Electric field optimization to improve multichannel TMS-based functional localization

112 

Abstract Submission 

Ole Numssen¹, Thomas Knösche², Evgenii Kim³, Mohammad Daneshzand⁴, Sergey Makarov⁵, Tommy Raij⁴, Aapo Nummenmaa⁴, Konstantin Weise^1,6

¹Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Saxony, ²Max Planck Institute, Leipzig, Saxony, ³Harvard University, Boston, MA, ⁴Massachusetts General Hospital, Boston, MA, ⁵Worcester Polytechnic Institute, Boston, MA, ⁶Leipzig University of Applied Sciences, Leizig, Germany

Ole Numssen  
Max Planck Institute for Human Cognitive and Brain Sciences
Leipzig, Saxony

Thomas Knösche  
Max Planck Institute
Leipzig, Saxony

Evgenii Kim  
Harvard University
Boston, MA

Mohammad Daneshzand  
Massachusetts General Hospital
Boston, MA

Sergey Makarov  
Worcester Polytechnic Institute
Boston, MA

Tommy Raij  
Massachusetts General Hospital
Boston, MA

Aapo Nummenmaa  
Massachusetts General Hospital
Boston, MA

Konstantin Weise  
Max Planck Institute for Human Cognitive and Brain Sciences|Leipzig University of Applied Sciences
Leipzig, Saxony|Leizig, Germany

Transcranial magnetic stimulation (TMS) is a powerful tool for non-invasive modulation of cortical activity. In our previous work, we employed a regression approach [1] relating the local electric field strength across stimuli with motor evoked potentials (MEPs) to pinpoint muscle representations in the primary motor cortex (M1) [2]. This method relies on differences in the cortical stimulation patterns across pulses to functionally differentiate cortical areas from one another and, thus, is limited by the significant spatial autocorrelation of induced e-fields from standard TMS coils. Here, we present a strategy to utilize multi-channel TMS techniques (Fig. 1a) for TMS mapping. Specifically, we aim to minimise the cross-correlation of electric fields across TMS pulses (Fig. 1b) by optimizing the channel currents to improve the mapping resolution and shorten the experimental duration by reducing the number of TMS pulses needed.

For a multichannel TMS array with nc channels (e.g. Nc = 6) the induced e-field etotal is the superposition of the Nc individual e-fields [3,4]. To take the individual head and brain anatomy into account, an initial e-field computation has to be computed for all Nc channels individually at the (to be) realized coil placements with an arbitrary stimulation intensity (e.g. 1A/µS) [5,6]. Due to the computational cost of the optimization procedure, etotal (Ncomp * Nelm; Ncomp = 3 spatial components: x, y, z) is optimized only within pre-defined region of interest (ROI) with Nroi (e.g. Nroi = 10,000) elements. We employ the SLSQP solver to determine the currents (Nchan * Npulse) for each channel that minimize the average correlation across Npulse TMS pulses. Two complementing optimization schemes solve the two major practical requirements: Pre-experimental optimization of a fixed number of pulses (1) and pulse-by-pulse optimization that includes previously realized currents (2). The optimization routine is implemented in our pyNIBS [1] Python package.

Downsampling of the region of interest from Nroi elements to a spatially equidistant subset of elements Nelm (Nelm = 100 to 1000) yields a considerable speed up of the optimization procedure without significantly impeding the results (Fig. 2a - 2c). Restraining the number of optimization iterations (Niter) does impact optimization duration as well as the optimization result (Fig. 2b & 2c), as the SLSQP solver does not yield the global optimum. As expected, optimization duration strongly depends on Niter and Nelm, ranging from < 1 min for Nelm = 100 and Niter = 100 to > 1 hr for Nelm = 1000 and Niter = 500 (Fig. 2a). The optimization score only marginally improves from 200 to 500 iterations for Nelm ≥ 500 (Fig. 2c). Across all tested combinations of Nelms and Niter the optimization routine significantly decreases the correlation of the induced e-fields compared to randomly chosen currents (Fig. 2d). The computation time to optimize a fixed number of pulses ('pre-experimental optimization') grows exponentially with the number of pulses, with computation times exceeding 20 min for Nelm = 1000 for 150 TMS pulses. In contrast, pulse-by-pulse optimization yields fast current results for subsequent stimuli without reaching the levels of decorrelation from the pre-experimental optimization (Fig. 2e).

In summary, our routine successfully decreases the spatial autocorrelation of induced e-fields from multichannel TMS arrays across pulses by optimizing the channel currents. Reducing the computational load, by restricting the optimizer and by subsampling the cortical region of interest, allows to complete optimizations in reasonable time. Importantly, tuning these hyperparameters does not significantly impede the overall optimization goal. Increasing the across-pulse variance is a strong lever to reduce the number of TMS pulses needed to perform structure-function mappings.

TMS ¹

Methods Development ²

Other - multichannel TMS; mapping; localization; FEM; e-field; regression; motor mapping; structure-function mapping