Fast and Accurate EEG/MEG BEM-Based Forward Problem Solution for High-Resolution Head Models.

A BEM (boundary element method) based approach is developed to accurately solve an EEG/MEG forward problem for a modern high-resolution head model in approximately 60 seconds using a common workstation. The method utilizes a charge-based BEM with fast multipole acceleration (BEM-FMM) and a "smart" mesh pre-refinement (called b-refinement) close to the singular source(s). No costly matrix-filling or direct solution steps typical for the standard BEM are required; the method generates on-skin voltages as well as MEG magnetic fields for high-resolution head models in approximately 60 seconds after initial model assembly. The method is verified both theoretically and experimentally.

Accuracy of dipole source reconstruction in the 3-layer BEM model against the 5-layer BEM-FMM model.

Objective: To compare cortical dipole fitting spatial accuracy between the widely used yet highly simplified 3-layer and modern more realistic 5-layer BEM-FMM models with and without adaptive mesh refinement (AMR) methods. Methods: We generate simulated noiseless 256-channel EEG data from 5-layer (7-compartment) meshes of 15 subjects from the Connectome Young Adult dataset. For each subject, we test four dipole positions, three sets of conductivity values, and two types of head segmentation. We use the boundary element method (BEM) with fast multipole method (FMM) acceleration, with or without (AMR), for forward modeling. Dipole fitting is carried out with the FieldTrip MATLAB toolbox. Results: The average position error (across all tested dipoles, subjects, and models) is ~4 mm, with a standard deviation of ~2 mm. The orientation error is ~20° on average, with a standard deviation of ~15°. Without AMR, the numerical inaccuracies produce a larger disagreement between the 3- and 5-layer models, with an average position error of ~8 mm (6 mm standard deviation), and an orientation error of 28° (28° standard deviation). Conclusions: The low-resolution 3-layer models provide excellent accuracy in dipole localization. On the other hand, dipole orientation is retrieved less accurately. Therefore, certain applications may require more realistic models for practical source reconstruction. AMR is a critical component for improving the accuracy of forward EEG computations using a high-resolution 5-layer volume conduction model. Significance: Improving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

Enabling Electric Field Modeling of Microscopically Realistic Brain.

Across all domains of brain stimulation (neuromodulation), conventional analysis of neuron activation involves two discrete steps: i) prediction of macroscopic electric field, ignoring presence of cells and; ii) prediction of cell activation from tissue electric fields. The first step assumes that current flow is not distorted by the dense tortuous network of cell structures. The deficiencies of this assumption have long been recognized, but - except for trivial geometries - ignored, because it presented intractable computation hurdles. This study introduces a novel approach for analyzing electric fields within a microscopically realistic brain volume. Our pipeline overcomes the technical intractability that prevented such analysis while also showing significant implications for brain stimulation. Contrary to the standard finite element method (FEM), we suggest using a nested iterative boundary element method (BEM) coupled with the fast multipole method (FMM). This approach allows for solving problems with multiple length scales more efficiently. A target application is a subvolume of the L2/3 P36 mouse primary visual cortex containing approximately 400 detailed densely packed neuronal cells at a resolution of 100 nm, which is obtained from scanning electron microscopy data. Our immediate result is a reduction of the stimulation field strength necessary for neuron activation by a factor of 0.85-0.55 (by 15%-45%) as compared to macroscopic predictions. This is in line with modern experimental data stating that existing macroscopic theories substantially overestimate electric field levels necessary for brain stimulation.

Electric Field Characteristics of Rotating Permanent Magnet Stimulation.

