Deriving macroscopic myocardial conductivities by homogenization of microscopic models

We derive the values for the intracellular and extracellular conductivities needed for bidomain simulations of cardiac electrophysiology using homogenization of partial differential equations. In our model, cardiac myocytes are rectangular prisms and gap junctions appear in a distributed manner as flux boundary conditions for Laplace's equation. Using directly measurable microproperties such as cellular dimensions and end-to-end and side-to-side gap junction coupling strengths, we inexpensively obtain effective conductivities close to those given by simulations with a detailed cyto-architecture (Stinstra et al. in Ann. Biomed. Eng. 33:1743-1751, 2005). This model provides a convenient framework for studying the effect on conductivities of aligned vs. brick-like arrangements of cells and the effect of different distributions of gap junctions along the myocyte membranes.