The FieldTripSimBio pipeline for EEG forward solutions
Abstract
Background
Accurately solving the electroencephalography (EEG) forward problem is crucial for precise EEG source analysis. Previous studies have shown that the use of multicompartment head models in combination with the finite element method (FEM) can yield high accuracies both numerically and with regard to the geometrical approximation of the human head. However, the workload for the generation of multicompartment head models has often been too high and the use of publicly available FEM implementations too complicated for a wider application of FEM in research studies. In this paper, we present a MATLABbased pipeline that aims to resolve this lack of easytouse integrated software solutions. The presented pipeline allows for the easy application of fivecompartment head models with the FEM within the FieldTrip toolbox for EEG source analysis.
Methods
The FEM from the SimBio toolbox, more specifically the St. Venant approach, was integrated into the FieldTrip toolbox. We give a short sketch of the implementation and its application, and we perform a source localization of somatosensory evoked potentials (SEPs) using this pipeline. We then evaluate the accuracy that can be achieved using the automatically generated fivecompartment hexahedral head model [skin, skull, cerebrospinal fluid (CSF), gray matter, white matter] in comparison to a highly accurate tetrahedral head model that was generated on the basis of a semiautomatic segmentation with very careful and timeconsuming manual corrections.
Results
The source analysis of the SEP data correctly localizes the P20 component and achieves a high goodness of fit. The subsequent comparison to the highly detailed tetrahedral head model shows that the automatically generated fivecompartment head model performs about as well as a highly detailed fourcompartment head model (skin, skull, CSF, brain). This is a significant improvement in comparison to a threecompartment head model, which is frequently used in praxis, since the importance of modeling the CSF compartment has been shown in a variety of studies.
Conclusion
The presented pipeline facilitates the use of fivecompartment head models with the FEM for EEG source analysis. The accuracy with which the EEG forward problem can thereby be solved is increased compared to the commonly used threecompartment head models, and more reliable EEG source reconstruction results can be obtained.
Keywords
Source analysis Forward modeling Finite element method Volume conductor modelingBackground
In many applications of electroencephalography (EEG), it is desirable to reconstruct the active brain areas that generate the measured signals to achieve a better understanding of the neural processes. The reconstruction of these sources is called EEG source analysis; this reconstruction can be split into two mathematical problems, the EEG forward and the EEG inverse problem. Whereas the EEG forward problem consists of simulating the electric potential at the head surface that is generated by a microscopic source of brain activity, the EEG inverse problem aims at reconstructing a distribution of such sources that can explain the measured signal. Therefore, the accuracy of EEG source analysis directly depends on the accuracy that is achieved in solving the EEG forward problem.
To solve the EEG forward problem with high accuracy, the volume conductor model \(\Omega \) should reflect the head geometry as well as possible. The importance of detailed volume conductor models for an accurate inverse analysis has been demonstrated in various studies [3, 4, 5], especially the influence of distinguishing gray matter, white matter, and cerebrospinal fluid (CSF) instead of modeling a homogeneous brain compartment [6].
In order to be able to incorporate realistic head geometries \(\Omega \), numerical methods to solve Eq. (1) are necessary. Different numerical methods have been proposed to solve the EEG forward problem (1), e.g., boundary element methods (BEM) [7, 8, 9], finite volume methods (FVM) [10], finite difference methods (FDM) [11, 12], or finite element methods (FEM) [13, 14, 15, 16, 17]. BEMs are commonly used in combination with simplified threelayer head models (skin, skull, brain), whereas FEM and FDM offer the possibility of modeling more complex geometries and also anisotropic conductivities, with only weak influence on the computational effort [6]. Finite element methods have been shown to achieve high numerical accuracies [13, 18], and the computational burden has been clearly reduced by the introduction of transfer matrices and fast solver techniques [19].
To solve (1) numerically, a discretization of the head domain \(\Omega \) has to be generated. The FEM can be used with different kinds of head models. Surfacebased tetrahedral head models generated from triangulations of the compartment boundaries allow for the accurate modeling of compartments of complicated shape, e.g., the strongly folded interface between cortex and CSF. These head models are generated based on surface triangulations of the compartment boundaries. Subsequently, a volume discretization of \(\Omega \) into tetrahedral elements respecting these boundaries is generated using methods such as the constrained Delaunay tetrahedralization [20]. The surfaces have to be nonintersecting/touching and should have a sufficient distance between each other, which are constraints shared with the surfaces generated for BEM approaches. A common argument against the use of realistic surfacebased tetrahedral head models that include more than the commonly used three compartments is the great effort that is necessary to construct these models.
The generation of the surface discretizations that are necessary for the construction of the tetrahedral head model can be especially complicated and time consuming. The additional consideration of skull holes—be it naturally existing ones such as the foramen magnum or those that are a consequence of brain surgery—as suggested by [12, 21], further complicates the generation of tetrahedral head models due to the more complicated compartment topologies. A possible approach to simplifying the head model generation is to use hexahedral head models generated directly out of segmented magnetic resonance images (MRIs) of the human head, which is done in this pipeline. To avoid the occurence of staircase effects, the generation of geometryadapted meshes is implemented [22].
