Session S32.1

An Efficient Technique for Determining the Steady-State Membrane Potential Profile in Tissues with Multiple Cell Types

V Jacquemet*, CS Henriquez

Duke University
Durham, NC, USA

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.
We developed 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. The equation to be solved establishes that membrane currents compensate intercellular diffusion fluxes. The iterations start with a membrane potential profile characterized by the cells being in their resting state. Then, each Newton step is a linear problem for the membrane potential field. Forming this linear system requires computing for each cell the steady-state membrane current at clamped potential as well as its derivative. This function was precomputed for each cell type using as far as possible analytical methods for determining the ionic concentrations at clamped potential.
This approached was applied to a 2D microstructural tissue model (size: 2 by 2 mm, discretization: 8 um) including patchy fibrosis covering 9.5% of the tissue. Fibroblasts were electrically coupled to adjacent myocytes and fibroblasts by a conductance of 3 uS. The Ramirez kinetics (Vrest=-83.7) was used for the myocytes and the McCannell kinetics (Vrest=-49.4) for the fibroblasts. In the resulting steady-state membrane potential profile, the myocyte membrane potential was depolarized by 3-5 mV near the clusters of fibroblasts. An accuracy of 0.01 mV was reached after 250 iterations. As a result, the root finding procedure was less demanding than simulating the system for 10 ms using a semi-implicit scheme.
Computing of the steady state through root-finding was found to be convenient and computationally efficient when applied to heterogeneous tissue incorporating multiple membrane kinetics models.

(Abstract Control Number: 131)