Biology subjects

Wartman, W. A.

Publications and source records attributed to Wartman, W. A..

9 recordsLinked to original sources

bioRxiv2026

Experimental Validation of Finite Element Models for Directional DBS: The Critical Role of Boundary Conditions on VTA Accuracy

ObjectiveComputational models and visualization toolboxes for Deep Brain Stimulation (DBS) increasingly rely on pre-computed electric field libraries to estimate the Volume of Tissue Activated (VTA). However, the boundary conditions (BCs) and source models used to generate these fields vary widely across studies, and there is currently no experimental consensus regarding which parameters most accurately reflect the physical device output. The objective of this study was to experimentally validate the electric potential distribution of directional DBS leads in order to determine the optimal Finite Element Method (FEM) configuration. ApproachThe voltage distribution surrounding a Boston Scientific Vercise Gevia directional lead was mapped in a saline phantom using a custom high-precision robotic scanning system. Experimental measurements were compared against six FEM configurations that varied in source formulation (Dirichlet vs. Neumann boundary conditions) and ground definitions. For each configuration, the resulting VTA volume was computed to assess the clinical impact of modeling assumptions. ResultsThe FEM configuration implementing a Dirichlet (voltage) boundary condition on the active contact with a grounded implantable pulse generator (IPG) surface demonstrated the highest accuracy, achieving a Symmetric Mean Absolute Percent Error (SMAPE) of less than 9% across all contact levels. In contrast, conventional current-controlled simulations employing Neumann boundary conditions with disparate ground definitions substantially overestimated electric field spread. Suboptimal boundary condition selection resulted in an approximate 67% overestimation of VTA volume (137 mm3 vs. 82 mm3) relative to the experimentally validated model. SignificanceAlthough clinical DBS systems operate as current sources, standard Neumann (current density) boundary conditions do not adequately represent the equipotential behavior of the electrode-tissue interface, resulting in nearly a two-fold error in predicted VTA volume. To improve the validity of predictive clinical models, we recommend the use of Dirichlet boundary conditions derived from the device operating impedance (V = Itarget x Zmeasured) rather than conventional current density specifications.

bioengineering↗

bioRxiv2024

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.

neuroscience↗

bioRxiv2024

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

ObjectiveTo 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. MethodsWe 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. ResultsThe 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{degrees} on average, with a standard deviation of [~]15{degrees}. 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{degrees} (28{degrees} standard deviation). ConclusionsThe 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. SignificanceImproving EEG source reconstruction accuracy is important for several clinical applications, including epilepsy and other seizure-inducing conditions.

bioinformatics↗

bioRxiv2024

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

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities. We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 x 140 x 90 m3. The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume. Our result shows that the microscopic field perturbations - an electric field spatial noise with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10% on average. Under the stated limitations and assumptions of our method, this result justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single- pulse stimulation time course. Significance statementThis study is arguably the first attempt to model brain stimulation at the microscopic scale, enabled by automated analysis of modern scanning electron microscopy images of the brain. It concentrates on modeling microscopic perturbations of the extracellular electric field caused by the physical cell structure and is applicable to any type of brain stimulation. Data availability statementPost-processed cell CAD models (383, stl format), microcapillary CAD models (34, stl format), post-processed neuron morphologies (267, swc format), extracellular electric field and potential distributions at different polarizations (267x3, MATLAB format), *.ses projects files for biophysical modeling with Neuron software (267x2, Neuron format), and computed neuron activating thresholds at different conditions (267x8, Excel tables, without the sample polarization correction from Section 2.8) are made available online through BossDB, a volumetric open-source database for 3D and 4D neuroscience data.

neuroscience↗

bioRxiv2023

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

ObjectiveThis study aims to describe a MATLAB software package for transcranial magnetic stimulation (TMS) coil analysis and design. ApproachElectric 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 ResultsThe 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. SignificanceThe developed software package is applicable to any quasistatic inductor design, not necessarily to the TMS coils only.

neuroscience↗

bioRxiv2023

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

ObjectiveIn 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. ApproachWe 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 methods 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 ResultsExcellent 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. SignificanceThis error has especially important implications for TES dosing prediction - where the stimula t ion 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.

neuroscience↗

bioRxiv2022

High-Resolution EEG Source Reconstruction with Boundary Element Fast Multipole Method Using Reciprocity Principle and TES Forward Model Matrix

BackgroundAccurate high-resolution EEG source reconstruction (localization) is important for several tasks, including rigorous and rapid mental health screening. ObjectiveThe present study has developed, validated, and applied a new source localization algorithm utilizing a charge-based boundary element fast multipole method (BEM-FMM) coupled with the Helmholtz reciprocity principle and the transcranial electrical stimulation (TES) forward solution. MethodsThe unknown cortical dipole density is reconstructed over the entire cortical surface by expanding into global basis functions in the form of cortical fields of active TES electrode pairs. These pairs are constructed from the reading electrodes. An analog of the minimum norm estimation (MNE) equation is obtained after substituting this expansion into the reciprocity principle written in terms of measured electrode voltages. Delaunay (geometrically balanced) triangulation of the electrode cap is introduced first. Basis functions for all electrode pairs connected by the edges of a triangular mesh are precomputed and stored in memory. A smaller set of independent basis functions is then selected and employed at every time instant. This set is based on the highest voltage differences measured. ResultsThe method is validated against the classic, yet challenging problem of median nerve stimulation and the tangential cortical sources located at the posterior wall of the central sulcus for an N20/P20 peak (2 scanned subjects). The method is further applied to perform source reconstruction of synthesized tangential cortical sources located at the posterior wall of the central sulcus (12 different subjects). In the second case, an average source reconstruction error of 7 mm is reported for the best possible noiseless scenario. ConclusionsOnce static preprocessing with TES electrodes has been done (the basis functions have been computed), our method requires fractions of a second to complete the accurate high-resolution source localization.

neuroscience↗

bioRxiv2020

A Software Toolkit for TMS Electric-Field Modeling with Boundary Element Fast Multipole Method: An Efficient MATLAB Implementation

BackgroundTranscranial magnetic stimulation (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 (E-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. ObjectiveTo present and disseminate our 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. MethodThe 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 field resolution close to and across cortical interfaces. Here, the previously proposed BEM-FMM algorithm has been improved in several novel ways. Results and ConclusionsThe improvements resulted in a threefold increase in computational speed while maintaining the same solution accuracy. The computational code based on the MATLAB(R) 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.

bioengineering↗

bioRxiv2020

A Note about the Individualized TMS Focality

A particular yet computationally successful solution of an inverse transcranial magnetic stimulation (TMS) problem is reported. The goal has been focusing the normal unsigned electric field at the inner cortical surface and its vicinity (the D wave activation site) given a unique high-resolution gyral pattern of a subject and a precise coil model. For 16 subjects and 32 arbitrary target points, the solution decreases the mean deviation of the maximum-field domain from the target by a factor of 2 on average. The reduction in the maximum-field area is expected to quadruple. The average final deviation is 6 mm. Rotation about the coil axis is the most significantly altered parameter, and the coil moves 10 mm on average during optimization. The maximum electric field magnitude decreases by 16% on average. Stability of the solution is enforced. The relative average de-focalization is below 1.2 when position/orientation accuracies are within 3 mm/6 degrees, respectively. The solution for the maximum normal field may also maximize the total field and its gradient for neighboring cortical layers III-V (I wave activation).

bioengineering↗