Multigrid Solution of the Potential Field in Modeling Electrical Nerve Stimulation

In this paper, multilevel techniques are introduced as a fast numerical method to compute 3-D potential field in nerve stimulation configurations. It is shown that with these techniques the computing time is reduced significantly compared to conventional methods. Consequently, these techniques greatly enhance the possibilities for parameter studies and electrode design. Following a general description of the model of nerve stimulation configurations, the basic principles of multilevel solvers for the numerical solution of partial differential equations are briefly summarized. Subsequently, some essential elements for successful application are discussed. Finally, results are presented for the potential field in a nerve bundle induced by tripolar stimulation with a cuff electrode surrounding part of the nerve.