tDCS Peripheral Nerve Stimulation: A Neglected Mode of Action?

In the November 13, 2020 episode of Shark Tank (Season 12, Episode 5), two earnest entrepreneurs, Ken and Allyson, try to persuade five investors, the “sharks,” to buy into their company. The entrepreneurs sell LIFTiD, a device that applies a small steady current to the forehead. Ken said it’s supposed to improve “productivity, focus, and performance.” Allyson claimed it’s a “smarter way to get a… boost of energy.”

The device is based on transcranial direct current stimulation (tDCS). In 2009 I published an editorial in the journal Clinical Neurophysiology to accompany a paper appearing in the same issue by Pedro Miranda and his colleagues (Clin. Neurophysiol., Volume 120, Pages 1183–1187, 2009), in which they calculated the electric field in the brain caused by a 1 mA current applied to the scalp. I wrote

Although Miranda et al.’s paper is useful and enlightening, one crucial issue is not addressed: the mechanism of tDCS. In other words, how does the electric field interact with the neurons to modulate their excitability? Miranda et al. calculate a current density in the brain on the order of 0.01 mA/cm², which corresponds to an electric field of about 0.3 V/m (a magnitude that is consistent with other studies (Wagner et al., 2007)). Such a small electric field should polarize a neuron only slightly. Hause’s model of a single neuron predicts that a 10 V/m electric field would induce a transmembrane potential of 6–8 mV (Hause, 1975), implying that the 0.3 V/m electric field during tDCS should produce a transmembrane potential of less than 1 mV. Can such a small polarization significantly influence neuron excitability? If so, how? These questions perplex me, yet answers are essential for understanding tDCS. Detailed models of the cortical geometry and brain heterogeneities may be necessary to address this issue (Silva et al., 2008), but ultimately the response of the neuron (or network of neurons) to the electric field must be included in the model in order to unravel the mechanism. Moreover, because the effect of tDCS can last for up to an hour after the current turns off (Nitsche et al., 2008), the mechanism is likely to be more complicated than just neural polarization.

van Boekholdt et al. (2021)

My participation in the field of transcranial direct current stimulation started and ended with writing this editorial. However, I still follow the literature, and was was fascinated by a recent article by Luuk van Boekholdt and his coworkers in Molecular Psychiatry (Volume 26, Pages 456–461, 2021). Their abstract says

Transcranial direct current stimulation (tDCS) is a noninvasive neuromodulation method widely used by neuroscientists and clinicians for research and therapeutic purposes. tDCS is currently under investigation as a treatment for a range of psychiatric disorders. Despite its popularity, a full understanding of tDCS’s underlying neurophysiological mechanisms is still lacking. tDCS creates a weak electric field in the cerebral cortex which is generally assumed to cause the observed effects. Interestingly, as tDCS is applied directly on the skin, localized peripheral nerve endings are exposed to much higher electric field strengths than the underlying cortices. Yet, the potential contribution of peripheral mechanisms in causing tDCS’s effects has never been systemically investigated. We hypothesize that tDCS induces arousal and vigilance through peripheral mechanisms. We suggest that this may involve peripherally-evoked activation of the ascending reticular activating system, in which norepinephrine is distributed throughout the brain by the locus coeruleus. Finally, we provide suggestions to improve tDCS experimental design beyond the standard sham control, such as topical anesthetics to block peripheral nerves and active controls to stimulate non-target areas. Broad adoption of these measures in all tDCS experiments could help disambiguate peripheral from true transcranial tDCS mechanisms.

When the sharks tried the LIFTiD device, they each could feel a tingling shock on their scalp. If van Boekholdt et al.’s suggestion is correct, the titillation and annoyance caused by that shock might be responsible for the effects associated with tDCS. In that case, the method would work even if you could somehow make the skull a perfect insulator, so no current whatsoever could enter the brain. I like how van Boekholdt suggests specific, simple experiments that could test their hypothesis.

If you’re trying to buy a device to improve brain performance, you might not care if it works by directly stimulating the brain or just by exciting peripheral nerves. In fact, you might be able to save money by hiring someone to poke you in the back every few seconds. Do whatever it takes to focus your attention.

None of the sharks invested in LIFTiD. My favorite shark, Mark Cuban, claimed the entrepreneurs “tried to sell science without using science.” I couldn’t have said it better myself. 

