Adjustment of Parameters in Ionic Models Using Optimal Control Problems

Abstract

We developed numerical methods to optimally adjust the parameters in cardiac electrophysiology models, using optimal control and non-differentiable optimization methods. We define three optimal control problems to capture the main features of the cardiac action potential (AP). The first two control problems adjust parameters in single-cell models to recover the duration of the various phases of the AP or the trans-membrane potential at a given cell recorded over time. A third control problem is defined to adjust the conductance in the monodomain model to recover the conduction speed of an AP wave. The methodology is used to adjust parameters in the monodomain model with Mitchell-Schaeffer ion kinetics to recover the phase durations and conduction velocity in three cardiac tissues. Error on the phase durations lies within 1–3%, except for the depolarization time. The Aliev-Panfilov and Mitchell-Schaeffer model are adjusted to experimental recording of the trans-membrane potential obtained through optical fluorescence imaging. The Mitchell-Schaeffer model achieves a better fit to the data.