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(Circulation Research. 2000;86:e23.)
© 2000 American Heart Association, Inc.

Response to Research Commentary

Effects of Cardiac Microstructure on Propagating Electrical Waveforms

Madison S. Spach, Roger C. Barr

From the Departments of Pediatrics (M.S.S., R.C.B.), Cell Biology (M.S.S.), and Biomedical Engineering (R.C.B.), Duke University Medical Center, Durham, NC.

Correspondence to Madison S. Spach, Box 3475, Duke University Medical Center, Durham, NC 27710. E-mail cspach{at}acpub.duke.edu

	Abstract

Top Abstract Introduction Points of Agreement Between... Perfusate Effects Waveform Variations Not... Conclusions References

 
Abstract—Electrical waveforms measured during propagation at microscopic level are considerably affected by normal variations in cardiac microstructure as well as by the superfusing fluid. On the basis of evidence we present in this article, we argue that the anisotropic waveform variations discussed here are explained primarily by the associated variations in different microstructural components of myocardial architecture rather than by the effects of the perfusing bath. The results suggest that different components of myocardial architecture have preferential effects on _max and on the shape of the foot of the transmembrane action potential (V_m foot). Resistive discontinuities primarily affect _max, and an additional capacitive component in the local circuit due to the capillaries in interstitial space primarily affects V_m foot. Resistive discontinuities also have an important influence on cardiac conduction. These discontinuities include spatial variations in the size of interstitial space (interstitial resistive discontinuities) and the role of cellular scaling (effects of cell size) when changes occur in the cellular and multicellular distribution of gap junctions during remodeling of normal mature myocardium to proarrhythmic structural substrates. The full text of this article is available at http://www.circresaha.org.

Key Words: discontinuous conduction • anisotropy • action potential foot • capillaries • interstitial discontinuities

	Introduction

Top Abstract Introduction Points of Agreement Between... Perfusate Effects Waveform Variations Not... Conclusions References

 
On the basis of well-known bidomain model studies,^{1 2 3 4 5 6 7 8 9 10} Roth¹¹ notes in his commentary about our 1981 and 1998 papers^{12 13} that directional differences in the shape of the foot of the transmembrane potential (V_m) and in _max cannot be taken as definitive evidence of discontinuous propagation or capillary effects. Specifically, he concludes^{4 11} that the directional differences in _max and V_m foot that we reported^{12 13} result from the way the tissue was perfused and the interaction of current flow in the tissue with that in the surrounding fluid.

For purposes of clarity, we limit our response to uniform anisotropic myocardium and begin by noting the following about our recent (1998) article.¹³ We considered our experimental tests (and "2-domain" model results) in this paper to provide strong support for the following hypothesis: interstitial electrical field interactions between the electrically passive capillaries and active myocytes produce an additional interstitial component in the local electrical circuit of propagating excitation waves in working myocardium. This extra capacitive component depends on the direction of propagation in relation to the anisotropic distribution of the capillaries, and it also depends on the density of the capillaries and the size of interstitial space. The extra capacitive component due to normal capillaries primarily affects V_m foot, with much less effect on _max. This mechanism represents an extension of the general model of 1-dimensional cardiac fiber interactions of Medvinskii and Pertsov.¹⁴ To formalize our new "capillary" hypothesis, we developed a 2-domain model of cardiac muscle represented as 2 separate but interconnected spaces, anisotropic intracellular space with or without 2-dimensional discrete ventricular cells¹⁵ and anisotropic interstitial space containing the anisotropic distribution of capillaries. The electrical model was based on the morphology of working myocardium. When the documented variations in microstructure (cell geometry, density of capillaries, and dimensions of interstitial space) were approximated in the model, its predictions for V_m foot and _max were in good agreement with the experimental data.¹³