LIFTiD Neurostimulation Personal Brain Stimulator; https://www.youtube.com/watch?v=hFzihXprRUM

Currents of Fear: In Which Power Lines Are Suspected of Causing Cancer

Voodoo Science,
by Robert Park

These days—when so many people believe crazy conspiracy theories, refuse life-saving vaccines, promote alternative medicine, fret about perceived 5G cell phone hazards, and postulate implausible microwave weapons to explain the Havana Syndrome—we need to understand better how science interacts with society. In particular, we should examine past controversies to see what we can learn. In this post, I review the power line/cancer debate of the 1980s and 90s. I remember it well, because it raged during my graduate school days. The dispute centered on the physics Russ Hobbie and I describe in Chapter 9 of Intermediate Physics for Medicine and Biology. 

To tell this tale, I’ve selected excerpts from Robert Park’s book Voodoo Science: The Road from Foolishness to Fraud. The story has important lessons for today. Enjoy!

Currents of Fear: In Which Power Lines Are Suspected of Causing Cancer

In 1979, an unemployed epidemiologist named Nancy Wertheimer obtained the addresses of childhood leukemia patients in Denver and drove about the city looking for some common environmental factor that might be responsible. What she noticed was that many of the homes of victims seemed to be near power transformers. Could it be that fields from the electric power distribution system were linked to leukemia? She teamed up with a physicist named Ed Leeper, who devised a “wiring code” based on the size and proximity of power lines to estimate the strength of the magnetic fields. Together they eventually produced a paper relating childhood leukemia to the fields from power lines…

In June of 1989, The New Yorker carried a new three-part series of highly sensational articles by Paul Brodeur… on the hazards of power-line fields…. The series reached an affluent, educated, environmentally concerned audience. Suddenly, Brodeur was everywhere: the Today show on NBC, Nightline on ABC, This Morning on CBS, and, of course, Larry King Live on CNN. In the fall, Brodeur published the New Yorker series as a book with the lurid title Currents of Death. A new generation of environmental activists, led by mothers who feared for their children’s lives, demanded government action…

By [1995], sixteen years had passed since Nancy Wertheimer took her historic drive around Denver. An entire industry had grown up around the power-line controversy. Armies of epidemiologists conducted ever larger studies; activists organized campaigns to relocate power lines away from schools; the courts were clogged with damage suits; a half dozen newsletters were devoted to reporting on EMF [electromagnetic fields]; a brisk business had developed in measuring 60 Hz magnetic fields in homes and workplaces; fraudulent devices of every sort were being marketed to protect against EMF; and, of course, Paul Brodeur’s books were selling well…

It was into this climate that the Stevens Report was released by the National Academy of Sciences in 1996 with it unanimous conclusion that “the current body of evidence does not show that exposure to these fields presents a human health hazard.”… The chair of the review panel, Charles Stevens, a distinguished neurobiologist with the Salk Institute, [explained] the difficulty of trying to identify weak environmental hazards. Scientists had labored for seventeen years to evaluate the hazards of power-line fields; they had conducted epidemiological studies, laboratory research, and computational analysis. “Our committee evaluated over five hundred studies,” Stevens said, “and in the end all we can say is that the evidence doesn’t point to these fields as being a health risk…”

On July 2, 1997, the National Cancer Institute (NCI) finally announced the results of its exhaustive epidemiological study, “Residential Exposure to Magnetic Fields and Acute Lymphoblastic Leukemia in Children”… It was the most unimpeachable epidemiological study of the connection between power lines and cancer yet undertaken. Every conceivable source of investigator bias was eliminated. There were 638 children under age fifteen with acute lymphoblastic leukemia enrolled in the study along with 620 carefully matched controls, ensuring reliable statistics. All measurements were double blind… [The study] concluded that any link between acute lymphoblastic leukemia in children and magnetic fields is too weak to detect or to be concerned about. But the most surprising result had to do with the proximity of power lines to the homes of leukemia victims: the study found no association at all. The supposed association between proximity to power lines and childhood leukemia, which had kept the controversy alive all these years, was spurious—just an artifact of the statistical analysis. As is so often the case with voodoo science, with every improved study the effect had gotten smaller. Now, after eighteen years, it was gone completely.

 

Power Line Fears, https://www.retroreport.org/video/power-line-fears

 

The Bragg Peak (Continued)

In last week’s post, I discussed the Bragg peak: protons passing through tissue lose most of their energy near the end of their path. In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I present a homework problem in which the student calculates the stopping power (energy lost per distance traveled), S, as a function of depth, x, given a relationship between stopping power and energy, T. This problem is a toy model illustrating the physical origin of the Bragg peak. Often it’s helpful to have two such exercises; one to assign as homework and one to work in class (or put on an exam). Here’s a new homework problem similar to the one in IPMB, but with a different assumption about how stopping power depends on energy.

