Reducing mesh size in 3-D finite element modeling of the field induced cardiac transmembrane potential

The objective of this study is to determine if ill-shaped tetrahedral elements can be used to reduce the mesh size in a 3D finite element (FEM) bidomain simulation of cardiac transmembrane potential (TMP) induced by a uniform field. The myocardium of the heart is modeled as a spherical shell. The curved and branching cardiac fibers are represented by anisotropic conductivity tensors with realistic intra and extracellular conductivity values. The TMP induced by a uniform electric field is simulated using a 3D FEM bidomain model. Ill shaped tetrahedral elements are utilized in the model to reduce the mesh size. The mesh has a high spatial sampling rate along the radial direction of the myocardium but low sampling rates on the other two directions (θ, φ). The simulation shows that the FEM result has an overall root mean squared error (RMSE) of less than 4% and a correlation coefficient (CCF) of 1.000 compared to an analytic solution. The use of such ill-shaped elements reduces the myocardial mesh size by a factor of approximately 10³ compared to the mesh size constructed by using well shaped elements. These results suggest that it is feasible to use ill-shaped elements to simulate the cardiac TMP arising from a uniform field. The approach greatly reduces the mesh size which in turn reduces the memory and computational cost tremendously