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 

Digital Subtraction Angiography

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 more clearly (Fig. 16.23).

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

One of the pioneers of digital subtraction angiography was Charles Mistretta. The first two paragraphs in the introduction of his article “Digital Angiography: A Perspective” (Radiology, Volume 139, Pages 273-276, 1981) puts his work into perspective (references removed).

Within weeks of Roentgen’s discovery of the x-ray in 1895, Haschek and Lindenthal performed post-mortem arteriography in a hand. For the next 60 years, radiology in general and angiography in particular were largely limited to using film as a means for permanent recording of x-ray images. Recently, new technical developments in television, digital electronics, and image intensifier design have improved the electronic recording of images, and have caused renewed interest in the techniques of intravenous angiocardiography and arteriography originally described by Castellanos et al. [and] Robb and Steinberg.

Prior to 1970, applications involving the subtraction of unprocessed video information stored on analog discs or tape were common. These methods were adequate for augmentation of arterial injection techniques but were not sensitive enough to be used in conjunction with intravenous injection of contrast media. However, techniques capable of imaging the small contrast levels produced after an intravenous injection of contrast media were reported by Ort et al. and Kelcz et al. In combination with analog storage devices, these investigators used both time and K-edge energy subtraction methods for iodine imaging. In spite of their greater sensitivity, the poor reliability of those analog systems made them unsuitable for clinical use and lead to the design of the University of Wisconsin digital video image processor. Over the next five years, this processor was used by a number of investigators for a variety of energy and time subtraction studies both in animals and humans…

Mistretta is now professor emeritus in the Department of Radiology at the University of Wisconsin, where he has been doing medical imaging research since 1971. Students will benefit from his advice for young medical physicists presented in a spotlight article from the University of Wisconsin.

Choose a career and position that you enjoy and that you are eager to go to every day. Pick a career that makes a difference in the world and hopefully helps people. When you get old some day and start becoming aware of your mortality, it really helps to look back and say “I did my best and I helped make the world a little better place”. As medical physicists we have an excellent chance of making this come true.

2016 IEEE Honors Ceremony - Medal for Innovations in Healthcare Technology — Charles Mistretta

https://www.youtube.com/watch?v=y55ZStb93II

A Bifurcation Diagram for the Heart

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

A bifurcation diagram for the logistic map, showing 300 values of x_j 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 a. 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.

While Problem 41 provides insight into chaos and its relation to cardiac arrhythmias, Russ and I don’t draw a bifurcation diagram that summarizes how the action potential duration, APD, depends on the cycle length, CL (the time between stimuli, it’s the parameter analogous to a in the logistic map). In this post I present such a diagram.

A bifurcation diagram associated with Homework Problem 41 in Intermediate Physics for Medicine and Biology. The plot shows 20 values of APD_j for values of CL between 100 and 400 ms.

I don’t have the software to create a beautiful diagram like in Fig. 10.26, so I made one using MATLAB. It doesn’t have as much detail as does the diagram for the logistic map, but it’s still helpful.

The region marked 1:1 (for CL = 310 to 400 ms) implies steady-state behavior: Each stimulus excites an action potential with a fixed duration. Transients existed before the system settled down to a steady state, so I discarded the first 10,000 iterations before I plotted 20 values of APD_j (j = 10,001 to 10,020). 

Between CL = 283 and 309 ms the system predicts alternans: the response to the stimulus alternates between two APDs (long, short, long, short, etc.). Sometimes this is called a 2:2 response. Alternans are occasionally seen in the heart, and are usually a sign of trouble.

From CL = 154 to 282 ms the response is 2:1, meaning that after a first stimulus excites an action potential the second stimulus occurs during the refractory period and therefore has no effect. The third stimulus excites another action potential with the same duration as the first (once the transients die away). This is a type of period doubling; the stimulus has period CL but the response has period 2CL. In cardiac electrophysiology, this behavior resembles second-degree heart block.

For a CL of 153 ms or shorter, the system is chaotic. I didn’t explore the diagram in enough detail to tell if self-similar regions of steady-state behavior exist within the chaotic region, as occurs for the logistic map (see Fig. 10.27 in IPMB).

A bifurcation diagram is a useful way to summarize the behavior of a nonlinear system, and provides insight into deadly heart arrhythmias such as ventricular fibrillation.