During longitudinal (LP) and transverse propagation (TP), there was considerable variability in the general pattern of _max and in the phase-plane trajectories of V_m foot; eg, there were variable deviations from an exponential rise of V_m foot. Our hypothesis and model did not include the perfusing bath effects that have been demonstrated in the bidomain model studies of Roth and others,^{1 2 3 4 5 6 7 8 9 10 11} because it focused on the tissue at a microscopic size scale. As detailed in an excellent review by Henriquez,¹⁰ bidomain models of bath effects have considered propagation at the larger macroscopic level where the stochastic effects of normal cardiac microstructure are averaged.¹⁵ We think these differences in size scale are highly important when considering our results^{12 13} in relation to the effects of the perfusing bath shown by bidomain models.^{1 2 3 4 5 6 7 8 9 10 11}

We wish to address the following 3 specific points in response to Roth’s commentary: (1) matters on which we agree with Roth; (2) ways in which our results are not accounted for by bidomain model results of the bath effect; (3) our conclusion, which we consider to emphasize the need to develop more comprehensive models with the salient characteristic of incorporating features of actual cardiac architecture at the microscopic level.^{13 15 16}

	Points of Agreement Between Experimental Data and Results of Perfusate Effect

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We agree that Roth’s results in his accompanying paper,¹¹ as well as the results of other bidomain model studies,¹⁰ clearly demonstrate the same general changes in the shape of V_m foot and in _max that we presented in our 1981 initial report of discontinuous conduction.¹² That is, the rise of the action potential foot is slower (greater _foot) and _max is less during fast LP (low-resistance direction) than slow TP (high-resistance direction). If these general features, consistent with those of Plonsey and Barr,^{1 2} were the only consideration, we would agree that one cannot distinguish between a mechanism due to the discrete structure of cardiac muscle^{12 13} and the effects of the perfusing bath described in bidomain model studies.^{1 2 3 4 5 6 7 8 9 10 11}

In retrospect, we also agree with Roth that comparison of the shape of V_m foot in mature myocardium with action potentials measured in single layers of cultured neonatal cells¹⁷ (no capillaries) does not distinguish between a capillary mechanism and the superfusate effect. On the other hand, our analysis of the optical action potentials of Fast and Kléber¹⁷ provided a necessary first step before proceeding to the major experimental test of the capillary hypothesis, ie, comparison of the phase-plane trajectory of V_m foot in neonatal versus mature ventricular muscle.¹³ At that time there were no available data about the shape of V_m foot in neonatal preparations, including the elegant data of Fast and Kléber¹⁷ in neonatal cell cultures. We therefore considered that their published optical action potentials provided an excellent opportunity for an initial experimental test of our hypothesis. Our analysis of their data also provided a rigorous test of the phase-plane analysis method to ensure that the deviations from an exponential rise of V_m foot we found in working myocardium were not the result of experimental artifact. That is, there were concave deviations from a linear (exponential) phase-plane trajectory of V_m foot during LP in ventricular muscle, and these deviations should not (and did not¹³ ) occur in the optical action potentials that Fast and Kléber¹⁷ had recorded in neonatal cell cultures.

Roth¹¹ suggests that a good experiment would be to remove the superfusing fluid in the bath. We attempted that experiment but could not achieve successful measurements. Although we were unable to cover the preparations with oil in our large tissue bath (15 cm in diameter), we lowered the level of the superfusate to the surface of the tissue. When there was no fluid covering the surface, beat-to-beat changes in the intracellular (_i) and extracellular (_e) potential waveforms occurred, which prevented stable measurements.