A further common argument against the wider use of FEM in praxis is the lack of easily accessible integrated software solutions. The goal of the pipeline presented in this paper is to resolve this problem. A MATLABbased—and therefore multiplatform—FEM pipeline that is integrated in the FieldTriptoolbox (http://www.fieldtriptoolbox.org, [23]) is presented and evaluated in this work. The pipeline allows for the easy computation of accurate solutions to the EEG forward problem using the FEM with automatically generated geometryadapted hexahedral head models. Through the integration into FieldTrip, this pipeline also directly makes data preprocessing, as well as other tools for further analysis, e.g., source reconstruction, available. Furthermore, the integration into FieldTrip makes this pipeline available for users of other toolboxes such as EEGLAB (https://sccn.ucsd.edu/eeglab/) and SPM (http://www.fil.ion.ucl.ac.uk/spm/) that rely on FieldTrip for EEG forward computations.
In this manuscript, we describe the methodology we used to establish the pipeline, the implementation and workflow of the pipeline, a source reconstruction of somatosensory evoked potentials (SEP), and a basic evaluation of the accuracy of forward solutions computed with the obtained realistic fivecompartment head model.
Methods
Segmentation and hexahedral mesh generation
As the first step to generate segmentations in the FieldTripSimBio pipeline, the SPM toolbox is used to compute masks of gray matter, white matter, and CSF based on a T1MRI. A rough skull segmentation is created by dilating the union of these three masks, and a segmentation of the skin compartment is obtained by thresholding the MR image and subtracting the other masks.
Subsequently, a hexahedral mesh is generated directly based on this segmentation. To avoid staircase effects, geometryadapted hexahedral meshes can be created in which mesh nodes at tissue boundaries are slightly shifted to obtain a more smooth representation of the boundaries [22, 24]. Examples of the use of geometryadapted hexahedral meshes can be found in the studies of [25, 26, 27]; evaluations of the numerical accuracy achieved using geometryadapted hexahedral meshes in sphere models were performed by [24, 28].
The finite element method for solving the EEG forward problem
Evaluation
Two kinds of evaluations are presented in this manuscript. To demonstrate the functionality of the pipeline, we performed a source reconstruction of SEP data using the FieldTripSimBio pipeline and visualized the results of the different computation steps. To offer a basic impression of the accuracy that can be achieved using the automatically generated fivecompartment head models, we compared forward solutions obtained with such a fivecompartment hexahedral head model generated using the FieldTripSimBio pipeline to forward solutions that were computed using highly detailed surfacebased tetrahedral head models of the same subject that distinguished between three (skin, skull, brain) and six compartments (skin, skull spongiosa, skull compacta, CSF, gray matter, white matter).
Source localization of SEP data
We measured and evaluated a singlesubject dataset consisting of MRIs and SEP data. All procedures were approved by the ethics committee of the University of Erlangen, Faculty of Medicine on 10. 05. 2011 (Ref. No. 4453). A healthy 23yearold male volunteer subject was informed about the purpose of the study and gave written consent to participate, in accordance with local ethical regulations.
A T1weighted (T1w)MRI scan of the subject was acquired with a 3 T MR scanner (Magnetom Prisma, Siemens, Munich, Germany) using a 32channel head coil. An MPRAGE pulse sequence (TR/TE/TI/FA = 2300 ms/3.5 ms/1100 ms/8°, FOV = 256 × 256 × 192 mm, voxel size = 1 × 1 × 1 mm) with water selective excitation was used. An 80channel EEG and electrocardiography (ECG) were measured simultaneously. The EEG cap had 74 Ag/AgCl sintered ring electrodes placed equidistantly according to the 10–10 system (EASYCAP GmbH, Herrsching, Germany). In addition to the 74 electrodes, 6 channels were available and used for both eye movement detection (with a bipolar software montage) and source reconstruction. The electrode locations were digitized with a Polhemus Fastrak system (Polhemus Incorporated, Colchester, Vermont, USA) prior to the measurement. The EEG was measured with the subject in supine position to prevent erroneous CSF effects due to brain shift when combining EEG and MRI, following the results of [32]. To generate SEP data, one measurement run with electrical stimulation of the left median nerve and varying interstimulus interval (ISI) to avoid habituation (ISI: 350–450 ms, pulse duration 0.5 ms) was recorded at a frequency of 1200 Hz, resulting in 967 trials.
