A Numerical Method for the Optimal Adjustment of Parameters in Ionic Models Accounting for Restitution Properties

Abstract

We developed new numerical methods to optimally adjust the parameters in cardiac electrophysiology models, using optimal control and non-differentiable optimization methods. We define an optimal control problem to adjust parameters in single-cell models so that the trans-membrane potential predicted by a model fits in a least-square (LS) sense the potential recorded over time. To account for restitution properties, this LS function measures the discrepancy between predictions and experiments for a cell paced at various heart rates (HR) of increasing frequency. The methodology is used to adjust parameters in the Mitchell-Schaeffer model to unscaled non-smoothed experimental recording of the trans-membrane potential obtained in pig heart using optical fluorescence imaging based on voltage-sensitive dye, and simultaneously identify scaling factors for the experimental data. The methodology is validated by adjusting the model for multiple heart beats at a single HR. The fit for a single HR is excellent (LS function = 0.0065–0.02). The methodology is applied to adjust the MS model to multiple heart beats at three different HR. It is observed that the fit remains good when the range of HR is moderately large (LS function = 0.052), while a larger HR gap is more challenging (LS function = 0.17).