The aim of this tutorial is to solve the EEG and MEG forward problems using the Finite Element Method (FEM).

As already mentioned, the goal of this session is to solve the EEG and MEG forward problem, more precisely we want to compute EEG and MEG leadfields so that the inverse problem can be solved in the next session ( inverse problem). In order to compute leadfields, there are five main steps that have to be followed.

1. create the mesh: in this step the MRI is loaded and processed, the segmentation is performed and finally the mesh is generated;
2. create the head-model: in this step the geometrical (mesh) and electrical (tissue conductivities) features are merged together;
3. create the source-model: in this step a grid of source positions in the gray matter is created;
4. handle the sensors: loading the electrodes and the gradiometers and aligning the electrodes to the scalp surface if needed;
5. compute the leadfield, i.e., solve the forward problem: this steps consists of two procedures. First, the so-called transfer matrix is computed; second, the leadfield matrix is estimated.

The first step is the same for solving both the EEG and MEG forward problem, the other four have to be executed separately for EEG and MEG. See Figure1.

Figure1: pipeline for forward computation using FEM, in the orange box there are the steps which differ between EEG and MEG

In particular, the EEG forward solution is computed via the method so-called simbio which relies on the code that you can find here, while the MEG forward solution calls the duneuro method, which makes use of the code developed in the University of Münster, visit this for further details.

This procedure consists in six steps. The input is a T1 weighted MRI and the output is a volumetric mesh with five compartments, i.e., scalp, skull, cerebrospinal fluid (CSF), gray and white matter.

mri_orig = ft_read_mri('subject01.nii');

Visualize the MRI

cfg = []; 
ft_sourceplot(cfg,mri_orig);

Figure2: visualization of the MRI

In this step we will interactively align the MRI to the CTF space. We will be asked to identify the three CTF landmarks (nasion, NAS; right pre-auricular point, RPA; left pre-auricular point, LPA) in the MRI.

cfg           = [];
cfg.method    = 'interactive';
cfg.coordsys  = 'ctf';
mri_realigned = ft_volumerealign(cfg, mri_orig);

We can visualize the realigned MRI

cfg = []; 
ft_sourceplot(cfg, mri_realigned);

cfg          = [];
mri_resliced = ft_volumereslice(cfg, mri_realigned);

We can visualize the resliced MRI

cfg = []; 
ft_sourceplot(cfg, mri_resliced);

Figure3: visualization of the replaced MRI

For visualization purposes, we produce surface meshes for three compartments: scalp, skull and brain. In order to do that, we first have to segment the MRI into the three compartments.

cfg                         = [];
cfg.output                  = {'scalp','skull', 'brain'};
mri_segmented_3_compartment = ft_volumesegment(cfg, mri_resliced);

Visualize the segmentation

seg_i = ft_datatype_segmentation(mri_segmented_3_compartment,'segmentationstyle','indexed');
 
cfg              = [];
cfg.funparameter = 'seg';
cfg.funcolormap  = gray(4); % distinct color per tissue
cfg.location     = 'center';
cfg.atlas        = seg_i;   
ft_sourceplot(cfg, seg_i);

Figure4: 3 compartment segmentation output

Once the segmentation is completed, the three surface meshes can be computed.

cfg  =[];
cfg.tissue      = {'scalp','skull','brain'};
cfg.numvertices = [3000 2000 1000];
mesh_surf       = ft_prepare_mesh(cfg,mri_segmented_3_compartment);

We can save the mesh obtained

save mesh_surf mesh_surf 

cfg                         = [];
cfg.output                  = {'scalp','skull','csf','gray','white'};
cfg.brainsmooth             = 2;
cfg.skullsmooth             = 2;
cfg.scalpsmooth             = 2; 
mri_segmented_5_compartment = ft_volumesegment(cfg, mri_resliced); 

Visualize the segmentation result

seg_i = ft_datatype_segmentation(mri_segmented_5_compartment,'segmentationstyle','indexed');
 
seg_i = ft_datatype_segmentation(mri_segmented_5_compartment,'segmentationstyle','indexed');
 
cfg              = [];
cfg.funparameter = 'seg';
cfg.funcolormap  = gray(6); % distinct color per tissue (air is included)
cfg.location     = 'center';
cfg.atlas        = seg_i;    % the segmentation can also be used as atlas
ft_sourceplot(cfg, seg_i);

Figure8: 5 compartment segmentation output

cfg            = [];
cfg.shift      = 0.3;
cfg.method     = 'hexahedral';
cfg.resolution = 2; % this is in mm
cfg.tissue     = {'scalp', 'skull', 'csf', 'gray','white'};
mesh_fem       = ft_prepare_mesh(cfg,mri_segmented_5_compartment);

For this tutorial we downsample the mesh to 2mm resolution, in order to reduce the computation time of the following steps.

