Activation of MAP2K signaling by genetic engineering or HF-rTMS promotes corticospinal axon sprouting and functional regeneration.

Facilitating axon regeneration in the injured central nervous system remains a challenging task. RAF-MAP2K signaling plays a key role in axon elongation during nervous system development. Here, we show that conditional expression of a constitutively kinase-activated BRAF in mature corticospinal neurons elicited the expression of a set of transcription factors previously implicated in the regeneration of zebrafish retinal ganglion cell axons and promoted regeneration and sprouting of corticospinal tract (CST) axons after spinal cord injury in mice. Newly sprouting axon collaterals formed synaptic connections with spinal interneurons, resulting in improved recovery of motor function. Noninvasive suprathreshold high-frequency repetitive transcranial magnetic stimulation (HF-rTMS) activated the BRAF canonical downstream effectors MAP2K1/2 and modulated the expression of a set of regeneration-related transcription factors in a pattern consistent with that induced by BRAF activation. HF-rTMS enabled CST axon regeneration and sprouting, which was abolished in MAP2K1/2 conditional null mice. These data collectively demonstrate a central role of MAP2K signaling in augmenting the growth capacity of mature corticospinal neurons and suggest that HF-rTMS might have potential for treating spinal cord injury by modulating MAP2K signaling.

The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement.

BACKGROUND: When modeling transcranial electrical stimulation (TES) and transcranial magnetic stimulation (TMS) in the brain, the meninges - dura, arachnoid, and pia mater - are often neglected due to high computational costs. OBJECTIVE: We investigate the impact of the meningeal layers on the cortical electric field in TES and TMS while considering the headreco segmentation as the base model. METHOD: We use T1/T2 MRI data from 16 subjects and apply the boundary element fast multipole method with adaptive mesh refinement, which enables us to accurately solve this problem and establish method convergence at reasonable computational cost. We compare electric fields in the presence and absence of various meninges for two brain areas (M1HAND and DLPFC) and for several distinct TES and TMS setups. RESULTS: Maximum electric fields in the cortex for focal TES consistently increase by approximately 30% on average when the meninges are present in the CSF volume. Their effect on the maximum field can be emulated by reducing the CSF conductivity from 1.65 S/m to approximately 0.85 S/m. In stark contrast to that, the TMS electric fields in the cortex are only weakly affected by the meningeal layers and slightly (∼6%) decrease on average when the meninges are included. CONCLUSION: Our results quantify the influence of the meninges on the cortical TES and TMS electric fields. Both focal TES and TMS results are very consistent. The focal TES results are also in a good agreement with a prior relevant study. The solver and the mesh generator for the meningeal layers (compatible with SimNIBS) are available online.

Visible Human Project® female surface based computational phantom (Nelly) for radio-frequency safety evaluation in MRI coils.

Quantitative modeling of specific absorption rate and temperature rise within the human body during 1.5 T and 3 T MRI scans is of clinical significance to ensure patient safety. This work presents justification, via validation and comparison, of the potential use of the Visible Human Project (VHP) derived Computer Aided Design (CAD) female full body computational human model for non-clinical assessment of female patients of age 50-65 years with a BMI of 30-36 during 1.5 T and 3 T based MRI procedures. The initial segmentation validation and four different application examples have been identified and used to compare to numerical simulation results obtained using VHP Female computational human model under the same or similar conditions. The first application example provides a simulation-to-simulation validation while the latter three application examples compare with measured experimental data. Given the same or similar coil settings, the computational human model generates meaningful results for SAR, B1 field, and temperature rise when used in conjunction with the 1.5 T birdcage MRI coils or at higher frequencies corresponding to 3 T MRI. Notably, the deviation in temperature rise from experiment did not exceed 2.75° C for three different heating scenarios considered in the study with relative deviations of 10%, 25%, and 20%. This study provides a reasonably systematic validation and comparison of the VHP-Female CAD v.3.0-5.0 surface-based computational human model starting with the segmentation validation and following four different application examples.

Application of a Neural Network Classifier to Radiofrequency-Based Osteopenia/Osteoporosis Screening.

