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Wang B, Peterchev AV, Gaugain G, Ilmoniemi RJ, Grill WM, Bikson M, Nikolayev D. Quasistatic approximation in neuromodulation. J Neural Eng 2024; 21:041002. [PMID: 38994790 DOI: 10.1088/1741-2552/ad625e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 06/28/2024] [Indexed: 07/13/2024]
Abstract
We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.
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Affiliation(s)
- Boshuo Wang
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC 27710, United States of America
| | - Angel V Peterchev
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC 27710, United States of America
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, United States of America
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, United States of America
- Department of Neurosurgery, Duke University, Durham, NC 27710, United States of America
| | - Gabriel Gaugain
- Institut d'Électronique et des Technologies du numéRique (IETR UMR 6164), CNRS / University of Rennes, 35000 Rennes, France
| | - Risto J Ilmoniemi
- Department of Neuroscience and Biomedical Engineering, Aalto University School of Science, Espoo, Finland
| | - Warren M Grill
- Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, United States of America
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, United States of America
- Department of Neurosurgery, Duke University, Durham, NC 27710, United States of America
- Department of Neurobiology, Duke University, Durham, NC 27710, United States of America
| | - Marom Bikson
- The City College of New York, New York, NY 11238, United States of America
| | - Denys Nikolayev
- Institut d'Électronique et des Technologies du numéRique (IETR UMR 6164), CNRS / University of Rennes, 35000 Rennes, France
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Wartman WA, Weise K, Rachh M, Morales L, Deng ZD, Nummenmaa A, Makaroff SN. An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling. Phys Med Biol 2024; 69:055030. [PMID: 38316038 PMCID: PMC10902857 DOI: 10.1088/1361-6560/ad2638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/20/2023] [Accepted: 02/05/2024] [Indexed: 02/07/2024]
Abstract
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.
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Affiliation(s)
- William A Wartman
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 United States of America
| | - Konstantin Weise
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, D-04103 Leipzig, Germany
- Department of Clinical Medicine, Aarhus University, DNK-8200, Aarhus, Denmark
| | - Manas Rachh
- Center for Computational Mathematics, Flatiron Institute, New York, NY 10012, United States of America
| | - Leah Morales
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 United States of America
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch, National Institute of Mental Health Intramural Research Program, National Institutes of Health, Bethesda, MD, United States of America
| | - Aapo Nummenmaa
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 United States of America
| | - Sergey N Makaroff
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 United States of America
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 United States of America
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Noetscher GM, Tang D, Nummenmaa AR, Bingham CS, McIntyre CC, Makaroff SN. Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields. IEEE Trans Biomed Eng 2024; 71:307-317. [PMID: 37535481 PMCID: PMC10837334 DOI: 10.1109/tbme.2023.3299734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
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.
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Jing Y, Numssen O, Weise K, Kalloch B, Buchberger L, Haueisen J, Hartwigsen G, Knösche TR. Modeling the effects of transcranial magnetic stimulation on spatial attention. Phys Med Biol 2023; 68:214001. [PMID: 37783213 DOI: 10.1088/1361-6560/acff34] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 10/02/2023] [Indexed: 10/04/2023]
Abstract
Objectives. Transcranial magnetic stimulation (TMS) has been widely used to modulate brain activity in healthy and diseased brains, but the underlying mechanisms are not fully understood. Previous research leveraged biophysical modeling of the induced electric field (E-field) to map causal structure-function relationships in the primary motor cortex. This study aims at transferring this localization approach to spatial attention, which helps to understand the TMS effects on cognitive functions, and may ultimately optimize stimulation schemes.Approach. Thirty right-handed healthy participants underwent a functional magnetic imaging (fMRI) experiment, and seventeen of them participated in a TMS experiment. The individual fMRI activation peak within the right inferior parietal lobule (rIPL) during a Posner-like attention task defined the center target for TMS. Thereafter, participants underwent 500 Posner task trials. During each trial, a 5-pulse burst of 10 Hz repetitive TMS (rTMS) was given over the rIPL to modulate attentional processing. The TMS-induced E-fields for every cortical target were correlated with the behavioral modulation to identify relevant cortical regions for attentional orientation and reorientation.Main results. We did not observe a robust correlation between E-field strength and behavioral outcomes, highlighting the challenges of transferring the localization method to cognitive functions with high neural response variability and complex network interactions. Nevertheless, TMS selectively inhibited attentional reorienting in five out of seventeen subjects, resulting in task-specific behavioral impairments. The BOLD-measured neuronal activity and TMS-evoked neuronal effects showed different patterns, which emphasizes the principal distinction between the neural activity being correlated with (or maybe even caused by) particular paradigms, and the activity of neural populations exerting a causal influence on the behavioral outcome.Significance. This study is the first to explore the mechanisms of TMS-induced attentional modulation through electrical field modeling. Our findings highlight the complexity of cognitive functions and provide a basis for optimizing attentional stimulation protocols.
