A Simple Absolute Estimate of Peak Eddy Currents Induced by Transcranial Magnetic Stimulation Using the GR Model

Although rigorous numerical modeling is a major and very reliable tool of transcranial magnetic stimulation (TMS) analyses, it requires significant computational resources and time to complete. Therefore, in certain cases, a quick analytical estimate for the peak TMS currents induced by the procedure would be very useful. For instance, maximum exposure due to currents induced in an operator's body, or eddy currents present in ancillary areas of the patient (e.g., the fetus of a pregnant woman) may be of interest. In such cases, a general simplified analytical solution that provides at least an upper absolute estimate of spatial eddy current distribution may be of value. In the present study, we suggest using an early model of Grandori and Ravazzani (GR model) related to an unbounded homogeneous space for that purpose. We formulate the model, implement it in software, and validate the model by comparison with a known numerical FEM solution. Finally, we apply the model in order to establish an upper absolute estimate for TMS eddy currents excited in a human body at various conditions.