| The purposes of this work is to compare the action potential and electrocardiogram computed with the monodomain and bidomain models, using a patient-based two-dimensional geometry of the heart-torso. The pipeline from CT scans to image segmentation with an in-house level set method, then to mesh generation is detailed in the article. Our segmentation technique is based on a new iterative Chan-Vese method. The bidomain model and its approximation called the ``adapted'' monodomain model are next introduced. The numerical methods used to solve these two models are briefly presented. Using both uni- and two-dimensional test cases, we next assess the mesh size required to control the error on the conduction velocities, a main source of error in cardiac action potential computations. We show with quantitative estimates that a main parameter controlling the mesh size is the cell membrane surface-to-volume ratio, noted $\am$. Realistic $\am$ of about $1500-2000$ cm$^{-1}$ for human hearts still require major computational resources. We then compare our numerical solutions and the electrocardiogram recovered with both models on our heart-torso geometry. Activation sites are chosen so that the depolarisation isochrons closely match experimental results in human hearts for healthy cardiac propagation. Both models give similar solutions whereas the bidomain model is about 20-50 times more CPU intensive than the adapted monodomain model. The main computational effort goes in the computation of the extra-cellular and extra-cardiac potentials in the heart-torso. We show that the equations for these potentials must be solved with sufficient accuracy, otherwise compromising the quality of the computed electrocardiograms. |
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