GPU Load Balancing Using Sparse Cartesian Grids: Making Interactive WebGL Simulations of Complex Ionic Models Even Faster on 3D Heart Structures

Cardiac modeling on supercomputers has limited arrhythmia studies to groups with specialized access and expertise. We previously showed that WebGL programs can simulate complex ionic models in 2D and 3D cardiac geometries in real time without the need for a supercomputer by utilizing parallel hardware through the graphics processing unit (GPU). In this work, we use sparse Cartesian grids to balance GPU load, conserve memory, and avoid unnecessary read/write operations, speeding up 3D simulations by up to a factor of 20. We also present a simple mapping technique to compress sparse data structures into compact structures, which allows us to access texture memory efficiently during the time-stepping portion of the computation. As examples, we present the implementation of phenomenological models for 3D atrial and ventricular simulations, as well as the 41-state-variable OVVR human ventricular cell model on 3D ventricular human anatomical structures. We show how our programs can be used to initiate and terminate scroll waves in 3D interactively.