Biology subjects

Makaroff, S. N.

Publications and source records attributed to Makaroff, S. N..

16 recordsLinked to original sources

bioRxiv2026

Low Intensity Multi-Channel Steering TMS Array for Network Level Neuromodulation

Objective: Low-intensity transcranial magnetic stimulation (LI-TMS) is being investigated as a gel-free alternative to transcranial electrical stimulation (tES), but existing systems remain almost exclusively single-channel and cannot electronically steer the induced electric field. We present the design, modeling, and experimental measurement of a wearable whole-head, multichannel, steerable LI-TMS array. Methods: The system comprises a 102-channel conformal coil array with independently controlled drivers capable of arbitrary waveform synthesis, together with a boundary element fast multipole method (BEM-FMM) framework that computes the coil currents required to produce prescribed cortical field patterns. A 12-channel prototype was characterized by coil-current, electric-field, and thermal measurements. Results: The prototype produced a peak primary electric field of approximately 1 V/m measured in air 4 cm from the inner helmet surface. Whole-array modeling attained cortical fields of up to 1.5 V/m, reproduced the field distribution of a clinically validated low-intensity stimulator to within 3%-5%, and demonstrated focal targeting of the dorsolateral prefrontal cortex, simultaneous delivery of electric field to the default mode network nodes, and synthesis of electric fields following the traveling alpha wave. Conclusion: Electronically steerable, whole-head LI-TMS is feasible using accessible microprocessor-controlled power electronics. Significance: The array reaches the cortical field regime of tES without scalp contact or the associated shunting of current through the scalp, offering a route to testing network-level, phaselocked weak-field neuromodulation.

bioengineering↗

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↗

bioRxiv2026

Direct Reconstruction of DC Cortical Conductivity from Large-Scale Electron Microscopy Data

Electrical conductivity of cortical gray matter governs the magnitude and spatial distribution of electric fields generated by brain stimulation and intrinsic neuronal activity measured with M/EEG and intracortical recordings. However, reported macroscopic conductivity values vary by more than threefold, limiting the fidelity of bioelectromagnetic models and leaving unresolved whether this variability reflects measurement uncertainty or genuine structural heterogeneity of cortical tissue. Here, we present a multiscale computational framework that, for the first time, attempts to derive mesoscale conductivity maps of mouse visual cortex at 50-{micro}m resolution directly from large-volume, segmented nanometer-scale electron microscopy data. The Minnie 65 subvolume of the MICrONS dataset is accurately subdivided into 1,224 50-{micro}m cubic blocks. Each block contains, on average, 40-50 million membrane facets of a highly convoluted and dense cellular structure. Three orthogonal electrode pairs are applied to each isolated block to estimate the three principal components of the conductivity tensor. Quasistatic electric modeling is enabled by an iterative boundary-element fast multipole method (BEM-FMM) under the approximation of non-conducting membranes (DC conductivity). Spatially averaged conductivity values predicted by our framework agree well with prior low-resolution measurements in rats, validating the approach. At the same time, the resulting mesoscale maps reveal pronounced conductivity granularity at 50-100 {micro}m scales as well as significant variations in both radial and tangential directions. These results indicate that mesoscale conductivity heterogeneity could be an intrinsic structural property of the cortex. Limitations and extensions of this study are discussed in detail.

neuroscience↗

bioRxiv2026

Charge Based Boundary Element Method with Residual Driven Adaptive Mesh Refinement for High Resolution Electrical Simulation Modeling

Accurate transcranial electrical stimulation (TES), electroconvulsive therapy (ECT), and electroencephalography (EEG) forward modeling requires resolving numerical singularities in the charge density near electrodes and tissue interfaces. We present an adaptive mesh refinement (AMR) strategy for the charge based boundary element method (BEM) accelerated by the fast multiple method (BEM-FMM) including electrode and interface singularities. We derive a new error estimator which considers both local and nonlocal contributions of the single-layer potential operator and construct a refinement criterion based on the difference in charge solution across AMR iterations. We evaluate this approach on a 5-layer sphere model and on multiple subject-specific head models derived from the 7-tissue SimNIBS (headreco) and 40-tissue Sim4Life (head40) segmentations, using both voltage-controlled and current-controlled electrode formulations. Through convergence analysis on the white matter and deep hippocampal targets, we find electric fields with relative residual errors below 0.1% and 1% for SimNIBS and Sim4Life models, respectively. Our results indicate that the residual based AMR applied to BEM-FMM leads to numerically stable TES and EEG forward solutions in realistic head models.

neuroscience↗

bioRxiv2025

High-Resolution EEG Source Reconstruction from PCA-Corrected BEM-FMM Reciprocal Basis Funcions: A Study with Visual Evoked Potentials from Intermittent Photic Stimulation

Modern automated human head segmentations can generate high-resolution computational meshes involving many non-nested tissues. However, most source reconstruction software is limited to 3 -4 nested layers of low resolution and a small number of dipolar sources[~] 10, 000. Recently, we introduced modeling techniques for source reconstruction of magnetoencephalographic (MEG) signals using the reciprocal approach and the boundary element fast multipole method (BEM-FMM). The technique of BEM-FMM can process both nested and non-nested models with as many as 4 million surface elements. In this paper, we present an analogue technique for source reconstruction of electroencephalographic (EEG) signals based on cortical global basis functions. The present work uses Helmholtz reciprocity to relate the reciprocally-generated lead-field matrices to their direct counterpart, while resolving the issue of possible biases toward the reference electrode. Our methodology is tested with experimental EEG data collected from a cohort of 12, young and healthy, volunteers subjected to intermittent photic stimulation (IPS). Our novel high-resolution source reconstruction models can have impact on mental health screening as well as brain-computer inter-faces.

