Abstract
Biophysically detailed cardiac cell models reconstruct the action potential and calcium dynamics of cardiac myocytes. They aim to capture the biophysics of current flow through ion channels, pumps, and exchangers in the cell membrane, and are highly detailed. However, the relationship between model parameters and model outputs is difficult to establish because the models are both complex and non-linear. The consequences of uncertainty and variability in model parameters are therefore difficult to determine without undertaking large numbers of model evaluations. The aim of the present study was to demonstrate how sensitivity and uncertainty analysis using Gaussian process emulators can be used for a systematic and quantitive analysis of biophysically detailed cardiac cell models. We selected the Courtemanche and Maleckar models of the human atrial action potential for analysis because these models describe a similar set of currents, with different formulations. In our approach Gaussian processes emulate the main features of the action potential and calcium transient. The emulators were trained with a set of design data comprising samples from parameter space and corresponding model outputs, initially obtained from 300 model evaluations. Variance based sensitivity indices were calculated using the emulators, and first order and total effect indices were calculated for each combination of parameter and output. The differences between the first order and total effect indices indicated that the effect of interactions between parameters was small. A second set of emulators were then trained using a new set of design data with a subset of the model parameters with a sensitivity index of more than 0.1 (10%). This second stage analysis enabled comparison of mechanisms in the two models. The second stage sensitivity indices enabled the relationship between the L-type Ca2+ current and the action potential plateau to be quantified in each model. Our quantitative analysis predicted that changes in maximum conductance of the ultra-rapid K+ channel IKur would have opposite effects on action potential duration in the two models, and this prediction was confirmed by additional simulations. This study has demonstrated that Gaussian process emulators are an effective tool for sensitivity and uncertainty analysis of biophysically detailed cardiac cell models.
Highlights
The cardiac action potential arises from the movement of ions through channels, pumps, and exchangers in the cell membrane
The first model of the action potential in a cardiac myocyte was developed over 50 years ago (Noble, 1962), and since a series of more detailed models have been developed as experimental techniques and data have improved
The present generation of models provide detailed reconstructions of the cardiac action potential (Fink et al, 2011), and computational models of cardiac cells and tissue have become valuable research tools because they can encode biophysical mechanisms into a quantitative framework, and so can be used to test and construct hypotheses (Clayton et al, 2011). These detailed models are capable of simulating the behavior of real cardiac myocytes, this veracity comes at the price of complexity
Summary
The cardiac action potential arises from the movement of ions through channels, pumps, and exchangers in the cell membrane. The present generation of models provide detailed reconstructions of the cardiac action potential (Fink et al, 2011), and computational models of cardiac cells and tissue have become valuable research tools because they can encode biophysical mechanisms into a quantitative framework, and so can be used to test and construct hypotheses (Clayton et al, 2011) These detailed models are capable of simulating the behavior of real cardiac myocytes, this veracity comes at the price of complexity. Experimental data are subject to variability and error arising from both limitations of experimental methods as well as intrinsic variability in cardiac cells Some of these inputs, such as binding affinities and reaction rate constants, can be considered to have fixed values because they have a physical basis. The equations for a particular ion channel, pump, or exchanger are often re-used in different models and so the provenance of model inputs may be very difficult to establish (Niederer et al, 2009)
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