Real-time electric field dosimetry for electric-field-informed neuronavigation of transcranial magnetic stimulation

Background. Neuronavigation systems position transcranial magnetic stimulation (TMS) coils relative to a subject’s MRI, but they display the coil position rather than the electric field actually induced in the brain. Our fast solvers can resolve electric fields for millions of precomputed coil placements, yet a new coil placement or a new coil type still required a full re-run of several hours.

Objective. Deliver the whole-brain electric field for any coil shape and position within the frame time of a neuronavigation display, so that TMS targeting can be guided by the electric field itself.

Approach. We combine electromagnetic surface equivalence and reciprocity to relate the solution coefficients for any new coil placement to its incident (primary) fields. The head model is factorized once; fields for arbitrary coil shapes and positions are then recovered without re-solving, with no predefined placement set or coil-type constraint, and with the accuracy of first-order finite element solvers.

Main results. In a comparative study of eight subjects, two head-model pipelines (SimNIBS headreco and mri2mesh), three coil types (circular, double-cone, and figure-8), and 1000 coil placements (48,000 simulations), the real-time solver reproduces finite element electric fields while returning the whole-brain field in under 4 ms per coil placement using 400 modes and less than 4 GB of GPU memory. This work received first-place student paper awards at the 2024 Applied Computational Electromagnetics Society Symposium and third place at the 2024 PhotonIcs and Electromagnetics Research Symposium.

Significance. Sub-4 ms electric field computation adds negligible overhead to neuronavigation frame generation (20 to 50 frames per second), which makes electric-field-guided targeting, adaptive treatment planning, and closed-loop stimulation workflows practical.

Ongoing work. The solver is being integrated into neuronavigation systems that combine co-registered MRI with camera-based tracking.

Publications.

N. I. Hasan (G), M. Dannhauer, D. Wang (PD), Z.-D. Deng, and L. J. Gomez, "Real-time computation of brain E-field for enhanced transcranial magnetic stimulation neuronavigation and optimization," Imaging Neuroscience, vol. 3, 2025. link

N. I. Hasan (G), D. Moritz, D. Wang (PD), Z.-D. Deng, and L. J. Gomez, "Real-Time Computation of Brain E-Field for Enhanced Transcranial Magnetic Stimulation Neuronavigation and Optimization," Progress In Electromagnetics Research Symposium, April 2024 (third place, student paper competition).

N. I. Hasan (G), D. Moritz, D. Wang (PD), Z.-D. Deng, and L. J. Gomez, "Real-Time Computation of E-Field for Transcranial Magnetic Stimulation," International Applied Computational Electromagnetics Society Symposium, May 2024 (first place, student paper competition).

N. I. Hasan (G), D. Moritz, D. Wang (PD), Z.-D. Deng, and L. J. Gomez, "Real-time Computation of E-field in Transcranial Magnetic Stimulation for Neuronavigation and Optimization," IEEE Latin American Conference on Antennas and Propagation, December 2024.

N. I. Hasan (G), D. Wang (PD), and L. J. Gomez, "Real-Time E-Field Dosimetry Estimation in Transcranial Magnetic Stimulation via Probabilistic Matrix Decomposition (PMD) and Huygens’ Principle," IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, July 2023.