Robust Graph-based Upscaling of Micro-scale Fibrotic Structures

Megan Farquhar1, Kevin Burrage1, Brodie Lawson2
1Queensland University of Technology, 2ARC Centre of Excellence for Mathematical and Statistical Frontiers (Queensland University of Technology)


Electrophysiological (and electromechanical) simulations are infamous for their computational runtimes, and remain a significant barrier to a full understanding of the electrical signalling process in the heart. These computational challenges are particularly impactful when it comes to understanding the important effects of small-scale heterogeneities, such as due to cardiac fibrosis, as refinement of cardiac meshes to even finer spatial resolutions incurs an insurmountable increase in simulation time. Therefore, methods that are able to appropriately {\it upscale} these micro-scale heterogeneities, that is, to appropriately represent their effects on conduction in a coarser mesh, are of critical importance to understanding how exactly, and under which circumstances, conditions such as cardiac fibrosis act to promote dangerous arrhythmia. In this work, we combine our recent ideas for upscaling using homogenisation via volume averaging and a unique graph-based approach to demonstrate a powerful tool for capturing some of the subtler and localisation-dependent effects of cardiac fibrosis with only minor impact on simulation runtimes.