1
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Czerwonky DM, Aberra AS, Gomez LJ. A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields. J Neural Eng 2024; 21:036050. [PMID: 38862011 DOI: 10.1088/1741-2552/ad5704] [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: 12/19/2023] [Accepted: 06/11/2024] [Indexed: 06/13/2024]
Abstract
Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.
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Affiliation(s)
- David M Czerwonky
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, United States of America
| | - Aman S Aberra
- Dartmouth Department of Biological Sciences, Dartmouth College, Hanover, NH 03755, United States of America
| | - Luis J Gomez
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, United States of America
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2
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Park TY, Franke L, Pieper S, Haehn D, Ning L. A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation. Biomed Eng Lett 2024; 14:393-405. [PMID: 38645587 PMCID: PMC11026361 DOI: 10.1007/s13534-024-00373-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2024] [Revised: 02/27/2024] [Accepted: 03/04/2024] [Indexed: 04/23/2024] Open
Abstract
Transcranial magnetic stimulation (TMS) is a device-based neuromodulation technique increasingly used to treat brain diseases. Electric field (E-field) modeling is an important technique in several TMS clinical applications, including the precision stimulation of brain targets with accurate stimulation density for the treatment of mental disorders and the localization of brain function areas for neurosurgical planning. Classical methods for E-field modeling usually take a long computation time. Fast algorithms are usually developed with significantly lower spatial resolutions that reduce the prediction accuracy and limit their usage in real-time or near real-time TMS applications. This review paper discusses several modern algorithms for real-time or near real-time TMS E-field modeling and their advantages and limitations. The reviewed methods include techniques such as basis representation techniques and deep neural-network-based methods. This paper also provides a review of software tools that can integrate E-field modeling with navigated TMS, including a recent software for real-time navigated E-field mapping based on deep neural-network models.
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Affiliation(s)
- Tae Young Park
- Bionics Research Center, Biomedical Research Division, Korea Institute of Science and Technology, Seoul, 02792 Republic of Korea
- Division of Biomedical Science and Technology, KIST School, Korea University of Science and Technology, Seoul, 02792 Republic of Korea
- Brigham and Women’s Hospital, Boston, MA 02115 USA
| | - Loraine Franke
- University of Massachusetts Boston, Boston, MA 02125 USA
| | | | - Daniel Haehn
- University of Massachusetts Boston, Boston, MA 02125 USA
| | - Lipeng Ning
- Brigham and Women’s Hospital, Boston, MA 02115 USA
- Harvard Medical School, Boston, MA 02115 USA
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3
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Czerwonky DM, Aberra AS, Gomez LJ. A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.12.15.571917. [PMID: 38168351 PMCID: PMC10760105 DOI: 10.1101/2023.12.15.571917] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Objective Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons. Methods Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios. Main Results Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh. Significance Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.
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Affiliation(s)
- David M Czerwonky
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA-47907
| | - Aman S Aberra
- Dartmouth Department of Biological Sciences Dartmouth College Hanover, NH 03755
| | - Luis J Gomez
- Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, USA-47907
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4
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Makaroff SN, Qi Z, Rachh M, Wartman WA, Weise K, Noetscher GM, Daneshzand M, Deng ZD, Greengard L, Nummenmaa AR. A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation. Sci Rep 2023; 13:18657. [PMID: 37907689 PMCID: PMC10618282 DOI: 10.1038/s41598-023-45602-5] [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: 06/18/2023] [Accepted: 10/21/2023] [Indexed: 11/02/2023] Open
Abstract
When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~ 200,000 or more arbitrarily selected observation points within approximately 5 s, with the solution time itself of 3 s. The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods-an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.
