Mark L. Trew

Laminar arrangement of ventricular myocytes influences electrical behavior of the heart.

The response of the heart to electrical shock, electrical propagation in sinus rhythm, and the spatiotemporal dynamics of ventricular fibrillation all depend critically on the electrical anisotropy of cardiac tissue. A long-held view of cardiac electrical anisotropy is that electrical conductivity is greatest along the myocyte axis allowing most rapid propagation of electrical activation in this direction, and that conductivity is isotropic transverse to the myocyte axis supporting a slower uniform spread of activation in this plane. In this context, knowledge of conductivity in two directions, parallel and transverse to the myofiber axis, is sufficient to characterize the electrical action of the heart. Here we present new experimental data that challenge this view. We have used a novel combination of intramural electrical mapping, and experiment-specific computer modeling, to demonstrate that left ventricular myocardium has unique bulk conductivities associated with three microstructurally-defined axes. We show that voltage fields induced by intramural current injection are influenced by not only myofiber direction, but also the transmural arrangement of muscle layers or myolaminae. Computer models of these experiments, in which measured 3D tissue structure was reconstructed in-silico, best matched recorded voltages with conductivities in the myofiber direction, and parallel and normal to myolaminae, set in the ratio 4:2:1, respectively. These findings redefine cardiac tissue as an electrically orthotropic substrate and enhance our understanding of how external shocks may act to successfully reset the fibrillating heart into a uniform electrical state. More generally, the mechanisms governing the destabilization of coordinated electrical propagation into ventricular arrhythmia need to be evaluated in the light of this discovery.

Three Distinct Directions of Intramural Activation Reveal Nonuniform Side-to-Side Electrical Coupling of Ventricular Myocytes

Background—The anisotropy of cardiac tissue is a key determinant of 3D electric propagation and the stability of activation wave fronts in the heart. The electric properties of ventricular myocardium are widely assumed to be axially anisotropic, with activation propagating most rapidly in the myofiber direction and at uniform velocity transverse to this. We present new experimental evidence that contradicts this view. Methods and Results—For the first time, high-density intramural electric mapping (325 electrodes at ≈4×4×1-mm spacing) from pig left ventricular tissue was used to reconstruct 3D paced activation surfaces projected directly onto 3D tissue structure imaged throughout the same left ventricular volume. These data from 5 hearts demonstrate that ventricular tissue is electrically orthotropic with 3 distinct propagation directions that coincide with local microstructural axes defined by the laminar arrangement of ventricular myocytes. The maximum conduction velocity of 0.67±0.019 ms−1 was aligned with the myofiber axis. However, transverse to this, the maximum conduction velocity was 0.30±0.010 ms−1, parallel to the myocyte layers and 0.17±0.004 ms−1 normal to them. These orthotropic conduction velocities give rise to preferential activation pathways across the left ventricular free wall that are not captured by structurally detailed computer models, which incorporate axially anisotropic electric properties. Conclusions—Our findings suggest that current views on uniform side-to-side electric coupling in the heart need to be revised. In particular, nonuniform laminar myocardial architecture and associated electric orthotropy should be included in future models of initiation and maintenance of ventricular arrhythmia.

A finite volume method for modeling discontinuous electrical activation in cardiac tissue

This paper describes a finite volume method for modeling electrical activation in a sample of cardiac tissue using the bidomain equations. Microstructural features to the level of cleavage planes between sheets of myocardial fibers in the tissue are explicitly represented. The key features of this implementation compared to previous modeling are that it represents physical discontinuities without the implicit removal of intracellular volume and it generates linear systems of equations that are computationally efficient to construct and solve. Results obtained using this method highlight how the understanding of discontinuous activation in cardiac tissue can form a basis for better understanding defibrillation processes and experimental recordings.

Solving the cardiac bidomain equations for discontinuous conductivities

Fast simulations of cardiac electrical phenomena demand fast matrix solvers for both the elliptic and parabolic parts of the bidomain equations. It is well known that fast matrix solvers for the elliptic part must address multiple physical scales in order to show robust behavior. Recent research on finding the proper solution method for the bidomain equations has addressed this issue whereby multigrid preconditioned conjugate gradients has been used as a solver. In this paper, a more robust multigrid method, called Black Box Multigrid, is presented as an alternative to conventional geometric multigrid, and the effect of discontinuities on solver performance for the elliptic and parabolic part is investigated. Test problems with discontinuities arising from inserted plunge electrodes and naturally occurring myocardial discontinuities are considered. For these problems, we explore the advantages to using a more advanced multigrid method like Black Box Multigrid over conventional geometric multigrid. Results will indicate that for certain discontinuous bidomain problems Black Box Multigrid provides 60% faster simulations than using conventional geometric multigrid. Also, for the problems examined, it will be shown that a direct usage of conventional multigrid leads to faster simulations than an indirect usage of conventional multigrid as a preconditioner unless there are sharp discontinuities.

