The forward module routines generate leadfields which are used used in different contexts (e.g. beamformer). To build the forward model we make use of various methods and we start from very different geometrical descriptions, generally representing the head shape.

Let's list some of the the methods currently supported by FieldTrip (in parentheses which modality they are used for):

• ASA bem (EEG)
• Bemcp (EEG)
• Dipoli bem (EEG)
• OpenMEEG bem (EEG/MEG)
• MNE bem (do we want to adopt this?)
• halfspace medium (EEG)
• Infinite medium (EEG/MEG)
• Infinite slab (EEG)
• Local spheres (EEG/MEG)
• Single shell (MEG)
• Concentric spheres (EEG)

According to the different anatomy acquisition techniques it is possible to distinguish among the following types of input:

• CT scan
• MRI scan
• Headshape, points
• Headshape, closed surface
• Nothing

All the routines which create a forward model need a description of the volume conductor model as input. This model is represented in a vol structure which contains a set of fields, among which vol.method (e.g. vol.method = 'dipoli'). All other fields are specific for the various methods and are generated in a pipeline which can be summarized in the following picture:

The leftmost box indicates a set of functions (Matlab/external toolboxes, FieldTrip) that deal with anatomical volumes (a 3D matrix filled with intensity values - a set of voxels). This step manages the volumetric information (MRI/CT scans) and transforms the anatomy into a processed anatomy ('ana2ana' functions), transforms the anatomy into a binary segmentation ('ana2seg' functions) or manipulates segmented images ('seg2seg' functions, i.e. morphology operators).

The content of the central box is a set of functions which refines the geometrical description derived from the volumetric analysis. Any visual quality control is processed in this section, including interactions with the operator. The input can be a segmented volume, a triangulated set of points or a cloud of points. The output is a geometry (geom), defined as a geometrical description other than volumetric, like for example a triangulated mesh, a cloud of points representing the head, a 3D lattice of tetrahedrons/hexahedrons, etc.

The third block (Post-processing) performs all automatic steps to build the description of the volume conductor ('vol' structure with various fields). This last step provides the piece of information which is fed to the forward solution algorithms (the various lead field computation routines). This post-processing functions are not supposed to change the meshes anymore and call method-specific head model functions (ft_headmodel_XXX routines)

As a general rule all volumetric geometry descriptions should not contain holes or be hollow. All mesh geometries (excluded 3D meshes for FEM) should not intersect with each other or be nested (apart for concentric spheres).

The table contains the cells that indicate FROM which kind of input TO which kind of method I want to go. The content is a set of programmatic steps which leads from a specific anatomical information (see the first column) to the costruction of the 'vol' structure for a forward model method (see the first row of the table).

The tables are different for EEG and MEG:

* For EEG:

* For MEG:

The following paragraphs describe in synthesis the pipelines for the various methods sketched in the tables. The methods are ordered according to the input type (e.g. CT scans) they use to generate the 'vol' structure.

From CT to Infinite space

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FROM CT TO Infinite halfspace

This applies for example when the set of electrodes is distributed on a flat surface (e.g. Utah array)
Method:

Back

FROM CT TO Infinite slab

This applies for example when the set of electrodes is distributed on a flat surface (e.g. Utah array)

Back

FROM CT TO Single sphere

This method applies to ECoG or iEEG and is normally not used for scalp EEG:

Back

FROM CT TO Concentric spheres

For a 3-sphere model the spheres represent the skin surface, the outside of the skull and the inside of the skull. For a 4-sphere model, the surfaces describe the skin, the outside-skull, the inside-skull and the inside of the cerebro-spinal fluid (CSF) boundaries.

Accordingly:
For 3 spheres:

5 - Extract the filled volume of the outer skull using morphological operators
6 - Dilate the outer skull to estimate the scalp compartment
7 - For each compartment fit a sphere (see SPH1 method)
8 - Assign the conductivity to each compartment (from literature)

For 4 spheres:
7 - Erode the inner skull to estimate the inside of the CSF compartment
8 - For each compartment fit a sphere (see SPH1 method)
9 - Assign the conductivity to each compartment (from literature)

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FROM CT TO FEM

For a FEM model we have to represent as many different volumetric compartments as wanted. In the case of a CT scan we can identify the following tissue compartments:
volume of the scalp, the skull, inside of the skull, inside of the CSF

5 - Dilate the outer skull to estimate the scalp compartment
6 - Erode the skull to obtain the inner CSF compartment
7 - Check that each compartment does not contain holes, and fill them
8a - Use one of the triangulation methods to obtain the:

1. - scalp surface
   
2. - scalp-skull interface
   
3. - skull-CSF interface
   

9a - Check the triangulations for intersections
10a - Using Tetgen to generate a set of tetrahedrons for:

1. -the inner CSF compartment
   
2. -the inner skull compartment
   
3. -the skull
   
4. -the scalp
   

OR
8-10b - Generate a set of hexahedrons using vgrid
11 - Assign the conductivity tensor to each -hedron element (from literature and DTI data)
12 - Check the consistency of tetrahedral/hexahedral normals (vertices order has to be consistent)