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Affiliation(s)
- S N Makaroff
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA, 02129, USA
| | - Z Qi
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA.
| | - M Rachh
- Center for Computational Mathematics, Flatiron Institute, New York, NY, 10010, USA
| | - W A Wartman
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
| | - K Weise
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103, Leipzig, Germany
- Advanced Electromagnetics Group, Technische Universität Ilmenau, Helmholtzplatz 2, 98693, Ilmenau, Germany
| | - G M Noetscher
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
| | - M Daneshzand
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA, 02129, USA
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics and Pathophysiology Branch, National Institute of Mental Health, NIH 10 Center Drive, Bethesda, MD, 20892, USA
| | - L Greengard
- Center for Computational Mathematics, Flatiron Institute, New York, NY, 10010, USA
- Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA
| | - A R Nummenmaa
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA, 02129, USA
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5
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Yadan Z, Jian L, Jian W, Yifu L, Haiying L, Hairui L. An expert review of the inverse problem in electrocardiographic imaging for the non-invasive identification of atrial fibrillation drivers. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 240:107676. [PMID: 37343376 DOI: 10.1016/j.cmpb.2023.107676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 06/06/2023] [Accepted: 06/09/2023] [Indexed: 06/23/2023]
Abstract
BACKGROUND AND OBJECTIVE Electrocardiographic imaging (ECGI) has emerged as a non-invasive approach to identify atrial fibrillation (AF) driver sources. This paper aims to collect and review the current research literature on the ECGI inverse problem, summarize the research progress, and propose potential research directions for the future. METHODS AND RESULTS The effectiveness and feasibility of using ECGI to map AF driver sources may be influenced by several factors, such as inaccuracies in the atrial model due to heart movement or deformation, noise interference in high-density body surface potential (BSP), inconvenient and time-consuming BSP acquisition, errors in solving the inverse problem, and incomplete interpretation of the AF driving source information derived from the reconstructed epicardial potential. We review the current research progress on these factors and discuss possible improvement directions. Additionally, we highlight the limitations of ECGI itself, including the lack of a gold standard to validate the accuracy of ECGI technology in locating AF drivers and the challenges associated with guiding AF ablation based on post-processed epicardial potentials due to the intrinsic difference between epicardial and endocardial potentials. CONCLUSIONS Before performing ablation, ECGI can provide operators with predictive information about the underlying locations of AF driver by non-invasively and globally mapping the biatrial electrical activity. In the future, endocardial catheter mapping technology may benefit from the use of ECGI to enhance the diagnosis and ablation of AF.
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Affiliation(s)
- Zhang Yadan
- Institute of Biomedical Engineering, Shenzhen International Graduate School, Tsinghua University, Shenzhen, Guangdong, China
| | - Liang Jian
- Fuwai Hospital Chinese Academy of Medical Sciences, Shenzhen, Guangdong, China
| | - Wu Jian
- Institute of Biomedical Engineering, Shenzhen International Graduate School, Tsinghua University, Shenzhen, Guangdong, China.
| | - Li Yifu
- Fuwai Hospital Chinese Academy of Medical Sciences, Shenzhen, Guangdong, China
| | - Li Haiying
- The University of Hong Kong-Shenzhen Hospital, Shenzhen, Guangdong, China
| | - Li Hairui
- The University of Hong Kong-Shenzhen Hospital, Shenzhen, Guangdong, China
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6
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Pérez-Benítez JA, Martínez-Ortiz P, Aguila-Muñoz J. A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields. Brain Sci 2023; 13:1142. [PMID: 37626498 PMCID: PMC10452852 DOI: 10.3390/brainsci13081142] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2023] [Revised: 07/22/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023] Open
Abstract
Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.
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Affiliation(s)
- J. A. Pérez-Benítez
- Laboratorio de Bio-Electromagnetismo, ESIME-SEPI, Edif. Z-4, Instituto Politécnico Nacional, Mexico City 07738, CDMX, Mexico;
| | - P. Martínez-Ortiz
- Laboratorio de Bio-Electromagnetismo, ESIME-SEPI, Edif. Z-4, Instituto Politécnico Nacional, Mexico City 07738, CDMX, Mexico;
| | - J. Aguila-Muñoz
- CONAHCYT—Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, km 107 Carretera Tijuana-Ensenada, Apartado Postal 14, Ensenada 22800, BC, Mexico
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7
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Makaroff SN, Qi Z, Rachh M, Wartman WA, Weise K, Noetscher GM, Daneshzand M, Deng ZD, Greengard L, Nummenmaa AR. A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation. RESEARCH SQUARE 2023:rs.3.rs-3079433. [PMID: 37503106 PMCID: PMC10371170 DOI: 10.21203/rs.3.rs-3079433/v1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Background When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. Objective We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~200,000 or more arbitrarily selected observation points within approximately 5 sec, with the solution time itself of 3 sec. Method The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods - an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Results Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. Conclusion The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.
