Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

Abstract

Background: Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level.

Methods: We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG.

Results: We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given.

Conclusions: Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described.

Figure 1

Quantitative cellular automata with different neighborhoods. (a) Moor neighborhood. (b) A user-defined neighborhood. The radius in both cases is 1.

Figure 2

The master-slave structure of distributed computing with MPI programming.

Figure 3

Digitalizing slices of the digital male cadaver. Yellow color indicates ventricular tissue, and pink color indicates atrial tissue.

Figure 6

The stratified heart walls. (a) The stratified 2-D model. (b) The epicardium-to-endocardium repolarization in the 2-D model based on stratified cardiac walls. Different color indicates different transmembrane potential. (c) Two ischemia areas based on stratified cardiac walls. (d) The stratified 3-D model (a section).

Figure 7

The simulated ECGs with the 2-D model. (a) The normal ECG; two leads are at the middle of left and right chests (<190,50 > and <-80,50 >). (b) The normal ECG; two leads are in the cardiac cavities (<75,50 > and <32,50 >). (c) The ECG of endocardial ischemia (top line) and epicardial ischemia (bottom line); two leads are at the same positions as in (A). Two ischemia areas are shown in Figure 6(c).

Figure 4

The channel level electrical activities of a ventricular cell. (a) The transjunctional currents from eight neighboring cells. (b) The state of gating variables. (c) The transmembrane ionic currents.

Figure 5

The cell level electrical activities of a ventricular cell. The top line is the transmembrane potential; the middle line is the transmembrane current; the bottom line is the stimulating current received from neighboring cells. The cell is under progressive ischemia, which can be reflected in the change of action potential.

Figure 8

Computing the field potential of single connected cells. This figure shows the distribution of gap junctions on the membrane of cells in a 2-D cell array and how gap junctions contribute to field potential. φ_i is the potential within the current cell; φ_1i is the potential within the first neighboring cell; is the normal direction of the transjunctional potential difference between the current cell and its first neighboring cell; ... Ω is the solid angle subtended by the current cell at field point P.

Figure 9

The performance of running the 3-D model on a cluster of SMP nodes. (a) When the 3-D cell space is sparsely occupied by the heart model (left), the evenly dispatch strategy does not produce the best performance. (b) When the cell space is fully occupied by ventricular cells (right), the best performance is guaranteed.