Modeling cardiac structural heterogeneity via space-fractional differential equations
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We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we consider the application of space-fractional operators in the context of cardiac electrophysiology, where the lack of clear separation of scales of the highly heterogeneous myocardium triggers peculiar features such as the dispersion of action potential duration, that have been observed experimentally, but cannot be described by the standard monodomain or bidomain models. We describe the methodology and compare the results of a standard monodomain model with results of a model with a non-local component in space.