Section 16.10

Problem 31 ½. Assume the stopping power of a particle, S = −dT/dx, as a function of kinetic energy, T, is S = S_o e^−T/T_o. 

(a) What are the units of S_o and T_o? 

(b) If the initial kinetic energy at x = 0 is T_i, calculate T(x). 

(c) Determine the range R of the particle as a function of T_o, S_o, and T_i. 

(d) Plot S(x) vs. x. Does this plot contain a Bragg peak? 

(e) Discuss the implications of the shape of S(x) for radiation treatment using this particle.

The answer to part (d) is difficult, because your conclusion is different depending on the relative magnitude of T_i and T_o. You might consider adding a part (f)

(f) Plot T(x), S(x), and R(T_i) for T_i >> T_o and for T_i << T_o.

The case T_i >> T_o has a conspicuous Bragg peak; the case T_i << T_o doesn’t. 

The homework problem in IPMB is more realistic than this new one, because Fig. 15.17 indicates that the stopping power decreases as 1/T (assumed in the original problem) rather than exponentially (assumed in the new problem). This changes the particle’s behavior, particularly at low energies (near the end of its range, in the Bragg peak). Nevertheless, having multiple versions of the problem is useful. 

The answer to part (e) is given in IPMB.

Protons are also used to treat tumors... Their advantage is the increase of stopping power at low energies. It is possible to make them come to rest in the tissue to be destroyed, with an enhanced dose relative to intervening tissue and almost no dose distally.

 Enjoy!

The Bragg Peak

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the Bragg peak.

Protons are also used to treat tumors (Khan 2010, Ch. 26; Goitein 2008). Their advantage is the increase of stopping power at low energies. It is possible to make them come to rest in the tissue to be destroyed, with an enhanced dose relative to intervening tissue and almost no dose distally (“downstream”) as shown by the Bragg peak in Fig.16.47.

Energy loss versus depth for a 150 MeV proton beam in water, with and without straggling (fluctuations in the range). The Bragg peak enhances the energy deposition at the end of the proton range. Adapted from Fig. 16.47 in Intermediate Physics for Medicine and Biology.

William Henry Bragg

Sir William Henry Bragg (1862 – 1942) was an English scientist who shared the 1915 Nobel Prize in Physics with his son Lawrence Bragg for their analysis of crystal structure using X-rays. In 2004, Andrew Brown and Herman Suit published an article commemorating “The Centenary of the Discovery of the Bragg Peak” (Radiotherapy and Oncology, Volume 73, Pages 265-268).

In December 1904, William Henry Bragg, Professor of Mathematics and Physics at the University of Adelaide and his assistant Richard Kleeman published in the Philosophical Magazine (London) novel observations on radioactivity. Their paper “On the ionization of curves of radium,” gave measurements of the ionization produced in air by alpha particles, at varying distances from a very thin source of radium salt. The recorded ionization curves “brought to light a fact, which we believe to have been hitherto unobserved. It is, that the alpha particle is a more efficient ionizer towards the extreme end of its course.” This was promptly followed by further results in the Philosophical Magazine in 1905. Their finding was contrary to the accepted wisdom of the day, viz. that the ionizations produced by alpha particles decrease exponentially with range. From theoretical considerations, they concluded that an alpha particle possesses a definite range in air, determined by its initial energy and produces increasing ionization density near the end of its range due to its diminishing speed.

Although Bragg discovered the Bragg peak for alpha particles, the same behavior is found for other heavy charged particles such as protons. It is the key concept underlying the development of proton therapy. Brown and Suit conclude

The first patient treatment by charged particle therapy occurred within a decade of Wilson’s paper [the first use of protons in therapy, published in 1946]. Since then, the radiation oncology community has been evaluating various particle beams for clinical use. By December 2004, a century after Bragg’s original publication, the approximate number of patients treated by proton–neon beams is 47,000 (Personal communication, Janet Sisterson, Editor, Particles) [over 170,000 today]. There have been several clear clinical gains. None of these would have been possible, were it not for the demonstration that radically different depth dose curves were feasible.

Alan Magee and the St. Nazaire Railroad Station

Alan Magee. Reproduced from the
website www.americanairmuseum.com.

