Transcranial Magnetic Stimulation : Magnetic Field Computation in empty free space

Transcranial magnetic stimulation (TMS) is a technique for brain stimulation using magnetic field generated by an external coil. As other techniques like ECT or the implantation of electrodes into motor cortex, TMS has several applications in medical and clinical research. The main benefit of TMS is to be non invasive and painless. TMS use increases but stimulation process remains still empirical and practician has to perform several stimulations to find the best coil position/direction. We propose to develop a simulator of transcranial magnetic stimulation which aims at computing the electromagnetic field induced in the cortex by TMS. We present in this article the first step of this tool, a parametrical coil model allowing the computation of potential magnetic field outside the head and some way to represent it