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.

I. Introduction

Cardiac simulations have recently become a fast-developing branch of computational science. They are helpful for many questions related to normal and abnormal cardiac function without expensive and time-consuming experimental and clinical work. As the heart works as an electromechanical pump, the simulations usually include four main parts: an anatomical heart model, an electrical tissue model, a mechanical model of the myocardium and a model of the blood flow. In the present work, we focus on a description which combines electrical and mechanical models. We apply this electromechanical model to study a basic biophysical problem of the low-voltage cardioversion (LVC) in a 2D slab of the myocardium with straight fibres parallel to one of the domain boundaries. In this domain, we initiate self-sustaining spiral waves which represent dangerous cardiac diseases (re-entry arrhythmias). We utilize LVC via local, periodic, small-amplitude, high-frequency electrical stimulation which was proposed several decades ago [1]. As a result, spiral waves start to drift away and disappear at the medium boundary. In the previous LVC simulations, the mechano-electrical feedback was not studied, though it strongly affects the spontaneous drift of spiral waves [2]. This limitation can explain the discrepancy between the theoretical and experimental studies [3].