Theoretical versus experimental estimates of the effective conductivities of cardiac muscle

Effective intracellular and extracellular conductivities of cardiac muscle are determined directly from its microscopic structure. The myocardium is represented by a periodic lattice of cells connected by low-resistance junctions and suspended in extracellular fluid. Effective conductivity tensors of this structure, found with the homogenization process based on two-scale asymptotic analysis, are expressed in terms of the cellular-level geometry and material constants. For nominal values of these parameters, the effective extracellular conductivities and the effective intracellular conductivity in the longitudinal direction are close to the measurements reported in the literature. However, the effective intracellular conductivity in the transverse direction is from 63 to 200 times smaller than experimentally measured values. The analysis of the results shows that small variations in fiber orientation influence effective conductivities measured on a tissue level and complicate their relation to the geometry and material constants measured on a cellular level