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Affiliation(s)
- S N Makaroff
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609 USA
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 USA
| | - Z Qi
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609 USA
| | - M Rachh
- Center for Computational Mathematics, Flatiron Institute, New York, NY 10010 USA
| | - W A Wartman
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609 USA
| | - K 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
| | - G M Noetscher
- Electrical and Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609 USA
| | - M Daneshzand
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 USA
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch, National Institute of Mental Health, NIH 10 Center Drive, Bethesda, MD 20892 USA
| | - L Greengard
- Center for Computational Mathematics, Flatiron Institute, New York, NY 10010 USA
- Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012 USA
| | - A R Nummenmaa
- Athinoula A. Martinos Ctr. for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA 02129 USA
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8
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Köhler M, Götz S. TMS coil design instrument (Kl/Codein Box): A toolbox for creating user-defined coils from conductor path data. Brain Stimul 2023; 16:698-700. [PMID: 36893961 DOI: 10.1016/j.brs.2023.02.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Revised: 02/16/2023] [Accepted: 02/20/2023] [Indexed: 03/09/2023] Open
Affiliation(s)
- Max Köhler
- TU Kaiserslautern, Paul-Ehrlich-Straße 11/372, 67663, Kaiserslautern, Germany.
| | - Stefan Götz
- TU Kaiserslautern, Paul-Ehrlich-Straße 11/372, 67663, Kaiserslautern, Germany
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9
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Lu H, Li J, Zhang L, Meng L, Ning Y, Jiang T. Pinpointing the precise stimulation targets for brain rehabilitation in early-stage Parkinson's disease. BMC Neurosci 2023; 24:24. [PMID: 36991320 PMCID: PMC10061909 DOI: 10.1186/s12868-023-00791-7] [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: 08/29/2022] [Accepted: 03/15/2023] [Indexed: 03/31/2023] Open
Abstract
BACKGROUND Transcranial magnetic stimulation (TMS) is increasingly used as a promising non-pharmacological treatment for Parkinson's disease (PD). Scalp-to-cortex distance (SCD), as a key technical parameter of TMS, plays a critical role in determining the locations of treatment targets and corresponding dosage. Due to the discrepancies in TMS protocols, the optimal targets and head models have yet to be established in PD patients. OBJECTIVE To investigate the SCDs of the most popular used targets in left dorsolateral prefrontal cortex (DLPFC) and quantify its impact on the TMS-induced electric fields (E-fields) in early-stage PD patients. METHODS Structural magnetic resonance imaging scans from PD patients (n = 47) and normal controls (n = 36) were drawn from the NEUROCON and Tao Wu datasets. SCD of left DLPFC was measured by Euclidean Distance in TMS Navigation system. The intensity and focality of SCD-dependent E-fields were examined and quantified using Finite Element Method. RESULTS Early-stage PD patients showed an increased SCDs, higher variances in the SCDs and SCD-dependent E-fields across the seven targets of left DLPFC than normal controls. The stimulation targets located on gyral crown had more focal and homogeneous E-fields. The SCD of left DLPFC had a better performance in differentiating early-stage PD patients than global cognition and other brain measures. CONCLUSION SCD and SCD-dependent E-fields could determine the optimal TMS treatment targets and may also be used as a novel marker to differentiate early-stage PD patients. Our findings have important implications for developing optimal TMS protocols and personalized dosimetry in real-world clinical practice.
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Affiliation(s)
- Hanna Lu
- G27, Multi-Centre, Department of Psychiatry, The Chinese University of Hong Kong, Tai Po Hospital, Hong Kong SAR, China.