On January 3, 1943, airman Alan Magee fell 22,000 feet (6700 meters, or about 4 miles) without a parachute from a damaged B-17 Flying Fortress and survived. How’d he do it?

Let’s examine Magee’s fall using elementary physics. Homework Problem 29 in Chapter 2 of Intermediate Physics for Medicine and Biology explains how someone falling through the air reaches a steady-state, or terminal, speed. A typical terminal speed, v, when skydiving is about 50 m/s. This may be a little slower than average, but v decreases with mass and ball turret gunners like Magee were usually small. Skydivers will reach their terminal speed after about 20 seconds. Magee fell for much longer than that, so starting four miles up didn’t matter. He could have begun forty miles up and his terminal speed would have been the same (presumably he would have suffocated, but that’s another story).

When falling, what kills you is the sudden deceleration when you hit the ground. Suppose you’re traveling at v = 50 m/s and you hit a hard surface like cement. You come to a stop over a distance, h, of a few centimeters (a person isn’t rigid, so there would be some distance that corresponds to the body splatting). Let’s estimate 10 cm, or h = 0.1 m. If the acceleration, a, is uniform, we can use an equation from kinematics to calculate a from v and h: a = v²/(2h) = 50²/0.2 = 12,500 m/s². This is about 1250g, where g is the acceleration of gravity (approximately 10 m/s²).

How much acceleration can a person survive? It’s hard to say. Some roller coasters can accelerate at up to 3g and you feel a thrill. Astronauts in the Mercury space program experienced about 10g during reentry and they survived. Flight surgeon John Stapp withstood 46g on a rocket sled, but that is probably near the maximum. Clearly 1250g is well over the threshold of survivability. You would die.

So, how did Magee survive? He didn’t hit cement. Instead, he crashed through the glass ceiling of the St. Nazaire railroad station. Most sources I’ve read claim that shattering the glass helped break his fall. Maybe, but I have another idea. Some of the articles I’ve examined have German soldiers finding Magee alive on the station floor, but others say he was found tangled in steel girders. Below is a picture of the railroad station as it looked during World War II. 

The Railroad Station in St. Nazaire, France. Modified from a photo posted by @ron_eisele on Twitter.

 

Notice the structures below the glass ceiling. I wouldn’t call them girders or struts. To me they look like a web of steel cables or ties. My hypothesis is that this web functioned as a net. Suppose Magee landed on one of the ties and it deflected downward, perhaps dragging part of the ceiling with it, or pulling down other ties, or breaking at one end, or stretching like a bungee cord. All this pulling and breaking and stretching would reduce his deceleration. Let’s guess that he came to rest about three meters below where he first hit a tie. Now his acceleration (assuming it’s uniform) is a = 50²/6 = 417 m/s², or about 42g. That’s a big deceleration, but it may be survivable. You would expect him to be hurt, and he was; he suffered from several broken bones, damage to a lung and kidney, and a nearly severed arm.

If my hypothesis is correct, the shattering of glass had little or nothing to do with breaking Magee’s fall. I’m sure it made a loud noise, and must have given the accident a dramatic flair, but the glass ceiling may have been irrelevant to his survival.

I don’t think we can ever know for sure why Magee didn’t die, short of building a replica of the train station, dropping corpses (or, more hygienically, crash dummies) through the roof, and video recording their fall. Still, it’s fun to speculate.

After the crash, what happened to Magee? He was captured, became a prisoner of war, and was treated for his injuries. In May 1945 the war in Europe ended and he was freed. He returned to the United States and lived another 58 years. He was awarded the Air Medal and a well-earned Purple Heart. Alan Magee's survival represents a fascinating example of physics applied to medicine and biology.

Triumph of Victory. A reenactment of Alan Magee’s fall.

Don’t expect much dialogue.

https://www.youtube.com/watch?v=WEZ97XsU2wQ&t=109s

Cerenkov Luminescence Imaging: Physics Principles and Potential Applications in Biomedical Sciences

When a particle travels faster than the speed of light, it emits Cerenkov radiation. This phenomenon has resulted in new medical imaging applications, as described in a 2017 review paper by Esther Ciarrocchi and Nicola Belcari (Cerenkov Luminescence Imaging: Physics Principles and Potential Applications in Biomedical Sciences, EJNMMI Physics, Volume 4, Article 14). This is an open access article, so you can read it for free.

