Various types of models have been developed in the past to study electrical conduction in cardiac tissue. Model types include macroscopic approaches e.g. cellular automata and reaction-diffusion systems. In general, macroscopic approaches are based on the assumption that myocytes are the exclusive cell type in cardiac muscle. However, cardiac tissue is known to be a composite material composed of various cell types including - in addition to myocytes - fibroblasts, myofibroblasts, endothelial, vascular smooth muscle, and neuronal cells. We hypothesize that heterogeneity of cell type affects electrical conduction. We tested this hypothesis by developing a novel approach for macroscopic multidomain modeling, applying the model in computational simulations, and analyzing the simulation results.
Our multidomain model represents cardiac tissue as a mixture of various cell types. The model is an extension of established cardiac bidomain models, which include a description of intra-myocyte and extracellular conductivities, currents and potentials in addition to transmembrane voltages of myocytes. Our extension added spatial and physical domains associated with other cell types. Cells in these domains can be electrically coupled with each other and with cells from other domains. We implemented the model equations based on finite differences and finite element methods applying the PETSc toolkit for scientific computation. We applied the model in exemplary computational simulations of electrical conduction in cardiac tissue composed of myocytes and fibroblasts. In these simulations, volume ratios of cells and their inter- and intracellular electrical coupling were varied.
In support of our hypothesis, the simulations showed that cellular heterogeneity, electrical coupling between myocytes and fibroblasts, and inter-fibroblast coupling have distinct effects on tissue conduction. For example, myocyte-fibroblast coupling reduced anisotropy of conduction velocity only for significant inter-fibroblast coupling. We suggest that these effects can be tested in experimental studies with engineered tissue. Furthermore, we believe that the presented modeling approach provides novel means to understand mechanisms of conduction in diseased and engineered cardiac tissue.
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