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Liu X, Chou KL, Patil PG, Malaga KA. Effect of Anisotropic Brain Conductivity on Patient-Specific Volume of Tissue Activation in Deep Brain Stimulation for Parkinson Disease. IEEE Trans Biomed Eng 2024; 71:1993-2000. [PMID: 38277250 DOI: 10.1109/tbme.2024.3359119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2024]
Abstract
OBJECTIVE Deep brain stimulation (DBS) modeling can improve surgical targeting by quantifying the spatial extent of stimulation relative to subcortical structures of interest. A certain degree of model complexity is required to obtain accurate predictions, particularly complexity regarding electrical properties of the tissue around DBS electrodes. In this study, the effect of anisotropy on the volume of tissue activation (VTA) was evaluated in an individualized manner. METHODS Tissue activation models incorporating patient-specific tissue conductivity were built for 40 Parkinson disease patients who had received bilateral subthalamic nucleus (STN) DBS. To assess the impact of local changes in tissue anisotropy, one VTA was computed at each electrode contact using identical stimulation parameters. For comparison, VTAs were also computed assuming isotropic tissue conductivity. Stimulation location was considered by classifying the anisotropic VTAs relative to the STN. VTAs were characterized based on volume, spread in three directions, sphericity, and Dice coefficient. RESULTS Incorporating anisotropy generated significantly larger and less spherical VTAs overall. However, its effect on VTA size and shape was variable and more nuanced at the individual patient and implantation levels. Dorsal VTAs had significantly higher sphericity than ventral VTAs, suggesting more isotropic behavior. Contrastingly, lateral and posterior VTAs had significantly larger and smaller lateral-medial spreads, respectively. Volume and spread correlated negatively with sphericity. CONCLUSION The influence of anisotropy on VTA predictions is important to consider, and varies across patients and stimulation location. SIGNIFICANCE This study highlights the importance of considering individualized factors in DBS modeling to accurately characterize the VTA.
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Patrick EE, Fleeting CR, Patel DR, Casauay JT, Patel A, Shepherd H, Wong JK. Modeling the volume of tissue activated in deep brain stimulation and its clinical influence: a review. Front Hum Neurosci 2024; 18:1333183. [PMID: 38660012 PMCID: PMC11039793 DOI: 10.3389/fnhum.2024.1333183] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2023] [Accepted: 03/26/2024] [Indexed: 04/26/2024] Open
Abstract
Deep brain stimulation (DBS) is a neuromodulatory therapy that has been FDA approved for the treatment of various disorders, including but not limited to, movement disorders (e.g., Parkinson's disease and essential tremor), epilepsy, and obsessive-compulsive disorder. Computational methods for estimating the volume of tissue activated (VTA), coupled with brain imaging techniques, form the basis of models that are being generated from retrospective clinical studies for predicting DBS patient outcomes. For instance, VTA models are used to generate target-and network-based probabilistic stimulation maps that play a crucial role in predicting DBS treatment outcomes. This review defines the methods for calculation of tissue activation (or modulation) including ones that use heuristic and clinically derived estimates and more computationally involved ones that rely on finite-element methods and biophysical axon models. We define model parameters and provide a comparison of commercial, open-source, and academic simulation platforms available for integrated neuroimaging and neural activation prediction. In addition, we review clinical studies that use these modeling methods as a function of disease. By describing the tissue-activation modeling methods and highlighting their application in clinical studies, we provide the neural engineering and clinical neuromodulation communities with perspectives that may influence the adoption of modeling methods for future DBS studies.