Russ Hobbie and I don’t discuss Cerenkov Luminescence Imaging in Intermediate Physics for Medicine and Biology, but you can learn a lot about it using the physics we do discuss. For example, can particles  travel faster than the speed of light? They can’t travel faster than the speed of light in a vacuum, but they can travel faster than the speed of light in a material such as water or tissue where light is slowed and the medium has an index of refraction. Below is a new homework problem, in which we consider electrons emitted in tissue by beta decay of the isotope iodine-131, used in many medical applications.

Problem 9 ¼. The end point kinetic energy (see Fig. 17.8) for beta decay of ¹³¹I is 606 keV, and tissue has an index of refraction of 1.4. Do any of the emitted electrons have a speed faster than the speed of light in the tissue? To determine this speed, use Eq. 14.1. Because the electrons move near the speed of light, to determine their speed as a function of their kinetic energy use a result from special relativity, Eq. 17.1.

For those who don’t have IPMB at your side (shame on you!), Eq. 14.1 is c_n = c/n, where c_n is the speed of light in the medium, c is the speed of light in a vacuum (3 × 10⁸ m/s), and n is the index of refraction, and Eq. 17.1 is T + mc² = mc²/√(1 − v²/c²), where v is the speed of the particle, T is its kinetic energy, and mc² is the rest mass of an electron expressed as energy (511 keV).

If you solved this problem correctly, you found that some of the more energetic electrons emitted during beta decay of ¹³¹I do travel faster than the speed of light in tissue.

Cerenkov radiation is emitted at an angle θ with respect to the direction that the particle is moving. This distribution of light is characteristic of a shock wave, and is similar to the distribution of sound in a sonic boom made by a plane when it flies faster than the speed of sound. The new problem below requires the reader to calculate θ.

Problem 9 ½. The drawing below shows a particle moving to the right faster than the speed of light in the medium. The position of the particle at several instants is indicated by the purple dots. The location of light emitted by the particle at each position is shown by the black circles. The light adds to form a conical wave front, shown by the green lines. 

(a) Use the red right triangle to calculate the angle θ as a function of the particle speed, v, and the index of refraction, n. 

(b) Compute the value of θ for the fastest electrons emitted by beta decay of ¹³¹I in tissue.

The number of photons emitted tends to be greatest at short wavelengths, so Cerenkov radiation often has a blue tinge. However, readers of IPMB learned in Chapter 14 that the spectrum of radiation can look different when viewed as a function of frequency (or energy) rather than as a function of wavelength. Below is a new problem to explore this effect.

Problem 9 ¾. The number of photons dN emitted with a wavelength between λ and λ + dλ is approximately dN = Cdλ/λ², where C is a constant.

(a) Sketch a plot of dN/dλ versus λ. Don’t worry about the scale of the axes (in other words, don't worry about the value of C); just make the plot qualitatively correct. 

(b) Use methods similar to those introduced in Section 14.8 to determine the number of photons emitted with an energy between E and E + dE. Don’t worry about constant factors, just determine how dN/dE varies with E. 

(c) Sketch a plot of dN/dE versus E. Again, just make the plot qualitatively correct.

If you solved part (c) correctly, you should have drawn a plot with a flat line, because dN/dE is independent of E. Of course, there must be some limits to this result, otherwise the particle would emit an infinite amount of energy when integrated over all photon energies. See Ciarrocchi and Belcari’s review for an explanation.

Perhaps the most interesting part of Ciarrocchi and Belcari’s article is their discussion of biomedical applications. You can use Cerenkov radiation to image beta emitters like ¹³¹I, positron emitters like ¹⁸F used in positron emission tomography, and high-energy protons required for proton therapy.

To learn more about Cerenkov radiation, watch this video by Don Lincoln. Enjoy!

How does Cerenkov radiation work?

https://www.youtube.com/watch?v=Yjx0BSXa0Ks

Science-Based Medicine

Why is my field—bioelectromagnetics—so prone to pseudoscience? I don’t know. But I do know that we need to be more skeptical about alternative medical treatments. That’s why I’m a fan of the website sciencebasedmedicine.org.

Science-Based Medicine is dedicated to evaluating medical treatments and products of interest to the public in a scientific light, and promoting the highest standards and traditions of science in health care. Online information about alternative medicine is overwhelmingly credulous and uncritical, and even mainstream media and some medical schools have bought into the hype and failed to ask the hard questions.

We provide a much needed “alternative” perspective—the scientific perspective.

