Multilevel Homogenization Applied to the Cardiac Bidomain Equations

Accurate cardiac tissue-based modeling using the bidomain equations requires the incorporation of fine-scale structures observed at the 50-100 micron level. By including such features we can more easily observe how defibrillation shocks lead to total depolarization of the heart. Several modeling studies that have investigated the effect of fine scale structures on defibrillation success have been completed. Results have shown that such structures aid, through the creation of virtual electrodes, in total depolarization. An obstacle that occurs with this modeling style is the massive amount of data that must be incorporated into detailed tissue models for even a cubic millimeter sample of cardiac tissue. In this paper, we discuss our approach to generating upscaled, or homogenized, versions of these models that can be used to perform simulations at a more reasonable modeling scale. They have the advantage of incorporating fine scale structure into the model at a reduced modeling cost. We introduce and briefly explore the advantages of this upscaling method