Derivative-based Inference for Cell and Channel Electrophysiology Models

Models of ionic currents or of the cardiac action potential (AP) are frequently calibrated by defining an error function that quantifies the mismatch between simulations and data, and using numerical optimisation to find the parameter values that minimise this function. Many optimisation algorithms assume knowledge of the derivatives of the error function with respect to the parameters, but for models formulated as differential equations these are typically unknown. In this study we extend our simulation tool, Myokit, with the capability to rapidly calculate derivatives of simulation output and couple it to our inference tool, PINTS, to calculate the derivatives of the error function. We measure the added overhead of the sensitivity calculations in a model of the ion current
$I_{Kr}$
and in a model of a stem-cell AP. Next we compare the performance of a state-of-the art derivative-free optimiser with that of a popular derivative-using method. For both problems, the derivative-based method requires fewer function evaluations, but this is offset by a significant increase in the computational cost of each evaluation. The derivative-free method is much faster for the
$I_{Kr}$
case, while the derivative-using method outper-forms on the AP case. However, the derivative-free method is more robust on both problems: providing the correct answer on a greater percentage of runs.