	Perfusate Effects

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The choice of the depth of perfusate in the volume conductor produces conflicting considerations in the study of anisotropic conduction events when measuring intracellular and extracellular potentials.^{18 19 20 21} In our first study of anisotropic conduction in uniform anisotropic muscle,¹⁸ we found systematic differences in the general shape and amplitude of _e waveforms when conduction progressed in different directions from a single stimulus site. The directionally dependent changes in _e at the tissue surface were accounted for by a "continuous" anisotropic model of directional differences in effective axial resistance, which ignored interstitial anisotropy in a preparation exposed to a large volume conductor.¹⁸ We then collaborated with David Geselowitz²² to evaluate the effects of the volume conductor on _e at the surface of tissue with and without interstitial anisotropy. The model of Geselowitz et al,²² and the associated experimental measurements, showed that as long as the level of the perfusate exceeded 1 mm above the tissue surface, there was good agreement with the measured _e waveforms and the bidomain model predictions; ie, interstitial anisotropy was not necessary to explain the _e waveforms.²² However, when the fluid level decreased to <1 mm above the surface, interstitial anisotropy became important; ie, the general _e wave shape was altered and the amplitude of the waveforms increased considerably.²² Consequently, to achieve extracellular measurements at the surface, we have maintained an adequate volume conductor in our tissue bath experiments.

	Waveform Variations Not Accounted for by Bath Effect

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Discontinuous Propagation Evident in Extracellular Waveforms
We subsequently found that the most straightforward evidence for discontinuous propagation in uniform anisotropic myocardium lies in the analysis of extracellular waveforms.²⁰ Superimposed on the smooth-appearing _e waveforms, which are accounted for by a continuous anisotropic medium,¹⁸ there is notching of the _e first and second derivative waveforms, and the notches become more frequent as the wavefront shifts from LP to TP.²⁰ Recent results with a 2-dimensional discrete cellular model¹⁵ of uniform anisotropic ventricular muscle produced good agreement with the experimental _e, d_e/dt, and d²_e/dt² waveforms during LP, oblique conduction, and TP.²³ The _e notching was found to be associated with more prominent conduction delays between cells and groups of cells during TP than LP in mature myocardium,^{15 23} ie, discontinuous propagation.

At this point, therefore, it is important to separate the question as to whether discontinuous propagation does or does not occur at a microscopic level from Roth’s¹¹ additional important question as to how one can distinguish between the effects of cardiac microstructure and the effects of the perfusing bath shown by bidomain models on propagating waveforms. We have not questioned the validity of the bidomain model predictions of the bath effects.^{1 2 3 4 5 6 7 8 9 10 11} Rather, we found that the experimental variations in _max and in the time course of V_m foot " ... were not explained by computer simulations based on bidomain models,"¹³ (p 1145) at least to the present time.

_max
On the basis of measurements in trabecula and papillary muscles from ferret hearts, in 1985 Suenson²⁴ reported that differences in resistance of the medium to which the tissue surface was exposed produces curved propagating wavefronts beneath the surface. He noted that when a wavefront deviates from a plane wave, the leading cells will be loaded electrically by the lagging neighboring cells. He also extended the interpretation of his results about curvature beneath the surface (along the z axis) to the x-y plane of the tissue surface by noting that "the effects of a curved wavefront may represent an alternative explanation of the findings [directional differences in _max and _foot] of Spach et al. (1981)¹² who introduced the theory of discontinuous propagation in dog myocardium ...."²⁴ (p 89).

Suenson was correct, given that, at that time, we had not considered the effects of the curvature of wavefronts in the x-y plane (along the surface) at a macroscopic size scale. Therefore, we challenged our 1981 data¹² by performing detailed measurements of _max for conditions under which there should be no x-y plane curvature effects. We produced "4-way conduction" of macroscopic plane waves at each microelectrode impalement site; ie, propagation occurred in both directions along the long axis of the fibers and in both directions along the transverse axis.²⁵ The results showed that mean TP _max was significantly greater than mean LP _max, as we had originally found.¹² We concluded, therefore, that our _max results were not explained by curvature of wavefronts.