Good science is the best and only way to determine which treatments and products are truly safe and effective. That idea is already formalized in a movement known as evidence-based medicine (EBM). EBM is a vital and positive influence on the practice of medicine, but it has limitations and problems in practice: it often overemphasizes the value of evidence from clinical trials alone, with some unintended consequences, such as taxpayer dollars spent on “more research” of questionable value. The idea of SBM is not to compete with EBM, but a call to enhance it with a broader view: to answer the question “what works?” we must give more importance to our cumulative scientific knowledge from all relevant disciplines.

To me, this means that medical claims must not violate the laws of physics. Some do. For instance, magnetic therapy suggests that permanent magnets can prevent many diseases. Powerline (60 Hz) magnetic fields are said to cause cancer. A few people claim to be hypersensitive to weak electromagnetic fields. Many people believe that electromagnetic radiation associated with cell phones is dangerous. This belief has increased recently with the development of 5G technology. Somehow (and this is really weird), doubts about covid-19 vaccines became mixed up with these 5G concerns.

Yet, bioelectromagnetics has enormous potential for medical applications: cardiac pacing and defibrillation, transcranial magnetic stimulation, functional electrical stimulation, deep brain stimulation, and prostheses such as cochlear implants.

How do we separate the wheat from the chaff? It’s not easy. Reading Intermediate Physics for Medicine and Biology is a good place to start. Many of these readers would benefit from a short course about science-based medicine. Does such a course exist? Yes! Harriet Hall (the SkepDoc, who I discussed previously in this blog) has recorded a series of ten videos about science-based medicine. She debunks much of the nonsense out there. Below, I link to the videos. Your homework assignment is to watch them.

If the coronavirus pandemic has taught us anything, it’s that we must base medicine on science.

 

Lecture 1: Science-based medicine versus evidence-based medicine

 

Lecture 2: Complimentary and alternative medicine

 

 

Lecture 3: Chiropractic

 

Lecture 4: Acupuncture

 

 

Lecture 5: Homeopathy

 

 

Lecture 6: Naturopathy

 

 

Lecture 7: Energy medicine

 

 

Lecture 8: Miscellaneous

 

 

Lecture 9: Pitfalls in research

 

 

Lecture 10: The media and politics

Inspire

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

An Inspire TV ad. 

https://www.youtube.com/watch?v=bn5-ydF4_QQ 

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 et al.2008); deep brain stimulation for Parkinson’s disease (Perlmutterand Mink 2006); for cardiac pacing (Moses andMullin 2007); and even for defibrillation (Dosdall et al.2009).

Like the cardiac pacemaker, the Inspire device is implanted in the upper chest. Instead of monitoring the electrocardiogram, the device monitors breathing; instead of stimulating the heart, it stimulates the hypoglossal nerve controlling muscles in the tongue.

A patient with obstructive sleep apnea has their airway blocked while sleeping, causing the body to crave oxygen. This results in a brief reawakening as the person opens their airway for better airflow. Once oxygen is restored, the patient goes back to sleep. Then, the entire process starts again, so sleep is frequently and repeatedly interrupted.

One way to treat obstructive sleep apnea is using continuous positive airway pressure (CPAP), which requires wearing a mask attached by a hose to a pump. Some people can’t or won’t tolerate CPAP, and it’s hard to imagine that anyone likes it.

When Inspire detects that you’re taking a breath it stimulates the tongue to contract, opening the airway. You only need it when sleeping, so it has a button you can push to turn it on before bed and turn it off when you wake up.

Inspire is yet one more example of how physics can be applied to medicine, and in particular how electrical stimulation can be used to treat patients. I’m into it. 

Dr. Ryan Soose explains the Stimulation Therapy for Apnea Reduction (STAR) clinical trial.

https://www.youtube.com/watch?v=AvQoxv7iDP4

The Bidomain Model of Cardiac Tissue: Predictions and Experimental Verification

“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. Now—after nearly thirty years—it’s obsolete, but provides a glimpse into the pressing issues of that time.

I was a impudent young buck back in those days. Three times in the chapter I recast the arguments of other scientists (my competitors) as syllogisms. Then, I asserted that their premise was false, so their conclusion was invalid (I'm sure this endeared me to them). All three syllogisms dealt with whether or not cardiac tissue could be treated as a continuous tissue, as opposed to a discrete collection of cells.

The Spach Experiment

The first example had to do with the claim by Madison Spach that the rate of rise of the cardiac action potential, and time constant of the action potential foot, varied with direction.

Continuous cable theory predicts that the time course of the action potential does not depend on differences in axial resistance with direction.

The rate of rise of the cardiac wave front is observed experimentally to depend on the direction of propagation.