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Affiliation(s)
- Erin E. Patrick
- Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL, United States
| | - Chance R. Fleeting
- College of Medicine, University of Florida, Gainesville, FL, United States
| | - Drashti R. Patel
- College of Medicine, University of Florida, Gainesville, FL, United States
| | - Jed T. Casauay
- College of Medicine, University of Florida, Gainesville, FL, United States
| | - Aashay Patel
- College of Medicine, University of Florida, Gainesville, FL, United States
| | - Hunter Shepherd
- College of Medicine, University of Florida, Gainesville, FL, United States
| | - Joshua K. Wong
- Department of Neurology, Fixel Institute for Neurological Diseases, University of Florida, Gainesville, FL, United States
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Malaga KA, Houshmand L, Costello JT, Chandrasekaran J, Chou KL, Patil PG. Thalamic Segmentation and Neural Activation Modeling Based on Individual Tissue Microstructure in Deep Brain Stimulation for Essential Tremor. Neuromodulation 2023; 26:1689-1698. [PMID: 36470728 DOI: 10.1016/j.neurom.2022.09.013] [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: 06/23/2022] [Revised: 08/08/2022] [Accepted: 09/13/2022] [Indexed: 12/05/2022]
Abstract
OBJECTIVE Thalamic deep brain stimulation (DBS) is the primary surgical therapy for essential tremor (ET). Thalamic DBS traditionally uses an atlas-based targeting approach, which, although nominally accurate, may obscure individual anatomic differences from population norms. The objective of this study was to compare this traditional atlas-based approach with a novel quantitative modeling methodology grounded in individual tissue microstructure (N-of-1 approach). MATERIALS AND METHODS The N-of-1 approach uses individual patient diffusion tensor imaging (DTI) data to perform thalamic segmentation and volume of tissue activation (VTA) modeling. For each patient, the thalamus was individually segmented into 13 nuclei using DTI-based k-means clustering. DBS-induced VTAs associated with tremor suppression and side effects were then computed for each patient with finite-element electric-field models incorporating DTI microstructural data. Results from N-of-1 and traditional atlas-based modeling were compared for a large cohort of patients with ET treated with thalamic DBS. RESULTS The size and shape of individual N-of-1 thalamic nuclei and VTAs varied considerably across patients (N = 22). For both methods, tremor-improving therapeutic VTAs showed similar overlap with motor thalamic nuclei and greater motor than sensory nucleus overlap. For VTAs producing undesirable sustained paresthesia, 94% of VTAs overlapped with N-of-1 sensory thalamus estimates, whereas 74% of atlas-based segmentations overlapped. For VTAs producing dysarthria/motor contraction, the N-of-1 approach predicted greater spread beyond the thalamus into the internal capsule and adjacent structures than the atlas-based method. CONCLUSIONS Thalamic segmentation and VTA modeling based on individual tissue microstructure explain therapeutic stimulation equally well and side effects better than a traditional atlas-based method in DBS for ET. The N-of-1 approach may be useful in DBS targeting and programming, particularly when patient neuroanatomy deviates from population norms.
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Affiliation(s)
- Karlo A Malaga
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Layla Houshmand
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Joseph T Costello
- Department of Electrical Engineering, University of Michigan, Ann Arbor, MI, USA
| | | | - Kelvin L Chou
- Department of Neurology, University of Michigan, Ann Arbor, MI, USA; Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA
| | - Parag G Patil
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA; Department of Neurology, University of Michigan, Ann Arbor, MI, USA; Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA.
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Charlebois CM, Anderson DN, Johnson KA, Philip BJ, Davis TS, Newman BJ, Peters AY, Arain AM, Dorval AD, Rolston JD, Butson CR. Patient-specific structural connectivity informs outcomes of responsive neurostimulation for temporal lobe epilepsy. Epilepsia 2022; 63:2037-2055. [PMID: 35560062 DOI: 10.1111/epi.17298] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2022] [Revised: 05/09/2022] [Accepted: 05/10/2022] [Indexed: 11/29/2022]
Abstract
OBJECTIVE Responsive neurostimulation is an effective therapy for patients with refractory mesial temporal lobe epilepsy. However, clinical outcomes are variable, few patients become seizure-free, and the optimal stimulation location is currently undefined. The aim of this study was to quantify responsive neurostimulation in the mesial temporal lobe, identify stimulation-dependent networks associated with seizure reduction, and determine if stimulation location or stimulation-dependent networks inform outcomes. METHODS We modeled patient-specific volumes of tissue activated and created probabilistic stimulation maps of local regions of stimulation across a retrospective cohort of 22 patients with mesial temporal lobe epilepsy. We then mapped the network stimulation effects by seeding tractography from the volume of tissue activated with both patient-specific and normative diffusion-weighted imaging. We identified networks associated with seizure reduction across patients using the patient-specific tractography maps and then predicted seizure reduction across the cohort. RESULTS Patient-specific stimulation-dependent connectivity was correlated with responsive neurostimulation effectiveness after cross-validation (p = .03); however, normative connectivity derived from healthy subjects was not (p = .44). Increased connectivity from the volume of tissue activated to the medial prefrontal cortex, cingulate cortex, and precuneus was associated with greater seizure reduction. SIGNIFICANCE Overall, our results suggest that the therapeutic effect of responsive neurostimulation may be mediated by specific networks connected to the volume of tissue activated. In addition, patient-specific tractography was required to identify structural networks correlated with outcomes. It is therefore likely that altered connectivity in patients with epilepsy may be associated with the therapeutic effect and that utilizing patient-specific imaging could be important for future studies. The structural networks identified here may be utilized to target stimulation in the mesial temporal lobe and to improve seizure reduction for patients treated with responsive neurostimulation.