The chronological appearance of "new" information based on bidomain models now becomes pertinent. Although in 1978 Tung²⁶ formalized in a bidomain model the mathematical representation of the separate intracellular and interstitial spaces as a single interpenetrating domain, the powerful applications using mathematical representations of this model to in vitro measurements (eg, virtual cathode²⁷ ) did not appear until after our 1981 paper.¹² Since then, a number of model results have demonstrated the effects of the perfusing bath on propagating depolarization.^{1 2 3 4 5 6 7 8 9 10 11} All of the bidomain models that we know of predict the following fixed relationships between _max and V_m foot: (1) at the surface, or at a specific depth below the surface, _max and the shape of V_m foot are constant during propagation along any given axis of conduction, and 2) when _max decreases, the rate of rise of V_m foot decreases (and vice versa).

In contrast to the bidomain model predictions of fixed values of _max along a given axis of propagation, our 4-way conduction analysis showed that the values of _max were different from cell to cell during LP (93 to 139 V/s) and TP (110 to 181 V/s), and at a few sites TP _max was less than LP _max.²⁵ That these considerable variations along the same axis of conduction were not measurement artifact, or due to the perfusing bath, was indicated by fact that the absolute values of LP _max and TP _max at the same impalement site varied independently of each other (some of the lowest values of LP _max occurred at the same site as the highest TP _max values). On the other hand, one might argue that the considerable cell-to-cell _max variation along the same axis of conduction was influenced by the tip of the microelectrode penetrating to different depths beneath the surface at different sites, which could produce different _max values according to bidomain model predictions.^{1 2 3 4 5 6 7 8 9 10 11} However, when we maintained the microelectrode tip in a fixed position (ie, no change in its depth), _max changed considerably at the same site when the direction of conduction was reversed 180 degrees during LP. Similarly, prominent _max changes occurred at the same site when conduction was reversed 180 degrees during TP.

Thus, undulating values of _max occur in any given direction of propagation, and it is the average _max value that is larger during TP than LP.^{15 25} This anisotropic feature of _max is explained by variations in cellular loading that generate variations in _max that are dependent on the complex distribution of r_i discontinuities produced by the gap junctions and cellular boundaries in the path of an advancing excitation wave.¹⁵

V_m Foot
Because there had been no detailed experimental analysis of the time course of V_m foot during anisotropic propagation, we performed a similar 4-way conduction analysis of V_m foot in which we used phase-plane analysis.¹³ Although the average values of _foot were greater during LP than TP, as found originally,¹² different sites demonstrated variable deviations from a linear (exponential) V_m foot trajectory during both LP and TP. Quite importantly, _max and V_m foot varied independently of one another. We therefore considered the major point established by the experimental results to be that " ... electrical loading due the microstructure of working myocardium can independently alter _max or the foot of the action potential."¹³ (p 1159). This experimental result is different from the predictions of continuous medium theory, as well as the bidomain model predictions for the effects of the perfusing bath as done to date.^{1 2 3 4 5 6 7 8 9 10 11}

To explain these results, several resistive models^{17 28 29 30 31} (including our two-dimensional cellular model¹⁵ ) were evaluated but discarded. None of the models of resistive discontinuities produced deviations from a linear phase-plane trajectory of V_m at any site for all directions of conduction. On the basis of the measurements by Crone and Olesen³² and Oleson and Crone³³ of the passive properties of cerebral capillaries, we then considered that the capillaries provided a structure in interstitial space for electrotonic interactions with the active myocytes. This structural arrangement is similar to that in the model of Medvinskii and Pertsov¹⁴ of electrical field interactions between active and inactive cardiac fibers. Thus, we hypothesized that the microstructure that could produce an effect as observed in the data was that of the capillaries.

Because the perfusing bath conditions were the same for all of our experiments, we consider the following to provide experimental support¹³ for the capillary hypothesis, rather than for the effects of the perfusing bath, as the explanation of our experimental V_m foot results.

