Variance Based Sensitivity Analysis of $I_{Kr}$ in a Model of the Human Atrial Action Potential Using Gaussian Process Emulators

Abstract

Cardiac cell models have become valuable research tools, but biophysically detailed models embed large numbers of parameters, which must be fitted from experimental data. The provenance of these parameters can be difficult to establish, and so it is important to understand how parameter values influence model behaviour. In this study we examined how model parameters influence the repolarising current $I_{Kr}$ in the Courtemenache-Ramirez-Nattel model of the human atrial action potential. We used a statistical approach in which Gaussian processes (GP) are used to emulate the model outputs. A GP emulator can treat model inputs and outputs as uncertain, and so can be used to directly calculate sensitivity indices. We found that 3 of the 10 parameters influencing $I_{Kr}$ had a strong influence on $APD_{70}$, $APD_{90}$, and Dome $V_m$. These three parameters scale the magnitude of the $I_{Kr}$ gating variable time constant and the voltage dependence of the steady state activation curve, and these mechanisms act to modify the amplitude of $I_{Kr}$ during repolarisation. This study highlights the potential value of statistical approaches for investigating cardiac models, and that uncertainties or errors in parameters resulting from attempts to fit experimental data during model development can ultimately affect model behaviour.