Speaker
Description
The well-established homogenized bidomain (BD) model represents averaged intra- and extracellular behavior, providing a good compromise between physiological accuracy and computational feasibility. However, as the myocyte is not present in the model, the BD model cannot account for cell-to-cell variations, which can be properly analyzed by adopting the cell-based EMI model, in which the extracellular (E) space, the cell membrane (M) and the intracellular space (I) are explicitly represented. However, its prohibitive computational cost restricts its application to small domains.
Finally, the recent Kirchhoff Network model (KNM) models each cell and its surrounding extracellular space as computational nodes. Although it cannot reach the subcellular resolution of the EMI model, it preserves essential conduction properties and has computational demands that are comparable to the bidomain model.
These observations highlight a general challenge in cardiac modeling: homogenized models are often inadequate for investigating pathological conditions, while highly detailed models are unnecessarily expensive in simulations where the majority of the myocardium is healthy. This scenario motivates a multiscale modeling strategy: reduce the overall computational cost by adopting fine-scale models in the diseased regions and coarser models in the surrounding healthy tissue, where efficiency is prioritized over accuracy.
To leverage the strengths of these complementary models, we employ a domain decomposition approach, in which each subdomain can be solved independently and the solutions are coupled through interface conditions. In the case of non-overlapping regions, we have to impose the continuity of both the solution and the flux, while in the case of overlapping subdomains, continuity of flux comes naturally from enforcing the solution is consistent pointwise in the overlapping region. This domain decomposition strategy not only facilitates parallel computation and handling of complex geometries but also provides flexibility to use different solvers in subdomains.