Efficient, cell-based simulations of cardiac electrophysiology; The Kirchhoff Network Model (KNM)

Figures

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  Fig. 1. Model comparison and convergence. a Illustration of the models. In BD, the extracellular space, the membrane and the intracellular space are assumed to exist everywhere in the tissue, and the computational mesh can therefore be chosen irrespective of the location of the cells. In KNM, each cell and an associated part of the extracellular space are represented as computational nodes connected to their neighbors. In EMI, the computational nodes are set up to spatially resolve the extracellular space, the cell membrane, and the intracellular space. Note that in the illustration, the extracellular space only partly covers the cells to make the cells visible, but in simulations, it surrounds the cells on all sides. b Convergence analysis. The tables display the difference, in percent, between the CV computed using the finest considered resolution (Δt = 1 μs, Δx = 3 μm) and coarser resolutions for three different adjustments of the default gap junction resistance, Rg. The discretization parameter that is not varied is fixed at the finest resolution. Note that for KNM, there is no spatial discretization since the computational nodes are the cells, and for EMI, the applied numerical…

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  Fig. 2. Micro-reentry and CPU efforts. a A spiral wave is generated for KNM and EMI, but not for BD. We consider a collection of 20 × 20 weakly coupled cells (500 × Rg) and apply an S2 stimulation (see, e.g., refs. 20,21) in the lower left quarter of the domain 240 ms after an S1 stimulation was applied in the left part of the domain. Note that also other tested timings of the S2 stimulation did not give reentry for BD (see Supplementary Figure S1). The time points displayed at the top of the plots report the time (after the S2 stimulation) when the snapshots are recorded. Note that the longitudinal axis is scaled for improved visibility. b CPU efforts associated with the simulations. We report the number of mesh nodes, the number of time steps and the CPU time required to run the simulation. The applied resolution is Δt = 10 μs (all models), Δx = 10 μm (BD), and Δx = 5 μm (EMI).