Improved Hierarchical Parameter Optimization Technique - Application for a cardiac myocyte model

We propose a hierarchical parameter optimization technique which further enhances our original technique for an accurate biological cell simulation. Our original technique generates a k-d tree and uses the coefficient of multiple determination (R²) for tree-branching, however it requires a huge computation time since it processes the response surface at every leaf node of the k-d tree, including those that do not have optimum parameters. In our parameter optimization problem, the objective function is defined as the difference between the measured and calculated waveform of action potentials in a cardiac myocyte. The function value is always non-negative, and is equal to zero if and only if the best optimized parameter is included in the leaf node. To minimize the computational cost problem, our proposed technique takes advantage of the aforementioned conditions and only processes a leaf node if the corresponding Hessian matrix of the objective function is found to be a positive definite matrix. We confirmed the effectiveness of the proposed parameter optimization technique by searching for some pre-determined parameters