that are often not covered in other science classes, such as fluid dynamics, diffusion, feedback, and tomography. Not all universities offer such courses. In that case, you might have to take them via independent study, or just do some outside reading. Okay, if you must you can use some other textbook (but you’ll break my heart). 

Any faculty thinking of starting a biological physics major should note that these two specialty courses are the only classes that probably don’t already exist at your institution. The vast majority of the courses I list are already being taught at most colleges and universities.

Capstone Courses

• Colloquium 
• Independent Research
  

If your physics department has a colloquium course take it, at least during your senior year. If not, just attend regularly any research seminars hosted by your physics, chemistry, or biology departments (sometimes these events have free food!). I encourage you to do undergraduate research, even if it means you take fewer advanced courses and electives. My undergraduate research experience was more valuable than any class I ever took.  If your school has few research opportunities, search for a National Science Foundation-supported REU (Research Experience for Undergraduates).

Some students may be attending a college that has no biological physics or biophysics major. In that case, you will just have to adjust this list as best you can to fit your situation. Be flexible. If you have some oddball class that you love, or that is being taught by an outstanding and beloved instructor, don’t hesitate to substitute it for one of the courses on this list. Remember, it’s your education, so do as you want.

I hope this helps you high school students as you plan your college experience. Good luck!

A Short Course in Vector Calculus

Want a short course in vector calculus? You can find one in Intermediate Physics for Medicine and Biology.

Divergence

The divergence is defined in Section 4.1 in IPMB, when discussing the continuity equation. The divergence is one way to differentiate a vector field. I our case, the vector field is the current density (or some other type of flux density), j. Its divergence is defined as 

When you take the divergence of a vector (a quantity that has both magnitude and direction), you get a scalar (a quantity that has magnitude but no direction). In electrostatics, the electrical charge is conserved, implying that the divergence of the electrical current density is zero.

Curl

The curl is defined in Section 8.6, when analyzing electromagnetic induction. It is another way to differentiate a vector,

The symbols x̂, ŷ, and ẑ are unit vectors, and the vertical lines indicate that you follow the rules for determinants when expanding this expression. The curl appears often when analyzing the magnetic field. In our case, the curl of the electric field equations the negative of the time derivative of the magnetic field (Faraday’s law of induction).

Gradient

The gradient is a way to differentiate a scalar field to get a vector. 

 

You can think of the gradient, ∇, as representing the vector x̂ ∂/∂x + ŷ ∂/∂y + ẑ ∂/∂z. The divergence is then found by taking the dot product of the gradient with a vector, and the curl is found by taking the cross product of the gradient with the vector. In electrostatics, V represents of the electric potential (a scalar) and E represents the electric field (a vector). The two are related by

Laplacian

The Laplacian, ∇², is just the dot product of the gradient operator with itself. In other words 

 

You can apply the Laplacian to a vector, but it is more commonly applied to a scalar (such as electrical potential, temperature, or concentration). The Europeans use ∆ to represent the Laplacian, but that’s just weird and we Americans know better than that.

Other Coordinate Systems

We have written the divergence, curl, gradient, and Laplacian in Cartesian coordinates. These operators are more complicated in other coordinate systems. Appendix L of IPMB provides expressions for these operators in cylindrical coordinats of spherical coordinates.

The Divergence Theorem

The divergence theorem says that the volume integral of div J is equal to the surface integral of the normal component of J. We don’t dwell on this theorem in IPMB, but we do ask the reader to derive it in Homework Problem 4 of Chapter 4.

Stokes’ Theorem

We don’t discuss Stokes’ Theorem in IPMB, but I’ve pointed out how we might include a homework problem about it in a previous blog post. Stokes’ theorem says that the line integral of a vector around a closed loop is equal to the surface integral of the curl of that vector of an area bounded by the loop.

div, grad, curl, and all that,
by h. m. schey.

So, almost all the big concepts of vector calculus are presented in IPMB. If, however, you want a little more detail, Russ and I recommend the wonderful book div, grad, curl, and all that, by Harry Schey. I learned vector calculus from the first edition of that book as an undergraduate physics major at the University of Kansas. Schey died five years ago, but his book lives on.

Integral of the Bessel Function

Have you ever been reading a book, making good progress with everything making sense, and then you suddenly stop at say “wait… what?”. That happened to me recently as I was reading Homework Problem 31 in Chapter 12 of Intermediate Physics for Medicine and Biology. (Wait…what? I’m a coauthor of IPMB! How could there be any surprises for me?) The problem is about calculating the two-dimensional Fourier transform of 1/r, and it supplies the following Bessel function identity 

The function J₀ is a Bessel function of the first kind of order zero. What surprised me is that if you let x = kr, you get that the integral of the Bessel function is one,

Really? Here’s a plot of J₀(x).

It oscillates like crazy and the envelope of those oscillations falls off very slowly. In fact, an asymptotic expansion for J₀ at large x is

The leading factor of 1/√x decays so slowly that its integral from zero to infinity does not converge. Yet, when you include the cosine so the function oscillates, the integral does converge. Here’s a plot of

The integral approaches one at large x, but very slowly. So, the expression given in the problem is correct, but I sure wouldn’t want to do any numerical calculations using it, where I had to truncate the endpoint of the integral to something less than infinity. That would be a mess!

Here’s another interesting fact. Bessel functions come in many orders—J₀, J₁, J₂, etc.—and they all integrate to one.

Who’s responsible for these strangely-behaved functions? They’re named after the German astronomer Friedrich Bessel but they were first defined by the Swiss mathematician Daniel Bernoulli (1700–1782), a member of the brilliant Bernoulli family. The Bernoulli equation, mentioned in Chapter 1 of IPMB, is also named for Daniel Bernoulli. 

There was a time when I was in graduate school that I was obsessed with Bessel functions, especially modified Bessel functions that don’t oscillate. I’m not so preoccupied by them now, but they remain my favorite of the many special functions encountered in physics.