Bidomain Model for Axon Bundles with Random Geometry

In this work a homogenized model for signal propagation in fascicles comprising many identical bundled axons is obtained. We consider the case when the axons are circular cylinders, and their centers in the cross section of the bundle are randomly distributed. For the action potential, we assume the FitzHugh-Nagumo dynamics on the axons’ membranes. Combining the tools of stochastic homogenization and the method of monotone operators, we derive a macroscopic bidomain model describing the action potential in the fascicle.