Neurostimulation devices that use rotating permanent magnets are being explored for their potential therapeutic benefits in patients with psychiatric and neurological disorders. This study aims to characterize the electric field (E-field) for ten configurations of rotating magnets using finite element analysis and phantom measurements. Various configurations were modeled, including single or multiple magnets, and bipolar or multipolar magnets, rotated at 10, 13.3, and 350 revolutions per second (rps). E-field strengths were also measured using a hollow sphere (r=9.2 cm) filled with a 0.9% sodium chloride solution and with a dipole probe. The E-field spatial distribution is determined by the magnets' dimensions, number of poles, direction of the magnetization, and axis of rotation, while the E-field strength is determined by the magnets' rotational frequency and magnetic field strength. The induced E-field strength on the surface of the head ranged between 0.0092 and 0.52 V/m. In the range of rotational frequencies applied, the induced E-field strengths were approximately an order or two of magnitude lower than those delivered by conventional transcranial magnetic stimulation. The impact of rotational frequency on E-field strength represents a confound in clinical trials that seek to tailor rotational frequency to individual neural oscillations. This factor could explain some of the variability observed in clinical trial outcomes.

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling.

Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

Electric field characteristics of rotating permanent magnet stimulation.

Neurostimulation devices that use rotating permanent magnets are being explored for their potential therapeutic benefits in patients with psychiatric and neurological disorders. This study aims to characterize the electric field (E-field) for ten configurations of rotating magnets using finite element analysis and phantom measurements. Various configurations were modeled, including single or multiple magnets, bipolar or multipolar magnets, rotated at 10, 13.3, and 400 Hz. E-field strengths were also measured using a hollow sphere ( r = 9.2 cm) filled with a 0.9% sodium chloride solution and with a dipole probe. The E-field spatial distribution is determined by the magnets' dimensions, number of poles, direction of the magnetization, and axis of rotation, while the E-field strength is determined by the magnets' rotational frequency and magnetic field strength. The induced E-field strength on the surface of the head ranged between 0.0092 and 0.59 V/m. At the range of rotational frequencies applied, the induced E-field strengths were approximately an order or two of magnitude lower than those delivered by conventional transcranial magnetic stimulation. The impact of rotational frequency on E-field strength represents a previously unrecognized confound in clinical trials that seek to personalize stimulation frequency to individual neural oscillations and may represent a mechanism to explain some clinical trial results.

Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields.

OBJECTIVE: Biophysical models of neural stimulation are a valuable approach to explaining the mechanisms of neuronal recruitment via applied extracellular electric fields. Typically, the applied electric field is estimated via a macroscopic finite element method solution and then applied to cable models as an extracellular voltage source. However, the field resolution is limited by the finite element size (typically 10's-100's of times greater than average neuronal cross-section). As a result, induced charges deposited onto anatomically realistic curved membrane interfaces are not taken into consideration. However, these details may alter estimates of the applied electric field and predictions of neural tissue activation. METHODS: To estimate microscopic variations of the electric field, data for intra-axonal space segmented from 3D scanning electron microscopy of the mouse brain genu of corpus callosum were used. The boundary element fast multipole method was applied to accurately compute the extracellular solution. Neuronal recruitment was then estimated via an activating function. RESULTS: Taking the physical structure of the arbor into account generally predicts higher values of the activating function. The relative integral 2-norm difference is 90% on average when the entire axonal arbor is present. A large fraction of this difference might be due to the axonal body itself. When an isolated physical axon is considered with all other axons removed, the relative integral 2-norm difference between the single-axon solution and the complete solution is 25% on average. CONCLUSION: Our result may provide an explanation as to why Deep Brain Stimulation experiments typically predict lower activation thresholds than commonly used FEM/Cable model approaches to predicting neuronal responses to extracellular electrical stimulation. SIGNIFICANCE: These results may change methods for bi-domain neural modeling and neural excitation.

An in silico testbed for fast and accurate MR labeling of orthopedic implants.