High-Resolution 3-Dimensional Reconstruction of the Infarct Border Zone Impact of Structural Remodeling on Electrical Activation

Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 &mgr;m across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry.Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 μm across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry. # Novelty and Significance {#article-title-38}

Structural Heterogeneity Alone is a Sufficient Substrate for Dynamic Instability and Altered Restitution

Background—Marked changes in ventricular APD restitution and associated alternans rhythm have been demonstrated in structural heart disease (SHD). However, whether this is due to structural heterogeneity or regional variation in cellular properties remains uncertain. In this study, we address the hypothesis that the structural heterogeneity associated with SHD is sufficient to alter dynamic restitution and increase the probability of electric instability. Methods and Results—Activation was simulated in a 14×14 mm2 domain in the presence and absence (control) of a central region containing nonuniform discontinuities resembling patchy fibrosis. A modified LR1 cardiac activation model was used in a bidomain formulation with isotropic conductivities. Bipolar stimulation was imposed above the central region with coupling intervals decreasing progressively from 500 ms and then maintained at 105 ms. Structural discontinuities had little effect on electric activation at low stimulus rates, but activation time and APD distributions became highly nonuniform within and adjacent to the discontinuous region at high rates. Discordant APD alternans occurred in both “fibrosis” and control, but at lower stimulus rates and with markedly greater extent in the former. Tortuous conduction through the discontinuous region resulted in large fluctuations of diastolic intervals giving rise to regional electric instability, which modulates dynamic conduction velocity and APD restitution. This led to heterogeneous conduction block and reentry not observed in control. Conclusions—We show that structural discontinuities can amplify discordant alternans and provide a rate-dependent substrate for reentry. This work provides new insights into the mechanisms by which fibrosis may contribute to arrhythmogenesis.

Three-Dimensional Impulse Propagation in Myocardium: Arrhythmogenic Mechanisms at the Tissue Level

Impulse propagation in the heart depends on the excitability of individual cardiomyocytes, impulse transmission between adjacent myocytes, and the 3-dimensional arrangement of those cells. Here, we review the role of each of these factors in normal and aberrant cardiac electric activation, with particular emphasis on the effects of 3-dimensional myocyte architecture at the tissue scale. The analysis draws on findings from in vivo and in vitro experiments, as well as biophysically based computer models that have been used to integrate and interpret these experimental data. It indicates that discontinuous arrangement of myocytes and extracellular connective tissue at the tissue scale can give rise to current source-to-sink mismatch, spatiotemporal distribution of refractoriness, and rate-sensitive electric instability, which contribute to the initiation and maintenance of reentrant cardiac arrhythmia. This exacerbates the risk of rhythm disturbance associated with heart disease. We conclude that structure-based, multiscale computer models that incorporate accurate information about local cellular electric activity provide a powerful platform for investigating the basis of reentrant cardiac arrhythmia. However, it is important that these models capture key features of structure and related electric function at the tissue scale.

Cardiac electrophysiology and tissue structure: bridging the scale gap with a joint measurement and modelling paradigm

Significant tissue structures exist in cardiac ventricular tissue that are of supracellular dimension. It is hypothesized that these tissue structures contribute to the discontinuous spread of electrical activation, may contribute to arrhymogenesis and also provide a substrate for effective cardioversion. However, the influences of these mesoscale tissue structures in intact ventricular tissue are difficult to understand solely on the basis of experimental measurement. Current measurement technology is able to record at both the macroscale tissue level and the microscale cellular or subcellular level, but to date it has not been possible to obtain large volume, direct measurements at the mesoscales. To bridge this scale gap in experimental measurements, we use tissue‐specific structure and mathematical modelling. Our models have enabled us to consider key hypotheses regarding discontinuous activation. We also consider the future developments of our intact tissue experimental programme.

High-Resolution 3-Dimensional Reconstruction of the Infarct Border Zone

Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 &mgr;m across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry.Rationale: Slow nonuniform electric propagation in the border zone (BZ) of a healed myocardial infarct (MI) can give rise to reentrant arrhythmia. The extent to which this is influenced by structural rather than cellular electric remodeling is unclear. Objective: To determine whether structural remodeling alone in the infarct BZ could provide a substrate for re-entry by (i) characterizing the 3-dimensional (3D) structure of the myocardium surrounding a healed MI at high spatial resolution and (ii) modeling electric activation on this structure. Methods and Results: Anterior left ventricular (LV) infarcts were induced in 2 rats by coronary artery ligation. Three-dimensional BZ volume (4.1 mm3 and 5.6 mm3) were imaged at 14 days using confocal microscopy. Viable myocytes were identified, and their connectivity and orientation were quantified. Preserved cell networks were observed in the subendocardium and subepicardium of the infarct. Myocyte tracts traversed the BZ, and there was heavy infiltration of collagen into the adjacent myocardium. Myocyte connectivity decreased by ≈65% over 250 μm across the BZ. This structure was incorporated into 3D network models on which activation was simulated using Luo–Rudy membrane dynamics assuming normal cellular electric properties. Repetitive stimulation was imposed at selected BZ sites. Stimulus site-specific unidirectional propagation occurred in the BZ with rate-dependent slowing and conduction block, and reentry was demonstrated in one substrate. Activation times were prolonged because of tract path length and local slowing. Conclusions: We have used a detailed image-based model of the infarct BZ to demonstrate that structural heterogeneity provides a dynamic substrate for electric reentry. # Novelty and Significance {#article-title-38}

A Tissue-Specific Model of Reentry in the Right Atrial Appendage

Introduction: Atrial fibrillation is prevalent in the elderly and contributes to mortality in congestive heart failure. Development of computer models of atrial electrical activation that incorporate realistic structures provides a means of investigating the mechanisms that initiate and maintain reentrant atrial arrhythmia. As a step toward this, we have developed a model of the right atrial appendage (RAA) including detailed geometry of the pectinate muscles (PM) and crista terminalis (CT) with high spatial resolution, as well as complete fiber architecture.