Limitations of the homogenized cardiac Monodomain model for the case of low gap junctional coupling

The cardiac Monodomain model is a mathematical model extensively used in studies of propagation of bioelectric wavefronts in the heart. To be able to use the model for complex and large cardiac simulations, such as the case of whole heart and 3D simulations, some parameters of the model that are known to physiologically vary in space, such as the intracellular conductivity, are traditionally kept constant at effective values. These effective values can be obtained via a mathematical procedure called homogenization. In this work we revisit the classical homogenized monodomain formulation to evaluate its ability to reproduce the situation of low gap junctional coupling. This situation arises in many pathological conditions such as during ischemia. Our numerical results suggest some limitations of the homogenized cardiac Monodomain model under these conditions in terms of computed conduction velocity and Action Potential waverforms.