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Affiliation(s)
- Ying Jing
- Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Lise Meitner Research Group Cognition and Plasticity, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
| | - Ole Numssen
- Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Lise Meitner Research Group Cognition and Plasticity, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
| | - Konstantin Weise
- Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Advanced Electromagnetics Group, Technische Universität Ilmenau, Helmholtzplatz 2, D-98693, Ilmenau, Germany
| | - Benjamin Kalloch
- Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, Gustav-Kirchhoff-Straße 2, D-98693, Ilmenau, Germany
| | - Lena Buchberger
- Lise Meitner Research Group Cognition and Plasticity, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
| | - Jens Haueisen
- Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, Gustav-Kirchhoff-Straße 2, D-98693, Ilmenau, Germany
| | - Gesa Hartwigsen
- Lise Meitner Research Group Cognition and Plasticity, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Wilhelm Wundt Institute for Psychology, Leipzig University, Neumarkt 9-19, D-04109, Leipzig, Germany
| | - Thomas R Knösche
- Methods and Development Group Brain Networks, Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstraße 1a, D-04103, Leipzig, Germany
- Institute of Biomedical Engineering and Informatics, Technische Universität Ilmenau, Gustav-Kirchhoff-Straße 2, D-98693, Ilmenau, Germany
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Wartman WA, Weise K, Rachh M, Morales L, Deng ZD, Nummenmaa A, Makaroff SN. An Adaptive H-Refinement Method for the Boundary Element Fast Multipole Method for Quasi-static Electromagnetic Modeling. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.08.11.552996. [PMID: 37645957 PMCID: PMC10461998 DOI: 10.1101/2023.08.11.552996] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/31/2023]
Abstract
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.
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Affiliation(s)
- William A Wartman
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 USA
| | - Konstantin Weise
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103 Leipzig, Germany
- Department of Clinical Medicine, Aarhus University, DNK-8200, Aarhus, Denmark
| | - Manas Rachh
- Center for Computational Mathematics, Flatiron Institute, New York, NY 10012, USA
| | - Leah Morales
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 USA
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch, National Institute of Mental Health Intramural Research Program, National Institutes of Health, Bethesda, MD, USA
| | - Aapo Nummenmaa
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 USA
| | - Sergey N Makaroff
- Electrical and Computer Engineering Department, Worcester Polytechnic Inst., Worcester, MA 01609 USA
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 USA
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Makaroff SN, Nummenmaa AR, Noetscher GM, Qi Z, McIntyre CC, Bingham CS. Influence of charges deposited on membranes of human hyperdirect pathway axons on depolarization during subthalamic deep brain stimulation. J Neural Eng 2023; 20:10.1088/1741-2552/ace5de. [PMID: 37429285 PMCID: PMC10542971 DOI: 10.1088/1741-2552/ace5de] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 07/10/2023] [Indexed: 07/12/2023]
Abstract
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.
