Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential

Twenty years ago this week, I published a Research Commentary in Circulation Research about the “ Influence of a Perfusing Bath on the Foot of the Cardiac Action Potential” (Volume 86, Pages e19-e22, 2000). I like this article for several reasons: it’s short and to the point; it’s a theoretical paper closely tied to data; it’s well written; and it challenges a widely-accepted interpretation of an experiment by a major figure in cardiac electrophysiology.

Back in my more pugnacious days, I wouldn’t hesitate to take on senior scientists when I disagreed with them. In this case, I critiqued the work of Madison Spach, a Professor at Duke University and a towering figure in the field. In 1981, Spach led an all-star team that measured cardiac action potentials propagating either parallel to or perpendicular to the myocardial fibers.

Spach MS, Miller WT III, Geselowitz DB, Barr RC, Kootsey JM, Johnson EA. “The Discontinuous Nature of Propagation in Normal Canine Cardiac Muscle: Evidence for Recurrent Discontinuities of Intracellular Resistance that Affect the Membrane Currents. Circulation Research, Volume 48, Pages 39–45, 1981.

They found that the rate-of-rise of the action potential and the time constant of the action potential foot depend on the direction of propagation. Continuous cable theory predicts that the rate-of-rise and time constant should be the same, regardless of direction. Therefore, they concluded, cardiac tissue is not continuous. Instead, they claimed that their experiment revealed the tissue’s discrete structure.

To be sure, cardiac tissue is discrete in a sense. It’s made of individual cells, coupled by intercellular junctions to form a “ syncytium.” Often, however, you can average over the cellular structure and treat the tissue as a continuum, just as you can often treat a material as a continuum even through it’s made from discrete atoms. For example, the bidomain model is a continuous description of the electrical properties of a microscopically heterogeneous tissue (See Section 7.9 of Intermediate Physics for Medicine and Biology for more about the bidomain model).

I’m skeptical of Spach’s interpretation of his data, and I’m not convinced that his observations imply the tissue’s discrete nature. I didn’t waste any time making this point in my article; I mention Spach by name in the first sentence of the Introduction. (In all quotes, I don’t include the references.)

In 1981, Spach et al observed a smaller maximum rate of rise of the action potential, max, and a larger time constant of the action potential foot,τfoot, during propagation parallel to the myocardiac [sic] fibers (longitudinal) than during propagation perpendicular to the fibers (transverse). They attributed these differences to the discrete cellular structure of the myocardium. Their research has been cited widely and is often taken as evidence for discontinuous propagation in cardiac tissue.

Several researchers have suggested that the observations of Spach et al may be caused by the bath perfusing the tissue rather than the discrete nature of the tissue itself… The purpose of this commentary is to model the experiment of Spach et al using a numerical simulation and to show that the perfusing bath plays an important role in determining the time course of the action potential foot.

I performed a computer simulation of wave fronts propagating through a slab of cardiac tissue that is perfused by a tissue bath. The tissue is represented as a bidomain, so its discrete nature was not incorporated into the model. I found that the rate-of-rise of the action potential is slower when propagation is parallel to the fibers compared to perpendicular to the fibers, just as Spach et al. observed. However, when I eliminated the purfusing bath this effect disappeared and the rate-of-rise was the same in both directions.

My favorite part of the article is in the Discussion, where I summarize my conclusion using a syllogism.

The data of Spach et al are cited widely as evidence for discontinuous propagation in cardiac tissue. Their hypothesis of discontinuous propagation is supported by the following logic: (1) During 1-dimensional propagation in a tissue with continuous electrical properties, the time course of the action potential (including max and τfoot) does not depend on the intracellular and interstitial conductivities; (2) experiments indicate that in cardiac tissue max and τfoot differ with the direction of propagation and therefore with conductivity; and (3) therefore, the conductivity of cardiac tissue is not continuous. A flaw exists in this line of reasoning: when a conductive bath perfuses the tissue, the propagation is not 1-dimensional. The extracellular conductivity is higher for the tissue near the surface (adjacent to the bath) than it is for the tissue far from the surface (deep within the bulk). Therefore, gradients in Vm exist not only in the direction of propagation, but also in the direction perpendicular to the tissue surface. Reasoning based on the 1-dimensional cable model (such as used in the first premise of the syllogism above) is not applicable.

In biology and medicine, the main purpose of computer simulations is to suggest new experiments, so I proposed one.

One way to distinguish between the 2 mechanisms ([the discrete structure] versus perfusing bath) would be to repeat the experiments of Spach et al with and without a perfusing bath present. The tissue would have to be kept alive when the perfusing bath was absent, perhaps by arterial perfusion. The results … indicate that when the bath is eliminated, the action potential foot should become exponential, with no differences between longitudinal and transverse propagation. Furthermore, the maximum rate of rise of the action potential should increase and become independent of propagation direction. Although this experiment is easy to conceive, it would be susceptible to several sources of error. If Vm were measured optically, the data would represent an average over a depth of a few hundred microns. Because the model predicts thatVm changes dramatically over such distances, the data would be difficult to interpret. Microelectrode measurements, on the other hand, are sensitive to capacitative [sic] coupling to the perfusing bath, and the degree of such coupling depends on the bath depth. The rapid depolarization phase of the action potential is particularly sensitive to electrode capacitance. Although it is possible to correct the data for the influence of electrode capacitance, these corrections would be crucial when comparing data measured at different bath depths.

A later paper by Oleg Sharifov and Vladimir Fast (Heart Rhythm, Volume 3, Pages 1063–1073, 2006) suggests a better way to perform this experiment: use optical mapping but with the membrane dye introduced through the perfusing bath so it stains only the surface tissue. In this case, there is no capacitive coupling (no microelectrode) and little averaging over depth (the optical signal arises from only surface tissue). This would be an important experiment, but it hasn’t been performed yet. Until it is, we can’t resolve the debate over discrete versus continuous behavior.

The last paragraph in the paper sums it all up. I particularly like the final sentence.

We cannot conclude from our study that [discrete structures] are not important during action potential propagation. Nor can we conclude that discontinuous propagation does not occur (particularly in diseased tissue). These factors may well play a role in propagation. We can conclude, however, that the influence of a perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction… Therefore, differences in action potential shape with direction cannot be taken as definitive evidence supporting discontinuous propagation… if a perfusing bath is present. Finally, without additional experiments, we cannot exclude the possibility that in healthy tissue the difference in the shape of the action potential upstroke with propagation direction is simply an artifact of the way the tissue was perfused.

Has my commentary had much impact? Nope. Compared to other papers I’ve written, this one is a citation dud. It has been cited only 27 times (22 if you remove self-citations); barely once a year. Spach’s 1981 paper has over 800 citations; over 20 per year. Even a response by Spach and Barr (Circ. Res., Volume 86, Pages e23-e28, 2000) to my commentary has almost twice as many citations as my original commentary. Does this difference in citation rate arise because I’m wrong and Spach’s right? Maybe. The only way to know is to do the experiment.

Originally published at



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Brad Roth

Brad Roth


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