Torge Worbs’s research while affiliated with Technical University of Denmark and other places

Objective. To provide a finite-element method (FEM) for rapid, repeated evaluations of the electric field induced by transcranial magnetic stimulation (TMS) in the brain for changing coil positions. Approach. Previously, we introduced a first-order tetrahedral FEM enhanced by super-convergent patch recovery (SPR), striking a good balance between computational efficiency and accuracy (Saturnino et al 2019 J. Neural Eng. 16 066032). In this study, we refined the method to accommodate repeated simulations with varying TMS coil position. Starting from a fast direct solver, streamlining the pre- and SPR-based post-calculation steps by implementing these steps as parallel sparse matrix multiplications strongly improved the computational efficiency. Additional speedups were achieved through efficient multi-core and GPU acceleration, alongside the optimization of the volume conductor model of the head for TMS. Main Results. For an anatomically detailed head model with ∼4.4 million tetrahedra, the optimized implementation achieves update rates above 1 Hz for electric field calculations in bilateral gray matter, resulting in a 60-fold speedup over the previous method with identical accuracy. An optimized model without neck and with adaptive spatial resolution scaled in dependence to the distance to brain grey matter, resulting in ∼1.9 million tetrahedra, increased update rates up to 10 Hz, with ∼3% numerical error and ∼4% deviation from the standard model. Region-of-interest (ROI) optimized models focused on the left motor, premotor and dorsolateral prefrontal cortices reached update rates over 20 Hz, maintaining a difference of <4% from standard results. Our approach allows efficient switching between coil types and ROI during runtime which greatly enhances the flexibility. Significance. The optimized FEM enhances speed, accuracy and flexibility and benefits various applications. This includes the planning and optimization of coil positions, pre-calculation and training procedures for real-time electric field simulations based on surrogate models as well as targeting and dose control during neuronavigated TMS.

Before, we've introduced voxel-wise TMS mapping [1]: This approach uses simulations of the TMS-induced E-field to perform voxel-wise regression, fitting the cortical stimulation to behavioral modulation. With this, we were able to significantly improve localization resolution. Here, we supercharge this mapping approach by utilizing multichannel TMS (mTMS) to generate highly varying E-fields to further increase stimulation accuracy while reducing the number of TMS pulses.

Background: Transcranial Magnetic Stimulation (TMS) therapies use both focal and unfocal coil designs. Unfocal designs often employ bendable windings and moveable parts, making realistic simulations of their electric fields in inter-individually varying head sizes and shapes challenging. This hampers comparisons of the various coil designs and prevents sys-tematic evaluations of their dose-response relationships. Objective: Introduce and validate a novel method for optimizing the position and shape of flexible coils taking individual head anatomies into account. Evaluate the impact of realistic modeling of flexible coils on the electric field simulated in the brain. Methods: Accurate models of four coils (Brainsway H1, H4, H7; MagVenture MST-Twin) were derived from computed tomography data and mechanical measurements. A generic representation of coil deformations by concatenated linear transformations was introduced and validated. This served as basis for a principled approach to optimize the coil positions and shapes, and to optionally maximize the electric field strength in a region of interest (ROI). Results: For all four coil models, the new method achieved configurations that followed the scalp anatomy while robustly preventing coil-scalp intersections on N=1100 head models. In contrast, setting only the coil center positions without shape deformation regularly led to physically impossible configurations. This also affected the electric field calculated in the cortex, with a median peak difference of ~16%. In addition, the new method outperformed grid search-based optimization for maximizing the electric field of a standard figure 8 coil in a ROI with a comparable computational complexity. Conclusion: Our approach alleviates practical hurdles that so far hampered accurate simula-tions of bendable coils. This enables systematic comparison of dose-response relationships across the various coil designs employed in therapy.

Background Transcranial Electrical Stimulation (TES), Temporal Interference Stimulation (TIS), Electroconvulsive Therapy (ECT) and Tumor Treating Fields (TTFields) are based on the application of electric current patterns to the brain. Objective The optimal electrode positions, shapes and alignments for generating a desired current pattern in the brain vary between persons due to anatomical variability. The aim is to develop a flexible and efficient computational approach to determine individually optimal montages based on electric field simulations. Methods We propose a leadfield-free optimization framework that allows the electrodes to be placed freely on the head surface. It is designed for the optimization of montages with a low to moderate number of spatially extended electrodes or electrode arrays. Spatial overlaps are systematically prevented during optimization, enabling arbitrary electrode shapes and configurations. The approach supports maximizing the field intensity in target region-of-interests (ROI) and optimizing for a desired focality-intensity tradeoff. Results We demonstrate montage optimization for standard two-electrode TES, focal center-surround TES, TIS, ECT and TTFields. Comparisons against reference simulations are used to validate the performance of the algorithm. The system requirements are kept moderate, allowing the optimization to run on regular notebooks and promoting its use in basic and clinical research. Conclusion(s) The new framework complements existing optimization methods that require small electrodes, a predetermined discretization of the electrode positions on the scalp and work best for multi-channel systems. It strongly extends the possibilities to optimize electrode montages towards application-specific aims and supports researchers in discovering innovative stimulation schemes. The framework is available in SimNIBS.

Objective To provide a Finite-Element Method (FEM) for rapid, repeated evaluations of the electric field induced by transcranial magnetic stimulation (TMS) in the brain for changing coil positions. Approach Previously, we introduced a first-order tetrahedral FEM enhanced by super- convergent patch recovery (SPR), striking a good balance between computational efficiency and accuracy (Saturnino et al 2019 J. Neural Eng . 16 066032). In this study, we refined the method to accommodate repeated simulations with varying TMS coil position. Starting from a fast direct solver, streamlining the pre- and SPR-based post-calculation steps using weight matrices computed during initialization strongly improved the computational efficiency. Additional speedups were achieved through efficient multi-core and GPU acceleration, alongside the optimization of the volume conductor model of the head for TMS. Main Results For an anatomically detailed head model with ∼4.4 million tetrahedra, the optimized implementation achieves update rates above 1 Hz for electric field calculations in bilateral gray matter, resulting in a 60-fold speedup over the previous method with identical accuracy. An optimized model without neck and with adaptive spatial resolution scaled in dependence to the distance to brain grey matter, resulting in ∼1.9 million tetrahedra, increased update rates up to 10 Hz, with ∼3% numerical error and ∼4% deviation from the standard model. Region-of-interest (ROI) optimized models focused on the left motor, premotor and dorsolateral prefrontal cortices reached update rates over 20 Hz, maintaining a difference of <4% from standard results. Our approach allows efficient switching between coil types and ROI during runtime which greatly enhances the flexibility. Significance The optimized FEM enhances speed, accuracy and flexibility and benefits various applications. This includes the planning and optimization of coil positions, pre-calculation and training procedures for real-time electric field simulations based on surrogate models as well as targeting and dose control during neuronavigated TMS.

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