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Affiliation(s)
- Sergey N Makaroff
- Electrical and Computer Engineering Department, Worcester Polytechnic Institution, Worcester, MA 01609, United States of America
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, United States of America
| | - Aapo R Nummenmaa
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129, United States of America
| | - Gregory M Noetscher
- Electrical and Computer Engineering Department, Worcester Polytechnic Institution, Worcester, MA 01609, United States of America
- ARMY DEVCOM-SC, General Greene Ave, Natick, MA 01760, United States of America
| | - Zhen Qi
- Electrical and Computer Engineering Department, Worcester Polytechnic Institution, Worcester, MA 01609, United States of America
| | - Cameron C McIntyre
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, United States of America
- Department of Neurosurgery, Duke University, Durham, NC 27710, United States of America
| | - Clayton S Bingham
- Department of Biomedical Engineering, Duke University, Durham, NC 27708, United States of America
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Makaroff SN, Nguyen H, Meng Q, Lu H, Nummenmaa AR, Deng ZD. Modeling transcranial magnetic stimulation coil with magnetic cores. J Neural Eng 2023; 20:016028. [PMID: 36548994 PMCID: PMC10481791 DOI: 10.1088/1741-2552/acae0d] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2022] [Revised: 12/15/2022] [Accepted: 12/22/2022] [Indexed: 12/24/2022]
Abstract
Objective.Accurate modeling of transcranial magnetic stimulation (TMS) coils with the magnetic core is largely an open problem since commercial (quasi) magnetostatic solvers do not output specific field characteristics (e.g. induced electric field) and have difficulties when incorporating realistic head models. Many open-source TMS softwares do not include magnetic cores into consideration. This present study reports an algorithm for modeling TMS coils with a (nonlinear) magnetic core and validates the algorithm through comparison with finite-element method simulations and experiments.Approach.The algorithm uses the boundary element fast multipole method applied to all facets of a tetrahedral core mesh for a single-state solution and the successive substitution method for nonlinear convergence of the subsequent core states. The algorithm also outputs coil inductances, with or without magnetic cores. The coil-core combination is solved only once i.e. before incorporating the head model. The resulting primary TMS electric field is proportional to the total vector potential in the quasistatic approximation; it therefore also employs the precomputed core magnetization.Main results.The solver demonstrates excellent convergence for typical TMS field strengths and for analyticalB-Happroximations of experimental magnetization curves such as Froelich's equation or an arctangent equation. Typical execution times are 1-3 min on a common multicore workstation. For a simple test case of a cylindrical core within a one-turn coil, our solver computed the small-signal inductance nearly identical to that from ANSYS Maxwell. For a multiturn rodent TMS coil with a core, the modeled inductance matched the experimental measured value to within 5%.Significance.Incorporating magnetic core in TMS coil design has advantages of field shaping and energy efficiency. Our software package can facilitate model-informed design of more efficiency TMS systems and guide selection of core material. These models can also inform dosing with existing clinical TMS systems that use magnetic cores.
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Affiliation(s)
- Sergey N Makaroff
- Department of Electrical & Computer Engineering, Worcester Polytechnic Institute, Worcester, MA,
United States of America
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical
School, Boston, MA, United States of America
| | - Hieu Nguyen
- Magnetic Resonance Imaging and Spectroscopy Section, Neuroimaging Research Branch, National Institute of Drug Abuse
Intramural Research Program, Baltimore, MD, United States
of America
| | - Qinglei Meng
- Magnetic Resonance Imaging and Spectroscopy Section, Neuroimaging Research Branch, National Institute of Drug Abuse
Intramural Research Program, Baltimore, MD, United States
of America
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical
School, Boston, MA, United States of America
| | - Hanbing Lu
- Magnetic Resonance Imaging and Spectroscopy Section, Neuroimaging Research Branch, National Institute of Drug Abuse
Intramural Research Program, Baltimore, MD, United States
of America
| | - Aapo R Nummenmaa
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical
School, Boston, MA, United States of America
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive
Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch,
National Institute of Mental Health Intramural
Research Program, National Institutes of Health, Bethesda, MD,
United States of America
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Weise K, Wartman WA, Knösche TR, Nummenmaa AR, Makarov SN. The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement. Brain Stimul 2022; 15:654-663. [PMID: 35447379 DOI: 10.1016/j.brs.2022.04.009] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Revised: 04/07/2022] [Accepted: 04/08/2022] [Indexed: 11/02/2022] Open
Abstract
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.
