An Inspire TV ad.

I suspect you’ve seen some of the recent ads for Inspire, a new treatment for obstructive sleep apnea.

How does Inspire work? It uses electrical stimulation, like Russ Hobbie and I discuss in Chapter 7 of Intermediate Physics for Medicine and Biology.

7.10 Electrical Stimulation

The information that has been developed in this chapter can also be used to understand some of the features of stimulating electrodes. These may be used for electromyographic studies; for stimulating muscles to contract called functional electrical stimulation (Peckham and Knutson 2005); for a cochlear implant to partially restore hearing (Zeng…


“The Bidomain Model of Cardiac Tissue:
Predictions and Experimental Verification”

In the early 1990s, I was asked to write a chapter for a book titled Neural Engineering. My chapter had nothing to do with nerves, but instead was about cardiac tissue analyzed with the bidomain model. (You can learn more about the bidomain model in Chapter 7 of Intermediate Physics for Medicine and Biology.)

“The Bidomain Model of Cardiac Tissue: Predictions and Experimental Verification” was submitted to the editors in January, 1993. Alas, the book was never published. However, I still have a copy of the chapter, and you can download it here. …


A drawing of insulin by David Goodsell, from Wikipedia.

Insulin was isolated and first used to treat diabetes in 1921, one hundred years ago. To celebrate this landmark, I will quote a few paragraphs from the section on blood hormones in Isaac Asimov’s A Short History of Biology.


Figure 16.23 in Intermediate Physics for Medicine and Biology. Digital subtraction angiography. (a) Brain image with contrast material. (b) Image without contrast material. © The difference image. Anterior view of the right internal carotid artery. Photograph courtesy of Richard Geise, Department of Radiology, University of Minnesota.

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss digital subtraction angiography.

16.6 Angiography and Digital Subtraction Angiography

One important problem in diagnostic radiology is to image portions of the vascular tree. Angiography can confirm the existence of and locate narrowing (stenosis), weakening and bulging of the vessel wall (aneurysm), congenital malformations of vessels, and the like. This is done by injecting a contrast material containing iodine into an artery. If the images are recorded digitally, it is possible to subtract one without the contrast medium from one with contrast and see the vessels…


In Figure 10.26 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I plot a bifurcation diagram for the logistic map: xj+1 = a xj (1 − xj).

A bifurcation diagram for the logistic map, showing 300 values of xj for values of a between 1 and 4. Figure 10.26 in Intermediate Physics for Medicine and Biology.

The bifurcation diagram summarizes the behavior of the map as a function of the parameter . Some values of a correspond to a steady state, others represent period doubling, and still others lead to chaos.

When I teach Biological Physics, I don’t introduce chaos using the logistic map. Instead, I solve IPMB’s Homework Problem 41, about cardiac restitution and the onset of fibrillation.


In Chapter 10 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss feedback and control. Homework Problem 12 analyzes the feedback circuit that controls blood pressure.

Problem 12 from Chapter 10 of Intermediate Physics for Medicine and Biology.

The reference to the article by Allen Scher and Allan Young is

Scher AM, Young AC (1963) “Servoanalysis of Carotid Sinus Reflex Effects on Peripheral Resistance,” Circulation Research, Volume 12, Pages 152–165.

I downloaded this paper to learn more about their experiment. Below are excerpts from their introduction.

The baroceptors of the carotid sinus (and artery) and the aortic arch are the major sense organs which reflexly control the systemic blood…


The electrocardiogram (ECG).

In Chapter 7 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the electrocardiogram. Today, I present twelve ECGs that everyone should know. I’ve drawn them in a stylized and schematic way, ignoring differences between individuals, changes from beat to beat, and noise.

When I taught medical physics at Oakland University, my lecture on ECGs was preceded by a lesson on cardiac anatomy. If some anatomical terms in this post are unfamiliar, I suggest reviewing the Texas Heart Institute website.

1. Normal Heartbeat

Electrocardiograms are plotted on graph paper that consists of large squares, each divided into a five-by-five grid…


Page 223 of Intermediate Physics for Medicine and Biology.

Figure 8.18 on page 223 of Intermediate Physics for Medicine and Biology contains a plot of the magnetic field produced by action currents in a slice of cardiac tissue. The measured magnetic field contours have approximately a four-fold symmetry. The experiment by Staton et al. that produced this data was a tour de force, demonstrating the power of high-spatial-resolution biomagnetic techniques.


The Code Breaker,
by Walter Isaacson

My favorite authors are Simon Winchester, David Quammen, and Walter Isaacson. This week I read Isaacson’s latest book: The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race. I would place it alongside The Eighth Day of Creation and The Making of the Atomic Bomb as one of the best books about the history of science.

In his introduction, Isaacson writes

The invention of CRISPR and the plague of COVID will hasten our transition to the third great revolution of modern times. …


Vitamin D

Two years ago my doctor recommended I start taking vitamin D. I’m annoyed at having to take a supplement every day, but I do what the doc says.

Your body needs exposure to ultraviolet light to produce its own vitamin D, but too much UV light causes skin cancer. Russ Hobbie and I address this trade-off in Section 14.10 of Intermediate Physics for Medicine and Biology.

There has been an alarming increase in the use of tanning parlors by teenagers and young adults. These emit primarily UVA, which can cause melanoma. Exposure rates are two to three times greater than…

Brad Roth

Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.

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