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FROM CT TO FDM

This method is based on anatomical description obtained from the segmentation of the CT scan. Normally the 'elements' of the FDM (Finite Differences Method) are the voxels of each compartment (as for example for the FNS method). Consequently it is important to obtain the segmentation of as many compartments as possible from the CT scan. Typically we will try to obtain:
the scalp, the skull, the inner skull, the inner CSF compartments

5 - Dilate the skull to estimate the scalp compartment
6 - Erode the skull to obtain the inner CSF compartment
7 - Assign the conductivity value to each compartment (from literature)
8 - Define the points in which the solution has to be calculated as:

1. Deep brain points, OR
   
2. The vertices of a previously defined surface (i.e. the scalp)
   

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FROM CT TO ASA BEM

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FROM CT TO BEMCP

This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

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FROM CT TO Dipoli

This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

Back

FROM CT TO OpenMEEG

This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

Back

From MRI to Infinite space

Back

FROM MRI TO Infinite halfspace

This applies for example when the set of electrodes is distributed on a very flat surface (e.g. Utah array)
Method:

Back

FROM MRI TO Infinite slab

This applies for example when the set of electrodes is distributed on a flat surface (e.g. Utah array)

Back

FROM MRI TO Single sphere

This method applies to ECoG or iEEG and is normally not used for scalp EEG:

Back

FROM MRI TO Concentric spheres

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FROM MRI TO FEM

Back

FROM MRI TO FDM

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FROM MRI TO ASA BEM

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FROM MRI TO BEMCP

This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

Back

FROM MRI TO Dipoli

This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

Back

FROM MRI TO OpenMEEG
This method generates a 'vol' structure which contains the conductivities of each compartment, the description of the triangulated surfaces and the system matrix (also called Head matrix), which accounts for the geometry of the head shape in the calculation of the lead fields.

Back

From Headshape points to Infinite space

Back

FROM Headshape points TO Infinite halfspace

Headshape points are the 3D electrodes positions in this case. This is the case, for example, of a set of points manually poked on a rendering of the brain surface (e.g. in the case of ECoG surgical pictures availability).

Method:
-With the available points consider if it is necessary to further process the inner skull surface. Avoid the next point if no further processing is necessary.

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FROM Headshape points TO Infinite slab

This case happens when I have a set of electrodes positions and an estimate of the average cortical thickness in the electrode's positions (i.e. Utah array)
-With the available points consider if it is necessary to further process the inner skull surface. Avoid the next point if no further processing is necessary.

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FROM Headshape points TO Single sphere

This method applies to ECoG or iEEG and is normally not used for scalp EEG:

- Load in the set of points of the head shape (these can be the electrodes positions as well)
- Fit a sphere to the points
Back

FROM Headshape points TO Concentric spheres

- Load in the set of points of the concentric shapes
- Fit a sphere to each shape
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FROM Headshape points TO ASA

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FROM Headshape points TO BEMCP

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FROM Headshape points TO Dipoli

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FROM Headshape points TO OpenMEEG

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FROM Headshape triangulation TO Infinite space

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FROM Headshape triangulation TO Infinite halfspace

Headshape points are read from an external software file, in form of a closed triangulated surface. This case applies to manual segmentations/triangulations performed (e.g.) in Solid Works/Blender and exported in STL format.

Method:
-With the available points consider if it is necessary to further process the inner skull surface. Avoid the next point if no further processing is necessary.

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FROM Headshape triangulation TO Slab

The user has a closed boundary, e.g. representing the brain, and an estimate of the average cortical thickness. This is the case for example of a boundary calculated in another software and read in Matlab, with points and edges.

Method:
-With the available points consider if it is necessary to further process the inner skull/brain surface. Avoid the next point if no further processing is necessary.

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FROM Headshape triangulation TO Single sphere

This method applies to ECoG or iEEG and is normally not used for scalp EEG:

1 - Load in the set of points of the head triangulation
2 - Get rid of the .tri (edges of the mesh) and exclude the points corresponding to the inferior part of the head
3 - Fit a sphere to the points
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FROM Headshape triangulation TO Concentric spheres

- Load the boundaries
- Discard the edges of the triangulations
- For each compartment fit a sphere
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FROM Headshape triangulation TO ASA BEM

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FROM Headshape triangulation TO BEMCP

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FROM Headshape triangulation TO Dipoli

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FROM Headshape triangulation TO OpenMEEG

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FROM Nothing TO Infinite halfspace

- determine a standard plane crossing (0,0,0) and with normal (e.g.) along the z axis
- Determine one point on the non-conductive side of the electrodes
- Electrodes are not allowed to be in the vacuum side, therefore faulty electrodes are automatically reprojected on the plane

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FROM Nothing TO Infinite slab

- Determine one point on the non-conductive side of the electrodes
- Determine the thickness of the slab (e.g. cortical thickness)
- Electrodes are not allowed to be in the vacuum side, therefore faulty electrodes are automatically reprojected on the plane

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FROM Nothing TO Single sphere

This method applies to ECoG or iEEG and is normally not used for scalp EEG:

1 - Use priors or informed guess about the radius and the center of the sphere (i.e. radius = 12cm and center = [0,0,4]cm in head coordinates is normally a good guess!)