Once the volumetric mesh has been created, the forward solution can be computed. In the following, steps 2-5 are described for EEG and MEG separately.

cfg               = [];
cfg.method        = 'simbio';
cfg.conductivity  = [0.43 0.01 1.79 0.33 14]; 
cfg.tissuelabel   = {'scalp', 'skull', 'csf', 'gray','white'};
headmodel_fem_eeg = ft_prepare_headmodel(cfg, mesh_fem); 

Visualize the headmodel and the electrodes (it might take time and memory)

% scalp: 1, skull: 2, csf: 3, gray: 4, wm: 5
ts = 1;
figure
mesh2 =[];
mesh2.hex = headmodel_fem_eeg.hex(headmodel_fem_eeg.tissue==ts,:); %mesh2.hex(1:size(mesh2.hex),:);
mesh2.pos =  headmodel_fem_eeg.pos;
mesh2.tissue =  headmodel_fem_eeg.tissue(headmodel_fem_eeg.tissue==ts,:);%mesh.tissue(1:size(mesh2.hex),:);
 
mesh_ed = mesh2edge(mesh2);
patch('Faces',mesh_ed.poly,...
    'Vertices',mesh_ed.pos,...
    'FaceAlpha',.5,...
    'LineStyle','none',...
    'FaceColor',[1 1 1],...
    'FaceLighting','gouraud');
 
xlabel('coronal');
ylabel('sagital');
zlabel('axial')
camlight; 
axis on;
 
ft_plot_sens(elec, 'style', '*g');

Figure9: visualization of headmodel_fem_eeg and electrodes

In this phase, source locations are selected within the gray matter compartment. During this tutorial we recommend to create a rather coarse grid (cfg.grid.resolution = 5;), in order to be able to compute the forward solution in the time available in this course.

cfg                 = [];
cfg.grid.resolution = 5; %in mm
cfg.vol             = headmodel_fem_eeg;
cfg.inwardshift     = 1; %shifts dipoles away from surfaces
sourcemodel         = ft_prepare_sourcemodel(cfg, headmodel_fem_eeg);

We can visualize the sources and the scalp surface mesh:

figure, ft_plot_mesh(sourcemodel.pos(sourcemodel.inside,:))
hold on, ft_plot_mesh(mesh_surf(1),'surfaceonly','yes','vertexcolor','none','facecolor',...
             'skin','facealpha',0.5,'edgealpha',0.1)
 

Figure9: visualization of the source model

In case the electrodes are not aligned to the MRI (i.e., CTF space), we can use the interactive function as follows

cfg           = [];
cfg.method    = 'interactive';
cfg.elec      = elec;
cfg.headshape = mesh_surf(1);
elec  = ft_electroderealign(cfg);

Figure9: visualization of headmodel_fem_eeg and electrodes

%% compute the transfer matrix
[headmodel_fem_eeg_tr, elec] = ft_prepare_vol_sens(headmodel_fem_eeg, elec); 

%% compute the leadfield
cfg               = [];
cfg.grid          = sourcemodel;
cfg.vol           = headmodel_fem_eeg_tr;
cfg.elec          = elec;
cfg.reducerank    = 3;
leadfield_fem_eeg = ft_prepare_leadfield(cfg); 

cfg               = [];
cfg.method        = 'duneuro';
cfg.conductivity  = [0.43 0.01 1.79 0.33 0.14]; % check that the order is the same as the one i the mesh_fem
headmodel_fem_meg = ft_prepare_headmodel(cfg, mesh_fem);

If the source-model was already created at the step 3(EEG), it can be simply loaded for this step.

cfg                 = [];
cfg.grid.resolution = 5; %in mm
cfg.vol             = headmodel_fem_meg;
cfg.inwardshift     = 1; %shifts dipoles away from surfaces
sourcemodel         = ft_prepare_sourcemodel(cfg, headmodel_fem_meg);

We can visualize the sources and the scalp surface mesh:

figure, ft_plot_mesh(sourcemodel.pos(sourcemodel.inside,:))
hold on, ft_plot_mesh(mesh_surf(1),'surfaceonly','yes','vertexcolor','none','facecolor',...
             'skin','facealpha',0.5,'edgealpha',0.1)

As already mentioned, the MRI was realigned to the CTF space, therefore there is no need to realign the sensors. We load them from the data.

hdr     = ft_read_header('subject01.ds','headerformat', 'ctf_ds');
grad_cm = hdr.grad;
grad    = ft_convert_units(grad_cm,'mm');

We can visualize both EEG and MEG sensors, together with the scalp surface mesh

figure
hold on
ft_plot_mesh(mesh_fem,'surfaceonly','yes','vertexcolor','none','edgecolor','none','facecolor',[0.5 0.5 0.5],'facealpha',0.1, 'edgealpha', 0.1);
camlight
axis on
ft_plot_sens(grad,'style', 'sr', 'coil', 'yes');
ft_plot_sens(elec);

%% compute the transfer matrix
[headmodel_fem_meg_tr, grad] = ft_prepare_vol_sens(headmodel_fem_meg, grad, 'channel', MEG_avg.label);

load headmodel_fem_meg_tr
meg_transfer = headmodel_fem_meg_tr.meg_transfer;
headmodel_fem_meg_tr =headmodel_fem_meg;
headmodel_fem_meg_tr.meg_transfer = meg_transfer;

%% compute the leadfield
cfg                = [];
cfg.grid           = sourcemodel;
cfg.headmodel      = headmodel_fem_meg_tr;
cfg.grad           = grad;
cfg.reducerank     = 2;
leadfield_fem_meg  = ft_prepare_leadfield(cfg); 

This tutorial was about the computation of leadfields that could be feed into the inverse problem which will be explain in: Inverse problem.

This tutorial was last tested on 14-06-2018 by Simon Homölle on Mac, Matlab 2015b.