Verification of computational models of cardiac electro-physiology

For computational models of cardiac activity to be used in safety-critical clinical decision-making, thorough and rigorous testing of the accuracy of predictions is required. The field of 'verification, validation and uncertainty quantification' has been developed to evaluate the credibility of computational predictions. The first stage, verification, is the evaluation of how well computational software correctly solves the underlying mathematical equations. The aim of this paper is to introduce novel methods for verifying multi-cellular electro-physiological solvers, a crucial first stage for solvers to be used with confidence in clinical applications. We define 1D-3D model problems with exact solutions for each of the monodomain, bidomain, and bidomain-with-perfusing-bath formulations of cardiac electro-physiology, which allow for the first time the testing of cardiac solvers against exact errors on fully coupled problems in all dimensions. These problems are carefully constructed so that they can be easily run using a general solver and can be used to greatly increase confidence that an implementation is correct, which we illustrate by testing one major solver, 'Chaste', on the problems. We then perform case studies on calculation verification (also known as solution verification) for two specific applications. We conclude by making several recommendations regarding verification in cardiac modelling.