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 nonuniform orientation of the cells within the tissue and for deformations of the tissue occurring as a result of the heart beat.