The increased incidence of arrhythmias in structural heart disease is accompanied by remodeling of the cellular distribution of gap junctions to a diffuse pattern like that of neonatal cardiomyocytes. Accordingly, it has become important to know how remodeling of gap junctions due to normal growth hypertrophy alters anisotropic propagation at a cellular level (V(max)) in relation to conduction velocities measured at a macroscopic level. To this end, morphological studies of gap junctions (connexin43) and in vitro electrical measurements were performed in neonatal and adult canine ventricular muscle. When cells enlarged, gap junctions shifted from the sides to the ends of ventricular myocytes. Electrically, normal growth produced different patterns of change at a macroscopic and microscopic level. Although the longitudinal and transverse conduction velocities were greater in adult than neonatal muscle, the anisotropic velocity ratios were the same. In the neonate, mean V(max) was not different during longitudinal (LP) and transverse (TP) propagation. However, growth hypertrophy produced a selective increase in mean TP V(max) (P<0.001), with no significant change in mean LP V(max). Two-dimensional neonatal and adult cellular computational models show that the observed increases in cell size and changes in the distribution of gap junctions are sufficient to account for the experimental results. Unexpectedly, the results show that cellular scaling (cell size) is as important (or more so) as changes in gap junction distribution in determining TP properties. As the cells enlarged, both mean TP V(max) and lateral cell-to-cell delay increased. V(max) increased because increases in cell-to-cell delay reduced the electric current flowing downstream up to the time of V(max), thus enhancing V(max). The results suggest that in pathological substrates that are arrhythmogenic, maintaining cell size during remodeling of gap junctions is important in sustaining a maximum rate of depolarization.

Available models of circus movement reentry in cardiac muscle and of drug action on reentrant arrhythmias are based on continuous medium theory, which depends solely on the membrane ionic conductances to alter propagation. The purpose of this study is to show that the anisotropic passive properties at a microscopic level highly determine the propagation response to modification of the sodium conductance by premature action potentials and by sodium channel-blocking drugs. In young, uniform anisotropic atrial bundles, propagation of progressively earlier premature action potentials continued as a smooth process until propagation ceased simultaneously in all directions. In older, nonuniform anisotropic bundles, however, premature action potentials produced either unidirectional longitudinal conduction block or a dissociated zigzag type of longitudinal conduction (a safer type of propagation, similar to transverse propagation). Directional differences in the velocity of premature action potentials demonstrated that anisotropic propagation was necessary for a reentrant circuit to be contained within an area of 50 mm2, even with very short refractory periods. Quinidine produced Wenckebach periodicity, which disappeared after acetylcholine shortened the action potential. Quinidine also produced use-dependent dissociated zigzag longitudinal conduction in the older, nonuniform anisotropic bundles but not in the young, uniform anisotropic bundles. The electrophysiological consequence was that propagation events differed in an age-related manner in response to the same modification of the sodium conductance. The electrical events at microscopic level showed that conditions leading to obliteration of side-to-side electrical coupling between fibers (e.g., aging and chronic hypertrophy) provide a primary mechanism for reentry to occur within very small areas (1-2 mm) due to a variety of propagation phenomena that do not occur in tissues with tight electrical coupling in all directions.

BACKGROUND-Aging is associated with a significant increase in atrial tachyarrhythmias, especially atrial fibrillation. A macroscopic repolarization gradient created artificially by a stimulus at one site prior to a premature stimulus from a second site is widely considered to be part of the experimental protocol necessary for the initiation of such arrhythmias in the laboratory. How such gradients occur naturally in aging atrial tissue has remained unknown.

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Having found the regional differences in right atrial action potentials shown in an accompanying article, we tested two seemingly paradoxical hypotheses: 1) The spatial pattern of repolarization provides a protective mechanism against reentry, and 2) repolarization inhomogeneities interact with anisotropic discontinuous propagation to produce reentry. Measurement of multidimensional refractory periods demonstrated an anisotropic distribution within large bundles with the longest refractory periods in the medial upper crista terminalis (sinus node area), a distribution similar to that of action potential durations. Also, discontinuities of repolarization were found at muscle bundle junctions. Early premature impulses originating in the sinus node area propagated throughout the right atrial preparations without conduction disturbances or reentry. Conversely, early premature impulses that originated at sites distal to the sinus node area resulted in localized conduction block at multiple sites, which frequently produced complex conduction changes and reentry. The critical nature of the site of origin of a premature impulse in initiating reentry was related to locations where the steepest repolarization gradients occurred: within anisotropic bundles in the direction of highest axial resistance (across fibers) and at muscle bundle junctions that represented localized discontinuities of axial resistance. The multiple conduction abnormalities at localized sites interacted to produce different types of reentry at a larger size scale (25 mm 1 to several cm 2 ). In each case, neither repolarization inhomogeneities (leading circle concept) nor anisotropic discontinuous propagation was the only "mechanism" involved. That is, reentry at a macroscopic size scale occurred as a result of a combined repolarization-anisotropic discontinuous propagation mechanism. (Circulation Research 1989;65:1612-1631) I t is generally thought that the only electrophysiological consequence of the spatial dispersion of repolarization of cardiac action potentials is the enhancement of reentry.1 -3 It is also widely considered that the spatial nonuniformity of refractory periods (spatial dispersion of action potential durations) is the only "mechanism" involved in the production of conduction disturbances that initiate circus movement reentry following premature impulses. 4 In this article, however, we present experiments that use new information to reassess both of these long-standing ideas.Approximately a decade ago, we presented new evidence that in cardiac muscle anisotropic propa- Received July 27, 1988; accepted June 28, 1989. gation was discontinuous, with directional differences in electrical load that lead to unidirectional block without requiring nonuniformities of refractory periods. 5 -6 Subsequently, we found that anisotropic discontinuous propagation can produce all of the conduction disturbances leading to reentry without the presence of spatial differences in refractory periods.7 That is, the passive anisotropic properties of car...

