1
|
Piastra MC, Oostenveld R, Homölle S, Han B, Chen Q, Oostendorp T. How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data. Front Hum Neurosci 2024; 18:1279183. [PMID: 38410258 PMCID: PMC10894995 DOI: 10.3389/fnhum.2024.1279183] [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: 08/17/2023] [Accepted: 01/25/2024] [Indexed: 02/28/2024] Open
Abstract
Introduction Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation. Methods In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients. Results Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes. Discussion Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.
Collapse
Affiliation(s)
- Maria Carla Piastra
- Clinical Neurophysiology, Faculty of Science and Technology, Technical Medical Centre, University of Twente, Enschede, Netherlands
- Department of Cognitive Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands
| | - Robert Oostenveld
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands
- NatMEG, Karolinska Institutet, Stockholm, Sweden
| | - Simon Homölle
- Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands
| | - Biao Han
- School of Psychology, South China Normal University, Guangzhou, China
| | - Qi Chen
- School of Psychology, South China Normal University, Guangzhou, China
| | - Thom Oostendorp
- Department of Cognitive Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands
| |
Collapse
|
2
|
Bruña R, Fuggetta G, Pereda E. One Definition to Join Them All: The N-Spherical Solution for the EEG Lead Field. SENSORS (BASEL, SWITZERLAND) 2023; 23:8136. [PMID: 37836967 PMCID: PMC10575356 DOI: 10.3390/s23198136] [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: 06/19/2023] [Revised: 09/07/2023] [Accepted: 09/26/2023] [Indexed: 10/15/2023]
Abstract
Albeit its simplicity, the concentric spheres head model is widely used in EEG. The reason behind this is its simple mathematical definition, which allows for the calculation of lead fields with negligible computational cost, for example, for iterative approaches. Nevertheless, the literature shows contradictory formulations for the electrical solution of this head model. In this work, we study several different definitions for the electrical lead field of a four concentric spheres conduction model, finding that their results are contradictory. A thorough exploration of the mathematics used to build these formulations, provided in the original works, allowed for the identification of errors in some of the formulae, which proved to be the reason for the discrepancies. Moreover, this mathematical review revealed the iterative nature of some of these formulations, which allowed us to develop a formulation to solve the lead field in a head model built from an arbitrary number of concentric, homogeneous, and isotropic spheres.
Collapse
Affiliation(s)
- Ricardo Bruña
- Center for Cognitive and Computational Neuroscience, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain;
- Department of Radiology, Rehabilitation and Physical Therapy, Universidad Complutense de Madrid (UCM), IdISSC, 28040 Madrid, Spain
| | - Giorgio Fuggetta
- School of Psychology, University of Roehampton, London SW15 4JD, UK;
| | - Ernesto Pereda
- Center for Cognitive and Computational Neuroscience, Universidad Complutense de Madrid (UCM), 28040 Madrid, Spain;
- Department of Industrial Engineering, Institute of Neuroscience & Institute of Biomedical Technology, Universidad de La Laguna, 38200 Tenerife, Spain
| |
Collapse
|
3
|
Maksymenko K, Clarke AK, Mendez Guerra I, Deslauriers-Gauthier S, Farina D. A myoelectric digital twin for fast and realistic modelling in deep learning. Nat Commun 2023; 14:1600. [PMID: 36959193 PMCID: PMC10036636 DOI: 10.1038/s41467-023-37238-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2022] [Accepted: 03/08/2023] [Indexed: 03/25/2023] Open
Abstract
Muscle electrophysiology has emerged as a powerful tool to drive human machine interfaces, with many new recent applications outside the traditional clinical domains, such as robotics and virtual reality. However, more sophisticated, functional, and robust decoding algorithms are required to meet the fine control requirements of these applications. Deep learning has shown high potential in meeting these demands, but requires a large amount of high-quality annotated data, which is expensive and time-consuming to acquire. Data augmentation using simulations, a strategy applied in other deep learning applications, has never been attempted in electromyography due to the absence of computationally efficient models. We introduce a concept of Myoelectric Digital Twin - highly realistic and fast computational model tailored for the training of deep learning algorithms. It enables simulation of arbitrary large and perfectly annotated datasets of realistic electromyography signals, allowing new approaches to muscular signal decoding, accelerating the development of human-machine interfaces.
