Cardiac cell and tissue models have many parameters, and these can have a strong influence on model behaviour. For example a reduced outward current may result in a failure to depolarise. However, these parameters are not fixed in the same way as a physical constant or a material parameter. Instead they may vary from cell to cell, and in a single cell parameters can change dynamically in response to the local environment. The present generation of cardiac cell models are not well equipped to study the effect of uncertainty and variability. While it is possible to evaluate models with different parameter settings, the potential parameter space is high-dimensional and so a thorough exploration of model behaviour is difficult. One way to approach this problem is to replace the computational model with an emulator, which can act as a fast running surrogate.
We have used Gaussian processes as emulators of cardiac cell models, where model parameters are treated as a vector of inputs to the Gaussian process. The Gaussian process hyperparameters are fitted to a set of model runs, and the quality of fit is assessed by comparing predicted outputs from the emulator against actual output from the model.
In this framework it is possible to treat model parameters and model outputs as uncertain, so that they are described by a distribution instead of a fixed value. Variance based sensitivity indices can then be calculated, which are the proportion of output variance that is accounted for by variance on each input or parameter. Since the emulator can be evaluated very quickly, it is possible to throughly explore the parameter space and identify regions of parameter space that are implausible given a set of experimental data. This approach is called history matching, and accounts properly for uncertainty in the experimental data as well as uncertainty in the emulator fit.