Head model accuracy
To evaluate the accuracy of the results achieved with the FieldTripSimBio pipeline, we compared forward solutions obtained with a fivecompartment hexahedral head model generated using the pipeline to forward solutions that were computed using highly detailed surfacebased tetrahedral head models of the same subject that distinguished between three (skin, skull, brain) and six compartments (skin, skull spongiosa, skull compacta, CSF, gray matter, white matter) and white matter anisotropy [6]. Otherwise, the computation pipeline to compute the forward solutions was not altered. The generation of the head models used in [6] involved extensive manual correction of the initial segmentation to obtain highly detailed surfaces of the compartment interfaces. This sixcompartment (skin, skull compacta, skull spongiosa, CSF, gray matter, white matter) head model contains numerous details, such as realistic skull openings and white matter anisotropy. The simplified versions of the highly detailed tetrahedral head model were generated by neglecting some model details, as described below, to evaluate the effects of modeling or neglecting certain conductive compartments. A tetrahedral head model with a higher resolution was used as a reference to obtain the numerical error. In this study, we generated a fivecompartment head model using the FieldTripSimBio pipeline within a few minutes, which is based on the same MRI data, and compared the accuracy of this simple model to that of the different versions of the tetrahedral head model.
The fivecompartment hexahedral head model that was generated based on the segmentation of a T1MRI using the FieldTripSimbio pipeline (Fig. 3) is denoted 5CI_hex_ft (5 Compartment Isotropic HEXahedral FieldTrip) hereinafter. To classify the accuracy of the newly generated head model 5CI_hex_ft, we compared it to different simplified head models as described in [6], starting from a threecompartment model (skin, skull, brain; 3CI—3 Compartment Isotropic). Subsequently, a CSF compartment (4CI), gray and white matter distinction (5CI), skull spongiosa and compacta distinction (6CI), and white matter anisotropy (6CA—6 Compartment Anisotropic) were also modeled.
The electrode positions were aligned with the model surface. We regularly distributed source positions in the gray matter [6]; those that are valid positions in both the tetrahedral and the hexahedral head models (i.e., the mesh vertex next to the source position is fully inside the gray matter compartment) were selected, which led to 89,902 remaining sources. For each source position, a normal constraint was applied, i.e., the source direction was chosen to be orthogonal to the white matter surface. Reference solutions were computed using a highresolution model 6CA_hr.
Implementation
The segmentation algorithm distinguishing the five compartments (white matter, gray matter, CSF, skull, skin) in the individual MRIs, as described in "Segmentation and hexahedral mesh generation" section, was already available in the FieldTrip toolbox (based on code of the SPM toolbox, http://www.fil.ion.ucl.ac.uk/spm/) through the function ft_volumesegment. Two additional features were required to enable the computation of EEG forward solutions using realistic multicompartment head volume conductor models: the generation of geometryadapted hexahedral meshes from the segmented images and the computation of FEM forward solutions using these meshes. To obtain these functionalities, the required lowlevel code was implemented and integrated into the highlevel functions of the common FieldTrip workflow.
Hexahedral mesh generation
For the generation of geometryadapted hexahedral meshes, the function prepare_mesh_hexahedral was created; a sketch of the function call is shown in Fig. 1. This function allows the generation of geometryadapted hexahedral meshes directly from segmented MR images. A basic fivecompartment segmentation of a T1MRI as input to this method can be generated using the function ft_volumesegment (cf. "Segmentation and hexahedral mesh generation" section). For more detailed (skull) segmentations, results from other toolboxes such as SPM (http://www.fil.ion.ucl.ac.uk/spm/), FSL (http://www.fmrib.ox.ac.uk/fsl), and BrainSuite (http://brainsuite.org) or from commercial tools like BESA (http://www.besa.de) and Curry (http://www.neuroscan.com) can be included at this point. Additional options for the mesh creation are generating geometryadapted meshes with varying nodeshift parameters (cf. "Segmentation and hexahedral mesh generation" section; [22, 24]), up/downsampling of the image resolution, or modeling/not modeling the image background. It should be noted that unlike implementing the generation of hexahedral meshes and the fully MATLABbased computation of FEM forward solutions on multiple platforms, improving the segmentation algorithm was not a main goal of the work presented here.
EEG forward solution computation
Following the mesh generation, the next necessary step was to enable the computation of FEM solutions for the EEG forward problem using a fully MATLABbased multiplatform pipeline. Therefore, it was necessary to be able to calculate the stiffness matrix A (cf. Eq. (3), "The finite element method for solving the EEG forward problem" section). The approach we employed was to make the isoparametric FEM implementation from the SimBio toolbox (https://www.mrt.unijena.de/simbio/, [24]) directly accessible in MATLAB. A MATLAB Executable (MEX function) was implemented that enables the execution of the core Fortran functions of the SimBio toolbox from within MATLAB. The MEX function is implemented in Fortran and can be compiled on any platform for which a supported compiler is available (for supported compilers in MATLAB R2017b, see https://www.mathworks.com/support/compilers.html). The resulting function is sb_calc_stiff; a sketch of the function call is shown in Fig. 2. Precompiled binaries of this function for, e.g., most Linux distributions, macOS, and Windows 7/8/10, are available with the FieldTriptoolbox.
