Realistic head model: FEM with DUNEuro

[TUTORIAL UNDER REVISION]

Authors: Takfarinas Medani, Juan Garcia-Prieto, Francois Tadel, Sophie Schrader, Anand Joshi, Christian Engwer, Carsten Wolters, John Mosher and Richard Leahy

This tutorial explains how to use DUNEuro to compute the forward model using the finite element method (FEM). The FEM methods use a realistic volume mesh of the head generated from the segmentation of the MRI. The FEM models provide more accurate results than the spherical forward models and more realistic geometry and tissue properties than the BEM methods.

The scope of this page is limited to a basic example (head model with 3 layers). More advanced options for mesh generation and forward model computation are discussed in other tutorials: FEM mesh generation, FEM tensors estimation, FEM median nerve example. We assume that you have already followed the introduction tutorials, we will not discuss the general principles of forward modeling here.

DUNEuro

DUNEuro is an open-source C++ software library for solving partial differential equations (PDE) in neurosciences using mesh-based methods. It is based on the DUNE library and its main features include solving the EEG and MEG forward problem and providing simulations for brain stimulation.

As distributed on the DUNEuro GitLab, the source code works only on Linux operating systems. Interfaces to Matlab and Python are possible, but you need to install and compile DUNEuro by yourself. For Brainstorm, we adapted this code and were able to generate binaries for the main operating systems (Windows, Linux and MacOS), which are downloaded automatically when needed as a Brainstorm plugin. This project is available on our GitHub repository bst-duneuro.

We would like to thank the DUNEuro team for their help with this integration work: Carsten Wolters, Christian Engwer, Sophie Schrader, Andreas Nuessing, Tim Erdbruegger, Marios Antonakakis, Johannes Vorwerk & Maria Carla Piastra.

Please cite the following papers if you use this software in your work:

• Medani T, Garcia-Prieto J, Tadel F, Schrader S, Antonakakis M, Joshi A, Engwer C, Wolters CH, Mosher JC, Leahy RM, Realistic head modeling of electromagnetic brain activity: an integrated Brainstorm-DUNEuro pipeline from MRI data to the FEM solutions (preprint), SPIE Medical Imaging (2021)

Publications that make use of, or extend the DUNEuro library (listed on the duneuro website):

• Piastra MC, Nüßing A, Vorwerk J, Bornfleth H, Oostenveld R, Engwer C, Wolters CH, The Discontinuous Galerkin Finite Element Method for Solving the MEG and the combined MEG/EEG Forward Problem, Frontiers in Neuroscience (2018)

• Engwer C, Vorwerk J, Ludewig J, Wolters CH, A discontinuous Galerkin method to solve the EEG forward problem using the subtraction approach, SIAM Journal on Scientific Computing (2017)

• Nüßing A, Wolters CH, Brinck H, Engwer C, The unfitted discontinuous Galerkin method for solving the EEG forward problem, IEEE Transactions on Biomedical Engineering (2016)

Requirements

In order to reproduce the computation present below on your computer, you need to fulfill all the conditions listed below. Alternatively, you can read this page as a reference documentation about DUNEuro and not try to reproduce the results.

• You have a working copy of Brainstorm installed on your computer.

• You have already followed the introduction tutorials, at least until #23.

• You have followed the tutorial EEG and Epilepsy, as it is used for illustrating the computation.

• DUNEuro: Software installed automatically as a Brainstorm plugin.

• Iso2mesh: Software installed automatically as a Brainstorm plugin.

FEM mesh

In order to use the FEM computations of the electromagnetic field (EEG/MEG), the volume mesh of the head is required. Brainstorm integrates most of the modern open-source tools to generate realistic head mesh, either from nested surface mesh or from individual MR images (T1 or T1 and T2). This tutorial describes only a simple approach based on three nested surfaces meshed in 3D with Iso2mesh. For the full list of available methods and description of options, please refer to the tutorial FEM mesh generation.