- Centre for Neuromodulation and Rehabilitation, The Affiliated Brain Hospital of Guangzhou Medical University, Guangzhou, China.
- The Affiliated Brain Hospital of Guangzhou Medical University, Guangzhou, China.
| | - Jing Li
- G27, Multi-Centre, Department of Psychiatry, The Chinese University of Hong Kong, Tai Po Hospital, Hong Kong SAR, China
| | - Li Zhang
- Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China
| | - Lin Meng
- Academy of Medical Engineering and Translational Medicine, Tianjin University, Tianjin, China
| | - Yuping Ning
- The Affiliated Brain Hospital of Guangzhou Medical University, Guangzhou, China
- The First School of Clinical Medicine, Southern Medical University, Guangzhou, China
| | - Tianzi Jiang
- Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing, China
- Research Center for Augmented Intelligence, Zhejiang Lab, Hangzhou, 311100, China
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10
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Gross J, Junghöfer M, Wolters C. Bioelectromagnetism in Human Brain Research: New Applications, New Questions. Neuroscientist 2023; 29:62-77. [PMID: 34873945 PMCID: PMC9902961 DOI: 10.1177/10738584211054742] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
Bioelectromagnetism has contributed some of the most commonly used techniques to human neuroscience such as magnetoencephalography (MEG), electroencephalography (EEG), transcranial magnetic stimulation (TMS), and transcranial electric stimulation (TES). The considerable differences in their technical design and practical use give rise to the impression that these are quite different techniques altogether. Here, we review, discuss and illustrate the fundamental principle of Helmholtz reciprocity that provides a common ground for all four techniques. We show that, more than 150 years after its discovery by Helmholtz in 1853, reciprocity is important to appreciate the strengths and limitations of these four classical tools in neuroscience. We build this case by explaining the concept of Helmholtz reciprocity, presenting a methodological account of this principle for all four methods and, finally, by illustrating its application in practical clinical studies.
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Affiliation(s)
- Joachim Gross
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany,Joachim Gross, Institute for Biomagnetism and Biosignalanalysis, University of Münster, Malmedyweg 15, Münster, 48149, Germany.
| | - Markus Junghöfer
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany
| | - Carsten Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany
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11
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Li H, Deng ZD, Oathes D, Fan Y. Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning. Neuroimage 2022; 264:119705. [PMID: 36280099 PMCID: PMC9854270 DOI: 10.1016/j.neuroimage.2022.119705] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2021] [Revised: 09/28/2022] [Accepted: 10/20/2022] [Indexed: 11/06/2022] Open
Abstract
Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.
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Affiliation(s)
- Hongming Li
- Center for Biomedical Image Computation and Analytics, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Zhi-De Deng
- Computational Neurostimulation Research Program, Noninvasive Neuromodulation Unit, Experimental Therapeutics & Pathophysiology Branch, National Institute of Mental Health, NIH, MD 20892, USA
| | - Desmond Oathes
- Center for Neuromodulation in Depression and Stress, Department of Psychiatry, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Yong Fan
- Center for Biomedical Image Computation and Analytics, Department of Radiology, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
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12
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Devices and Technology in Transcranial Magnetic Stimulation: A Systematic Review. Brain Sci 2022; 12:brainsci12091218. [PMID: 36138954 PMCID: PMC9496961 DOI: 10.3390/brainsci12091218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2022] [Revised: 09/05/2022] [Accepted: 09/07/2022] [Indexed: 01/18/2023] Open
Abstract
The technology for transcranial magnetic stimulation (TMS) has significantly changed over the years, with important improvements in the signal generators, the coils, the positioning systems, and the software for modeling, optimization, and therapy planning. In this systematic literature review (SLR), the evolution of each component of TMS technology is presented and analyzed to assess the limitations to overcome. This SLR was carried out following the PRISMA 2020 statement. Published articles of TMS were searched for in four databases (Web of Science, PubMed, Scopus, IEEE). Conference papers and other reviews were excluded. Records were filtered using terms about TMS technology with a semi-automatic software; articles that did not present new technology developments were excluded manually. After this screening, 101 records were included, with 19 articles proposing new stimulator designs (18.8%), 46 presenting or adapting coils (45.5%), 18 proposing systems for coil placement (17.8%), and 43 implementing algorithms for coil optimization (42.6%). The articles were blindly classified by the authors to reduce the risk of bias. However, our results could have been influenced by our research interests, which would affect conclusions for applications in psychiatric and neurological diseases. Our analysis indicates that more emphasis should be placed on optimizing the current technology with a special focus on the experimental validation of models. With this review, we expect to establish the base for future TMS technological developments.
