Application of Order and Sample Selection in Uncertainty Quantification of Cardiac Models

Simulating the electrical behavior of the heart requires accounting for parameter errors, model inaccuracies, and individual variations in settings, which can all be influenced by user choices or disease conditions. To map the effects of parameter uncertainty, we built on previous findings employing bi-ventricular activation simulations and robust uncertainty quantification (UQ) techniques based on polynomial chaos expansion (PCE) that maps variability in propagation simulations. The PCE approach offers efficient stochastic exploration with reduced computational demands. To ensure reliable results, we focused here on the importance of testing for polynomial order and sample size, aiming to obtain accurate outcomes with minimal computational burden. Order testing involves determining the polynomial degree used for calculating statistics, whereas sample testing pertains to identifying the necessary number and values of the parameters from which the UQ model is estimated. The guide for both steps was to ensure consistency in the results, roughly emulating a convergence analysis. We applied this approach to a bi-ventricular activation simulation using UncertainSCI and quantified the effects of physiological variability in conduction velocity. Our results show that the selection of the appropriate polynomial degree order and sample dataset influences the outcomes of simulations and should be a required step before performing a UQ analysis.