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Affiliation(s)
- Chantel M Charlebois
- Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, USA
- Scientific Computing & Imaging Institute, University of Utah, Salt Lake City, Utah, USA
| | - Daria Nesterovich Anderson
- Department of Neurosurgery, University of Utah, Salt Lake City, Utah, USA
- Department of Pharmacology & Toxicology, University of Utah, Salt Lake City, Utah, USA
| | - Kara A Johnson
- Norman Fixel Institute for Neurological Diseases, University of Florida, Gainesville, Florida, USA
- Department of Neurology, University of Florida, Gainesville, Florida, USA
| | - Brian J Philip
- Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, USA
- Department of Neurosurgery, University of Utah, Salt Lake City, Utah, USA
| | - Tyler S Davis
- Department of Neurosurgery, University of Utah, Salt Lake City, Utah, USA
| | - Blake J Newman
- Department of Neurology, University of Utah, Salt Lake City, Utah, USA
| | - Angela Y Peters
- Department of Neurology, University of Utah, Salt Lake City, Utah, USA
| | - Amir M Arain
- Department of Neurology, University of Utah, Salt Lake City, Utah, USA
| | - Alan D Dorval
- Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, USA
| | - John D Rolston
- Department of Biomedical Engineering, University of Utah, Salt Lake City, Utah, USA
- Scientific Computing & Imaging Institute, University of Utah, Salt Lake City, Utah, USA
- Department of Neurosurgery, University of Utah, Salt Lake City, Utah, USA
| | - Christopher R Butson
- Norman Fixel Institute for Neurological Diseases, University of Florida, Gainesville, Florida, USA
- Department of Neurology, University of Florida, Gainesville, Florida, USA
- Department of Neurosurgery, University of Florida, Gainesville, Florida, USA
- Department of Biomedical Engineering, University of Florida, Gainesville, Florida, USA
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Rao AT, Lu CW, Askari A, Malaga KA, Chou KL, Patil PG. Clinically-derived oscillatory biomarker predicts optimal subthalamic stimulation for Parkinson's disease. J Neural Eng 2022; 19. [PMID: 35272281 DOI: 10.1088/1741-2552/ac5c8c] [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: 01/10/2022] [Accepted: 03/10/2022] [Indexed: 11/11/2022]
Abstract
OBJECTIVE Choosing the optimal electrode trajectory, stimulation location, and stimulation amplitude in subthalamic nucleus deep brain stimulation (STN DBS) for Parkinson's disease (PD) remains a time-consuming empirical effort. In this retrospective study, we derive a data-driven electrophysiological biomarker that predicts clinical DBS location and parameters, and we consolidate this information into a quantitative score that may facilitate an objective approach to STN DBS surgery and programming. APPROACH Random-forest feature selection was applied to a dataset of 1046 microelectrode recordings sites across 20 DBS implant trajectories to identify features of oscillatory activity that predict clinically programmed volumes of tissue activation (VTA). A cross-validated classifier was used to retrospectively predict VTA regions from these features. Spatial convolution of probabilistic classifier outputs along MER trajectories produced a biomarker score that reflects the probability of localization within a clinically optimized VTA. MAIN RESULTS Biomarker scores peaked within the VTA region and were significantly correlated with percent improvement in postoperative motor symptoms (MDS-UPRDS Part III, R = 0.61, p = 0.004). Notably, the length of STN, a common criterion for trajectory selection, did not show similar correlation (R = -0.31, p = 0.18). These findings suggest that biomarker-based trajectory selection and programming may improve motor outcomes by 9 ± 3 percentage points (p = 0.047) in this dataset. SIGNIFICANCE A clinically defined electrophysiological biomarker not only predicts VTA size and location but also correlates well with motor outcomes. Use of this biomarker for trajectory selection and initial stimulation may potentially simplify STN DBS surgery and programming.
