TMS coil and TMS coil array designer with fast multipole method: Fields and self/mutual inductances optimization
Year: 2023
Type: article
Abstract: For TMS coil design, it is important to know both electric and magnetic field distributions as well as the self-inductance of a single coil and the mutual inductances of individual radiators in a coil array. It is also important to perform computations fast and for many possible designs. We present a platform for performing these modeling tasks based on the fast multipole method (FMM). Every physical coil conductor is discretized into a very large number of “elementary currents” - small straight segments of electric current. The currents could either be distributed uniformly (a Litz wire-based design) or flow close to the surface (the skin effect for a solid conductor). The electric field (following Faraday’s law of induction) and the magnetic field of all these segments are found anywhere in space using FMM. The computation is very fast; it requires ∼0.5 sec for 50,000 elementary current segments within coil conductors and 1,000,000 observation points. FMM is also applied to find the coil inductance(s) via the Neumann formula for self- and mutual inductances. Here, an accurate discretization might be necessary. Typical execution times are under 0.1 sec. The coil design may start with a conductor centerline given as a set of 3D nodes. Next, conductor’s cross-sectional shape (circular/elliptical/rectangular) needs to be specified. Then, we automatically create the “wire” mesh of small elementary current segments filling every cross -section of the physical conductor. This is done using the method of a moving cross-section. We also generate a 2-manifold surface CAD mesh for the entire volumetric conductor. Finally, the computations are performed. After that, the initial coil’s centerline can be modified as required, and the process continues. The same method applies to multiple coils with multiple centerlines. Our base platform is college MATLAB. Research Category and Technology and Methods Basic Research: 10. Transcranial Magnetic Stimulation (TMS) Keywords: TMS Coil Design, TMS Coil Array Design, Self and Mutual Inductances, Fast Multipole Method (FMM))
Source: Brain stimulation
Authors: Jonathan Ferreira, Leah Morales, Rosti Lemdiasov, Hanbing Lu, Zhi-De Deng, Tommi Raij, Aapo Nummenmaa, Sergey Makaroff
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,830
OpenAlex ID: W4320908350