Collapse
Affiliation(s)
| | | | | | | | - Dario Farina
- Department of Bioengineering, Imperial College London, London, UK.
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
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: 3] [Impact Index Per Article: 1.0] [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.
Collapse
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
| |
Collapse
|
6
|
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.
Collapse
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:
| |
Collapse
|
7
|
Piastra MC, Nüßing A, Vorwerk J, Clerc M, Engwer C, Wolters CH. A comprehensive study on electroencephalography and magnetoencephalography sensitivity to cortical and subcortical sources. Hum Brain Mapp 2021; 42:978-992. [PMID: 33156569 PMCID: PMC7856654 DOI: 10.1002/hbm.25272] [Citation(s) in RCA: 32] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Revised: 10/19/2020] [Accepted: 10/21/2020] [Indexed: 12/31/2022] Open
Abstract
Signal-to-noise ratio (SNR) maps are a good way to visualize electroencephalography (EEG) and magnetoencephalography (MEG) sensitivity. SNR maps extend the knowledge about the modulation of EEG and MEG signals by source locations and orientations and can therefore help to better understand and interpret measured signals as well as source reconstruction results thereof. Our work has two main objectives. First, we investigated the accuracy and reliability of EEG and MEG finite element method (FEM)-based sensitivity maps for three different head models, namely an isotropic three and four-compartment and an anisotropic six-compartment head model. As a result, we found that ignoring the cerebrospinal fluid leads to an overestimation of EEG SNR values. Second, we examined and compared EEG and MEG SNR mappings for both cortical and subcortical sources and their modulation by source location and orientation. Our results for cortical sources show that EEG sensitivity is higher for radial and deep sources and MEG for tangential ones, which are the majority of sources. As to the subcortical sources, we found that deep sources with sufficient tangential source orientation are recordable by the MEG. Our work, which represents the first comprehensive study where cortical and subcortical sources are considered in highly detailed FEM-based EEG and MEG SNR mappings, sheds a new light on the sensitivity of EEG and MEG and might influence the decision of brain researchers or clinicians in their choice of the best modality for their experiment or diagnostics, respectively.
Collapse
Affiliation(s)
- Maria Carla Piastra
- Institute for Biomagnetism and BiosignalanalysisUniversity of MünsterMünsterGermany
- Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
- Cognitive Neuroscience, Donders Institute for Brain, Cognition and Behaviour, Radboud University Nijmegen Medical CenterNijmegenThe Netherlands
| | - Andreas Nüßing
- Institute for Biomagnetism and BiosignalanalysisUniversity of MünsterMünsterGermany
- Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
| | - Johannes Vorwerk
- Institute of Electrical and Biomedical Engineering, University for Health SciencesMedical Informatics and TechnologyHall in TirolAustria
| | - Maureen Clerc
- Inria Sophia Antipolis‐MediterranéeBiotFrance
- Université Côte d'AzurNiceFrance
| | - Christian Engwer
- Institute for Computational and Applied MathematicsUniversity of MünsterMünsterGermany
- Cluster of Excellence EXC 1003, Cells in Motion, CiM, University of MünsterMünsterGermany
| | - Carsten H. Wolters
- Institute for Biomagnetism and BiosignalanalysisUniversity of MünsterMünsterGermany
- Otto Creutzfeldt Center for Cognitive and Behavioral Neuroscience, University of MünsterMünsterGermany
| |
Collapse
|
8
|
Avery J, Dowrick T, Witkowska-Wrobel A, Faulkner M, Aristovich K, Holder D. Simultaneous EIT and EEG using frequency division multiplexing. Physiol Meas 2019; 40:034007. [DOI: 10.1088/1361-6579/ab0bbc] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
9
|
Aristovich K, Donegá M, Blochet C, Avery J, Hannan S, Chew DJ, Holder D. Imaging fast neural traffic at fascicular level with electrical impedance tomography: proof of principle in rat sciatic nerve. J Neural Eng 2018; 15:056025. [DOI: 10.1088/1741-2552/aad78e] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
10
|
