Numerical simulation of mechanoelectric feedback in a deformed myocardium

Abstract

Abstract—Mechanoelectric feedback manifests itself as a change in myocardial conductivity and the appearance of additional transmembrane currents associated with stretch-activated ion channels. The deformation-conductivity relations were derived by analyzing the microstructural model using the homogenization method. The cardiac tissue was considered as a periodic lattice, where the cells are rectangular prisms filled with an isotropic electrolyte. The conductivity of the gap junctions was taken into account through the boundary conditions on the sides of these prisms and was deemed constant. It is shown that the tensor that is the inverse of the myocardial conductivity tensor can be represented as a sum of the inverse reduced conductivity tensors of the myoplasm and gap junctions. The chosen model is compared with the model from the book by F.B. Sachse, Computational Cardiology, Springer (2004). For the longitudinal conductivity both models agree well for relative extensions in the range from 0.8 to 1.2. When studying the propagation of an excitation wave, the effect of deformation is “diluted” by the extracellular conductivity. In the processes where the extracellular and intracellular media act individually, the effect of deformation on the myocardium is more significant. A model for the activation of channels under complex deformation based on the assumptions that these channels are uniformly distributed over the lateral surface of the cell and respond to a local increase in membrane patch area has been constructed. This model allows the activation of channels to be considered not only when stretched along the fiber, but also when deformed in an arbitrary direction.