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13
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Precise Modulation Strategies for Transcranial Magnetic Stimulation: Advances and Future Directions. Neurosci Bull 2021; 37:1718-1734. [PMID: 34609737 DOI: 10.1007/s12264-021-00781-x] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2021] [Accepted: 06/23/2021] [Indexed: 10/20/2022] Open
Abstract
Transcranial magnetic stimulation (TMS) is a popular modulatory technique for the noninvasive diagnosis and therapy of neurological and psychiatric diseases. Unfortunately, current modulation strategies are only modestly effective. The literature provides strong evidence that the modulatory effects of TMS vary depending on device components and stimulation protocols. These differential effects are important when designing precise modulatory strategies for clinical or research applications. Developments in TMS have been accompanied by advances in combining TMS with neuroimaging techniques, including electroencephalography, functional near-infrared spectroscopy, functional magnetic resonance imaging, and positron emission tomography. Such studies appear particularly promising as they may not only allow us to probe affected brain areas during TMS but also seem to predict underlying research directions that may enable us to precisely target and remodel impaired cortices or circuits. However, few precise modulation strategies are available, and the long-term safety and efficacy of these strategies need to be confirmed. Here, we review the literature on possible technologies for precise modulation to highlight progress along with limitations with the goal of suggesting future directions for this field.
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Makarov SN, Golestanirad L, Wartman WA, Nguyen BT, Noetscher GM, Ahveninen JP, Fujimoto K, Weise K, Nummenmaa AR. Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes. J Neural Eng 2021; 18. [PMID: 34311449 DOI: 10.1088/1741-2552/ac17d7] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 07/26/2021] [Indexed: 01/03/2023]
Abstract
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.
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Affiliation(s)
- Sergey N Makarov
- Electrical & Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, United States of America.,Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02115, United States of America
| | - Laleh Golestanirad
- Biomedical Engineering and Radiology Depts., Northwestern University, Chicago, IL 60611, United States of America
| | - William A Wartman
- Electrical & Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, United States of America
| | - Bach Thanh Nguyen
- Biomedical Engineering and Radiology Depts., Northwestern University, Chicago, IL 60611, United States of America
| | - Gregory M Noetscher
- Electrical & Computer Engineering Department, Worcester Polytechnic Institute, Worcester, MA 01609, United States of America
| | - Jyrki P Ahveninen
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02115, United States of America
| | - Kyoko Fujimoto
- Center for Devices and Radiological Health (CDRH), FDA, Silver Spring, MD 20993, United States of America
| | - Konstantin Weise
- Max Planck Institute for Human Cognitive and Brain Sciences, Stephanstr. 1a, 04103 Leipzig, Germany
| | - Aapo R Nummenmaa
- Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA 02115, United States of America
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15
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Schrader S, Westhoff A, Piastra MC, Miinalainen T, Pursiainen S, Vorwerk J, Brinck H, Wolters CH, Engwer C. DUNEuro-A software toolbox for forward modeling in bioelectromagnetism. PLoS One 2021; 16:e0252431. [PMID: 34086715 PMCID: PMC8177522 DOI: 10.1371/journal.pone.0252431] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Accepted: 05/14/2021] [Indexed: 01/19/2023] Open
Abstract
Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software's aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended.