Therefore, cardiac tissue does not behave like a continuous tissue.

I then argued that their first premise is incorrect. In one-dimensional cable theory, the time course of the action potential doesn’t depend on axial resistance, as Spach claimed. But in a three-dimensional slab of tissue superfused by a bath, the time course of the action potential depends on the direction of propagation. Therefore, I contended, their conclusion didn’t hold; their experiment did not prove that cardiac tissue isn’t continuous. To this day the issue is unresolved.

Defibrillation

A second example considered the question of defibrillation. When a large shock is applied to the heart, can its response be predicted using a continuous model, or are discrete effects essential for describing the behavior?

An applied current depolarizes or hyperpolarizes the membrane only in a small region near the ends of a continuous fiber.

For successful defibrillation, a large fraction of the heart must be influenced by the stimulus.

Therefore, defibrillation cannot be explained by a continuous model.

I argued that the problem is again with the first premise, which is true for tissue having “equal anisotropy ratios” (the same ratio of conductivity parallel and perpendicular to the fibers, in both the intracellular and extracellular spaces), but is not true for “unequal anisotropy ratios.” (Homework Problem 50 in Chapter 7 of IPMB examines unequal anisotropy ratios in more detail). If the premise is false, the conclusion is not proven. This issue is not definitively resolved even today, although the sophisticated simulations of realistically shaped hearts with their curving fiber geometry, performed by Natalia Trayanova and others, suggest that I was right.

Reentry Induction

The final example deals with the induction of reentry by successive stimulation through a point electrode. As usual, I condensed the existing dogma to a syllogism.

In a continuous tissue, the anisotropy can be removed by a coordinate transformation, so reentry caused by successive stimulation through a single point electrode cannot occur, since there is no mechanism to break the directional symmetry.

Reentry has been produced experimentally by successive stimulation through a single point electrode.

Therefore, cardiac tissue is not continuous.

Once again, that pesky first premise is the problem. In tissue with equal anisotropy ratios you can remove anisotropy by a coordinate transformation, so reentry is impossible. However, if the tissue has unequal anisotropy ratios the symmetry is broken, and reentry is possible. Therefore, you can’t conclude that the observed induction of reentry by successive stimulation through a point electrode implies the tissue is discrete.

I always liked this book chapter, in part because of the syllogisms, in part because of its emphasis on predictions and experiments, but mainly because it provides a devastating counterargument to claims that cardiac tissue acts discretely. Although it was never published, I did send preprints around to some of my friends, and the chapter took on a life of its own. This unpublished manuscript has been cited 13 times!

Trayanova N, Pilkington T (1992) “The use of spectral methods in bidomain studies,” Critical Reviews in Biomedical Engineering, Volume 20, Pages 255–277.

Winfree AT (1993) “How does ventricular tachycardia turn into fibrillation?” In: Borgreffe M, Breithardt G, Shenasa M (eds), Cardiac Mapping, Mt. Kisco NY, Futura, Chapter 41, Pages 655–680.

Henriquez CS (1993) “Simulating the electrical behavior of cardiac tissue using thebidomain model,” Critical Reviews of Biomedical Engineering, Volume 21, Pages 1–77.

Wikswo JP (1994) “The complexities of cardiac cables: Virtual electrode effects,” Biophysical Journal, Volume 66, Pages 551–553.

Winfree AT (1994) “Puzzles about excitable media and sudden death,” Lecture Notes in Biomathematics, Volume 100, Pages 139–150.

Roth BJ (1994) “Mechanisms for electrical stimulation of excitable tissue,” Critical Reviews in Biomedical Engineering, Volume 22, Pages 253–305.

Roth BJ (1995) “A mathematical model of make and break electrical stimulation ofcardiac tissue by a unipolar anode or cathode,” IEEE Transactions on Biomedical Engineering, Volume 42, Pages 1174–1184.

Wikswo JP Jr, Lin S-F, Abbas RA (1995) “Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation,” Biophysical Journal, Volume 69, Pages 2195–2210.

Roth BJ, Wikswo JP Jr (1996) “The effect of externally applied electrical fields on myocardial tissue,” Proceedings of the IEEE, Volume 84, Pages 379–391.

Goode PV, Nagle HT (1996) “On-line control of propagating cardiac wavefronts,” The 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam.

Winfree AT (1997) “Rotors, fibrillation, and dimensionality,” In: Holden AV, Panfilov AV (eds): Computational Biology of the Heart, Chichester, Wiley, Pages 101–135.

