Abstract
Models of electrical activity in cardiac cells have become important research tools as they can provide a quantitative description of detailed and integrative physiology. However, cardiac cell models have many parameters, and how uncertainties in these parameters affect the model output is difficult to assess without undertaking large numbers of model runs. In this study we show that a surrogate statistical model of a cardiac cell model (the Luo-Rudy 1991 model) can be built using Gaussian process (GP) emulators. Using this approach we examined how eight outputs describing the action potential shape and action potential duration restitution depend on six inputs, which we selected to be the maximum conductances in the Luo-Rudy 1991 model. We found that the GP emulators could be fitted to a small number of model runs, and behaved as would be expected based on the underlying physiology that the model represents. We have shown that an emulator approach is a powerful tool for uncertainty and sensitivity analysis in cardiac cell models.
Highlights
To explain the way that Gaussian process (GP) emulators were used in this study, we concentrate initially on the action potential duration to 90% repolarisation (APD90) emulator, before presenting our findings for the other emulators
The evaluation of the APD90 emulator against test data is shown in Fig 3, which shows the difference between the output of the emulator and the output of the simulator for each of the 20 test data
The Mahalanobis Distance (MD) for these test data was 28.22, which is within the plausible range given the reference distribution [29]
Summary
Since the publication of the first model describing the cardiac action potential over 50 years ago [1], models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools. These models have explanatory power as they express quantitatively our knowledge of the biophysical processes that generate the cardiac action potential. The present generation of models include detailed descriptions of the dynamics of transmembrane current flowing through ion channels, pumps and exchangers in the cell membrane, coupled to detailed models of Ca2+ storage and release within the cell [4], and there has been an increasing trend from models of animal cells towards detailed models of human atrial
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