One limitation on the ability to monitor health in older adults using magnetic resonance (MR) imaging is the presence of implants, where the prevalence of implantable devices (orthopedic, cardiac, neuromodulation) increases in the population, as does the pervasiveness of conditions requiring MRI studies for diagnosis (musculoskeletal diseases, infections, or cancer). The present study describes a novel multiphysics implant modeling testbed using the following approaches with two examples: (1) an in silico human model based on the widely available Visible Human Project (VHP) cryo-section dataset; (2) a finite element method (FEM) modeling software workbench from Ansys (Electronics Desktop/Mechanical) to model MR radio frequency (RF) coils and the temperature rise modeling in heterogeneous media. The in silico VHP-Female model (250 parts with an additional 40 components specifically characterizing embedded implants and resultant surrounding tissues) corresponds to a 60-year-old female with a body mass index of 36. The testbed includes the FEM-compatible in silico human model, an implant embedding procedure, a generic parameterizable MRI RF birdcage two-port coil model, a workflow for computing heat sources on the implant surface and in adjacent tissues, and a thermal FEM solver directly linked to the MR coil simulator to determine implant heating based on an MR imaging study protocol. The primary target is MR labeling of large orthopedic implants. The testbed has very recently been approved by the US Food and Drug Administration (FDA) as a medical device development tool for 1.5 T orthopedic implant examinations.

Detailed high quality surface-based mouse CAD model suitable for electromagnetic simulations.

Transcranial magnetic stimulation (TMS) studies with small animals can provide useful knowledge of activating regions and mechanisms. Along with this, functional magnetic resonance imaging (fMRI) in mice and rats is increasingly often used to draw important conclusions about brain connectivity and functionality. For cases of both low- and high-frequency TMS studies, a high-quality computational surface-based rodent model may be useful as a tool for performing supporting modeling and optimization tasks. This work presents the development and usage of an accurate CAD model of a mouse that has been optimized for use in computational electromagnetic modeling in any frequency range. It is based on the labeled atlas data of the Digimouse archive. The model includes a relatively accurate four-compartment brain representation (the 'whole brain' according to the original terminology, external cerebrum, cerebellum, and striatum [9]) and contains 21 distinct compartments in total. Four examples of low- and high frequency modeling have been considered to demonstrate the utility and applicability of the model.

High inductance magnetic-core coils have enhanced efficiency in inducing suprathreshold motor response in rats.

Objective. Transcranial magnetic stimulation (TMS) coil design involves a tradeoff among multiple parameters, including magnetic flux density (B), inductance (L), induced electric (E) field, focality, penetration depth, coil heating, etc. Magnetic materials with high permeability have been suggested to enhance coil efficiency. However, the introduction of magnetic core invariably increases coil inductance compared to its air-core counterpart, which in turn weakens theEfield. Our lab previously reported a rodent-specific TMS coil with silicon steel magnetic core, achieving 2 mm focality. This study aims to better understand the tradeoffs amongB,L,andEin the presence of magnetic core.Approach. The magnetic core initially operates within the linear range, transitioning to the nonlinear range when it begins to saturate at high current levels and reverts to the linear range as coil current approaches zero; both linear and nonlinear analyses were performed. Linear analysis assumes a weak current condition when magnetic core is not saturated; a monophasic TMS circuit was employed for this purpose. Nonlinear analysis assumes a strong current condition with varying degrees of core saturation.Main results. Results reveal that, the secondaryEfield generated by the silicon steel core substantially changed the dynamics during TMS pulse. Linear and nonlinear analyses revealed that higher inductance coils produced stronger peakEfields and longerEfield waveforms. On a macroscopic scale, the effects of these two factors on neuronal activation could be conceptually explained through a one-time-constant linear membrane model. Four coils with differentB,L,andEcharacteristics were designed and constructed. BothEfield mapping and experiments on awake rats confirmed that inductance could be much higher than previously anticipated, provided that magnetic material possesses a high saturation threshold.Significance. Our results highlight the novel potentials of magnetic core in TMS coil designs, especially for small animals.

Miniaturized Dual Antiphase Patch Antenna Radiating into the Human Body at 2.4 GHz.

An on-body antenna, comprised of two closely-spaced antiphase patch elements, for microwave imaging may provide enhanced signal penetration into the tissue. By further integrating a 180-degree on-chip power combiner with the dual antiphase patch antenna element, a low-profile miniaturized antenna, integrated into a single 18.5 mm x 10 mm x 1.6 mm circuit board assembly, is designed and evaluated both numerically and experimentally. This is the smallest on-body antenna known to the authors for the given frequency band. This linearly polarized antenna may potentially serve as a building block of a dense antenna array for prospective high-resolution microwave imaging. A 2.4 GHz band was chosen as the design target. The final antenna size was a compromise between the miniaturization, the SNR (Signal-to-Noise Ratio), and the targeted antenna bandwidth (2.3-2.5 GHz). The effect of surface waves (the secondary radiating components) was also factored in the design consideration, while maximizing the detected signals' SNR.

