Authors: Takfarinas Medani

[TUTORIAL UNDER DEVELOPMENT: NOT READY FOR PUBLIC USE]

Introduction

In this tutorial, we review and compare the forward models computation methods available in brainstorm.

We apply these methods in spherical head model and in realistic models. we caompare the forward solution in different scenarios.

This is a qualitative comparison and not an advanced study. You can find at the end of this page a list of references that investigate deeply the differents forward models.

At this time, the FEM implementation is available for the EEG and the MEG computation. We will integrate and test soon the FEM for sEEG and ECOG.

EEG within a spherical model

The volume conductor or the head model:

In this part we used the spherical head model distributed by the duneuro team (sphere). The following figure shows on the left the surface model and on right the tetrahedral mesh.

The model has three layers, the brain (inner skull), the outer skull and the scalp.

The source space

For the source space or dipole position, we will use a realistic cortex distributed with the ICBM default subject of brainstorm.

The sensor model

Regarding the electrode's positions, we use the same position defined in this file. The total number of electrodes is 200 regularly distributed on the outer layer.

The forward model

Now, we have all the components of the model, we can start the process to compute the head model. For the EEG, brainstorm offers three methods. We perform these three computations on this model.

1. 3-shell sphere: best-fitting sphere based on the scalp, then OK.

2. OpenMeeg BEM: use the conductivity 0.33, 0.004 and 0.33, and keep the default options.

3. DUNEuro FEM: use the default option with the same conductivity value as the previous method.

Qualitative comparison of the methods

In this tutorial, we use the display of the lead field vector to compare visually the performances of the three methods.

Right-click on the head model, and then select 'View lead field vector'. You can select more than the head model in order to overlay the vectors.

In this figure, we show all of these methods and zoom to focus on the vectors. For more documentations about these lead field vectors, please refere to these pages (page1, page2)

We can easily see that the three vectors are pointing in the same direction and have the same length.

The computation time

Regarding the computation time:

• 3-shell sphere: less than 30 secondes

• OpenMeeg BEM: ~ 12 minutes.

• DUNEuro FEM: ~ 2 minutes.

This example has 15000 dipoles (x3) and 200 electrodes.

There are many studies and publications that compare these methods and highlights the advantages and weakness of each method.

From the brainstorm side, we recommend to use either openmeeg or duneuro for a realistic head model. If you have the FEM mesh*, Duneuro is faster for the same mesh resolution as the surface (OpenMeeg).

Duneuro can be used for a more realistic model (more than 3 layers with the complex shape).

*You can generate the FEM if you have the surfaces or the MRI, this process is explained in this tutorial.

EEG within brainstorm template (3 layers)

In this example, we will present the process of FEM mesh generation from surface model and highlight the effect of the mesh resolution.

The head model

We will use the default subject, then right-click and generate FEM mesh, and follow the same steps as explained in this section.

We repeated this process four times, and hen we generate four FEM head models with four different values of the 'Max tetrahedral volume'.

Here is a view of the obtained mesh with MaxVol = 10, 1, 0.1 and 0.01 (clockwise order).

Let's give the name V10, V1, V01, and V001 respectively for these head models.

MaxVol: is the maximum volume of the tetrahedral, in this example, we use the ctf coordinate system, therefore MaxVol here is a volume with units of cm3.

The FEM generation time is quite fast, it varies from 15 secondes (V10) to less than 2 minutes (V001).

The source and sensor space

We use a protocol with EEG data, you can reproduce with any protocol with available channels position and EEG recording, this is not important in this tutorial.

For the source space, we use the default cortex with 15000 dipoles. The number of channels is 31, regularly distributed on the scalp surface, the model is shown on this figure.

The forward model & lead field visualisation

Switch to the "functional data" view, right click on the subject => Compute Head model => Duneuro FEM ==> keep the defaults parameters and set the conductivity to 0.33, 0.04 and 0.33.

Repeat the same process for four head models.

The computation time in these models is not expensive, it varies from 1 minute (V10) to 6 minutes(V001).

As in the previous example, we will display the lead field vectors for these head models.