Witkowska-Wrobel A, Aristovich K, Faulkner M, Avery J, Holder D. Feasibility of imaging epileptic seizure onset with EIT and depth electrodes. Neuroimage 2018; 173:311-321. [DOI: 10.1016/j.neuroimage.2018.02.056] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2017] [Revised: 02/22/2018] [Accepted: 02/26/2018] [Indexed: 11/27/2022] Open
|
11
|
Pursiainen S, Lew S, Wolters CH. Forward and inverse effects of the complete electrode model in neonatal EEG. J Neurophysiol 2016; 117:876-884. [PMID: 27852731 PMCID: PMC5338621 DOI: 10.1152/jn.00427.2016] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2016] [Accepted: 11/10/2016] [Indexed: 11/24/2022] Open
Abstract
The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary. This paper investigates finite element method-based modeling in the context of neonatal electroencephalography (EEG). In particular, the focus lies on electrode boundary conditions. We compare the complete electrode model (CEM) with the point electrode model (PEM), which is the current standard in EEG. In the CEM, the voltage experienced by an electrode is modeled more realistically as the integral average of the potential distribution over its contact surface, whereas the PEM relies on a point value. Consequently, the CEM takes into account the subelectrode shunting currents, which are absent in the PEM. In this study, we aim to find out how the electrode voltage predicted by these two models differ, if standard size electrodes are attached to a head of a neonate. Additionally, we study voltages and voltage variation on electrode surfaces with two source locations: 1) next to the C6 electrode and 2) directly under the Fz electrode and the frontal fontanel. A realistic model of a neonatal head, including a skull with fontanels and sutures, is used. Based on the results, the forward simulation differences between CEM and PEM are in general small, but significant outliers can occur in the vicinity of the electrodes. The CEM can be considered as an integral part of the outer head model. The outcome of this study helps understanding volume conduction of neonatal EEG, since it enlightens the role of advanced skull and electrode modeling in forward and inverse computations. NEW & NOTEWORTHY The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary.
Collapse
Affiliation(s)
- S Pursiainen
- Department of Mathematics, Tampere University of Technology, Tampere, Finland;
| | - S Lew
- Newborn Medicine in the Boston Children's Hospital, Boston, Massachusetts.,Department of Engineering, Olivet Nazarene University, Bourbonnais, Illinois; and
| | - C H Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany
| |
Collapse
|
12
|
Nusing A, Wolters CH, Brinck H, Engwer C. The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem. IEEE Trans Biomed Eng 2016; 63:2564-2575. [PMID: 27416584 DOI: 10.1109/tbme.2016.2590740] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
OBJECTIVE The purpose of this study is to introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the electroencephalography (EEG) forward problem. METHODS This new approach for source analysis does not use a geometry conforming volume triangulation, but instead uses a structured mesh that does not resolve the geometry. The geometry is described using level set functions and is incorporated implicitly in its mathematical formulation. As no triangulation is necessary, the complexity of a simulation pipeline and the need for manual interaction for patient-specific simulations can be reduced and is comparable with that of the FEM for hexahedral meshes. In addition, it maintains conservation laws on a discrete level. Here, we present the theory for UDG-FEM forward modeling, its verification using quasi-analytical solutions in multilayer sphere models and an evaluation in a comparison with a discontinuous Galerkin (DG-FEM) method on hexahedral and on conforming tetrahedral meshes. We furthermore apply the UDG-FEM forward approach in a realistic head model simulation study. RESULTS The results show convergence to the quasi-analytical solution and indicate a good accuracy of UDG-FEM. UDG-FEM performs comparable or even better than DG-FEM on a conforming tetrahedral mesh while providing a less complex simulation pipeline. When compared to DG-FEM on hexahedral meshes, an overall better accuracy is achieved. CONCLUSION The UDG-FEM approach is an accurate, flexible, and promising method to solve the EEG forward problem. SIGNIFICANCE This study shows the first application of the UDG-FEM approach to the EEG forward problem.
