Derivation of the Bidomain Equations for a Beating Heart with a General Microstructure

A novel multiple scales method is formulated that can be applied to problems which have an almost periodic microstructure not in Cartesian coordinates but in a general curvilinear coordinate system. The method is applied to a model of the electrical activity of cardiac myocytes and used to derive a version of the bidomain equations describing the macroscopic electrical activity of cardiac tissue. The treatment systematically accounts for the non-uniform orientation of the cells within the tissue and for deformations of the tissue occurring as a result of the heart beat.