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

Abstract

Mathematical models based on homogenized representation of cardiac tissue have greatly improved our understanding of cardiac electrophysiology. However, these models are too coarse to investigate the dynamics at the level of the myocytes since the cells are not present in homogenized models. Recently, fine scale models have been proposed to allow for cell-level resolution of the dynamics, but these models are too computationally expensive to be used in applications like whole heart simulations of large animals. To address this issue, we propose a model that balances computational demands and physiological accuracy. The model is founded on Kirchhoff’s current law, and represents every myocyte in the tissue. This allows specific properties to be assigned to individual cardiomyocytes, and other cell types like fibroblasts can be added to the model in an accurate manner while keeping the computing efforts reasonable.

The simplified Kirchhoff network model (SKNM): a cell-based reaction–diffusion model of excitable tissue

“…KNM was introduced in Jæger et al 27 and consists of a collection of N cells with associated extracellular space, see Fig. 1 .…”

“…In the recent paper 27 we presented the Kirchhoff Network Model (KNM) which aims at balancing the need for cell-level accuracy with computational efficiency. The model represents every individual cell and the associated extracellular space of the tissue under consideration, but does not allow for spatial variation of parameters along the individual cell membrane or inside the cell.…”

“…In other words, KNM allows the properties of individual cells to vary and can thus obtain cell-level accuracy, but cannot obtain sub-cellular accuracy. It was demonstrated in this paper 27 that KNM required computational efforts comparable to BD and much smaller than the cell-based Extracellular-Membrane-Intracellular (EMI) model. For one example the CPU efforts of KNM was about 0.01% of the CPU efforts needed to solve the EMI model.…”

A possible path to persistent re-entry waves at the outlet of the left pulmonary vein

“…However, we will apply the more computationally efficient 'simplified Kirchhoff's network model' (SKNM) [34] as opposed to the more detailed and considerably more computationally expensive extracellular-membrane-intracellular (EMI) model (see, e.g., [35,36,37,38,39,40]) applied in [33]. The SKNM is a simplification of Kirchhoff's network model (KNM), and KNM has been shown to provide good approximations of the EMI model in simulations of cardiac tissue [41].…”

“…Figure S2 shows a comparison of the solutions of the Kirchhoff network model (KNM) and the simplified Kirchhoff network model (SKNM) [41,34].…”