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Affiliation(s)
- Sophie Schrader
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Munster, Germany
| | - Andreas Westhoff
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Munster, Germany
- Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Munster, Germany
- Institute for Bioinformatics and Chemoinformatics, Westphalian University of Applied Sciences, Gelsenkirchen, Germany
| | - Maria Carla Piastra
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Munster, Germany
- Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Munster, Germany
- Radboud University Nijmegen Medical Centre, Donders Institute for Brain, Cognition and Behaviour, Nijmegen, The Netherlands
| | - Tuuli Miinalainen
- Computing Sciences, Tampere University, Tampere, Finland
- Department of Applied Physics, University of Eastern Finland, Kuopio, Finland
| | | | - Johannes Vorwerk
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Munster, Germany
- Institute of Electrical and Biomedical Engineering, UMIT - Private University for Health Sciences, Medical Informatics and Technology, Hall in Tyrol, Austria
| | - Heinrich Brinck
- Institute for Bioinformatics and Chemoinformatics, Westphalian University of Applied Sciences, Gelsenkirchen, Germany
| | - Carsten H. Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Munster, Germany
- Otto Creutzfeldt Center for Cognitive and Behavioral Neuroscience, University of Münster, Munster, Germany
| | - Christian Engwer
- Applied Mathematics: Institute for Analysis and Numerics, University of Münster, Munster, Germany
- * E-mail:
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16
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Rapid computation of TMS-induced E-fields using a dipole-based magnetic stimulation profile approach. Neuroimage 2021; 237:118097. [PMID: 33940151 PMCID: PMC8353625 DOI: 10.1016/j.neuroimage.2021.118097] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Revised: 03/25/2021] [Accepted: 04/23/2021] [Indexed: 12/25/2022] Open
Abstract
BACKGROUND TMS neuronavigation with on-line display of the induced electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, but present commercially available solutions are limited by simplified approximations. OBJECTIVE Developing a near real-time method for accurate approximation of TMS induced E-fields with subject-specific high-resolution surface-based head models that can be utilized for TMS navigation. METHODS Magnetic dipoles are placed on a closed surface enclosing an MRI-based head model of the subject to define a set of basis functions for the incident and total E-fields that define the subject's Magnetic Stimulation Profile (MSP). The near real-time speed is achieved by recognizing that the total E-field of the coil only depends on the incident E-field and the conductivity boundary geometry. The total E-field for any coil position can be obtained by matching the incident field of the stationary dipole basis set with the incident E-field of the moving coil and applying the same basis coefficients to the total E-field basis functions. RESULTS Comparison of the MSP-based approximation with an established TMS solver shows great agreement in the E-field amplitude (relative maximum error around 5%) and the spatial distribution patterns (correlation >98%). Computation of the E-field took ~100 ms on a cortical surface mesh with 120k facets. CONCLUSION The numerical accuracy and speed of the MSP approximation method make it well suited for a wide range of computational tasks including interactive planning, targeting, dosing, and visualization of the intracranial E-fields for near real-time guidance of coil positioning.
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Makarov SN, Hamalainen M, Okada Y, Noetscher GM, Ahveninen J, Nummenmaa A. Boundary Element Fast Multipole Method for Enhanced Modeling of Neurophysiological Recordings. IEEE Trans Biomed Eng 2021; 68:308-318. [PMID: 32746015 PMCID: PMC7704617 DOI: 10.1109/tbme.2020.2999271] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
OBJECTIVE A new numerical modeling approach is proposed which provides forward-problem solutions for both noninvasive recordings (EEG/MEG) and higher-resolution intracranial recordings (iEEG). METHODS The algorithm is our recently developed boundary element fast multipole method or BEM-FMM. It is based on the integration of the boundary element formulation in terms of surface charge density and the fast multipole method originating from its inventors. The algorithm still possesses the major advantage of the conventional BEM - high speed - but is simultaneously capable of processing a very large number of surface-based unknowns. As a result, an unprecedented spatial resolution could be achieved, which enables multiscale modeling. RESULTS For non-invasive EEG/MEG, we are able to accurately solve the forward problem with approximately 1 mm anatomical resolution in the cortex within 1-2 min given several thousand cortical dipoles. Targeting high-resolution iEEG, we are able to compute, for the first time, an integrated electromagnetic response for an ensemble (2,450) of tightly packed realistic pyramidal neocortical neurons in a full-head model with 0.6 mm anatomical cortical resolution. The neuronal arbor is comprised of 5.9 M elementary 1.2 μm long dipoles. On a standard server, the computations require about 5 min. CONCLUSION Our results indicate that the BEM-FMM approach may be well suited to support numerical multiscale modeling pertinent to modern high-resolution and submillimeter iEEG. SIGNIFICANCE Based on the speed and ease of implementation, this new algorithm represents a method that will greatly facilitate simulations at multi-scale across a variety of applications.