neuroscience↗

bioRxiv2025

Improved Source Localization of Auditory Evoked Fields using Reciprocal BEM-FMM

The precise localization of auditory evoked fields (AEFs) from magnetoencephalography (MEG) data is very important for the functional understanding of the auditory cortex in medicine and cognitive neuroscience. The numerical solution of the field equations in the human head using the boundary element method (BEM) is a powerful tool for achieving this. We hypothesized that the spatial resolution of the BEM is crucial for the achievable accuracy. However, in classical BEM (as implemented, e.g., in MNE-Python), very high resolutions are impractical due to the associated prohibitive computational effort. In contrast, our recently introduced reciprocal boundary element fast multipole method (reciprocal BEM-FMM) allows for hitherto unprecedented spatial resolution. In this work, we apply our reciprocal BEM-FMM technique for source estimation to localize AEFs, and we compare our results with the source estimates produced using a 3-layer BEM model (standard BEM) via MNE-Python. We first validate our methodology through comparison of source estimates of simulated N1m components of AEFs using a receiver operating characteristic (ROC) measure. While we obtain ROC measures of about 80% for the standard BEM, reciprocal BEM-FMM reaches about 90%, a significant statistical improvement. We then apply this methodology to analyze the source estimates of experimental data obtained from a cohort of 7 participants subjected to binaural auditory stimulation. Using a dispersion measurement to quantify the focality of localized sources, we find improvements upwards of 30% using reciprocal BEM-FMM over the standard BEM. Analyses from both simulated and experimental data show localization of AEFs using high-resolution reciprocal BEM-FMM is significantly better in terms of accuracy and focality than those estimates of the low-resolution standard BEM. We therefore recommend using the high-resolution reciprocal BEM-FMM to utilize high spatial anatomical precision for the modeling of neural activity.

neuroscience↗

bioRxiv2025

Construction of Accurate Turtle Cerebellum Models and their use in Simulating Neuromodulation using the BEM-FMM

Digital representations of Purkinje cells from turtle cerebellum, which have long been to study cellular transmission dynamics and neuroplasticity, are necessary to conduct simulations of neuromodulation methods, including Transcranial Magnetic Stimulation (TMS). Methods: Data collected using microCT with 0.6 um isometric resolution are processed, segmented, and arranged to enable high resolution simulation via the Boundary Element Fast Multipole Method. Results: Fully computer aided design compatible, manifold triangular surface meshes were generated from microCT data and used to simulate cellular electromagnetic response to TMS. Conclusion: Accurate Purkinje cells may be readily generated and manipulated to create representative models of turtle cerebellum. Significance: The techniques employed herein may be used to generate accurate surface mesh of Purkinje cells which can enable computational electromagnetics code verification and serve as the basis for skeletal models used for bidomain biophysical simulations in tools such as NEURON to study neurostimulation dynamics and neuromodulation.

neuroscience↗

bioRxiv2025

High-Definition MEG Source Estimation using the Reciprocal Boundary Element Fast Multipole Method

Magnetoencephalographic (MEG) source estimation relies on the computation of the gain (lead-field) matrix, which embodies the linear relationship between the amplitudes of the sources and the recorded signals. However, with a realistic forward model, the calculation of the gain matrix in a "direct" fashion is a computationally expensive task because the number of dipolar sources in standard MEG pipelines is often limited to [~]10,000. We propose a fast approach based on the reciprocal relationship between MEG and transcranial magnetic stimulation (TMS). This approach couples naturally with the charge-based boundary element fast multipole method (BEM-FMM), which allows us to efficiently generate gain matrices for high-resolution multi-layer non-nested meshes involving source spaces of up to a [~]1 million dipoles. We evaluate our approach by performing MEG source reconstruction against simulated data (at varying noise levels) obtained from the direct computation of MEG readings from 2000 different dipole positions over the cortical surface of 5 healthy subjects. Additionally, we test our methods with real MEG data from evoked somatosensory fields by right-hand median nerve stimulation in these same 5 subjects. We compare our experimental source reconstruction results against the standard MNE-Python source reconstruction pipeline.

neuroscience↗

bioRxiv2024

Statistical method accounts for microscopic electric field distortions around neurons when simulating activation thresholds

IntroductionNotwithstanding advances in computational models of neuromodulation, there are mismatches between simulated and experimental activation thresholds. Transcranial Magnetic Stimulation (TMS) of the primary motor cortex generates motor evoked potentials (MEPs). At the threshold of MEP generation, whole-head models predict macroscopic (at millimeter scale) electric fields (50-70 V/m) which are considerably below conventionally simulated cortical neuron thresholds (175-350 V/m). MethodsWe hypothesize that this apparent contradiction is in part a consequence of electrical field warping by brain microstructure. Classical neuronal models ignore the physical presence of neighboring neurons and microstructure and assume that the macroscopic field directly acts on the neurons. In previous work, we performed advanced numerical calculations considering realistic microscopic compartments (e.g., cells, blood vessels), resulting in locally inhomogeneous (micrometer scale) electric field and altered neuronal activation thresholds. Here we combine detailed neural threshold simulations under homogeneous field assumptions with microscopic field calculations, leveraging a novel statistical approach. ResultsWe show that, provided brain-region specific microstructure metrics, a single statistically derived scaling factor between microscopic and macroscopic electric fields can be applied in predicting neuronal thresholds. For the cortical sample considered, the statistical methods match TMS experimental thresholds. ConclusionsOur approach can be broadly applied to neuromodulation models, where fully coupled microstructure scale simulations may not be computationally tractable.

neuroscience↗

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↗

bioRxiv2023

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

AO_SCPLOWBSTRACTC_SCPLOWOne 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.

biophysics↗

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↗