Reducing Non-Through Body Energy Transfer in Microwave Imaging Systems.

On-body antennas for use in microwave imaging (MI) systems can direct energy around the body instead of through the body, thus degrading the overall signal-to-noise ratio (SNR) of the system. This work introduces and quantifies the usage of modern metal-backed RF absorbing foam in conjunction with on-body antennas to dampen energy flowing around the body, using both simulations and experiments. A head imaging system is demonstrated herein but the principle can be applied to any part of the body including the torso or extremities. A computational model was simulated numerically using Ansys HFSS. A physical prototype in the form of a helmet with embedded antennas was built to compare simulations with measured data. Simulations and measurements demonstrate that usage of such metal-backed RF-absorbing foams can significantly reduce around-body coupling from Transmit (Tx) and Receive (Rx) antennas by approximately 10dB. Thus, the overall SNR of the MI system can be substantially improved using this low-cost and affordable method.

Software Package for Transcranial Magnetic Stimulation Coil and Coil Array Analysis and Design.

Objective: This study aims to describe a MATLAB software package for transcranial magnetic stimulation (TMS) coil analysis and design. Approach: Electric and magnetic fields of the coils as well as their self- and mutual (for coil arrays) inductances are computed, with or without a magnetic core. Solid and stranded (Litz wire) conductors are also taken into consideration. The starting point is the centerline of a coil conductor(s), which is a 3D curve defined by the user. Then, a wire mesh and a computer aided design (CAD) mesh for the volume conductor of a given cross-section (circular, elliptical, or rectangular) are automatically generated. Self- and mutual inductances of the coil(s) are computed. Given the conductor current and its time derivative, electric and magnetic fields of the coil(s) are determined anywhere in space.Computations are performed with the fast multipole method (FMM), which is the most efficient way to evaluate the fields of many elementary current elements (current dipoles) comprising the current carrying conductor at a large number of observation points. This is the major underlying mathematical operation behind both inductance and field calculations. Main Results: The wire-based approach enables precise replication of even the most complex physical conductor geometries, while the FMM acceleration quickly evaluates large quantities of elementary current filaments. Agreement to within 0.74% was obtained between the inductances computed by the FMM method and ANSYS Maxwell 3D for the same coil model. Although not provided in this study, it is possible to evaluate non-linear magnetic cores in addition to the linear core exemplified. An experimental comparison was carried out against a physical MagVenture C-B60 coil; the measured and simulated inductances differed by only 1.25%, and nearly perfect correlation was found between the measured and computed E-field values at each observation point. Significance: The developed software package is applicable to any quasistatic inductor design, not necessarily to the TMS coils only.

An Adaptive H-Refinement Method for the Boundary Element Fast Multipole Method for Quasi-static Electromagnetic Modeling.

Objective: In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems. Approach: We propose, describe, and systematically investigate an AMR method using the Boundary Element Method with Fast Multipole Acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy.The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a "silver-standard" solution found by subsequent 4:1 global refinement of the adaptively-refined model. Main Results: Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models. Significance: This error has especially important implications for TES dosing prediction - where the stimulation strength plays a central role - and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

An In-Silico Testbed for Fast and Accurate MR Labeling of Orthopaedic Implants.

