bioRxiv Science⌕ Search
Home/Archive/bioRxiv

bioRxiv · 10.1101/300616

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

Gomez, L.·Goetz, S.·Peterchev, A. V.
View original source ↗Export metadata ↓

Abstract

BackgroundTranscranial 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.\n\nObjectiveThis 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.\n\nMethodsA 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 trade-offs for specific target depths.\n\nResultsAcross 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%.\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=153 SRC=\"FIGDIR/small/300616_fig8.gif\" ALT=\"Figure 8\">\nView larger version (14K):\norg.highwire.dtl.DTLVardef@af0b5org.highwire.dtl.DTLVardef@4118d8org.highwire.dtl.DTLVardef@1c61f80org.highwire.dtl.DTLVardef@3e23fa_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 8.C_FLOATNO Energy, W, vs. spread, S1/2, curves for hand knob stimulation for a conventional figure-8 coil and optimized fdTMS coil on a 32 x 32 cm square plane.\n\nC_FIG ConclusionComputational design of TMS coils could enable more selective targeting of the induced E-field. 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.\n\nDECLARATION 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.

Source connections

Explore related subjects

bioengineeringPreprint

Keep this discovery

BibTeXRIS

Gomez, L., Goetz, S., Peterchev, A. V.. 2018-04-13. Design of Transcranial Magnetic Stimulation Coils with Optimal Trade-off between Depth, Focality, and Energy. https://doi.org/10.1101/300616

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related preprints

bioRxiv2026

Comparative study of chlorophyll measurement in Physcomitrium patens moss using a conventional microscope adapted for combined 2D+1D imaging and spectral analysis

Imaging spectroscopy often requires expensive and complex equipment. Here we show a simple procedure for attaching a standard miniature fiber spectrometer to a conventional microscope, allowing easy integration of 2D imaging with 1D high-resolution spectral measurements. This combination provides much of the benefit of a full imaging spectrometer without the large equipment investment, and we provide instructions for modifying microscopes to this setup and the present measurements of living cells that demonstrate their performance. Using this setup, we compare the quantitative measurement of chlorophyll concentration in Physcomitrium patens moss using color imaging and spectral sampling.

bioengineering↗
bioRxiv2026

De novo designed single-domain antibodies protect against lethal cobra venom neurotoxicity in vivo

Generative protein design can now rapidly produce de novo binders with high affinity and functional activity against a wide range of targets, including lethal snake venom toxins. However, so far most reported successes rely on new-to-nature scaffolds with limited therapeutic precedent. Single-domain antibodies (VHHs) offer a clinically validated alternative scaffold that can bind and neutralize long-chain -neurotoxins, which are some of the most lethal components in snake venoms. Here we compare three recently established de novo design models with VHH-design capabilities (Germinal, RFantibody, and BoltzGen) for their ability to generate VHHs against the neurotoxin -cobratoxin from the monocled cobra (Naja kaouthia). Using standardized model inputs and evaluation criteria based on AlphaFold3 interface confidence (ipTM) and RMSD self-consistency, we find that Germinal was the only method to generate designs passing stringent in silico criteria for experimental testing. We therefore performed a larger Germinal design campaign employing three different VHH frameworks and experimentally validated 46 designs in vitro. Of these, 42 expressed as soluble proteins and we identified four binding hits derived from two of the three tested frameworks. Of the four binders, two lead candidates were further characterized and demonstrated high affinity (KDs of 4.1 nM and 10.8 nM), monomeric behavior and low polyreactivity, indicating favorable biophysical and developability properties, as well as functional toxin neutralization in vitro. To assess their therapeutic potential we investigated their ability to protect against -cobratoxin toxicity in vivo. Both candidates fully protected mice after -cobratoxin challenge, with 100% survival compared to a lethal control. One candidate also retained notable neutralization capacity against whole venom of Naja kaouthia with a survival of 56%, while the other protected 22% when tested in a rescue setting. Together, we demonstrate that de novo VHH design can generate high affinity single-domain antibodies with in vivo protection against lethal cobra venom neurotoxicity, and provide practical insights into method- and framework-dependent performance.

bioengineering↗
bioRxiv2026

Simple Feedback for Complex Movement: Capturing Whole-Limb Reorganization during Single-IMU Gait Retraining

Clinical gait retraining typically relies on multi-sensor arrays and high-dimensional feedback displays, imposing setup and interpretation burdens that limit routine clinical deployment. We developed a single-IMU visual biofeedback system that delivers real-time feedback of Lower Limb Trajectory Error (LLTE), a composite kinematic error metric integrating knee position and shank angle across the stance phase. Twenty able-bodied adults walked on a treadmill under two visual biofeedback targets (flexed-knee, extended-knee) while receiving either corrected (n=10) or uncorrected (n=8) feedback, where the correction accounted for limb orientation at initial contact. LLTE and stance-phase knee kinematics adapted consistently under the flexed-knee target for both feedback groups, with feedback formulation moderating the temporal trajectory of change. Adaptation toward the extended-knee target was limited, likely because participants were already operating near terminal knee extension and because the scalar error metric provided limited directional information for correction. Ankle range of motion (ROM) changed significantly across the stance phase under both target conditions, while hip ROM did not. Multiscale multivariate sample entropy (MSMVSE) increased monotonically with time scale across all conditions, with no statistically distinguishable difference between corrected and uncorrected feedback. These results suggest that single-IMU LLTE biofeedback can modify gait mechanics and that adaptation was expressed across multiple lower-limb segments rather than through changes at a single joint.

bioengineering↗