The Physiome Project aims to explain how each component of the human body operates as part of an integrated whole. Developing mathematical and computational models that represent interacting physical mechanisms and are informed by experimental and clinical data is a key component of this activity. Increasingly, this approach is moving from qualitative studies of laboratory experiments to clinical applications by providing quantitative predictions to aid diagnosis, facilitate drug and device development and guide treatment. Models of the heart have been a prominent feature of this enterprise, and it is now possible to construct models that represent the electromechanical behaviour of the heart of an individual patient. However, to be clinically useful, mathematical and computational models of the heart need to predict outcomes in a specific patient given available information. The inherent variability in patient physiology, pathology and therapies, combined with the sparsity and noise inherent in medical images and physiological data, necessitates quantification of uncertainty in these models to inform clinicians and decision makers of how much to rely on a prediction, to quantify confidence in model parameters, and to assist model developers in improving their predictions.

Models of the heart are typically systems of nonlinear ordinary differential equations and nonlinear systems of partial differential equations constrained by conservation laws. These are solved using numerical techniques, on a space scale from single cells up to meshes derived from medical images of the heart. Earlier work focused on developing efficient numerical methods and software solutions to reduce the time and computational cost of cardiac model simulations. Increasingly, with new software and hardware this is no longer the largest challenge. The latest major challenges facing cardiac modelling include parameter inference from uncertain experimental measurements, model personalisation to patient data, model selection, model discrepancy from reality, and most importantly how these factors affect the confidence in model predictions. To address these new challenges requires better links between statistics, mathematics and cardiac modelling communities to develop new mathematical techniques that are tailored to the challenges of patient-specific model development and its applications. This Isaac Newton Institute programme will bring together the statistics and cardiac modelling communities to identify challenging problems in cardiac modelling and novel mathematical and statistical solutions to these problems.

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