Steady-state Approximations for Hodgkin-Huxley Cell Models: Towards Multi-scale Models of Uterine Smooth Muscle

Abstract

The Tong, et al. 2011 publication presents a comprehensive mathematical model of electro- mechanical behaviour in a uterine smooth muscle cell. It incorporates ion channel currents into a classic Hodgkin-Huxley membrane voltage formulation as well as Ca2+ concentration dynamics with pumps and exchangers. Mechanical force generation by way of the Hai-Murphy smooth muscle cell model is computed based on the Ca2+ concentrations. The ‘full’ Tong, 2011 model (FTM) includes nineteen ordinary differential equations for the ion channel activation/inactivation variables out of a total of 105 equations overall. An effort at reducing the FTM into a smaller number of equations for computational efficiency – the ‘reduced’ Tong model (RTM) – aims at reproducing the overall behaviour of the FTM without excessive detail. We present here the CellML implementation of the RTM for simulating the FTM within the context of the reduced model’s primary publication as derived from the Tong, et al. 2011 model.