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Monin MY, Rahmouni L, Merlini A, Andriulli FP. A Hybrid Volume-Surface-Wire Integral Equation for the Anisotropic Forward Problem in Electroencephalography. ACTA ACUST UNITED AC 2020. [DOI: 10.1109/jerm.2020.2966121] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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19
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Navarro de Lara LI, Daneshzand M, Mascarenas A, Paulson D, Pratt K, Okada Y, Raij T, Makarov SN, Nummenmaa A. A 3-axis coil design for multichannel TMS arrays. Neuroimage 2020; 224:117355. [PMID: 32916290 PMCID: PMC7837414 DOI: 10.1016/j.neuroimage.2020.117355] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2020] [Revised: 08/13/2020] [Accepted: 09/04/2020] [Indexed: 01/24/2023] Open
Abstract
Purpose: Multichannel Transcranial Magnetic Stimulation (mTMS) arrays enable
multiple sites to be stimulated simultaneously or sequentially under
electronic control without moving the system’s stimulation coils.
Here, we build and characterize the performance of a novel modular 3-axis
TMS coil that can be utilized as a unit element in large-scale multichannel
TMS arrays. Methods: We determined the basic physical characteristics of the 3-axis TMS
coil x-, y- and
z-elements using a custom 2-channel programmable stimulator
prototype. We mapped the temporal rate-of-change of the induced magnetic
field (dB/dt) on a 2D plane parallel to the coil surface
(including an extended line for full spatial coverage) and compared those
values with predictions from magnetic field simulations. Temperature
measurements were carried out to assess the incorporated air-cooling method.
We measured the mutual and self-inductances of the
x/y/z-elements to assess coupling between them.
Additionally, we measured and calculated the coupling between
z-elements in the array configuration. Finally, we
performed electric field simulations to evaluate the stimulation intensity
and focality of the coil and compared the results to conventional TMS coils
as well as demonstrated suitability of the 3-axis coil for a multichannel
array configuration. Results: The experimentally obtained dB/dt values validated
the computational model of the 3-axis coil and therefore confirmed that both
the coil and stimulator system are operating as intended. The air-cooling
system was effective for brief high-frequency pulse trains and extended
single- and paired-pulse TMS protocols. The electromagnetic simulations
suggested that an array of the 3-axis coils would have comparable
stimulation intensity to conventional TMS coils, therefore enabling clearly
suprathreshold stimulation of the human brain. The recorded coil coupling
between the x/y/z-elements was < 1%
and the maximal coupling between z-elements in the array
configuration was 1.8% and 3.4% for the measured and calculated values,
respectively. Conclusion: We presented a 3-axis coil intended for multichannel TMS arrays. The
electromagnetic measurements and simulations verified that the coil
fabrication met the desired specifications and that the inductive coupling
between the elements was negligible. The air-cooled 3-axis TMS coil appears
suitable to be used as an element in multichannel TMS arrays.
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Affiliation(s)
- Lucia I Navarro de Lara
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Harvard Medical School, Massachusetts General Hospital, Charlestown, MA 02129, USA.
| | - Mohammad Daneshzand
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Harvard Medical School, Massachusetts General Hospital, Charlestown, MA 02129, USA
| | | | | | - Kevin Pratt
- Tristan Technologies, San Diego, CA 92121, USA
| | | | - Tommi Raij
- Center for Brain Stimulation, Shirley Ryan AbilityLab, Chicago IL 60611 USA; Department of Physical Medicine and Rehabilitation, Department of Neurobiology, Northwestern University, Chicago IL 60611 USA
| | - Sergey N Makarov
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Harvard Medical School, Massachusetts General Hospital, Charlestown, MA 02129, USA; Department of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, MA 01609, USA
| | - Aapo Nummenmaa
- Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Harvard Medical School, Massachusetts General Hospital, Charlestown, MA 02129, USA.