Winfree AT (1997) “Heart muscle as a reaction-diffusion medium: The roles of electric potential diffusion, activation front curvature, and anisotropy,” International Journal of Bifurcation and Chaos, Volume 7, Pages 487–526.

Winfree AT (1998) “A spatial scale factor for electrophysiological models of myocardium,” Progress in Biophysics and Molecular Biology, Volume 69, Pages 185–203.

I’ll end with the closing paragraph of the chapter.

The bidomain model ignores the discrete nature of cardiac cells, representing the tissue as a continuum instead. Experimental evidence is often cited to support the hypothesis that the discrete nature of the cells plays a key role in cardiac electrophysiology. In each case, the bidomain model offers an alternative explanation for the phenomena. It seems wise at this point to reconsider the evidence that indicates the significance of discrete effects in healthy cardiac tissue. The continuous bidomain model explains the data, recorded by Spach and his colleagues, showing different rates of rise during propagation parallel and perpendicular to the fibers, anodal stimulation, arrhythmia development by successive stimulation from a point source, and possibly defibrillation. Of course, these alternative explanations do not imply that discrete effects are not responsible for these phenomena, but only that two possible mechanisms exist rather than one. Experiments must be found that differentiate unambiguously between alternative models. In addition, discrete junctional resistance must be incorporated into the bidomain model. Only when such experiments are performed and the models are further developed will we be able to say with any certainty that cardiac tissue can be described as a continuum.

Insulin

A drawing of insulin by David Goodsell, from Wikipedia.

 
Chapter 10 of Intermediate Physics for Medicine and Biology discusses feedback. The homework problems of that chapter include an example of the classic feedback loop controlling the amount of glucose in the blood by the hormone insulin. 

A Short History of Biology,
by Isaac Asimov.

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.

The most spectacular early result of hormone work… was in connection with the disease, diabetes mellitus. This involved a disorder in the manner in which the body broke down sugar for energy, so that a diabetic accumulated sugar in his blood to abnormally high levels. Eventually, the body was forced to get rid of the excess sugar through the urine, and the appearance of sugar in the urine was symptomatic of an advanced stage of the disease. Until the twentieth century, the disease was certain death.

Suspicion arose that the pancreas was somehow connected with the disease, for in 1893, two German physiologists, Joseph von Mering (1849–1908) and Oscar Minkowski (1858–1931), had excised the pancreas of experimental animals and found that severe diabetes developed quickly. Once the hormone concept had been propounded by Starling and Bayliss, it seemed logical to suppose that the pancreas produced a hormone which controlled the manner in which the body broke down sugar.

Attempts to isolate the hormone from the pancreas… failed, however. Of course, the chief function of the pancreas was to produce digestive juices, so that it had a large content of protein-splitting enzymes. If the hormone were itself a protein (as, eventually, it was found to be) it would break down in the very process of extraction.

In 1920, a young Canadian physician, Frederick Grant Banting (1891–1941), conceived the notion of tying off the duct of the pancreas in the living animal and then leaving the gland in position for some time. The digestive-juice apparatus of the gland would degenerate, since no juice could be delivered, while those portions secreting the hormone directly into the blood stream would (he hoped) remain effective. In 1921, he obtained some laboratory space at the University of Toronto and with an assistant, Charles Herbert Best (1899–[1978]), he put his notion into practice. He succeeded famously and isolated the hormone “insulin.” The use of insulin has brought diabetes under control, and while a diabetic cannot be truly cured even so and must needs submit to tedious treatment for all his life, that life is at least a reasonably normal and prolonged one.

Charles Best and Frederick Banting, circa 1924, University of Toronto Library, from Wikipedia.

Where does physics, engineering, and technology enter this story? Consider the insulin pump. This modern medical device includes a battery-powered pump, an insulin reservoir, and a cannula and tubing for delivery of the insulin under the skin. It is controlled by a computer the size of a cell phone.

 

To learn more about the discovery of insulin, see the University of Toronto website: https://insulin100.utoronto.ca.

Happy 100th birthday, insulin! 

New Heritage Minute: The Discovery of Insulin.

https://www.youtube.com/watch?v=amCeBhkNo50

Who is Banting?

https://www.youtube.com/watch?v=V0_9LzAYLRY 

 

Insulin 2021

https://www.youtube.com/watch?v=q0EdNC1Fq7k

 

Insulin Pump

https://www.youtube.com/watch?v=Crkyl9bqfC0