Collapse
|
13
|
Wagner S, Lucka F, Vorwerk J, Herrmann CS, Nolte G, Burger M, Wolters CH. Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem. Neuroimage 2016; 140:163-73. [PMID: 27125841 DOI: 10.1016/j.neuroimage.2016.04.005] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2015] [Revised: 03/14/2016] [Accepted: 04/03/2016] [Indexed: 01/12/2023] Open
Abstract
To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.
Collapse
Affiliation(s)
- S Wagner
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany
| | - F Lucka
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany; Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany; Centre for Medical Image Computing, University College London, WC1E 6BT London, UK
| | - J Vorwerk
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany
| | - C S Herrmann
- Experimental Psychology Lab, Center for Excellence Hearing4all, European Medical School, University of Oldenburg, Oldenburg, Germany
| | - G Nolte
- Department of Neurophysiology and Pathophysiology, University Medical Center Hamburg-Eppendorf, Hamburg, Germany
| | - M Burger
- Institute for Computational and Applied Mathematics, University of Münster, Münster, Germany; Cells in Motion Cluster of Excellence, University of Münster, Münster, Germany
| | - C H Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany; Cells in Motion Cluster of Excellence, University of Münster, Münster, Germany.
| |
Collapse
|
14
|
A finite-element reciprocity solution for EEG forward modeling with realistic individual head models. Neuroimage 2014; 103:542-551. [DOI: 10.1016/j.neuroimage.2014.08.056] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2014] [Revised: 08/27/2014] [Accepted: 08/30/2014] [Indexed: 11/21/2022] Open
|
15
|
Steinsträter O, Sillekens S, Junghoefer M, Burger M, Wolters CH. Sensitivity of beamformer source analysis to deficiencies in forward modeling. Hum Brain Mapp 2010; 31:1907-27. [PMID: 21086549 DOI: 10.1002/hbm.20986] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
Abstract
Beamforming approaches have recently been developed for the field of electroencephalography (EEG) and magnetoencephalography (MEG) source analysis and opened up new applications within various fields of neuroscience. While the number of beamformer applications thus increases fast-paced, fundamental methodological considerations, especially the dependence of beamformer performance on leadfield accuracy, is still quite unclear. In this article, we present a systematic study on the influence of improper volume conductor modeling on the source reconstruction performance of an EEG-data based synthetic aperture magnetometry (SAM) beamforming approach. A finite element model of a human head is derived from multimodal MR images and serves as a realistic volume conductor model. By means of a theoretical analysis followed by a series of computer simulations insight is gained into beamformer performance with respect to reconstruction errors in peak location, peak amplitude, and peak width resulting from geometry and anisotropy volume conductor misspecifications, sensor noise, and insufficient sensor coverage. We conclude that depending on source position, sensor coverage, and accuracy of the volume conductor model, localization errors up to several centimeters must be expected. As we could show that the beamformer tries to find the best fitting leadfield (least squares) with respect to its scanning space, this result can be generalized to other localization methods. More specific, amplitude, and width of the beamformer peaks significantly depend on the interaction between noise and accuracy of the volume conductor model. The beamformer can strongly profit from a high signal-to-noise ratio, but this requires a sufficiently realistic volume conductor model.
Collapse
Affiliation(s)
- Olaf Steinsträter
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Münster, Germany.
| | | | | | | | | |
Collapse
|