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20
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Saturnino GB, Wartman WA, Makarov SN, Thielscher A. Accurate TMS Head Modeling: Interfacing SimNIBS and BEM-FMM in a MATLAB-Based Module. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2020; 2020:5326-5329. [PMID: 33019186 DOI: 10.1109/embc44109.2020.9175802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
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.
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21
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Gomez LJ, Dannhauer M, Koponen LM, Peterchev AV. Conditions for numerically accurate TMS electric field simulation. Brain Stimul 2019; 13:157-166. [PMID: 31604625 DOI: 10.1016/j.brs.2019.09.015] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2019] [Revised: 09/25/2019] [Accepted: 09/29/2019] [Indexed: 12/28/2022] Open
Abstract
BACKGROUND Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking. OBJECTIVE To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup. METHOD We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods. RESULTS To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled. CONCLUSION BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.
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Affiliation(s)
- Luis J Gomez
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC, 27710, USA.
| | - Moritz Dannhauer
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC, 27710, USA.
| | - Lari M Koponen
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC, 27710, USA.
| | - Angel V Peterchev
- Department of Psychiatry and Behavioral Sciences, Duke University, Durham, NC, 27710, USA; Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708, USA; Department of Neurosurgery, Duke University, Durham, NC, 27710, USA; Department of Biomedical Engineering, Duke University, Durham, NC, 27708, USA.
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Stenroos M, Koponen LM. Real-time computation of the TMS-induced electric field in a realistic head model. Neuroimage 2019; 203:116159. [PMID: 31494248 DOI: 10.1016/j.neuroimage.2019.116159] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2019] [Revised: 08/10/2019] [Accepted: 09/02/2019] [Indexed: 11/25/2022] Open
Abstract
Transcranial magnetic stimulation (TMS) is often targeted using a model of TMS-induced electric field (E). In such navigated TMS, the E-field models have been based on spherical approximation of the head. Such models omit the effects of cerebrospinal fluid (CSF) and gyral folding, leading to potentially large errors in the computed E-field. So far, realistic models have been too slow for interactive TMS navigation. We present computational methods that enable real-time solving of the E-field in a realistic five-compartment (5-C) head model that contains isotropic white matter, gray matter, CSF, skull and scalp. Using reciprocity and Geselowitz integral equation, we separate the computations to coil-dependent and -independent parts. For the Geselowitz integrals, we present a fast numerical quadrature. Further, we present a moment-matching approach for optimizing dipole-based coil models. We verified and benchmarked the new methods using simulations with over 100 coil locations. The new quadrature introduced a relative error (RE) of 0.3-0.6%. For a coil model with 42 dipoles, the total RE of the quadrature and coil model was 0.44-0.72%. Taking also other model errors into account, the contribution of the new approximations to the RE was 0.1%. For comparison, the RE due to omitting the separation of white and gray matter was >11%, and the RE due to omitting also the CSF was >23%. After the coil-independent part of the model has been built, E-fields can be computed very quickly: Using a standard PC and basic GPU, our solver computed the full E-field in a 5-C model in 9000 points on the cortex in 27 coil positions per second (cps). When the separation of white and gray matter was omitted, the speed was 43-65 cps. Solving only one component of the E-field tripled the speed. The presented methods enable real-time solving of the TMS-induced E-field in a realistic head model that contains the CSF and gyral folding. The new methodology allows more accurate targeting and precise adjustment of stimulation intensity during experimental or clinical TMS mapping.
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Affiliation(s)
- Matti Stenroos
- Aalto University, Department of Neuroscience and Biomedical Engineering, P.O. Box 12200, FI-00076, Aalto, Finland.
| | - Lari M Koponen
- Aalto University, Department of Neuroscience and Biomedical Engineering, P.O. Box 12200, FI-00076, Aalto, Finland
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