The object of this study is to present evidence that the myocardial architecture creates inhomogeneities of electrical load at the cellular level that cause cardiac propagation to be stochastic in nature; ie, the excitatory events during propagation are constantly changing and disorderly in the sense of varying intracellular events and delays between cells. At a macroscopic level, however, these stochastic events become averaged and appear consistent with a continuous medium. We examined this concept in a two-dimensional (2D) model of myocardial architecture by exploring whether experimentally observed Vmax variability reflected different patterns of intracellular excitation events and junctional delays. The patterns of Vmax variability at randomly chosen intracellular sites were similar experimentally and in the 2D model. The 2D cellular model produced marked variability in gap junction delays; however, on the average, different gap junctions were used for cell-to-cell charge flow during conduction in different directions. During longitudinal propagation (LP), the velocity increased from the proximal to the distal end of each myocyte, and Vmax was lowest proximally, increased to a maximum at the distal fourth of the cell, and decreased distally. Transverse propagation (TP) produced rapid intracellular conduction with variable intracellular excitation sequences. TP Vmax was greater than LP Vmax in most subcellular regions, but near the ends of some myocytes, a reversed "TP > LP Vmax" relation occurred. Total charge carried by the sodium current varied inversely with Vmax, demonstrating feedback effects of cellular loading on the subcellular sodium current and the kinetics of the sodium channels. The results suggest that the stochastic nature of normal propagation at a microscopic level provides a considerable protective effect against arrhythmias by reestablishing the general trend of wave-front movement after small variations in excitation events occur.

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Abstract-It has become of fundamental importance to understand variations in the shape of the upstroke of the action potential in order to identify structural loading effects. One component of this goal is a detailed experimental analysis of the time course of the foot of the cardiac action potential (V m foot) during propagation in different directions in anisotropic cardiac muscle.To this end, we performed phase-plane analysis of transmembrane action potentials during anisotropic propagation in adult working myocardium. The results showed that during longitudinal propagation there was initial slowing of V m foot that resulted in deviations from a simple exponential; corollary changes occurred at numerous sites during transverse propagation. We hypothesized that the effect on V m foot observed in the experimental data was created by the microscopic structure, especially the capillaries. This hypothesis predicts that the phase-plane trajectory of V m foot will deviate from linearity in the presence of a high density of capillaries, and that a linear trajectory will occur in the absence of capillaries. Comparison of the results of Fast and Kléber (Circ Res. 1993;73:914 -925) in a monolayer of neonatal cardiac myocytes, which is devoid of capillaries, and our results in newborn ventricular muscle, which is rich in capillaries, showed drastic differences in V m foot as predicted. Because this comparison provided experimental support for the capillary hypothesis, we explored the underlying biophysical mechanisms due to interstitial electrical field effects, using a "2-domain" model of myocytes and capillaries separated by interstitial space. The model results show that a propagating interstitial electrical field induces an inward capacitive current in the inactive capillaries that causes a feedback effect on the active membrane (source) that slows the initial rise of its action potential. The results show unexpected mechanisms related to extracellular structural loading that may play a role in selected conduction disturbances, such as in a reperfused ischemic region surrounded by normal myocardium. (Circ Res. 1998;83:1144-1164.)Key Words: action potential foot Ⅲ interstitial discontinuity Ⅲ capillary Ⅲ interstitial potential Ⅲ electrical field effect I t has become of fundamental importance to understand variations in shape of the upstroke of the action potential in order to identify structural loading effects on the action potential. For example, we used the finding of a greater value of the maximum rate of rise of the action potential (V max ) during transverse propagation (TP) compared with longitudinal propagation (LP) to suggest that cardiac propagation is discontinuous at a microscopic level because of recurrent discontinuities of internal resistance (r i ) produced by the gap junctions.1 Other laboratories have repeatedly reproduced these directional differences in V max in adult cardiac muscle, 2-4 and it is now generally accepted that cardiac conduction is discontinuous at a microscopic level.5 Recent resul...