 sb_rhs_venant:

calculates the rhsvector \(b^{ven}\) (cf. (4); [24, 30, 31]); takes the mesh geometry and source position and direction as input; output is the rhsvector \(b^{ven}\);
 sb_set_bndcon:

sets the Dirichlet boundary conditions necessary to achieve a unique solution of Eq. (3); takes the stiffness matrix A, the rhsvector b, the Dirichlet nodes, and the Dirichlet values as input; outputs are the stiffness matrix \(\tilde{A}\) and rhsvector \(\tilde{b}\) with implemented Dirichlet boundary conditions;
 sb_solve:

solves the equation system (2) using a conjugate gradient solver with incomplete Cholesky preconditioning and zero fillin (IC(0)CG) [13]; takes the output from sb_set_bndcon, i.e., the stiffness matrix \(\tilde{A}\) and rhsvector \(\tilde{b}\), as input; output is the solution vector u;
 sb_transfer:

computes the EEG transfer matrix \(T^{eeg}\) [19]; takes the stiffness matrix, the mesh geometry, and the sensor positions as input; output is the transfer matrix.
These lowlevel functions were integrated into the highlevel functions of the FieldTrip toolbox to create an easytouse pipeline for FEMbased EEG forward simulations. The resulting pipeline is sketched in Fig. 3. Due to the FieldTrip workflow—which was originally designed for forward analysis using BEM or analytic spherical models—the main computational effort, i.e., the setup of the transfer matrix, is not included in the function ft_prepare_headmodel as one might expect from Fig. 3; instead, only the stiffness matrix A is computed in this function. The transfer matrix \(T^{eeg}\) is subsequently computed in the function ft_prepare_vol_sens, where the sensor information is available to the pipeline functions for the first time (cf. Fig. 3).
Results
Source localization of SEP data
Step  Time [h:min:s] 

Overall  7:17:10 
ft_volumerealign, ft_volumereslice  0:00:01 
ft_volumesegment  0:01:30 
ft_prepare_mesh  0:00:22 
ft_prepare_headmodel  0:03:11 
ft_prepare_vol_sens  6:28:53 
ft_prepare_sourcemodel  0:00:04 
ft_prepare_leadfield  0:42:52 
ft_dipolefitting  0:00:14 
Head model accuracy
Comparing the fully automatic and the manually corrected segmentations (Fig. 7), it is clear that the main inaccuracies of the automatic segmentation are found for the skull mask, which is simply generated by a dilation of the inner skull surface in the FieldTrip pipeline, and in the nose/mouth area, where the contrast of the original image is low. The automatic segmentation of the brain compartments seems to be accurate, possibly even more accurate than the previously generated and manually corrected segmentation underlying the tetrahedral head model, where a minimal distance between outer brain and inner skull surface had to be assured to enable the tetrahedralization, and the ventricles were modeled as white matter to achieve a closed topology of the surfaces.
Figure 8 depicts the deviation of the forward solutions computed with model 5CI_hex_ft in comparison to the modeling effects. At this point, only the errors of model 5CI_hex_ft compared to the models 3CI—6CA are discussed. For a detailed analysis of the differences between the models 3CI—6CA, we refer the reader to the original publication [6]. With regard to the RDM, the errors are similar to those of model 4CI, i.e., a highly detailed fourcompartment model distinguishing skin, skull, CSF, and brain. Looking at the lnMAG, the results for the hexahedral model show a tendency toward an underestimation of source magnitudes. About 70% of the sources have a negative lnMAG value, and 90% of the lnMAG values are in the range from – 0.4 to 0.2. The error range is similar to model 5CI.
Discussion
In this paper, we presented and evaluated the FieldTripSimBio pipeline for finite element EEG forward computations in MATLAB. The pipeline was implemented to allow neuroscientists working with EEG to easily perform computations of EEG forward and inverse solutions using automatically generated fivecompartment (skin, skull, CSF, gray matter, white matter) hexahedral head models and the finite element method. Our goal was to close the gap between methodological studies that show the high accuracy of the FEM and the practial challenges encountered by researchers in scientific praxis. We showed a source reconstruction of SEP data using this pipeline, and we evaluated the forward simulation accuracy that can be achieved with such a simplified head model in comparison to a highly detailed, manually corrected sixcompartment tetrahedral head model for a test subject.
When comparing the simulation accuracy that was achieved with the head model generated using the FieldTripSimbio pipeline, 5CI_hex_ft, with head models 3CI—6CA, the fivecompartment head model 5CI_hex_ft performs about as well as the tetrahedral model 4CI with regard to the RDM (Fig. 8). This result means that the RDM for model 5CI_hex_ft is about the same as that of a highly detailed head model that includes the CSF compartment, but no distinction between gray and white matter, skull compacta and spongiosa, and also no anisotropic white matter conductivity (Fig. 8). With regard to the lnMAG, the absolute values of the error are of less interest, but a small spread of the errors to guarantee the comparability of the strength of different reconstructed sources is more important. Although the lnMAG values for model 5CI_hex_ft are lower than for all other models in the comparison, the spread of the lnMAG is in the same range as that of model 5CI. These results are remarkable given the negligible amount of time invested in model generation. As no manual corrections were applied for the segmentation, the pipeline presented here can be considered a buttonpress pipeline. The results show that through the distinction of CSF, gray matter, and white matter, accuracies that are at least comparable to model 4CI are achieved, which is an important result given the influence of the highly conductive CSF compartment on the EEG forward solution [6]. Although only one test subject was considered here, the underlying segmentation algorithms have been evaluated in previous studies and shown to be accurate [37]. We therefore believe that these results offer the possibility to obtain an estimate of the expected accuracy of the EEG forward simulations calculated using the FieldTripSimBio pipeline in general.