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Affiliation(s)
- Konstantin Weise
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103, Leipzig, Germany; Technische Universität Ilmenau, Advanced Electromagnetics Group, Helmholtzplatz 2, 98693, Ilmenau, Germany.
| | - William A Wartman
- Electrical & Computer Engineering Dept., Worcester Polytechnic Institute, Worcester, MA, 01609, USA.
| | - Thomas R Knösche
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103, Leipzig, Germany; Technische Universität Ilmenau, Institute of Biomedical Engineering and Informatics, Gustav-Kirchhoff Str. 2, 98693, Ilmenau, Germany.
| | - Aapo R Nummenmaa
- Electrical & Computer Engineering Dept., Worcester Polytechnic Institute, Worcester, MA, 01609, USA; Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, 02115, USA.
| | - Sergey N Makarov
- Electrical & Computer Engineering Dept., Worcester Polytechnic Institute, Worcester, MA, 01609, USA; Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, 02115, USA.
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Mercadal B, Salvador R, Biagi MC, Bartolomei F, Wendling F, Ruffini G. Modeling implanted metals in electrical stimulation applications. J Neural Eng 2022; 19. [PMID: 35172293 DOI: 10.1088/1741-2552/ac55ae] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 02/16/2022] [Indexed: 11/11/2022]
Abstract
OBJECTIVE Metal implants impact the dosimetry assessment in electrical stimulation techniques. Therefore, they need to be included in numerical models. While currents in the body are ionic, metals only allow electron transport. In fact, charge transfer between tissues and metals requires electric fields to drive electrochemical reactions at the interface. Thus, metal implants may act as insulators or as conductors depending on the scenario. The aim of this paper is to provide a theoretical argument that guides the choice of the correct representation of metal implants in electrical models while considering the electrochemical nature of the problem Approach: We built a simple model of a metal implant exposed to a homogeneous electric field of various magnitudes. The same geometry was solved using two different models: a purely electric one (with different conductivities for the implant), and an electrochemical one. As an example of application, we also modeled a transcranial electrical stimulation (tES) treatment in a realistic head model with a skull plate using a high and low conductivity value for the plate. MAIN RESULTS Metal implants generally act as electric insulators when exposed to electric fields up to around 100 V/m and they only resemble a perfect conductor for fields in the order of 1000 V/m and above. The results are independent of the implant's metal, but they depend on its geometry. tES modeling with implants incorrectly treated as conductors can lead to errors of 50% or more in the estimation of the induced fields Significance: Metal implants can be accurately represented by a simple electrical model of constant conductivity, but an incorrect model choice can lead to large errors in the dosimetry assessment. Our results can be used to guide the selection of the most appropriate model in each scenario.
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Affiliation(s)
- Borja Mercadal
- Neuroelectrics Barcelona SL, Av. del Tibidabo, 47B, Barcelona, Catalunya, 08035, SPAIN
| | - Ricardo Salvador
- Neuroelectrics Barcelona SL, Av. del Tibidabo, 47B, Barcelona, Catalunya, 08035, SPAIN
| | - Maria Chiara Biagi
- Neuroelectrics Barcelona SL, Av. del Tibidabo, 47B, Barcelona, Catalunya, 08035, SPAIN
| | - Fabrice Bartolomei
- INS, Institut de Neurosciences des Systèmes, Aix-Marseille Universite, 27, Boulevard Jean Moulin, Marseille, Provence-Alpes-Côte d'Azu, 13284, FRANCE
| | - Fabrice Wendling
- INSERM, LTSI (Laboratoire de Traitement du Signal et de l'Image) U1099, Universite de Rennes 1, Campus Beaulieu, Rennes, Bretagne, 35065, FRANCE
| | - Giulio Ruffini
- Neuroelectrics Barcelona SL, Av. del Tibidabo, 47B, Barcelona, Catalunya, 08035, SPAIN
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