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Affiliation(s)
- Akshay T Rao
- Biomedical Engineering, University of Michigan, 1500 East Medical Center Dr., SPC 5338, Ann Arbor, Michigan, 48109-5338, UNITED STATES
| | - Charles W Lu
- Biomedical Engineering, University of Michigan, 1500 E. Medical Center Drive, Ann Arbor, Michigan, 48109-5338, UNITED STATES
| | - Asra Askari
- Biomedical Engineering, University of Michigan, 1500 E Medical Center Drive, SPC 5338, Ann Arbor, Ann Arbor, Michigan, 48109-5338, UNITED STATES
| | - Karlo A Malaga
- Biomedical Engineering, Bucknell University, 316 Academic East Building, Lewisburg, Pennsylvania, 17837, UNITED STATES
| | - Kelvin L Chou
- Neurosurgery, University of Michigan, 1500 E. Medical Center Drive, Ann Arbor, Michigan, 48109-5338, UNITED STATES
| | - Parag G Patil
- Neurosurgery, University of Michigan, 1500 E. Medical Center Drive, Ann Arbor, Michigan, 48109-5338, UNITED STATES
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Askari A, Zhu BJ, Lyu X, Chou KL, Patil PG. Characterization and localization of upper and lower extremity motor improvements in STN DBS for Parkinson's disease. Parkinsonism Relat Disord 2021; 94:84-88. [PMID: 34896928 DOI: 10.1016/j.parkreldis.2021.11.036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 06/27/2021] [Revised: 11/02/2021] [Accepted: 11/30/2021] [Indexed: 10/19/2022]
Abstract
INTRODUCTION Subthalamic deep brain stimulation (STN DBS) may have differential effects on cardinal motor signs of Parkinson's disease (PD) in the upper and lower extremities. In addition, sites of maximally effective DBS for each sign and extremity may be distinct. Our study seeks to elucidate these structure-function relationships. METHODS We applied an ordinary least squares linear regression model to measure motor effects of STN DBS on upper (UE) and lower (LE) extremity tremor, rigidity, and bradykinesia. We then applied an atlas-independent electrical-field model to identify sites of maximally effective stimulation for each sign and each extremity. Distances between sites and statistical power to resolve differences were calculated. RESULTS In our study population (n = 78 patients), STN DBS improved all cardinal motor signs (β = 0.64, p < .05). Improvement magnitudes were tremor > rigidity > bradykinesia. Effects of STN DBS on UE versus LE signs were statistically equal for tremor and bradykinesia, but greater for UE rigidity than LE rigidity (β = 0.19, p < .05). UE maximal-effect loci were lateral, anterior, and dorsal to LE loci, but were not statistically resolved, despite sufficient statistical power to resolve differences of ≤0.48 mm (p < .05) between maximally effective loci of stimulation. CONCLUSION STN DBS produces differential effects on UE and LE rigidity, but not for tremor or bradykinesia. This finding is not explained by distinct UE and LE loci of maximally effective stimulation. Instead, we hypothesize that downstream effects of STN DBS on motor networks and limb biomechanics are responsible for observed differences in UE and LE responses.
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Affiliation(s)
- Asra Askari
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA
| | - Brandon J Zhu
- Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA
| | - Xiru Lyu
- Department of Statistics, University of Michigan, Ann Arbor, MI, USA
| | - Kelvin L Chou
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA; Department of Neurology, University of Michigan, Ann Arbor, MI, USA
| | - Parag G Patil
- Department of Neurosurgery, University of Michigan, Ann Arbor, MI, USA; Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA; Department of Neurology, University of Michigan, Ann Arbor, MI, USA.
