Electromagnetic Modeling within a Microscopically Realistic Brain - Implications for Brain Stimulation.

Across all electrical stimulation (neuromodulation) domains, conventional analysis of cell polarization involves two discrete steps: i) prediction of macroscopic electric field, ignoring presence of cells and; ii) prediction of cell polarization from tissue electric fields. The first step assumes that electric 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. We leverage: i) recent electron microscopic images of the brain that have made it possible to reconstruct microscopic brain networks over relatively large volumes and; ii) a charge-based formulation of boundary element fast multipole method (BEM-FMM) to produce the first multiscale stimulations of realistic neuronal polarization by electrical stimulation that consider current flow distortions by a microstructure. The dataset under study is a 250×140×90 µm section of the L2/L3 mouse visual cortex with 396 tightly spaced neurite cells and 34 microcapillaries. We quantify how brain microstructure significantly distorts the primary macroscopic electric field. Although being very local, such distortions constructively accumulate along the neuronal arbor and reduce neuronal activating thresholds by 0.55-0.85-fold as compared to conventional theory. Data availability statement: Post-processed cell CAD models (383), microcapillary CAD models (34), post-processed neuron morphologies (267), extracellular field and potential distributions at different polarizations (267×3), *.ses projects files for biophysical modeling with Neuron software (267×2), and computed neuron activating thresholds at different conditions (267×8) are made available online through BossDB, a volumetric open-source database for 3D and 4D neuroscience data. Significance statement: This study introduces a novel method for modeling perturbations of impressed electric fields within a microscopically realistic brain volume, including densely populated neuronal cells and blood microcapillaries. It addresses a limitation present across decades of macroscopic-level electromagnetic models for electrical stimulation. For the investigated brain volume, our model predicted a neural activation threshold reduction factor of 0.85-0.55 when compared to the macroscopic approach. The present study begins to bridge a long-recognized gap in our analysis of bioelectricity and provides a framework to evaluate (and compensate) for the adequacy of macroscopic models in brain stimulation and electrophysiology.

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.

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.

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.

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.

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.