Data-driven Uncertainty Quantification on Manifolds for Cardiac Digital Twins
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Organ-scale heart digital twins have shown considerable promise for improving clinical decision making in cardiac electrophysiology (EP). Currently, heart digital twins incorporate patient-specific organ-scale features, such as cardiac geometry and fibrosis distributions, by using noninvasive clinical imaging data. However, for tissue- and cell- scale properties, model values are mainly derived from literature. While patient-specific variation in cell-scale and tissue-scale properties may play an important role in EP behavior, it is not feasible to obtain this data noninvasively. Therefore, the impact of these uncertain parameters on patient-specific EP prediction accuracy is largely unstudied. We propose a manifold learning-based surrogate modeling framework for assessing confidence in patient-specific cardiac EP simulations while accounting for uncertainty of the unknown EP properties. More specifically, we will utilize the formulation of polynomial chaos expansion on principal geodesic Grassmannian manifolds. In this approach, principal geodesic analysis (PGA) on the Grassmann manifold of the response identifies a set of disjoint geodesic submanifolds that capture the variation in the response. This is performed using a minimization of the sample Frechet variance on the Grassmann manifold. Polynomial chaos expansion is then used to construct a mapping between the random parameter space and the projection of the response on the local submanifold. The projection back to the original space allows to quantify the uncertainty in the system. The model consists of sixteen EP parameters: 6 ionic conductances, each for the healthy and fibrotic cell models, and 4 for fiber conductivities.