Servoanalysis of Carotid Sinus Reflex Effects on Peripheral Resistance

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 pressure. Since the demonstration of the reflex function of these receptors… there has been much work on the responses of the blood pressure, heart, and peripheral vessels to changes in pressure in the carotid arteries and the aorta…. In our study, we subjected the isolated perfused carotid sinus to maintained pressures at different levels… and measured the resultant systemic pressures and pressure changes.

Two variables were measured: the systemic pressure (Russ and I call this the arterial pressure, p_art, in the homework problem) and the pressure in the carotid sinus (p_sinus). Let’s consider them one at a time.

Below I have drawn a schematic diagram of the circulatory system, consisting of the pulmonary circulation (blood flow through the lungs, pumped by the right side of the heart) and the systemic circulation (blood flow to the various organs such as the liver, kidneys, and brain, pumped by the left side of the heart). Scher and Young measured the arterial pressure in the systemic circulation. Most of the pressure drop occurs in the arterioles, capillaries, and venules, so you can measure the arterial pressure in any large artery (such a the femoral artery in the leg) and it is nearly equal to the pressure produced by the left side of the heart. Arterial pressure is pulsatile, but Scher and Young used blood reservoirs to even out the variation in pressure throughout the cardiac cycle, providing a mean pressure. 

The circulatory system.

My second drawing shows the carotid sinus, a region near the base of the carotid artery (the artery that feeds the brain) that contains baroceptors (nowadays commonly called baroreceptors; pressure sensors that send information about the arterial pressure to the brain so it can maintain the proper blood pressure). Scher and Young isolated the carotid sinus. They didn’t remove it completely from the animal—after all, they still needed to supply blood to the brain to keep it alive—but it was effectively removed from the circulatory system. In the drawing below I show it as being separate from the body. However, the nerves connecting the baroreceptors to the brain remain intact, so changes in the carotid sinus pressure still signal the brain to do whatever’s necessary to adjust the systemic pressure.

The carotid sinus was attached to a feedback circuit, similar to the voltage clamp used by Hodgkin and Huxley to study the electrical behavior of a nerve axon (see Sec. 6.13 of IPMB). I drew the feedback circuit as an operational amplifier (the green triangle), but this is metaphor for the real instrument. An operational amplifier will produce whatever output is required to keep the two inputs equal. In an electrical circuit, the output would be current and the inputs would be voltage. In Scher and Young’s experiment, the output was flow and the inputs were pressure. Specifically, one of the inputs was the pressure measured in the carotid sinus, and the other was a user-specified constant pressure (p_o in the drawing). The feedback circuit set p_sinus = p_o, allowing the sinus pressure to be specified by the experimenter.

A schematic diagram to represent the feedback circuit that controlled the sinus pressure.

 

Once this elaborate instrumentation was perfected, the experiment itself was simple: Adjust p_sinus to whatever value you want by varying p_o, wait several seconds for the system to come to a new equilibrium (so p_sinus and p_art have adjusted to a new constant value), and then measure p_art. Scher and Young obtained a plot of p_art versus p_sinus, similar to that given in our homework problem.

As always, details affect the results.

• Any contribution from pressure sensors in the aortic arch was eliminated by cutting the vagus nerve. Only baroreceptors in the carotid sinus contributed to controlling blood pressure.
• Scher and Young performed experiments on both dogs and cats. The data in Homework Problem 12 is from a cat.
• The blood reservoirs acted like capacitors in an electrical circuit, smoothing changes with time.
• In some experiments, a dog was given a large enough dose of anesthetic that the nerves sending information from the sinus baroreceptors to the brain were blocked. In other experiments, the nerve from the baroreceptors to the brain was cut. In both cases, the change in p_art with p_sinus disappeared.
  
• Many of Scher and Young’s experiments examined how the feedback circuit varied with time in response to either a step change or a sinusoidal variation in p_sinus. All of these experiments were ignored in the homework problem, which considers steady state. 
• Often my students are confused by Problem 12. They think there is only one equation relating p_art and p_sinus, but to solve a feedback problem they need two. To resolve this conundrum, realize that when the carotid sinus is not isolated but instead is just one of many large arteries in the body, its pressure is simply the arterial pressure and the second equation is p_sinus = p_art.
• The study provided hints about how the brain adjusted arterial pressure—by changing heart rate, stroke volume, or systemic resistance—but didn’t resolve this issue. 
• The experiments were performed at the University of Washington School of Medicine in Seattle. 
  