In "Source localization of SEP data" section, a source analysis using measured SEP data (P20/N20 component) was performed. The results of the localization of SEP generated by medianus nerve stimulation are in line with the literature results (cf. Fig. 6; [36]). The overall computation time was about 7 h 17 min. The most timeconsuming steps were the computation of the transfer matrix (in ft_prepare_vol_sens) and the leadfield matrix (ft_prepare_leadfield), with a time effort of about 6 h 29 min and 43 min, respectively. However, both steps can be easily parallelized within MATLAB with an optimal speedup by using parallel loops (parfor). Several lines of the transfer matrix and several forward solutions can thereby be computed in parallel. For a fully parallel implementation, an overall computation time of less than one hour can already be achieved with an eightcore CPU, which can nowadays even be found in portable computers.
The main novelty that is presented in this paper is the possibility for researchers to easily use the St. Venant FEM approach for EEG forward computations from within the FieldTrip toolbox [35]. The St. Venant FEM approach was shown to achieve high numerical accuracies in a variety of studies, both in multicompartment sphere models, where an analytical solution exists and can be used as reference, and in realistic head models. The approach was also shown to be robust, e.g., achieving an accuracy that is essentially independent of the type of mesh, i.e., tetrahedral or hexahedral, the position of the source within the mesh, and the orientation of the source within the mesh, and to allow for fast computation times. The St. Venant FEM approach was compared to other FEM approaches, i.e., partial integration, subtraction, and Whitney, in multiple sphere model studies in both hexahedral and tetrahedral meshes and was shown to achieve the best combination of accuracy, robustness, and computation speed [13, 15, 31, 38]. Furthermore, the St. Venant FEM was also compared to two BEM approaches, the symmetric BEM as implemented in OpenMEEG [39] and a doublelayer BEM approach, in both (tetrahedral) sphere models and in a realistic head model. Again, the St. Venant FEM was shown to achieve high accuracies and fast computation speeds [18]. This study also gave a first hint that differences in numerical accuracy between FEM and BEM approaches are often negligible compared to the effects of model simplifications, such as the use of threecompartment head models. Such head models are commonly used in combination with the BEM, which is the standard forward computation method in the FieldTrip toolbox. The effects of head model simplifications on EEG forward solutions in comparison to the numerical errors were later more thoroughly investigated [6], and a recommendation to distinguish at least five conductive compartments (skin, skull, CSF, gray matter, white matter) was formulated. Through the developments presented in this paper, it is now easy to address this recommendation using the FieldTrip toolbox. In "Head model accuracy" section, we demonstrated the improvements in forward simulation accuracy that can be achieved using a fivecompartment head model generated with the FieldTripSimbio pipeline (head model 5CI_hex_ft) in comparison to a threecompartment head model (head model 3CI), which is commonly used in combination with BEM approaches. Given that the accuracy of the skull segmentation strongly differs in these two models, the improvements achieved by using a fivecompartment head model over a threecompartment head model with the same skull segmentation are expected to be even greater and can be estimated by comparing the results for models 3CI and 5CI.
The main limitations of the presented pipeline concern the (skull) segmentation accuracy. As mentioned in the introduction, little work was invested in this study to improve the accuracy of the MRI segmentation. Differences between the automatically generated and the manually corrected segmentation were found for the segmentation of skull and brain compartment (cf. Figs. 5 and 7). The skull segmentation is generated by a dilation of the inner skull/outer brain surface in the FieldTripSimBio pipeline, which is a simple but robust approach. This segmentation results in a constant skull thickness and thereby a missestimation of the original skull thickness in many areas, which negatively affects the forward solution accuracy due to the major influence of an accurate modeling of the skull on EEG forward solutions [5, 12, 16, 17, 40]. The open nature of the pipeline presented here allows its users to include more accurate skull segmentations from other toolboxes such as SPM, FSL, or BrainSuite. A comparison study including these toolboxes was conducted in [37].