(1) The magnitude of the concave deviations from linearity in the phase-plane trajectory of V_m foot varied considerably at different sites during LP. During TP, 30% of the impalement sites demonstrated an initial slur in the trajectory of V_m foot, whereas 70% of the sites had a linear V_m foot trajectory. These directionally different variations were accounted for in our 2-domain model results by known variations in capillary density and the variations we measured in the size of interstitial space (see Fig. 9 in Reference 13¹³ ). That is, the greater the density of capillaries and the smaller the size of interstitial space, the greater the deviation from a linear V_m foot trajectory.¹³

(2) In adult canine working myocardium, the concave deviations from linearity during LP were greater in ventricular than in atrial muscle (see Table 1 in Reference 13¹³ ). Our subsequent analysis has shown that the density of capillaries is significantly greater (P<0.001) in adult canine ventricular muscle than in atrial muscle bundles (ie, number of capillaries adjacent to each myocyte). This morphological result is consistent with that of Ludwig.³⁴

(3) Neonatal ventricular muscle produced the most prominent concave deviations from a linear trajectory of V_m foot that we encountered; ie, the maximum difference from linearity during V_m foot was greater in neonatal than in adult ventricular muscle (P<0.02).¹³ Neonatal ventricular myocardium has the highest density of capillaries that occurs during any time interval from early life to adulthood.^{35 36}

(4) The relationship between the average values of _max during LP and TP are different in neonatal than adult canine ventricular muscle. That is, in contrast to adult ventricular muscle, in neonatal ventricular muscle the mean value of LP _max is not significantly different from mean TP _max.^{13 16} However, at a macroscopic level the LP/TP velocity ratios are the same in neonatal and adult canine ventricular muscle.¹⁶ It is difficult to understand how the same bath effects could produce different adult and neonatal patterns in _max, in addition to the differences in V_m foot, in preparations that are normal with similar uniform anisotropic properties and the same LP/TP velocity ratio at a macroscopic level. On the other hand, our recent results show that growth effects with associated increases in cell size, along with remodeling of the cellular distribution of gap junctions from birth to maturity, can explain the different neonatal and adult anisotropic _max patterns at a microscopic level in the presence of the same neonatal-adult LP/TP velocity ratios at a macroscopic level.¹⁶

(5) We encountered other trajectories with atypical phase-plane trajectories of V_m foot that are described, but not illustrated, in our 1998 article.¹³ Figure 1 shows an example of the unusual V_m foot shape changes we encountered at a single site when LP conduction was reversed along the long axis of the fibers. In a left-to-right direction (Figure 1, left), there was the usual concave deviation from a linear trajectory of V_m foot. However, when the direction of conduction was reversed along the same axis, the trajectory of V_m foot changed to a convex shape (Figure 1, right).

View larger version (10K): [in this window] [in a new window]   Figure 1. Atypical phase-plane trajectories of Vm foot at the same site during reversal of propagation along the longitudinal axis of the fibers in adult ventricular epimyocardium. Propagation in a left-to-right direction (arrow) produced a prominent concave deviation from a linear (exponential) trajectory of Vm foot. However, when LP was reversed to the right-to-left direction (arrow), the trajectory of Vm foot changed to a convex shape. We encountered atypical Vm foot trajectories during LP at 10 of 50 microelectrode impalement sites in adult canine ventricular muscle (see Table 1 of Reference 13).

We have not been able to account for this behavior of V_m foot by branching,²⁸ by any model of internal resistance (r_i) discontinuities,^{15 17 29 30 31} or by an effect of the perfusing bath.^{1 2 3 4 5 6 7 8 9 10 11} However, in our morphological studies of serial sections viewed rapidly (in motion) with computer displays, abrupt changes (discontinuities) in the size of interstitial space became apparent without apparent changes in the distribution of the gap junctions or density of the capillaries.¹³ When we included an abrupt change in the size of interstitial space (ie, an abrupt change in interstitial resistance) in our 2-domain model with capillaries,¹³ the model results (Figure 2) were in good agreement with the experimental results shown in Figure 1. Contrariwise, when the capillaries were removed from the 2-domain model, both the concave and convex shapes of the trajectory of V_m foot disappeared and the V_m foot trajectory was linear at all sites during conduction across the r_is discontinuity.