• Allen Scher was a World War II veteran, serving as a Marine in the Pacific. He contributed to our understanding of the electrocardiogram, and was a coauthor on the Textbook of Physiology, cited often as “Patton et al. 1989” in IPMB.
  
• Scher was born on April 17, 1921 and died May 12, 2011 at the age of ninety. Recently we celebrated the the hundred-year anniversary of his birth. Happy birthday, Dr. Scher!

A Dozen Electrocardiograms Everyone Should Know

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

The electrocardiogram (ECG).

Electrocardiograms are plotted on graph paper that consists of large squares, each divided into a five-by-five grid of small squares. The horizontal axis is time and the vertical axis is voltage. Each large square (or box) corresponds to a fifth of a second and a half of a millivolt.

The normal ECG contains three deflections: a small P wave associated with depolarization of the atria, a large narrow QRS complex associated with depolarization of the ventricles, and a T wave associated with repolarization of the ventricles.

A normal heart rate ranges from 60 to 100 beats per minute. The ECG below repeats every four boxes, so the time between beats is 0.8 seconds or 0.0133 minutes, which is equivalent to a heart rate of 75 beats per minute. 

Normal heartbeat.

2. Sinus Bradycardia

A sinus bradycardia is a slow heart beat (slower than 60 beats per minute, or five boxes). The term sinus means the sinoatrial node is causing the slow rate. This node in the right atrium is the heart’s natural pacemaker. Other than its slow rate, the ECG looks normal. A sinus bradycardia may need to be treated by drugs or an implantable pacemaker, or it may represent the healthy heartbeat of a trained athlete who pumps a large amount of blood with each beat. 

Sinus bradycardia.

3. Sinus Tachycardia

A sinus tachycardia is the opposite of a sinus bradycardia. It’s a fast heart beat (faster than 100 beats per minute, or three boxes). The rapid rate arises because the sinoatrial node paces the heart too quickly. A sinus tachycardia may trigger other more severe arrhythmias we discuss later.

Sinus tachycardia.

4. Atrial Flutter

During atrial flutter a reentrant circuit exists in the atria. That is, a wave front propagates in a loop, constantly chasing its tail. The nearly sinusoidal, small-magnitude signal in the ECG originates in the atria. Every few rotations around the circuit, the wave front passes through the atrioventricular node—the only connection between the atria and the ventricles—giving rise to a normal-looking QRS complex (the T wave is buried in the atrial signal).

Atrial flutter.

5. Atrial Fibrillation

Atrial fibrillation is similar to atrial flutter, except the wave fronts in the atrium are not as well organized, propagating in complicated, chaotic patterns resembling turbulence. The part of the ECG arising from the atria looks like noise. Occasionally the wave front passes through the atrioventricular node and produces a normal QRS complex. During atrial fibrillation the ventricles do not fill with blood effectively because the atria and ventricles are not properly synchronized.

Atrial fibrillation.

6. First-Degree Atrioventricular Block

In first-degree atrioventricular block, the time between the end of the P wave and the start of the QRS complex is longer than it should be. Otherwise, the ECG appears normal. This rarely results in a problem for the patient, but does imply that the atrioventricular node is not healthy and trouble with it may develop in the future.

First-degree atrioventricular block.

7. Second-Degree Atrioventricular Block

In second-degree atrioventricular block, the P waves appear like clockwork. The signal often passes through the atrioventricular node to the ventricles, but occasionally it does not. Different types of second-degree block exist. Sometimes the delay between the P wave and the QRS complex gets progressively longer with each beat until propagation through the atrioventricular node fails. Other times, the node will periodically drop a beat; for example if every second beat fails you have 2:1 AV block. Still other times, the node fails sporadically. 

Second-degree atrioventricular block.

8. Third-Degree Atrioventricular Block

If your atrioventricular node stops working entirely, you have third-degree atrioventricular block (also known as complete heart block). A ventricular beat exists because some other part of the conduction system (say, the Bundle of His or the Purkinje fibers) serves as the pacemaker. In this case, the P wave and QRS complex are unsynchronized, like two metronomes set to different rates. In complete heart block, the ventricles typically fire at a slow rate. Sometimes a patient will intermittently go in and out of third-degree block, causing fainting spells.