• Select the protocol TutorialEpilepsy, created while following the tutorial EEG and epilepsy.

• Go to the anatomy view.

• Select the three BEM surfaces: scalp, outer skull, inner skull.

• Right-click > Generate FEM mesh > Iso2mesh-2021 > MergeMesh > Default options.
  
  
  

• The FEM mesh appears in the database explorer after a short while. The first number indicates the number of vertices (i.e. nodes) of the tetrahedral mesh. To get the number of 3D elements (i.e. tetrahedrons) in this geometric model of the head: right-click on the file > File > View file contents. The structure of the file is describe in the tutorial FEM mesh generation.
  
  

• Double-click on the FEM file to display it. From the Surface tab, you can change the resection locations by moving the bottom sliders, and you can control the display of each of the three layers individually. Click on the layer button in the toolbar, then adjust the color and transparency of the corresponding mesh. The figure below represents the FEM mesh in the center and the initial BEM layers on the right.
  
  

FEM forward model

The forward model (or head model in the Brainstorm documentation and interface) describes how the electric activity in the source space (the cortex surface or a regular grid of volume points) influences the electric potential (EEG) or magnetic fields (MEG) at the level of the sensors. The FEM method uses the tetrahedral mesh computed above to establish this relationship.

• Go the Anatomy view. Select the default FEM mesh and cortex surface you'd like to use for the computation (in case there is more than one in each category). The selected elements appear in green, double-click or right-click > Set as default to change the selection.

• Go to the Functional view. Right-click on the channel file > Compute head model.
  
  

• Select MRI volume, EEG: DUNEuro FEM, Regular grid: brain 5mm.
  
  

• Start the computation. If you selected the correct files, it should only take a few minutes. You may be prompted to download or update the bst-duneuro plugin.

Basic DUNEuro options

At this level, the basic options are the list head's tissues and their conductivities. Brainstorm reads these parameters from the selected head model.

• FEM tissues or layers: Brainstorm detects automatically the number of layers on your model. Users can select the desired layers to include for the FEM computation. According to the modalities, the recommended selections are:

  • For EEG: select all the layers
  • For MEG: use only select the inner layers (here brain)
  • For SEEG: use only the inner layers
  • For ECOG: use only the inner layers
  • Any combinations that include MEG: use all the layers
  In this case, there is Scalp (=head), Skull (=outer skull), and Brain (=inner skull).

• FEM conductivities: Brainstorm detects automatically the number of layers and assigns the default isotropic value for each layer. However, you have the possibility to change these values according to your model.

For advanced users, check the advanced section and a more detailed example at this page FEM tensor.

Brainstorm will download the latest version of the bst-duneuro binaries for your operating system from the Github, and install it in Brainstorm user folder (~username/.brainstorm/bst-duneuro/). The calculation of the head model will start automatically. You may wait for a very long time, which depends on the mesh resolution, the number of sensors, and of course the capacity of your computer.

So, be patient, it's worth it... (for this model it's quite fast ... less than 10 min)

When it's finished, you have now a new head model for this subject in your database and can be used for the next steps/(back to tutorial 20 : Head modeling)

Anisotropy tensor from the DUNEuro options

In the case where the conductivity tensor are computed, Brainstorm detects and uses them for the FEM forward computation.

In this case, users can not change the conductivities values, since they are already computed as explained in this FEM tensor.

If at some points, for any reason, where users want to remove these FEM tensors, this can be done from the Brainstorm anatomy panel, select the FEM head model, right-click on the subject, and then "clear FEM tensor".

Advanced models and options

DUNEuro advanced options panel [to be completed]

From the previous panel, for advanced duneuro panel, click on the button "Show details", the following panel is displayed.

A set of advanced options are made available and can be easily changed. Here a short explanation is given for each option.

• FEM layers & conductivities: same explanation as in the previous section. Moreover, in the case where the conductivity tensor are previously computed, Brainstorm detects these tensors and load them. In this case, the users can't change the conductivities scalar values, since they are not used. The following is displayed panel is displayed.