The restrictions of the tetrahedral mesh generation necessitate a sufficient distance between the inner skull and outer brain surface. This distance had to be artificially introduced and is a main cause for the visible differences in the brain segmentation. The significant effect of varying CSF thickness caused by movement of the brain with changing body position of the subject, as demonstrated by [32], may indicate that hexahedral meshes possibly allow for even more realistic modeling in this aspect as they facilitate realistically touching skull and brain compartments. The inaccurate segmentation of the nose/mouth area with FieldTrip should have only a minor influence because the model is nevertheless not cut off directly below the skull following the advice of [21]. The problem of accurately segmenting the scalp surface in the nose/mouth area occurred for only this single dataset, whereas the scalp surface could be nicely estimated using the FieldTripSimBio pipeline in "Source localization of SEP data" section (cf. Fig. 5). Thus, this erroneous segmentation is not a general problem of the segmentation algorithm, but occurs for only some MRI recordings.
Compared to the possible inaccuracies introduced through the limitations of the segmentation, the influence of numerical errors in the forward simulation is expected to be insignificant. As previously discussed, the St. Venant FEM approach achieves a high accuracy and is robust with regard to the possible influence of mesh type and structure. In general, socalled leakage effects, which occur when the thickness of the skull segmentation is only one layer of voxels, so that skull voxels are connected only via edges and nodes but not necessarily faces [41], are a possible source of error for the St. Venant FEM. However, in the presented pipeline, the thickness of the skull layer is ensured to be at least 3 mm, so that such effects would occur only at mesh resolutions of 4 mm or even coarser, which are not recommended due to the generally reduced simulation accuracy. The occurrence of leakage effects can be avoided for general head models with any skull thickness by the use of currentpreserving FEM approaches, such as MixedFEM or discontinuous Galerkin (DG) FEM [16, 17]. A future development goal is to make the approaches implemented in duneuro (http://www.duneuro.org) directly accessible in FieldTrip.
Our results have shown that, using the easytouse and essentially automatic FieldTripSimBio pipeline, EEG forward solutions with accuracies that are comparable to those obtained with a manually corrected four or fivecompartment surfacebased tetrahedral head model can be reached. Previously, the generation of such an accurate head model required a significant amount of nonautomatic model generation work. The pipeline thus offers a clear advantage when compared to the current standard of isotropic threecompartment head models that is still frequently used in EEG source analysis [39, 42, 43].
Conclusion
This paper presented the FieldTripSimBio pipeline for the easy use of FEMbased EEG source analysis. Although the advantages of highly realistic multicompartment volume conductor models have been shown in multiple studies, the issue of the often high workload to create these models remained, especially for tetrahedral models. To allow the practical use of FEM approaches for EEG source analysis on several platforms, the FEM originally implemented in SimBio was integrated into a FieldTrip pipeline. We demonstrated that an automatically generated fivecompartment head model achieved an accuracy that is clearly superior to that of the commonly used isotropic threecompartment head models. Furthermore, we demonstrated the analysis of SEP data using this pipeline, and obtained results that are in line with the literature.
Notes
Authors' contributions
CHW is one of the main developers of the SimBio toolbox that is the basis for the FEM approach implemented here. RO is the main developer of the FieldTrip toolbox. JV performed the majority of the implementation efforts for the integration of the SimBio FEMapproach into the FieldTrip toolbox and designed and conducted the presented evaluations. LM performed implementation work necessary for the integration of the SimBioFEM into the regular FieldTrip processing pipeline. LM and MCP contributed to the optimization and evaluation of the pipeline. All coauthors participated in writing the paper. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
All data generated or analysed during this study are included in this published article (and its Additional files).
Availability and requirements
Project name: FieldTripSimBio; Project home page: http://www.fieldtriptoolbox.org/; Operating systems: Multiplatform (macOS, Linux, Windows); Programming language: MATLAB, Fortran; License: GPL
Ethics approval and consent to participate
The participants signed a written consent form and all procedures were approved by the ethics committee of the University of Erlangen, Faculty of Medicine on 10.05.2011 (Ref. No. 4453).
Funding
This work was supported by the Innovative Training Network ChildBrain, funded by the Marie Curie Actions of the European Commission (H2020MSCAITN2014, Grant Agreement No. 641652), by the Deutsche Forschungsgemeinschaft (DFG) (WO1425/71), by the National Science Foundation (NSF) (US IGNITE  10037840), and by the National Institutes of Health (NIH) (P41, GM102545, “Center for Integrative Biomedical Computing”).