Third-degree atrioventricular block.

9. Premature Ventricular Contraction

Sometimes the heart will beat with a normal ECG, and than sporadically have an extra ventricular beat: a premature ventricular contraction. Usually these beats originate within the ventricle, so they are not distributed through the cardiac conduction system and therefore produce a wide, bizzare QRS complex. As long as these premature contractions are rare they are not too dangerous, but they risk triggering more severe ventricular arrhythmias.

Premature ventricular contraction.

10. Ventricular Tachycardia

A ventricular tachycardia is a rapid heartbeat arising from a reentrant circuit in the ventricles. The ECG looks like a series of premature ventricular contractions following one after another. The VT signal typically has a large amplitude, and the atrial signal is often too small to be seen. This is a serious arrhythmia, because at such a fast rate the heart doesn’t pump blood effectively. It’s not lethal itself, but can become deadly if it decays into ventricular fibrillation.

Ventricular tachycardia.

11. Ventricular Fibrillation

In ventricular fibrillation, different parts of the ventricles contract out of sync, resulting in the heart quivering rather than beating. A heart in VF does not pump blood, and the patient will die in ten to fifteen minutes unless defibrillated by a strong electric shock. Ventricular fibrillation is the most common cause of sudden cardiac death.

Ventricular fibrillation.

12. Asystole

In asystole, the heart has no electrical activity, so the ECG is a flat line. Asystole is the end stage of ventricular fibrillation, when the chaotic electrical activity dies away and nothing remains.

Asystole.

Once you master these twelve ECGs, you’ll be on your way to understanding the electrical behavior of the heart. If you want to learn more, I suggest trying the SkillStat six-second ECG game, which includes 27 ECGs. It’s fun.

Electric and Magnetic Fields From Two-Dimensional Anisotropic Bisyncytia

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. 

 

Sepulveda and Wikswo (1987).

In this post, I discuss the theoretical prediction by Nestor Sepulveda and John Wikswo in the mid 1980s that preceded and motivated the experiment.

Sepulveda NG, Wikswo JP (1987) “Electric and Magnetic Fields From Two-Dimensional Anisotropic Bisyncytia,” Biophysical Journal, Volume 51, Pages 557-568.

Their abstract is presented below.

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium [a synonym for bidomain] with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue.

Sepulveda and Wikswo assumed the tissue was excited by a brief stimulus through an electrode (purple dot in the illustration below), resulting in a circular wave front propagating outward. The transmembrane potential coutours at one instant are shown in red. The assumption of a circular wave front is odd, because cardiac tissue is anisotropic. A better assumption would have been an elliptical wave front with its long axis parallel to the fibers. Nevertheless, the circular wave front captures the essential features of the problem.

If the tissue were isotropic, the intracellular current density would point radially outward and the extracellular current density would point radially inward. The intracellular and extracellular currents would exactly cancel, so the net current (their sum) would be zero. Moreover, the net current would vanish if the tissue were anisotropic but had equal anisotropy ratios. That is, if the ratios of the electrical conducivities parallel and perpendicular to the fibers were the same in the intracellular and extracellular spaces. The only way to produce a net current (shown as the blue loops in the illustration below) is if the tissue has unequal anisotropy ratios. In that case, the loops are four-fold symmetric, rotating clockwise in two quadrants and counterclockwise in the other two.

Current loops produce magnetic fields. The right-hand-rule implies that the magnetic field points up out of the plane in the top-right and the bottom-left quadrants, and down into the plane in the other two. The contours of magnetic field are green in the illustration below, and the peak magnitude for a 1 mm thick sheet of is about one fourth of a nanotesla.

Jut for fun, I superimposed the transmembrane potential, net current density, and magnetic field plots in the picture below.

Notes:

1. The measurement of the magnetic field is a null detector of unequal anisotropy ratios. In other words, in tissue with equal anisotropy ratios the magnetic field vanishes, so the mere existence of a magnetic field implies the anisotropy ratios are unequal. The condition of unequal anisotropy ratios has many implications for cardiac tissue. One is discussed in Homework Problem 50 in Chapter 7 of IPMB. 
2. If the sheet of cardiac tissue is superfused by a saline bath, the magnetic field distribution changes.
   
