An inverse boundary element method computational framework for designing optimal TMS coils

An inverse boundary element method and efficient optimisation techniques were combined to produce a versatile framework to design optimal TMS coils. The presented approach can be seen as an improvement and extension of the work introduced by Cobos Sanchez et al. [1] where the optimality of the resulting coil solutions was not guaranteed. This new numerical framework based on a constant boundary element method has been efficiently applied to produce optimal TMS coils with arbitrary geometry, allowing the inclusion of new coil features in the design process, such as optimised maximum current density or reduced temperature. Even the structural properties of the human head were considered using this approach at the design stage to produce more realistic TMS stimulators. Several examples of TMS coils were designed and simulated to demonstrate the validity of the proposed boundary element method approach, and the obtained results show that the described method is an efficient tool for the design of optimal TMS stimulators, which can be applied to a wide range of coil geometries and performance requirements considering the natural variability in the human head properties.