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.

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.

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.

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.

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.

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.

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.

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.

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.

Comparative analysis of different versions of a human model located inside a 1.5T MRI whole body RF coil.

Power deposition in tissues of a person subject to MRI examination is a significant point of concern today. Numerical electromagnetic simulation offers a way to model this complex problem with a sufficient degree of accuracy. Assessment of power deposition due to presence of implantable leads has been widely applied using the transfer function method. It relays on the incident tangential electric field (Etan) along the lead trajectory. This paper investigates how the precision of a numerical human model influences calculated Etan.

Virtual Human Models for Electromagnetic Studies and Their Applications.

Numerical simulation of electromagnetic, thermal, and mechanical responses of the human body to different stimuli in magnetic resonance imaging safety, antenna research, electromagnetic tomography, and electromagnetic stimulation is currently limited by the availability of anatomically adequate and numerically efficient cross-platform computational models or "virtual humans." The objective of this study is to provide a comprehensive review of modern human models and body region models available in the field and their important features.

CAD-Based Virtual Humans : Design and Safety Assessment of MRI Coils.

Magnetic resonance imaging (MRI) is a ubiquitous tool used in clinical settings around the world to provide detailed three-dimensional information on the internal anatomy and physiology of human patients without the use of ionizing radiation, which is the primary safety concern associated with computed tomography. This information is obtained noninvasively and can be used in the diagnosis of pathological conditions as well as the monitoring of treatments.

VHP-Female full-body human CAD model for cross-platform FEM simulations: recent development and validations.

Simulation of the electromagnetic response of the human body relies heavily upon efficient computational models or phantoms. The first objective of this paper is to present an improved platform-independent full-body electromagnetic computational model (computational phantom), the Visible Human Project® (VHP)-Female v. 3.1 and to describe its distinct features and enhancements compared to VHP-Female v. 2.0. The second objective is to report phantom simulation for electric stimulation studies using the commercial FEM electromagnetic solver ANSYS MAXWELL.