This preliminary study reports application of a neural network classifier to the processing of previously collected data on low power radiofrequency propagation through the wrist with the goal to detect osteoporotic/osteopenic conditions. The data set used includes 67 subjects (23-94 years old, 50 females, 17 males, 27 osteoporotic/osteopenic, 40 healthy). We process the entire spectrum of the propagation coefficient through the wrist from 30 kHz to 2 GHz, with 201 sampling points in total. We found that the dichotomic diagnostic test of raw non-normalized radiofrequency data performed with the trained neural network approaches 90% specificity and ~70% sensitivity. These results are obtained without inclusion of any additional clinical risk factors. They justify that the radio transmission data are usable on their own as a predictor of bone density. With the inclusion of additional clinical risk factors, both specificity and sensitivity improve to 95% and 76% respectively. Our approach correlates well with the available DXA measurements and has the potential for screening patients at risk for fragility fractures, given the ease of implementation and low costs associated with both the technique and the equipment.Clinical Relevance- Dichotomic diagnostic test of raw non-normalized radiofrequency data performed with the trained neural network approaches 90% specificity and ~70% sensitivity. With the inclusion of other clinical risk factors, specificity and sensitivity increase to 95% and 76% respectively.

Fast Individualized High-resolution Electric Field Modeling for Computational TMS Neuronavigation.

Transcranial Magnetic Stimulation (TMS) is a non-invasive method for safe and painless activation of cortical neurons. On-line visualization of the induced Electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, however present commercially available systems are limited by simplified approximations of the anatomy. Here, we developed a near real-time method to accurately approximate the induced E-field of a freely moving TMS coil with an individualized high-resolution head model. We use a set of magnetic dipoles around the head to approximate the total E-field of a moving TMS coil. First, we match the incident field of the dipole basis set with the incident E-field of the moving coil. Then, based on the principle of superposition and uniqueness of the solutions, we apply same basis coefficients to the total E-field of the basis set. The computed E-fields results show high similarity with an established TMS solver both in terms of the amplitude and the spatial distribution patterns. The proposed method enables rapid visualization of the E-field with ~100 ms of computation time enabling interactive planning, targeting, dosing and coil positioning tasks for TMS neuronavigation.

Electric Field Comparison for TMS Using Different Neuroimaging Segmentation Methods.

Computational electromagnetic modeling is a powerful technique to evaluate the effects of electrical stimulation of the human brain. The results of these simulations can vary depending on the specific segmentation of the head and brain generated from the patient images. Using an existing boundary element fast multipole method (BEM-FMM) electromagnetic solver, this work evaluates the electric field differences modeled using two neuroimaging segmentation methods. A transcranial magnetic stimulation (TMS) coil targeting both the primary motor cortex and the dorsolateral prefrontal cortex (DLPFC) was simulated. Average field differences along a 100 mm line from the coil were small (2% for motor cortex, 3% for DLPFC) and the average field differences in the regions directly surrounding the target stimulation point were 5% for the motor cortex and 2% for DLPFC. More studies evaluating different coils and other segmentation options may further improve the computational modeling for robust TMS treatment.Clinical relevance- Patient-specific computational modeling will provide more information to clinicians for improved localization and targeting of neuromodulation therapies.

Application of a Neural Network Classifier to Radiofrequency-Based Osteopenia/Osteoporosis Screening.

OBJECTIVE: There is an unmet need for quick, physically small, and cost-effective office-based techniques that can measure bone properties without the use of ionizing radiation. METHODS: The present study reports the application of a neural network classifier to the processing of previously collected data on very-low-power radiofrequency propagation through the wrist to detect osteoporotic/osteopenic conditions. Our approach categorizes the data obtained for two dichotomic groups. Group 1 included 27 osteoporotic/osteopenic subjects with low Bone Mineral Density (BMD), characterized by a Dual X-Ray Absorptiometry (DXA) T-score below - 1, measured within one year. Group 2 included 40 healthy and mostly young subjects without major clinical risk factors such as a (family) history of bone fracture. We process the complex radiofrequency spectrum from 30 kHz to 2 GHz. Instead of averaging data for both wrists, we process them independently along with the wrist circumference and then combine the results, which greatly increases the sensitivity. Measurements along with data processing require less than 1 min. RESULTS: For the two dichotomic groups identified above, the neural network classifier of the radiofrequency spectrum reports a sensitivity of 83% and a specificity of 94%. SIGNIFICANCE: These results are obtained without including any additional clinical risk factors. They justify that the radio transmission data are usable on their own as a predictor of bone density. This approach has the potential for screening patients at risk for fragility fractures in the office, given the ease of implementation, small device size, and low costs associated with both the technique and the equipment.

