Effects of cardiac mechanical heterogeneity on the electrical function of the heart are difficult to assess experimentally, yet they pose a serious (patho-)physiological challenge. Here, we present an in silico study of the effects of mechanical heterogeneity on action potential duration (APD) in mechanically interacting muscle regions and consequent effects on the dispersion of repolarization, a well-established determinant of cardiac arrhythmogenesis. Using a novel mathematical description of ventricular electromechanical activity (virtual muscle), we first assessed how differences in intrinsic contractile properties affect the electrical behavior of cardiac muscle representations. In spite of identical electrophysiological model descriptions in virtual muscle samples, faster muscle models show shorter APD than their slower counterparts. This is a consequence of Ca 2+-mediated feedback from mechanical to electrical activity in the individual muscle models. This mechano-electric feedback (MEF) is, of course, significantly more complex in native cardiac tissue, as the heterogeneous muscle elements interact both mechanically and electrically. Cardiac mechanical heterogeneity, in its most reduced form, can be represented by a duplex consisting of two mechanically interacting muscle segments. Our in silico model of heterogeneous myocardium therefore consists of two individual virtual muscles that are mechanically interconnected in-series to form a virtual heterogeneous duplex. During isometric contraction of the duplex (i.e. at constant external length), internal mechanical interactions affect Ca 2+ handling and APD of muscle elements, resulting in an increased dispersion of repolarization beyond the intrinsic APD differences. Duplex electromechanical activity is strongly affected by the activation sequence of its elements. Late activation of the faster (subepicardial type) duplex element, postponed by time-lags that correspond to normal transmural activation delays, optimizes duplex contractility and smoothes out intrinsic APD differences, thereby reducing dispersion in repolarization. This smoothing effect is not observed upon delayed activation of the slower (subendocardial type) duplex element. In both settings, changes in repolarization timing follow a nonlinear dependence of APD on activation delay. Furthermore, asynchronous activation of identical elements in a homogeneous duplex causes an impairment of contractile function and increases dispersion of repolarization. This suggests that the normal electrical activation sequence in the heart requires matching mechanical and electrical heterogeneity for optimal cardiac performance. On the subcellular level, our results suggest that mechanical modulation of Ca 2+ handling is a key mechanism of MEF in heterogeneous myocardium, which contributes to the matching of local mechanical and/or electrical activity to global hemodynamic demand.

Using one-dimensional models of myocardial tissue, implemented as chains of virtual ventricular muscle segments that are kinematically connected in series, we studied the role of the excitation sequence in spatio-temporal organization of cardiac function. Each model element was represented by a well-verified mathematical model of cardiac electro-mechanical activity. We found that homogeneous chains, consisting of identical elements, respond to non-simultaneous stimulation by generation of complex spatio-temporal heterogeneities in element deformation. These are accompanied by the establishment of marked gradients in local electro-mechanical properties of the elements (heterogeneity in action potential duration, Ca2+ transient characteristics and sarcoplasmic reticulum Ca2+ loading). In heterogeneous chains, composed of elements simulating fast and slow contracting cardiomyocytes from different transmural layers, we found that only activation sequences where stimulation of the slower elements preceded that of faster ones gave rise to optimization of the system's electro-mechanical function, which was confirmed experimentally. Based on the results obtained, we hypothesize that the sequence of activation of cardiomyocytes in different ventricular layers is one of the key factors of spatio-temporal organization of myocardium. Moreover, activation sequence and regional differences in intrinsic electro-mechanical properties of cardiac muscle must be matched in order to optimize myocardial function.

This paper reviews the development and application of paired muscle preparations, called duplex, for the investigation of mechanisms and consequences of intra-myocardial electro-mechanical heterogeneity. We illustrate the utility of the underlying combined experimental and computational approach for conceptual development and integration of basic science insight with clinically relevant settings, using previously published and new data. Directions for further study are identified.

We utilized our earlier developed 1D mathematical model of the heart muscle strand to study contribution of the bilateral interactions between excitation and contraction on the cellular and tissue levels to the local and global myocardium function. Numerical experiments on the model showed that an initially uniform strand, formed on the inherently identical cells, became functionally heterogeneous due to the asynchronous excitation via the electrical wave spread. Mechanical interactions between the cells and the mechano-electric feedback beat-to-beat affect the functional characteristics of coupled cardiomyocytes further, adjusting their electrical and mechanical heterogeneity to the activation timing. Model simulations showed that functional heterogeneity increases with an enlarged spatial extension of the myocardial strand (in terms of the longer slack length not a higher stretch of the strand), demonstrating a special role of the heart size in its function. Model analysis suggests that cooperative mechanisms of myofilament calcium activation contribute essentially to the generation of cellular functional heterogeneity in contracting cardiac tissue.

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