Fitting two human atrial cell models to experimental data using Bayesian history matching

Sam Coveney,Richard H Clayton

doi:10.1016/j.pbiomolbio.2018.08.001

Abstract

Cardiac cell models are potentially valuable tools for applications such as quantitative safety pharmacology, but have many parameters. Action potentials in real cardiac cells also vary from beat to beat, and from one cell to another. Calibrating cardiac cell models to experimental observations is difficult, because the parameter space is large and high-dimensional. In this study we have demonstrated the use of history matching to calibrate the maximum conductance of ion channels and exchangers in two detailed models of the human atrial action potential against measurements of action potential biomarkers. History matching is an approach developed in other modelling communities, based on constructing fast-running Gaussian process emulators of the model. Emulators were constructed from a small number of model runs (around 102), and then run many times (>106) at low computational cost, each time with a different set of model parameters. Emulator outputs were compared with experimental biomarkers using an implausibility measure, which took into account experimental variance as well as emulator variance. By repeating this process, the region of non-implausible parameter space was iteratively reduced. Both cardiac cell models were successfully calibrated to experimental datasets, resulting in sets of parameters that could be sampled to produce variable action potentials. However, model parameters did not occupy a small range of values. Instead, the history matching process exposed inputs that can co-vary across a wide range and still be consistent with a particular biomarker. We also found correlations between some biomarkers, indicating a need for better descriptors of action potential shape.

Highlights

Cardiac cell models have become valuable research tools, underpinning models of electrical excitation in cardiac tissue and increasingly applied to drug safety testing (Colatsky et al, 2016; Mirams et al, 2012)
In this paper we report on the application of Bayesian history matching to the problem of selecting a set of inputs for two cardiac cell models that produce outputs consistent with experimental observations
As cardiac cell models are increasingly used for applications such as quantitative safety pharmacology, these new questions are likely to have implications for future work in this area

Summary

Introduction

Cardiac cell models have become valuable research tools, underpinning models of electrical excitation in cardiac tissue and increasingly applied to drug safety testing (Colatsky et al, 2016; Mirams et al, 2012). A cardiac cell model can be thought of as a simulator, where outputs (either action potentials or a set of biomarkers e.g. action potential duration) depend on model parameters or inputs (e.g. maximum ion channel conductances). This relation can be described as: y 1⁄4 fSðxÞ: (1). Given a set of model inputs and corresponding outputs, called design data fxi; yig, the emulator is trained to reconstruct the output surface of the simulator, and so can make rapid predictions for outputs y* from inputs x* that have not been tested with the simulator. It is possible to designate the inputs x* to be uncertain

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