3. Wikswo was a pioneer in the field of biomagnetism. In particular, he developed small scanning magnetometers that had sub-millimeter spatial resolution. He was in a unique position of being able to measure the magnetic fields that he and Sepulveda predicted, which led to the figure included in IPMB. 
4. I was a graduate student in Wikswo’s laboratory when Sepulveda and Wikswo wrote this article. Sepulveda, a delightful Columbian biomedical engineer and a good friend of mine, worked as a research scientist in Wikswo’s lab. He was an expert on the finite element method—the numerical technique used in his paper with Wikswo—and had written his own finite element code that no one else in the lab understood. He died a decade ago, and I miss him. 
5. Sepulveda and Wikswo were building on a calculation published in 1984 by Robert Plonsey and Roger Barr (“Current Flow Patterns in Two Dimensional Anisotropic Bisyncytia With Normal and Extreme Conductivities,” Biophys. J., 45:557-571). Wikswo heard either Plonsey or Barr give a talk about their results at a scientific meeting. He realized immediately that their predicted current loops implied a biomagnetic field. When Wikswo returned to the lab, he described Plonsey and Barr’s current loops at a group meeting. As I listened, I remember thinking “Wikswo’s gone mad,” but he was right.
   
6. Two years after their magnetic field article, Sepulveda and Wikswo (now with me included as a coauthor) calculated the transmembrane potential produced when cardiac tissue is stimulated by a point electrode. But that’s another story.
   

I’ll give Sepulveda and Wikswo the last word. Below is the concluding paragraph of their article, which looks forward to the experimental measurement of the magnetic field pattern that was shown in IPMB.

The bidomain model of cardiac tissue provides a tool that can be explored and used to study and explain features of cardiac conduction. However, it should be remembered that “a model is valid when it measures what it is intended to measure” (31). Thus, experimental data must be used to evaluate the validity of the bidomain model. This evaluation must involve comparison of the model's predictions not only with measured intracellular and extracellular potentials but also with the measured magnetic fields. When the applicability of the bidomain model to a particular cardiac preparation and the validity and reliability of our calculations have been determined experimentally, this mathematical approach should then provide a new technique for analyzing normal and pathological cardiac activation.

Members of Wikswo's lab at Vanderbilt University in the mid 1980s: John Wikswo is on the phone, Nestor Sepulveda is in the white shirt and gray pants, and I am on the far right. The other people are Frans Gielen (the tall guy with arms crossed on the left), Ranjith Wijesinghe (between Gielen and Sepulveda), Peng Zhang (between Wikswo and Sepulveda), and Pat Henry (knelling).

The Code Breaker: Jennifer Doudna, Gene Editing, and the Future of the Human Race

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. These revolutions arose from the discovery, beginning just over a century ago, of the three fundamental kernels of our existence: the atom, the bit, and the gene.

The first half of the twentieth century, beginning with Albert Einstein’s 1905 papers on relativity and quantum theory, featured a revolution driven by physics. In the five decades following his miracle year, his theories led to atom bombs and nuclear power, transistors and spaceships, lasers and radar.

The second half of the twentieth century was an information-technology era, based on the idea that all information could be encoded by binary digits—known as bits—and all logical processes could be performed by circuits with on-off switches. In the 1950s, this led to the development of the microchip, the computer, and the internet. When these three innovations were combined, the digital revolution was born.

Now we have entered a third and even more momentous era, a life-science revolution. Children who study digital coding will be joined by those who study genetic code.

Early in the book, Isaacson describes Francisco Mojica’s discovery that bacteria have “CRISPR spacer sequences”: strands of DNA that serve as an immune system protecting them from viruses.

As we humans struggle to fight off novel strains of viruses, it’s useful to note that bacteria have been doing this for about three billion years, give or take a few million centuries. Almost from the beginning of life on this planet, there’s been an intense arms race between bacteria, which developed elaborate methods of defending against viruses, and the ever-evolving viruses, which sought ways to thwart those defenses.