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Liu Y, Xiao B, Zhang C, Li J, Lai Y, Shi F, Shen D, Wang L, Sun B, Li Y, Jin Z, Wei H, Haacke EM, Zhou H, Wang Q, Li D, He N, Yan F. Predicting Motor Outcome of Subthalamic Nucleus Deep Brain Stimulation for Parkinson's Disease Using Quantitative Susceptibility Mapping and Radiomics: A Pilot Study. Front Neurosci 2021; 15:731109. [PMID: 34557069 PMCID: PMC8452872 DOI: 10.3389/fnins.2021.731109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2021] [Accepted: 08/17/2021] [Indexed: 12/02/2022] Open
Abstract
Background Emerging evidence indicates that iron distribution is heterogeneous within the substantia nigra (SN) and it may reflect patient-specific trait of Parkinson’s Disease (PD). We assume it could account for variability in motor outcome of subthalamic nucleus deep brain stimulation (STN-DBS) in PD. Objective To investigate whether SN susceptibility features derived from radiomics with machine learning (RA-ML) can predict motor outcome of STN-DBS in PD. Methods Thirty-three PD patients underwent bilateral STN-DBS were recruited. The bilateral SN were segmented based on preoperative quantitative susceptibility mapping to extract susceptibility features using RA-ML. MDS-UPDRS III scores were recorded 1–3 days before and 6 months after STN-DBS surgery. Finally, we constructed three predictive models using logistic regression analyses: (1) the RA-ML model based on radiomics features, (2) the RA-ML+LCT (levodopa challenge test) response model which combined radiomics features with preoperative LCT response, (3) the LCT response model alone. Results For the predictive performances of global motor outcome, the RA-ML model had 82% accuracy (AUC = 0.85), while the RA-ML+LCT response model had 74% accuracy (AUC = 0.83), and the LCT response model alone had 58% accuracy (AUC = 0.55). For the predictive performance of rigidity outcome, the accuracy of the RA-ML model was 80% (AUC = 0.85), superior to those of the RA-ML+LCT response model (76% accuracy, AUC = 0.82), and the LCT response model alone (58% accuracy, AUC = 0.42). Conclusion Our findings demonstrated that SN susceptibility features from radiomics could predict global motor and rigidity outcomes of STN-DBS in PD. This RA-ML predictive model might provide a novel approach to counsel candidates for STN-DBS.
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Affiliation(s)
- Yu Liu
- Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Bin Xiao
- School of Biomedical Engineering, Institute for Medical Imaging Technology, Shanghai Jiao Tong University, Shanghai, China
| | - Chencheng Zhang
- Department of Neurosurgery, Center for Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Junchen Li
- Department of Radiology, Changshu Hospital Affiliated to Nanjing University of Chinese Medicine, Changshu, China
| | - Yijie Lai
- Department of Neurosurgery, Center for Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Feng Shi
- Shanghai United Imaging Intelligence Co., Ltd., Shanghai, China
| | - Dinggang Shen
- Shanghai United Imaging Intelligence Co., Ltd., Shanghai, China.,School of Biomedical Engineering, ShanghaiTech University, Shanghai, China.,Department of Artificial Intelligence, Korea University, Seoul, South Korea
| | - Linbin Wang
- Department of Neurosurgery, Center for Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Bomin Sun
- Department of Neurosurgery, Center for Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Yan Li
- Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Zhijia Jin
- Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Hongjiang Wei
- School of Biomedical Engineering, Med-X Research Institute, Shanghai Jiao Tong University, Shanghai, China
| | - Ewart Mark Haacke
- Department of Radiology, Wayne State University, Detroit, MI, United States
| | - Haiyan Zhou
- Department of Neurology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Qian Wang
- School of Biomedical Engineering, Institute for Medical Imaging Technology, Shanghai Jiao Tong University, Shanghai, China
| | - Dianyou Li
- Department of Neurosurgery, Center for Functional Neurosurgery, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Naying He
- Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
| | - Fuhua Yan
- Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai, China
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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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