With the FEM, it's known that increasing the mesh increases the accuracy of the solution. Therefore we will use the V001 as a reference solution and we compare the other model to this reference.

From visual checking and for different electrodes configurations(tap H for more help on the figure), we observe that there is less or difference between the V001 and V01. Also, we noticed differences in the model V1 and higher difference in the model V10 (coarse mesh). These basics observations are expected regarding the quality of the mesh.

source estimation

In this section, we perform a source estimation using the previous four head models.

Right-click on the head model ==> compute source [2018] and keep all the parameters as they are.

We repeat the process for the four head models and then we display the results on the cortex. We select a time point to highlight cortical activation.

The name of each figure is displayed on the title bare. We notice that the V01 and V001 have the same range on the scaling (0-300), whereas the V1 and V10 are lower (0-200). V001 and V01 give almost the same regions and are more focal than V1 and V10.

From these observations, we recommend using MaxVol = 0.1 and we set is as the default value for mesh resolutionin within brainstorm.

Comparaison between the different forward methods

In this section, we compute the forward model using the three available methods (3-shell, OpenMeeg, and DUNEuro). For these three methods, we use the same head model, with the same source and sensor space (as shown on the previous sections). For the Duneuro FEM, we select the head model V01 (the default value for the mesh generation).

Lead field visualisation

the BEM, FEM forward computation in basic model (realistic head model 3 layer) and also within a spherical head model with an analytical solution.

When the forward computation is completed with the three methods, we can display the lead vector.

We can see that the LF arrows of Duneuro and 3-shell are pointing in the same direction. Whereas, for OpenMeeg, there are some outliers (big blue arrows) pointing on wrongs and random directions.

When we check closely the values of the OpenMeeg LF, we notice that the vectors are pointing in the correct direction in most of the source points. The outliers have big value and could not be displayed on the same scale (we are working on that).

These points are some dipoles that are to close to the interface. The OpenMeeg BEM solution is not accurate in these positions. In the literature, similar problems are observed even with the FEM, however, this kind of instability is investigated and Duneuro offers many source models to avoid/minimize these errors.

source estimation

Following the same logic as in the previous section, we perform source localization using the three head model described below.

We select the Minimum norm and we keep the default parameters.

We do the same process, but with sLoreta option :

In this, basic example, we show that all the methods point to the same area with more or less precision.

As said, in this tutorial the objectify is to present how to use these tools.

MEG within a spherical model

In this part of the tutorial, we describe similar approcah for the MEG. We will use the data of the PhantomCTF, we recommend you to read the PhantomCTF tutorial for better understanding of this section.

The volume conductor and the source space:

With a similar approach as explained in the introduction tutorial, we can generate the BEM surfaces from the MRI of the phantom. Right-click on the subject ==> Generate BEM surfaces.

This process will generate three surfaces, the inner skull, outer skull, and scalp. We will use these surfaces for the OpenMeeg BEM computation. When these surfaces are available, we can generate the FEM mesh as explained in the previous section. Right-click on the subject, then Generate FEM Mesh, Iso2mesh, MergeMesh and then keep the default options. The following figure shows the BEM and the FEM head model.

From the ICBM head model, we import the cortex and then align it within the phantom as shown in the figure.

The sensor model

We use a similar configuration as explained on the CTF phantom tutorial. The following figure shows the model of the sensor and the head model.

The forward model

For the MEG, brainstorm has four methods.

1. single sphere: fitting sphere on the cortex, 20 secondes
2. Overlapping spheres: 30 secondes

3. OpenMeeg BEM: use only the inner tissue, ~10 minutes,

4. DUNEuro FEM: use only the inner mesh, ~ 15 min

We use these four methods in this section.

lead field visualisation

We use a similar process to display the lead field vectors.

These figures show the LF arrows, we can easily check the similarity on the different methods.

Brainstorm recommend the use of the Overlapping spheres since it's fast and its shown that the MEG is less affected by the head geometry and the jump on the conductivity.

In this section, we showed the methods available on the brainstorm.

source estimation

For each head model, we estimate the source activation on the cortex. The following figure shows the results.

References