Mojica found that bacteria with CRISPR space sequences seems to be immune from infection by a virus that had the same sequence. But bacteria without the spacer did get infected. It was a pretty ingenious defense system, but there was something even cooler: it appeared to adapt to new threats. When new viruses came along, the bacteria that survived were able to incorporate some of that virus’s DNA and thus create, in its progeny, an acquired immunity to that new virus. Mojica recalls being so overcome by emotion at this realization that he got tears in his eyes. The beauty of nature can sometimes do that to you.

The Code Breaker focuses on the life and work of Jennifer Doudna, who won the 2020 Nobel Prize in Chemistry. However, the star of the book is not Doudna, nor Emmanuelle Charpentier (who shared the prize with Doudna), nor Mojica, nor any of the other scientific heroes. The star is RNA, the molecule that carries genetic information from DNA in the nucleus to the cytoplasm where proteins are produced.

By 2008, scientists had discovered a handful of enzymes produced by genes that are adjacent to the CRISPR sequences in a bacteria’s DNA. These CRISPR-associated (Cas) enzymes enable the system to cut and paste new memories of viruses that attack the bacteria. They also create short segments of RNA, known as CRISPR RNA (crRNA), that can guide a scissors-like enzyme to a dangerous virus and cut up its genetic material. Presto! That’s how the wily bacteria create an adaptive immune system!

Doudna and Charpentier’s Nobel Prize resulted from their developing the CRISPR-Cas9 system into a powerful technique for gene editing.

The study of CRISPR would become a vivid example of the call-and-response duet between basic science and translational medicine. At the beginning it was driven by the pure curiosity of microbe-hunters who wanted to explain an oddity they had stumbled upon when sequencing the DNA of offbeat bacteria. Then it was studied in an effort to protect the bacteria in yogurt cultures from attacking viruses. That led to a basic discovery about the fundamental workings of biology. Now a biochemical analysis was pointing the way to the invention of a tool with potential practical uses. “Once we figured out the components of the CRISPR-Cas9 assembly, we realized that we could program it on our own,” Doudna says. “In other words, we could add a different crRNA and get it to cut any different DNA sequence we chose.”

Several other themes appear throughout The Code Breaker: 

• The role of competition and collaboration in science, 
• How industry partnerships and intellectual property affect scientific discovery, 
• The ethics of gene editing, and
• The epic scientific response to the COVID-19 pandemic. 

I’m amazed that Isaacson’s book is so up-to-date. I received my second dose of the Pfizer-BioNTech vaccine last Saturday and then read The Code Breaker in a three-day marathon. My arm was still sore while reading the chapter near the end of the book about RNA Covid vaccines like Pfizer’s.

There’s a lot of biology and medicine in The Code Breaker, but not much physics. Yet, some of the topics discussed in Intermediate Physics for Medicine and Biology appear briefly. Doudna uses x-ray diffraction to decipher the structure of RNA. Electroporation helps get vaccines and drugs into cells. Electrophoresis, microfluidics, and electron microscopy are mentioned. I wonder if injecting more physics and math into this field would supercharge its progress. 

CRISPR isn’t the first gene-editing tool, but it increases the precision of the technique. As Winchester noted in The Perfectionists, precision is a hallmark of technology in the modern world. Quammen’s book Spillover suggests that humanity may be doomed by an endless flood of viral pandemics, but The Code Breaker offers hope that science will provide the tools needed to prevail over the viruses.

I will close with my favorite passage from The Code Breaker: Isaacson’s paean to curiosity-driven scientific research.

The invention of easily reprogrammable RNA vaccines was a lightning-fast triumph of human ingenuity, but it was based on decades of curiosity-driven research into one of the most fundamental aspects of life on planet earth: how genes encoded by DNA are transcribed into snippets of RNA that tell cells what proteins to assemble. Likewise, CRISPR gene-editing technology came from understanding the way that bacteria use snippets of RNA to guide enzymes to chop up dangerous viruses. Great inventions come from understanding basic science. Nature is beautiful that way.

 

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“How CRISPR lets us edit our DNA,” a TED talk by Jennifer Doudna. 

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

Nobel Lecture, Jennifer Doudna, 2020 Nobel Prize in Chemistry.

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

Walter Isaacson, The Code Breaker, Talks at Google.

https://www.youtube.com/watch?v=-LuAuZ09uSs

 

CRISPR-Cas9 (“Mr. Sandman” Parody), by Tim Blais at A Capella Science.

https://www.youtube.com/watch?v=k99bMtg4zRk