Hybrid finite elements and spectral method for computation of the electric potential generated by a nerve cuff electrode

An original numerical method is developed to compute the 3D electric potential generated by a dot-contact cuff electrode implanted around an axisymmetrical, inhomogeneous, anisotropic nerve. The technique is based on a 2D finite-element approach coupled with a semi-analytical Fourier spectral decomposition to approximate the solution behaviour in the azymuthal direction. The method only requires a 2D FEM mesh and allows an accurate electrode description, with any number of contacts at different angular positions. Results show that the convergence of the Fourier series is very fast: typically, the relative error due to series truncation (estimated by the norm of the difference between the solution computed with M modes and the one computed with M— 1 modes, normalised by the norm of the solution computed with M modes) reaches the order of 10−3 with six spectral modes (M=6). As a consequence, the whole algorithm has the complexity of a 2D approach.