Design of Transcranial Magnetic Stimulation Coils with Optimal Trade-off between Depth, Focality, and Energy

Abstract

DECLARATION OF INTERESTThe fdTMS technology described in this paper is subject to a provisional patent application by Duke University with the authors as inventors. Additionally: L.J.G. is inventor on a patent pertaining to the design of focal multicoil TMS systems. S.M.G. is inventor on patents and patent applications; he has received royalties from Rogue Research, TU Muenchen, and Porsche; furthermore, he has been provided with research support and patent fee reimbursement from Magstim Co. A.V.P. is inventor on patents and patent applications, and has received research and travel support as well as patent royalties from Rogue Research; research and travel support, consulting fees, as well as equipment loan from Tal Medical / Neurex; patent application and research support from Magstim; and equipment loans from MagVenture, all related to technology for transcranial magnetic stimulation. ABSTRACTBackground: Transcranial magnetic stimulation (TMS) is a noninvasive brain stimulation technique used for research and clinical applications. Existent TMS coils are limited in their precision of spatial targeting (focality), especially for deeper targets.Objective: This paper presents a methodology for designing TMS coils to achieve optimal trade-off between the depth and focality of the induced electric field (E-field), as well as the energy required by the coil. Methods:A multi-objective optimization technique is used for computationally designing TMS coils that achieve optimal trade-offs between stimulation focality, depth, and energy (fdTMS coils). The fdTMS coil winding(s) maximize focality (minimize stimulated volume) while reaching a target at a specified depth and not exceeding predefined peak E-field strength and required coil energy. Spherical and MRI-derived head models are used to compute the fundamental depth-focality trade-off as well as focality-energy tradeoffs for specific target depths.Results: Across stimulation target depths of 1.0-3.4 cm from the brain surface, the stimulated volume can be theoretically decreased by 42%-55% compared to existing TMS coil designs. The stimulated volume of a figure-8 coil can be decreased by 36%, 44%, or 46%, for matched, doubled, or quadrupled energy. For matched focality and energy, the depth of a figure-8 coil can be increased by 22%. Conclusion:Computational design of TMS coils could enable more selective targeting of the induced Efield. The presented results appear to be the first significant advancement in the depth-focality trade-off of TMS coils since the introduction of the figure-8 coil three decades ago, and likely represent the fundamental physical limit.

Conditions for numerically accurate TMS electric field simulation

“…(In SimNIBS v2.0 this mesh was updated with one having nearly doubled resolution; however, we employed the lower-resolution version since it enables more barycentric refinements while maintaining computational tractability.) The mesh consisted of five homogenous compartments including white/gray matter, CSF, skull, and skin with conductivity of 0.126, 0.276, 1.65, 0.01 and 0.465 S/m, respectively [39]. Starting from the SimNIBS v1.0 example mesh, we generated refined meshes, each time by subdividing each tetrahedron of the earlier mesh into eight equal sized tetrahedrons using the GMSH 'refine by splitting' option [37].…”

Review on biophysical modelling and simulation studies for transcranial magnetic stimulation

“…Despite the inability to model the effects of individual anatomy on the induced EF, simpler spherical EF models are sufficient for the optimisation and characterisation of magnetic coils (Deng, Lisanby and Peterchev, 2013). Computation cannot overcome physical limitations, such as the depth focality trade-off that makes it difficult to design coils to target deep brain areas (Deng, Lisanby and Peterchev, 2013;Gomez, Goetz and Peterchev, 2018;Gomez-Tames et al, 2020).…”

“…Among standard commercial coils for deep TMS, the double cone coil offers a balance between stimulated volume and superficial field strength (Deng, Lisanby and Peterchev, 2014;Guadagnin et al, 2016;Gomez-Tames et al, 2020). Multi-objective optimisation of the coil windings can reduce the required power and reach the physical limits of the trade-off between depth and spread (Hernandez-Garcia et al, 2010;Koponen, Nieminen and Ilmoniemi, 2015;Koponen et al, 2017;Gomez, Goetz and Peterchev, 2018;Wang et al, 2018). The spherical head model provides a standardised platform to evaluate and compare coil designs but with limitations (refer subsection 3.1).…”

“…Wei et al 2017Homogeneous sphere (8.5 cm) (Deng, Lisanby and Peterchev, 2013;Guadagnin et al, 2016;Gomez, Goetz and Peterchev, 2018;Gomez-Tames et al, 2020) Focality Area (A1/x) Cortical area where EF is larger than Emax/x (Im and Lee, 2006;Salvador et al, 2009;Koponen, Nieminen and Ilmoniemi, 2015;Yamamoto et al, 2015;Rastogi et al, 2017) Volume (VΩ )…”

“…Usually normalised by brain volume (Deng, Lisanby and Peterchev, 2014;Lu andUeno, 2015a, 2017;Wei et al, 2017;Gomez, Goetz and Peterchev, 2018) Spread…”