Optimization of a Cardiac Electromechanics Simulation Program for Parallel Implementation

The modified mass-spring system for the soft tissue mechanics proposed by O. Jarrousse has a computationally intensive loop that updates the states of all mesh elements such as triangles in 2D or tetrahedra in 3D. Each iteration of the loop computes forces acting at the vertices of an element, leading to a deformation of the mesh. Although the result does not depend on the order of the update, its direct parallelization causes a data race. In this paper, we propose a parallelization approach that divides the set of the mesh elements into subsets so that the elements of each subset can be processed in a parallel way, while the subsets themselves must be processed in a serial way. We show that this problem can be reduced to dividing the set of graph vertices into independent sets, or the well-known graph colouring problem. We use the program to simulate the low-voltage cardioversion in a square model of the myocardium and show how the results depend on the stimulation period and mechano-electrical feedback intensity.