View larger version (40K): [in this window] [in a new window]   Figure 2. Two-domain capillary model demonstration of the effect of a discontinuity of interstitial resistance (abrupt change in interstitial volume) on the trajectory of Vm foot during LP. Results were obtained with the 2-domain capillary model using the same parameters detailed in Table 2 of Reference 13. The drawings illustrate spatial differences along the long axis of the fibers in the interstitial resistance (ris) and the discontinuity of interstitial resistance produced by the abrupt change in ris. For purposes of focusing on the effects of the interstitial discontinuity, the anisotropic active layer was continuous with a homogeneous longitudinal internal resistance (ri) of 133 M/cm. The same maximum density of capillaries was present in all interstitial space. However, in the left side of the model, ris was assigned a value of 236 M/cm (high ris) to represent an average interstitial width of 2.1 µm; in the right side of the model, ris was assigned a value of 118 M/cm (low ris) to represent an average interstitial width of 4.2 µm. (The dimensions of interstitial space were obtained from morphological measurements.13 ) A, During left-to-right LP, the concave deviation of the trajectory of Vm foot was more prominent in the region of high ris than low ris, as expected.13 B, When the direction of propagation was reversed to occur from the low to the high ris region, the trajectory of Vm foot changed to a convex shape (*) in same high ris area that had produced a prominent concave deviation in panel A. That is, over a distance of ~1 mm in the high ris region adjacent to the ris discontinuity, the trajectory of Vm foot changed to a convex shape when the direction of conduction was reversed. However, as propagation continued in the high ris area, at sites farther away from the ris discontinuity the prominent concave deviation from linearity in the trajectory of Vm foot returned to that shown for the high ris region in panel A. When the capillaries were removed, the trajectory of Vm foot was linear at all sites for both directions of conduction.

	Conclusions

Top Abstract Introduction Points of Agreement Between... Perfusate Effects Waveform Variations Not... Conclusions References

 
We agree with Roth¹¹ that the depolarization potential waveforms can be affected by the superfusing volume conductor, consistent with his publications^{3 4 11} and also our own.^{1 2 22} We do not agree, however, that such effects are sufficient or the most significant in accounting for the range of detailed changes that we observed in our studies.^{12 13} Our understanding of Roth’s¹¹ article is that he does not question whether discontinuous conduction occurs in cardiac muscle, a phenomenon that is supported by several converging lines of investigation since 1981.³⁷ Rather, he points out that care should be exerted when interpreting experimental data that may include the effects of the tissue bath as described by bidomain models. Here, we have attempted to point out the detailed anisotropic variations in _max and the shape of V_m foot that thus far have been explained only by specific features of the documented natural architecture of cardiac bundles. However, because of the relative paucity of available information about the effects of different components of cardiac microstructure, both Roth’s¹¹ admonition and our results emphasize the need for future study of variations in the depolarization shape of cardiac action potentials and their cause.

The results presented here provide an evolving picture that suggests that resistive discontinuities primarily affect _max, and an additional capacitive component due to capillaries in interstitial space primarily affects V_m foot. Therefore, the results emphasize that there are yet important, unexplored resistive discontinuities at a microscopic level. These include spatial variations in the size of interstitial space¹³ and the role of cellular scaling (effects of cell size)¹⁶ when changes occur in the cellular and multicellular distribution of gap junctions during remodeling of mature myocardium into structural substrates that are arrhythmogenic.^{21 38}

	Acknowledgments

 
The work reported here was supported by the National Heart, Lung, and Blood Institute of the NIH (Grant HL 50537) and the North Carolina Supercomputing Center.

Received December 2, 1999; accepted December 30, 1999.

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