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary material
References
 1.Hämäläinen MS, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV. Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev Mod Phys. 1993;65(2):413–97.CrossRefGoogle Scholar
 2.Brette R, Destexhe A. Handbook of neural activity measurement. Cambridge: Cambridge University Press; 2012.CrossRefGoogle Scholar
 3.Cho JH, Vorwerk J, Wolters CH, Knösche TR. Influence of the head model on EEG and MEG source connectivity analyses. NeuroImage. 2015;110:60–77.CrossRefGoogle Scholar
 4.Neugebauer F, Möddel G, Rampp S, Burger M, Wolters CH. The effect of head model simplification on beamformer source localization. Front Neurosci. 2017;11:625.CrossRefGoogle Scholar
 5.Dannhauer M, Lanfer B, Wolters CH, Knösche TR. Modeling of the human skull in EEG source analysis. Hum Brain Mapp. 2011;32(9):1383–99.CrossRefGoogle Scholar
 6.Vorwerk J, Cho JH, Rampp S, Hamer H, Knösche TR, Wolters CH. A guideline for head volume conductor modeling in EEG and MEG. NeuroImage. 2014;100:590–607.CrossRefGoogle Scholar
 7.Hämäläinen MS, Sarvas J. Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans Biomed Eng. 1989;36(2):165–71.CrossRefGoogle Scholar
 8.Gramfort A, Papadopoulo T, Olivi E, Clerc M. Forward field computation with OpenMEEG. Comput Intell Neurosci. 2011;2011:1–13.CrossRefGoogle Scholar
 9.Stenroos M, Sarvas J. Bioelectromagnetic forward problem: isolated source approach revis(it)ed. Phys Med Biol. 2012;57:3517–35.CrossRefGoogle Scholar
 10.Cook, MJD, Koles ZJ. A highresolution anisotropic finitevolume head model for EEG source analysis. In: Proceedings of the 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society; 2006. p. 4536–9.Google Scholar
 11.Vatta F, Meneghini F, Esposito F, Mininel F, Di Salle F. Solving the forward problem in EEG source analysis by spherical and fdm head modeling: a comparative analysis. Biomed Sci Instrum. 2009;45:382–8.Google Scholar
 12.MontesRestrepo V, van Mierlo P, Strobbe G, Staelens S, Vandenberghe S, Hallez H. Influence of skull modeling approaches on EEG source localization. Brain Topogr. 2014;27(1):95–111.CrossRefGoogle Scholar
 13.Lew S, Wolters CH, Dierkes T, Röer C, MacLeod RS. Accuracy and runtime comparison for different potential approaches and iterative solvers in finite element method based EEG source analysis. Appl Numer Math. 2009;59(8):1970–88.MathSciNetCrossRefzbMATHGoogle Scholar
 14.Drechsler F, Wolters CH, Dierkes T, Si H, Grasedyck L. A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation. NeuroImage. 2009;46(4):1055–65.CrossRefGoogle Scholar
 15.Wolters CH, Köstler H, Möller C, Härdtlein J, Anwander A. Numerical approaches for dipole modeling in finite element method based source analysis. Int Congr Ser. 2007;1300:189–92.CrossRefGoogle Scholar
 16.Engwer C, Vorwerk J, Ludewig J, Wolters CH. A discontinuous Galerkin method to solve the EEG forward problem using the subtraction approach. SIAM J Sci Comput. 2017;39(1):138–64.MathSciNetCrossRefzbMATHGoogle Scholar
 17.Vorwerk J, Engwer C, Pursiainen S, Wolters CH. A mixed finite element method to solve the EEG forward problem. IEEE Trans Med Imaging. 2017;36(4):930–41.CrossRefGoogle Scholar
 18.Vorwerk J, Clerc M, Burger M, Wolters CH. Comparison of boundary element and finite element approaches to the EEG forward problem. Biomed Eng/Biomedizinische Technik. 2012;57(Suppl. 1):795–8.Google Scholar
 19.Wolters CH, Grasedyck L, Hackbusch W. Efficient computation of lead field bases and influence matrix for the FEMbased EEG and MEG inverse problem. Inverse Probl. 2004;20(4):1099–116.MathSciNetCrossRefzbMATHGoogle Scholar
 20.Si H. TetGen: a quality tetrahedral mesh generator and threedimensional delaunay triangulator, V1.3, user’s manual. Technical Report 9, Weierstrass Institute for Applied Analysis and Stochastics; 2004. http://tetgen.berlios.de.
 21.Lanfer B, Scherg M, Dannhauer M, Knösche TR, Burger M, Wolters CH. Influences of skull segmentation inaccuracies on EEG source analysis. NeuroImage. 2012;62(1):418–31.CrossRefGoogle Scholar
 22.Camacho D, Hopper R, Lin G, Myers B. An improved method for finite element mesh generation of geometrically complex structures with application to the skullbase. J Biomech. 1997;30(10):1067–70.CrossRefGoogle Scholar
 23.Oostenveld R, Fries P, Maris E, Schoffelen JM. FieldTrip: open source software for advanced analysis of MEG, EEG, and invasive electrophysiological data. Comput Intell Neurosci. 2011;2011:1.CrossRefGoogle Scholar
 24.Wolters CH, Anwander A, Berti G, Hartmann U. Geometryadapted hexahedral meshes improve accuracy of finite element method based EEG source analysis. IEEE Trans Biomed Eng. 2007;54(8):1446–53.CrossRefGoogle Scholar
 25.Aydin Ü, Rampp S, Wollbrink A, Kugel H, Cho JH, Knösche T, Grova C, Wellmer J, Wolters CH. Zoomed MRI guided by combined EEG/MEG source analysis: A multimodal approach for optimizing presurgical epilepsy workup and its application in a multifocal epilepsy patient case study. Brain Topogr. 2017;30(4):417–33.CrossRefGoogle Scholar
 26.Aydin Ü, Vorwerk J, Dümpelmann M, Küpper P, Kugel H, Heers M, Wellmer J, Kellinghaus C, Haueisen J, Rampp S, Wolters CH. Combined EEG/MEG can outperform single modality EEG or MEG source reconstruction in presurgical epilepsy diagnosis. PLoS ONE. 2015;10(3):e0118753.CrossRefGoogle Scholar
 27.Wagner S, Rampersad SM, Aydin Ü, Vorwerk J, Oostendorp TF, Neuling T, Herrmann CS, Stegeman DF, Wolters CH. Investigation of tDCS volume conduction effects in a highly realistic head model. J Neural Eng. 2014;11:016002.CrossRefGoogle Scholar
 28.Vorwerk J. Comparison of numerical approaches to the EEG forward problem. Diploma thesis in Mathematics, Institut für Biomagnetismus und Biosignalanalyse, Westfälische WilhelmsUniversität Münster; 2011. http://www.sci.utah.edu/%7Ewolters/PaperWolters/2011/VorwerkDiplom.pdf.