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes.

Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.

Rapid computation of TMS-induced E-fields using a dipole-based magnetic stimulation profile approach.

BACKGROUND: TMS neuronavigation with on-line display of the induced electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, but present commercially available solutions are limited by simplified approximations. OBJECTIVE: Developing a near real-time method for accurate approximation of TMS induced E-fields with subject-specific high-resolution surface-based head models that can be utilized for TMS navigation. METHODS: Magnetic dipoles are placed on a closed surface enclosing an MRI-based head model of the subject to define a set of basis functions for the incident and total E-fields that define the subject's Magnetic Stimulation Profile (MSP). The near real-time speed is achieved by recognizing that the total E-field of the coil only depends on the incident E-field and the conductivity boundary geometry. The total E-field for any coil position can be obtained by matching the incident field of the stationary dipole basis set with the incident E-field of the moving coil and applying the same basis coefficients to the total E-field basis functions. RESULTS: Comparison of the MSP-based approximation with an established TMS solver shows great agreement in the E-field amplitude (relative maximum error around 5%) and the spatial distribution patterns (correlation >98%). Computation of the E-field took ~100 ms on a cortical surface mesh with 120k facets. CONCLUSION: The numerical accuracy and speed of the MSP approximation method make it well suited for a wide range of computational tasks including interactive planning, targeting, dosing, and visualization of the intracranial E-fields for near real-time guidance of coil positioning.

A 3-axis coil design for multichannel TMS arrays.

PURPOSE: Multichannel Transcranial Magnetic Stimulation (mTMS) arrays enable multiple sites to be stimulated simultaneously or sequentially under electronic control without moving the system's stimulation coils. Here, we build and characterize the performance of a novel modular 3-axis TMS coil that can be utilized as a unit element in large-scale multichannel TMS arrays. METHODS: We determined the basic physical characteristics of the 3-axis TMS coil x-, y- and z-elements using a custom 2-channel programmable stimulator prototype. We mapped the temporal rate-of-change of the induced magnetic field (dB/dt) on a 2D plane parallel to the coil surface (including an extended line for full spatial coverage) and compared those values with predictions from magnetic field simulations. Temperature measurements were carried out to assess the incorporated air-cooling method. We measured the mutual and self-inductances of the x/y/z-elements to assess coupling between them. Additionally, we measured and calculated the coupling between z-elements in the array configuration. Finally, we performed electric field simulations to evaluate the stimulation intensity and focality of the coil and compared the results to conventional TMS coils as well as demonstrated suitability of the 3-axis coil for a multichannel array configuration. RESULTS: The experimentally obtained dB/dt values validated the computational model of the 3-axis coil and therefore confirmed that both the coil and stimulator system are operating as intended. The air-cooling system was effective for brief high-frequency pulse trains and extended single- and paired-pulse TMS protocols. The electromagnetic simulations suggested that an array of the 3-axis coils would have comparable stimulation intensity to conventional TMS coils, therefore enabling clearly suprathreshold stimulation of the human brain. The recorded coil coupling between the x/y/z-elements was < 1% and the maximal coupling between z-elements in the array configuration was 1.8% and 3.4% for the measured and calculated values, respectively. CONCLUSION: We presented a 3-axis coil intended for multichannel TMS arrays. The electromagnetic measurements and simulations verified that the coil fabrication met the desired specifications and that the inductive coupling between the elements was negligible. The air-cooled 3-axis TMS coil appears suitable to be used as an element in multichannel TMS arrays.

Boundary Element Fast Multipole Method for Enhanced Modeling of Neurophysiological Recordings.

OBJECTIVE: A new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG). METHODS: The algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling. RESULTS: For non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 µm long dipoles. On a standard server, the computations require about 5 min. CONCLUSION: Our results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG. SIGNIFICANCE: Based on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.

Accurate TMS Head Modeling: Interfacing SimNIBS and BEM-FMM in a MATLAB-Based Module.

We interface the head modelling, coil models, Graphical User Interface (GUI), and post-processing capabilities of the SimNIBS package with the boundary element fast multipole method (BEM-FMM), implemented in a MATLAB-based module. The resulting pipeline combines the best of both worlds: the individualized head modelling and ease-of-use of SimNIBS with the numerical accuracy of BEM-FMM. The corresponding TMS (transcranial magnetic stimulation) modeling package is developed and made available online. It imports a SimNIBS surface segmentation and a coil field, and then exports electric-field values in selected surfaces or volumes. Additional information is also made available, such as discontinuous compartment surface electric fields and associated surface electric charge distributions.

