Improved hybrid/GPU algorithm for solving cardiac electrophysiology problems on Purkinje networks

Abstract

SUMMARYCardiac Purkinje fibres provide an important pathway to the coordinated contraction of the heart. We present a numerical algorithm for the solution of electrophysiology problems across the Purkinje network that is efficient enough to be used in in-silico studies on realistic Purkinje networks with physiologically detailed models of ion exchange at the cell membrane. The algorithm is based on operator splitting and is provided with three different implementations: pure CPU, hybrid CPU/GPU, and pure GPU. Compared to our previous work, we modify the explicit gap junction term at network bifurcations in order to improve its mathematical consistency. Due to this improved consistency of the model, we are able to perform an empirical convergence study against analytical solutions. The study verified that all three implementations produce equivalent convergence rates, which shows that the algorithm produces equivalent result across different hardware platforms. Finally, we compare the efficiency of all three implementations on Purkinje networks of increasing spatial resolution using membrane models of increasing complexity. Both hybrid and pure-GPU implementations outperform the pure-CPU implementation, but their relative performance difference depends on the size of the Purkinje network and the complexity of the membrane model used.

Computational assessment of arrhythmia potential in the heterogeneously perfused ventricle

“…It can be appreciated that real time detailed simulations may become possible when issues such as identified in Figure 4, as well as other hitherto unidentified issues are addressed. Further to the algorithmic developments, it is also necessary to exploit the upcoming GPU and GPU-CPU hybrid technologies to accelerate the simulations [36,37]. Figure 6.…”

Numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network

“…To model the potential propagation through the Purkinje network, we follow the approach proposed in Vigmond and Clements, which is briefly discussed in this section. For further details, see also Vergara et al and Lange et al…”

“…To model the potential propagation through the Purkinje network, we follow the approach proposed in Vigmond and Clements, 10 which is briefly discussed in this section. For further details, see also Vergara et al 15 and Lange et al 45 The basic idea is to solve the 1D monodomain equation in each segment S i , for i ∈ {1,…,P}. The monodomain model emerges as a simplification of the bidomain equations 2, when the hypothesis of equal anisotropy ratio in the intracellular and extracellular domains is made.…”

“…For the space discretization of the 1D Equation 20 we follow the strategy proposed in. 10 See also 15,45 for further details. The first 3 steps in the time-marching scheme described above are explicit problems that do not involve any space derivatives (see Vigmond and Clements 10 and Vergara et al 15 ).…”

“…The time discretization of the Purkinje network activation problem given by Equation 14 is performed via a semi‐implicit scheme, based on the operator splitting approach introduced in Vigmond and Clements . Basically, the time marching of the problem is split into 4 sequential stages (see Vigmond and Clements, Vergara et al, and Lange et al), with the reaction and diffusion terms being solved in different steps. The reaction term and the ionic model are solved in an explicit way, whereas the diffusion term is solved implicitly.…”