 29.Braess D. Finite elements: theory. Cambridge: Fast Solvers and Applications in Solid Mechanics. Cambridge University Press; 2007.CrossRefzbMATHGoogle Scholar
 30.Buchner H, Knoll G, Fuchs M, Rienäcker A, Beckmann R, Wagner M, Silny J, Pesch J. Inverse localization of electric dipole current sources in finite element models of the human head. Electroencephalogr Clin Neurophysiol. 1997;102(4):267–78.CrossRefGoogle Scholar
 31.Pursiainen S, Vorwerk J, Wolters CH. Electroencephalography (EEG) forward modeling via H(div) finite element sources with focal interpolation. Phys Med Biol. 2016;61(24):8502.CrossRefGoogle Scholar
 32.Rice JK, Rorden C, Little JS, Parra LC. Subject position affects EEG magnitudes. NeuroImage. 2013;64:476–84.CrossRefGoogle Scholar
 33.Meijs JWH, Weier OW, Peters MJ, van Oosterom A. On the numerical accuracy of the boundary element method. IEEE Trans Biomed Eng. 1989;36:1038–49.CrossRefGoogle Scholar
 34.Güllmar D, Haueisen J, Reichenbach JR. Influence of anisotropic electrical conductivity in white matter tissue on the EEG/MEG forward and inverse solution. A highresolution whole head simulation study. NeuroImage. 2010;51(1):145–63.CrossRefGoogle Scholar
 35.Buchner H, Knoll G, Fuchs M, Rienäcker A, Beckmann R, Wagner M, Silny J, Pesch J. Inverse localization of electric dipole current sources in finite element models of the human head. Electroencephalogr Clin Neurophysiol. 1997;102:267–78.CrossRefGoogle Scholar
 36.Buchner H, Fuchs M, Wischmann HA, Dössel O, Ludwig I, Knepper A, Berg P. Source analysis of median nerve and finger stimulated somatosensory evoked potentials: multichannel simultaneous recording of electric and magnetic fields combined with 3DMR tomography. Brain Topogr. 1994;6(4):299–310.CrossRefGoogle Scholar
 37.Kazemi K, Noorizadeh N. Quantitative comparison of SPM, FSL, and Brainsuite for brain MR image segmentation. J Biomed Phys Eng. 2014;4(1):13.Google Scholar
 38.Bauer M, Pursiainen S, Vorwerk J, Köstler H, Wolters CH. Comparison study for Whitney (Raviart–Thomas)type source models in finite element method based EEG forward modeling. IEEE Trans Biomed Eng. 2015;62(11):2648–56.CrossRefGoogle Scholar
 39.Gramfort A, Papadopoulo T, Olivi E, Clerc M. OpenMEEG: opensource software for quasistatic bioelectromagnetics. Biomed Eng Online. 2010;9(1):45.CrossRefGoogle Scholar
 40.Lanfer B, PaulJordanov I, Scherg M, Wolters CH. Influence of interior cerebrospinal fluid compartments on EEG source analysis. Biomed Eng/Biomedizinische Technik. 2012;57(Suppl. 1):236.Google Scholar
 41.Sonntag H, Vorwerk J, Wolters CH, Grasedyck L, Haueisen J, Maess B. Leakage effect in hexagonal FEM meshes of the EEG forward problem. In: International Conference on Basic and Clinical Multimodal Imaging (BaCI); 2013.Google Scholar
 42.Stenroos M, Nummenmaa A. Incorporating and compensating cerebrospinal fluid in surfacebased forward models of magnetoand electroencephalography. PLoS ONE. 2016;11(7):0159595.CrossRefGoogle Scholar
 43.Fuchs M, Wagner M, Wischmann HA, Köhler T, Theißen A, Drenckhahn R, Buchner H. Improving source reconstructions by combining bioelectric and biomagnetic data. Electroencephalogr Clin Neurophysiol. 1998;107:93–111.CrossRefGoogle Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.