An efficient technique for determining the steady-state membrane potential profile in tissues with multiple cell types

Most simulations of cardiac electrophysiology use the steady state as initial condition. Spatial variations in steady-state membrane potential may arise due to ischemia, coupling with fibroblasts, or local changes in intrinsic resting potential. In large scale models, simulating free evolution until the steady-state is reached may be computationally expensive when long time constants or slow concentration drifts are involved in the cell models. This paper describes a dedicated Newton-based root-finding solver to determine the steady state of a tissue in which two or more cell types coexist in the monodomain framework. This approach was applied to a 2D microstructural tissue model in which myocytes were coupled to fibroblasts, leading to an inhomogeneous elevation of the myocyte resting potential.