A software toolkit for TMS electric-field modeling with boundary element fast multipole method: an efficient MATLAB implementation.

Objective: To present and disseminate our transcranial magnetic stimulation (TMS) modeling software toolkit, including several new algorithmic developments, and to apply this software to realistic TMS modeling scenarios given a high-resolution model of the human head including cortical geometry and an accurate coil model. Approach: The recently developed charge-based boundary element fast multipole method (BEM-FMM) is employed as an alternative to the 1st order finite element method (FEM) most commonly used today. The BEM-FMM approach provides high accuracy and unconstrained numerical field resolution close to and across cortical interfaces. Here, the previously proposed BEM-FMM algorithm has been improved in several novel ways. Main results: The improvements resulted in a threefold increase in computational speed while maintaining the same solution accuracy. The computational code based on the MATLAB® platform is made available to all interested researchers, along with a coil model repository and examples to create custom coils, head model repository, and supporting documentation. The presented software toolkit may be useful for post-hoc analyses of navigated TMS data using high-resolution subject-specific head models as well as accurate and fast modeling for the purposes of TMS coil/hardware development. Significance: TMS is currently the only non-invasive neurostimulation modality that enables painless and safe supra-threshold stimulation by employing electromagnetic induction to efficiently penetrate the skull. Accurate, fast, and high resolution modeling of the electric fields may significantly improve individualized targeting and dosing of TMS and therefore enhance the efficiency of existing clinical protocols as well as help establish new application domains.

Concept of a Radiofrequency Device for Osteopenia/Osteoporosis Screening.

Osteoporosis represents a major health problem, resulting in substantial increases in health care costs. There is an unmet need for a cost-effective technique that can measure bone properties without the use of ionizing radiation. The present study reports design, construction, and testing of a safe, and easy to use radiofrequency device to detect osteoporotic bone conditions. The device uses novel on-body antennas contacting the human wrist under an applied, operator-controlled pressure. For the dichotomous diagnostic test, we selected 60 study participants (23-94 years old, 48 female, 12 male) who could be positively differentiated between healthy and osteopenic/osteoporotic states. The band-limited integral of the transmission coefficient averaged for both wrists, multiplied by age, and divided by BMI has been used as an index. For a 100 MHz frequency band centered about 890-920 MHz, the maximum Youden's J index is 81.5%. Both the sensitivity and specificity simultaneously reach 87% given the calibration device threshold tolerance of ±3%. Our approach correlates well with the available DXA measurements and has the potential for screening patients at risk for fragility fractures, given the ease of implementation and low costs associated with both the technique and the equipment. The inclusion of radiofrequency transmission data does add supplementary useful information to the available clinical risk factors.

Evaluation of RF interactions between a 3T birdcage transmit coil and transcranial magnetic stimulation coils using a realistically shaped head phantom.

PURPOSE: Multichannel transcranial magnetic stimulation (TMS)1 is an emerging technology that allows multiple sites to be stimulated simultaneously or sequentially under electronic control without movement of the coils. A multichannel TMS/MRI head coil array for 3 Tesla is currently under development to mitigate challenges of concurrent TMS/fMRI as well as enable potential new applications. The influence of the multichannel TMS system on the MR image quality and safety must be carefully investigated. METHODS: A standard birdcage volume coil for 3 Tesla systems was simulated using a commercial numerical electromagnetic solver. Two setups, consisting of 1) a MR-compatible TMS coil, and 2) a 3-axis TMS coil array, were simulated to quantify changes in the transmit field B1+ and the SAR. A realistically shaped homogeneous head model was used in the computations. RESULTS: The stimulation coils produced enhancements and attenuations on the transmit field with effects greater than 5% up to 2.4 cm and 3.3 cm under the scalp for the MR-compatible TMS coil and 3-axis TMS coil array, respectively. The 10 g-SAR distribution did not change significantly in either of the cases; however, the nominal SAR maximum locus was shifted between existing hot spots. CONCLUSION: The simulated B1+ variations found near the TMS coils indicate the possibility of inducing sequence-dependent image artefacts predominatly limited to the vicinity of the coil(s). However, we conclude that neither the MR-compatible commercial TMS coil nor the 3-axis TMS coil array siginificantly elevate SAR in the head or neck beyond accepted safety limits.

