Numerical simulation of mechanoelectric feedback in a deformed myocardium

Mechanoelectric feedback is the effect of deformation on the contractile apparatus of the muscle cell, the change in myocardial conductivity, the appearance of additional transmembrane currents (stretch-activated channels). The first type of feedback is closely related to the electromechanical coupling process and is taken into account in the corresponding models. The derivation of the strain-to-conductance ratios was carried out based on the analysis of the microstructural model using the homogenization method. Cardiac tissue was considered as a periodic lattice, where cells are rectangular prisms filled with an isotropic electrolyte, and the conductivity of the gap junctions was taken into account through the boundary conditions on the sides of these prisms and was considered constant. It is shown that the tensor, the inverse of the myocardial conductivity tensor, can be represented as the sum of the inverse reduced conductivity tensors of myoplasma and gap junctions. A comparison was made with the model from the book F.B. Sachse. Computational Cardiology. Springer 2004. For longitudinal conductivity, both models are well matched for extensions, ranging from 0.8 to 1.2. When studying the propagation of an excitation wave, the effect of strain is “diluted” by extracellular conductivity. In the processes, where the extracellular and intracellular environments act individually, the effect of strain on myocardium is greater. The model describing the activation of channels under complex deformation has been constructed assuming that these channels are evenly distributed along the lateral surface of the cell and respond to the local increase in the region of a cell membrane segment. The model allows studying the activation of channels both during stretching along the fiber and during deformation in an arbitrary direction.