Parameter optimization technique using the response surface methodology

In this paper, we propose a parameter optimization technique using the Response Surface Methodology (RSM) for the accurate biological cell simulation which calculates cell behavior by numerically integrating the differential equation and generates action potentials, intracellular Ca transient, contraction, and intracellular ATP consumption by using parameter values of major ion permeability and amplitude of Ko dependency. Since most of these parameters cannot be directly measured by experiment, these are searched for by applying an optimization technique, that is, by minimizing an objective function defined as a difference between a measured and a calculated waveform of action potentials in a cardiac myocyte. We employ the RSM as the optimization technique. In the RSM, a quadratic polynomial is used in general, and a mathematical technique is used to calculate the extreme points. Because our parameter space cannot be approximated by a single quadratic polynomial surface, we adopt a recursive subdivision technique and use the coefficient of multiple determination to representing a response surface in each subspace for a criteria of the subdivision. We confirmed the effectiveness of the proposed technique by searching for parameters which are determined in advance.