Electrically Small Dipole Antenna Probe for Quasistatic Electric Field Measurements in Transcranial Magnetic Stimulation.

The present paper designs, constructs, and tests an electrically small dipole antenna probe for the measurement of electric field distributions with the ultimate purpose to directly measure electric fields induced by a transcranial magnetic stimulation (TMS) coil. Its unique features include applicability to measurements in both air and conducting medium, high spatial resolution, large frequency band from 100 Hz to 300 KHz, efficient feedline isolation via a printed Dyson balun, and accurate mitigation of noise. Prior work in this area is thoroughly reviewed. The proposed probe design is realized in hardware; implementation details and design tradeoffs are described. Test data are presented for the measurement of a constant wave capacitor electric field, demonstrating the probe's ability to properly measure electric fields caused by a charge distribution. Test data are also presented for the measurement of a constant wave solenoidal electric field, demonstrating the probe's ability to measure electric fields caused by Faraday's law of induction. Those are the primary fields for the transcranial magnetic stimulation. Further steps necessary for the application of this probe as an instrument for TMS coil design are discussed.

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS).

OBJECTIVE: A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. APPROACH: We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. MAIN RESULTS: In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. SIGNIFICANCE: This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

Review of Computational Techniques for Performance Evaluation of RF Localization Inside the Human Body.

Location estimation within the human body by means of wireless signals is becoming popular for a variety of purposes, including wireless endoscopy using camera pills. The precision of wireless ranging in any medium is contingent upon the methodology employed. Two of the most popular wireless tracking methods are received signal strength (RSS) and time of arrival (TOA). The scope of this study is an assessment of the precision of TOA- and RSS-based ranging in the proximity of anthropomorphic tissue by means of simulation software designed to mimic signal transmission in the human body environment. Software simulations of wireless signals traveling within a human body are exceptionally challenging and require extensive computational resources. We created a rudimentary, MATLAB script using the finite-difference time-domain (FDTD) method to simulate the signal transmission inside and outside a human body and correlated the simulation outcomes of this script with the high-end commercial finite-element method (FEM) tool, ANSYS HFSS. First, we demonstrated that the FDTD modeling produces similar outcomes. Next, we employed the script to emulate the RSS and TOA of the wide bandwidth radio transmission within the human body for wireless ranging and estimated the accuracy of each technology. The precision of both methods was also evaluated with the Cramer-Rao lower bound (CRLB), which is frequently used to estimate the ranging methodologies and the effect of human tissue and its motion.

Simulations of a birdcage coil B1+ field on a human body model for designing a 3T multichannel TMS/MRI head coil array.

This article considers a new type of integrated multichannel Transcranial Magnetic Stimulator and Magnetic Resonance Imaging (TMS/MRI) system at 3T that is currently being designed. The system will enable unprecedented spatiotemporal control of the TMS-induced electric fields (Efields) with simultaneous rapid whole-head MRI acquisition to record the brain activity. A critical design question is how TMS coil elements interact with the transmit field (${\mathrm B}_{1}^{+}$) of the volume coil integrated in 3T MRI systems. In general, the TMS coils are not designed to have any resonant characteristics at the MRI frequency, they may potentially disturb the RF field due to the eddy currents induced. This is especially a concern with a multichannel TMS setup where the subject's head will be largely covered with the stimulation coils. Therefore, we investigated this problem by computational simulations with realistic TMS coil geometries and a birdcage transmit coil in conjunction with a human body model. We compared the ${\mathrm B}_{1}^{+}$ interaction effects of a commercially available MR-compatible TMS coil with our coil prototype. In both cases, the results show small local changes in the transmit field ${\mathrm B}_{1}^{+}$of the birdcage coil. Maximal Average Specific Absorption Rate (SAR) values over 1g tissue were found to be slightly lower when the TMS elements were present. We conclude that it should be feasible and safe to use the conventional body transmit coil even when an array of TMS coils is used.

A Quasi-Static Boundary Element Approach With Fast Multipole Acceleration for High-Resolution Bioelectromagnetic Models.

OBJECTIVE: We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals. RESULTS: The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case. SIGNIFICANCE: At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement. CONCLUSIONS: Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.