One limitation on the ability to monitor health in older adults using Magnetic Resonance (MR) imaging is the presence of implants, where the prevalence of implantable devices (orthopedic, cardiac, neuromodulation) increases in the population, as does the pervasiveness of conditions requiring MRI studies for diagnosis (musculoskeletal diseases, infections, or cancer). The present study describes a novel multiphysics implant modeling testbed using the following approaches with two examples: - an in-silico human model based on the widely available Visible Human Project (VHP) cryo-section dataset; - a finite element method (FEM) modeling software workbench from Ansys (Electronics Desktop/Mechanical) to model MR radio frequency (RF) coils and the temperature rise modeling in heterogeneous media. The in-silico VHP Female model (250 parts with an additional 40 components specifically characterizing embedded implants and resultant surrounding tissues) corresponds to a 60-year-old female with a body mass index (BMI) of 36. The testbed includes the FEM-compatible in-silico human model, an implant embedding procedure, a generic parameterizable MRI RF birdcage two-port coil model, a workflow for computing heat sources on the implant surface and in adjacent tissues, and a thermal FEM solver directly linked to the MR coil simulator to determine implant heating based on an MR imaging study protocol. The primary target is MR labeling of large orthopaedic implants. The testbed has very recently been approved by the US Food and Drug Administration (FDA) as a medical device development tool (MDDT) for 1.5 T orthopaedic implant examinations.

Influence of charges deposited on membranes of human hyperdirect pathway axons on depolarization during subthalamic deep brain stimulation.

Objective.The motor hyperdirect pathway (HDP) is a key target in the treatment of Parkinson's disease with deep brain stimulation (DBS). Biophysical models of HDP DBS have been used to explore the mechanisms of stimulation. Built upon finite element method volume conductor solutions, such models are limited by a resolution mismatch, where the volume conductor is modeled at the macro scale, while the neural elements are at the micro scale. New techniques are needed to better integrate volume conductor models with neuron models.Approach.We simulated subthalamic DBS of the human HDP using finely meshed axon models to calculate surface charge deposition on insulting membranes of nonmyelinated axons. We converted the corresponding double layer extracellular problem to a single layer problem and applied the well-conditioned charge-based boundary element fast multipole method (BEM-FMM) with unconstrained numerical spatial resolution. Commonly used simplified estimations of membrane depolarization were compared with more realistic solutions.Main result.Neither centerline potential nor estimates of axon recruitment were impacted by the estimation method used except at axon bifurcations and hemispherical terminations. Local estimates of axon polarization were often much higher at bifurcations and terminations than at any other place along the axon and terminal arbor. Local average estimates of terminal electric field are higher by 10%-20%.Significance. Biophysical models of action potential initiation in the HDP suggest that axon terminations are often the lowest threshold elements for activation. The results of this study reinforce that hypothesis and suggest that this phenomenon is even more pronounced than previously realized.

Modeling transcranial magnetic stimulation coil with magnetic cores.

Objective.Accurate modeling of transcranial magnetic stimulation (TMS) coils with the magnetic core is largely an open problem since commercial (quasi) magnetostatic solvers do not output specific field characteristics (e.g. induced electric field) and have difficulties when incorporating realistic head models. Many open-source TMS softwares do not include magnetic cores into consideration. This present study reports an algorithm for modeling TMS coils with a (nonlinear) magnetic core and validates the algorithm through comparison with finite-element method simulations and experiments.Approach.The algorithm uses the boundary element fast multipole method applied to all facets of a tetrahedral core mesh for a single-state solution and the successive substitution method for nonlinear convergence of the subsequent core states. The algorithm also outputs coil inductances, with or without magnetic cores. The coil-core combination is solved only once i.e. before incorporating the head model. The resulting primary TMS electric field is proportional to the total vector potential in the quasistatic approximation; it therefore also employs the precomputed core magnetization.Main results.The solver demonstrates excellent convergence for typical TMS field strengths and for analyticalB-Happroximations of experimental magnetization curves such as Froelich's equation or an arctangent equation. Typical execution times are 1-3 min on a common multicore workstation. For a simple test case of a cylindrical core within a one-turn coil, our solver computed the small-signal inductance nearly identical to that from ANSYS Maxwell. For a multiturn rodent TMS coil with a core, the modeled inductance matched the experimental measured value to within 5%.Significance.Incorporating magnetic core in TMS coil design has advantages of field shaping and energy efficiency. Our software package can facilitate model-informed design of more efficiency TMS systems and guide selection of core material. These models can also inform dosing with existing clinical TMS systems that use magnetic cores.