• FEM solver type:

  • CG or Continuous Galerkin: This is the standard Lagrangian method.
  • DC or the Discontinuous Galerkin:

In this version, only the Fitted FEM approaches are integrated, that require the FEM mesh of the head model. Unfitted methods are also available within DUNEuro, and will be integrated soon in Brainstorm.

• FEM source model: The list of the available source are
  • Venant
  • Subtraction
  • Partial Integration

For more information about these methods, users can check this thesis (Vorwek thesis).

• Source space
  • Shrink source space: the location of dipoles are moved inward by the specified value in this field(in mm).
  • Force source space: this is required in the case where the dipoles are not within the GM matter.
• Outputs options
  • Save transfer matrix:

All these parameters are stored and passed to the DUNEuro as a text file. This file is the main interface that passes the parameters from Brainstorm to DUNEuro. More details about the integration can be found in these links:

• GitHub repository for the Brainstorm-DUNEuro compilation and integration

• GitHub repository for the matlab-duneuro interface

• Brainstorm-DUNEuro integration discussions:

  • Brainstorm-simbio/DUNEuro implementation/head model generation

  • Integrate the DUNEuro FEM computation

  • Genration of the FEM tensor

  • Generation of the FEM source space

FEM head model generation from MRI data

One of the advantages of the FEM is its ability to use more complex head models with realistic geometry. In this tutorial, we have shown a basic example, as an introduction.

For the generation of a more realistic head model, users can follow this FEM mesh tutorial to learn how to generate advanced FEM head models form magnetic resonance data.

FEM conductivity tensors generation from DWI data

Among the advantages of the FEM, the use of tissue anisotropy (conductivity). The estimation of the tissue anisotropy is performed with the Brainsuite diffusion pipeline (BDP). The diffusion tensor images (DTI) are estimated with Brainsuite from the diffusion-weighted images (DWI) and then converted to conductivity tensor using the effective medieum approach. In order to use this tool, you need to install Brainsuite software, the rest of the process is distributed within bst-duneuro.

For more information, users can follow this FEM tensor tutorial.

Troubleshooting

DUNEuro binaries may crash for various reasons: we tried to list the possible causes here. Many FEM forward modeling issues are related with memory overload or extremely long computation times. Reducing the size of the problem may help in many cases. If you cannot find a solution, please post the full error message on the Brainstorm user forum (you can copy-paste the error message from the Matlab command window after closing the error message box).

Grid error messages

• Error message: Coordinate is outside of the grid, or grid is not convex
• Explanation: Some dipoles are probably outside of the cortex, users need to correct the source space.
• Solution: ?

Remove the neck

One way to reduce the size of the forward problem is to decrease the number of FEM elements in the head model. When the field of the MRI is large, you may have the mesh of the neck and even the shoulders. In most cases, it is safe to remove the lower part of the FEM mesh, below the nose and the brainstem. Right-click on the FEM mesh > Resect Neck.

Once the process is finished, a new FEM mesh appears in the database, with a tag "resect". The following figure shows the model before (743828 vertices / 4079587 elements) and after resection (613955 vertices / 3400957 elements). It will reduce the size of the problem by 20%.

Additional documentation

Related tutorials

• FEM mesh generation

• FEM tensors estimation

• FEM median nerve example

DUNEuro references

• DUNEuro wiki: https://gitlab.dune-project.org/duneuro/duneuro/wikis/home

• DUNEuro website: http://duneuro.org/

• List of the parameters: https://docs.google.com/spreadsheets/d/1MqURQsszn8Qj3-XRX_Z8qFFnz6Yl2-uYALkV-8pJVaM/edit#gid=0

Brainstorm-DUNEuro integration

• https://github.com/brainstorm-tools/bst-duneuro/issues/1

• https://github.com/brainstorm-tools/brainstorm3/issues/242

• https://github.com/brainstorm-tools/brainstorm3/issues/185