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For all inputs we consider the same approaches of EEG to be valid. A couple of methods described below are typical for MEG only (single shell Nolte method and the local spheres method).

FROM CT TO Single shell (MEG only)

The single shell method is also know as the Nolte method and consists in creating a realistic description of the geometry by fitting a series of spherical harmonics to the points describing the geometry of the outer skull.

Therefore:

1 - [SH1 only] Segment the skull with threshold and morph operators
OR
1 - [SH1 only] Segment the skull using BET-FSL
2 - Create a filled outer skull compartment
3 - Use marching cubes (isosurface.m) to determine the mesh
OR
3 - Project lines out of a inner icosaedron onto the outer skull to determine the mesh

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FROM CT TO Local spheres (MEG only)

For all we apply the same algorithms defined in SPH1-6, except that the point 4 of SPH1 (fit a sphere) becomes:

4 - define a maximum radius for each sensor
5 - define the points of the head shape included in this radius
6 - for every sensor fit a sphere to the points define in 5

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FROM MRI TO Single shell (MEG only)

The single shell method is also know as the Nolte method and consists in creating a realistic description of the geometry by fitting a series of spherical harmonics to the points describing the geometry of the outer skull.

- Segment the brain using SPM/Freesurfer
- Obtain the inner skull compartment by using csf+white+gray
- smooth and threshold the obtained volume
- Use one of the known Triangulation methods to obtain a surface

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FROM MRI TO Local spheres (MEG only)

For all we apply the same algorithms defined in SPH1-6, except that the point 4 of SPH1 (fit a sphere) becomes:

4 - define a maximum radius for each sensor
5 - define the points of the head shape included in this radius
6 - for every sensor fit a sphere to the points define in 5

Back

FROM Headshape points TO Single shell (MEG only)

1 - Load the outer skull boundary points
2 - Discard the .tri field (if any)

Back

FROM Headshape points TO Local spheres (MEG only)

For all we apply the same algorithms defined in SPH1-6, except that the point 4 of SPH1 (fit a sphere) becomes:

4 - define a maximum radius for each sensor
5 - define the points of the head shape included in this radius
6 - for every sensor fit a sphere to the points define in 5

Back

FROM Headshape boundary TO Single shell (MEG only)

1 - Load the outer skull boundary points
2 - Discard the .tri field (if any)

Back

FROM Headshape boundary TO Local spheres (MEG only)

For all we apply the same algorithms defined in SPH1-6, except that the point 4 of SPH1 (fit a sphere) becomes:

4 - define a maximum radius for each sensor
5 - define the points of the head shape included in this radius
6 - for every sensor fit a sphere to the points define in 5

Back

The triangulation methods are generally applied to pre-processed volumetric objects (e.g. segmented brain compartments) to generate a geometrical description expressed in terms of points and edges (a connectivity matrix).

These methods are commonly used in FieldTrip:

- The marching cubes algorithm implemented by the Matlab function isosurface.m
- The projection of lines from the center of an icosaedron, to obtain the points of the volume that correspond to the transition between inside and outside of the volume
- The use of edge detection to determine the points of the volumetric boundaries (see the edge function in the Image Processing Toolbox)

The second method is more stable in case of noise in the volumetric compartment

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The morphology operators are a set of functions which manipulates volumetric data. Some of the most common operators are imfill, imdilate, bwlabeln, etc.

In particular imdilate can be used to augment the volume of a closed surface (e.g. the inner skull) in order to render the other surrounding tissues (e.g. the outer skull). An example is reported below:

The code used to generate the figure is:

seg = imdilate(seg,strel_bol(3));
figure,volplot(seg);

An example of the imfill function is given below. This is the case, for example, in which we want to fill the volume so that it constitutes a single entity. It results in being useful for triangulation, as explained in one of the techniques to obtain the outer-most surface (i.e. the skin).

The code used to generate the figure is:

seg = imfill(seg,'holes');
figure,volplot(seg);

The same effect can be reached with the use of another morphology function: bwlabeln. This function classifies the cluster of neighboring voxels and attaches a label to them, so that different objects can be easily distinguished (and processed) in the successive steps.

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ft_headmodel_asa ft_headmodel_dipoli ft_headmodel_openmeeg ft_headmodel_bemcp ft_headmodel_concentricspheres ft_headmodel_fns ft_headmodel_simbio ft_headmodel_halfspace ft_headmodel_infinite ft_headmodel_localspheres ft_headmodel_singleshell ft_headmodel_singlesphere ft_headmodel_strip

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This functions are responsible to generate the lead fields for the different available methods. They are contained in the Forwrd/private folder.

eeg_halfspace_medium_leadfield.m leadfield_simbio.m eeg_leadfield1.m eeg_leadfield4.m meg_leadfield1.mexXXX eeg_leadfield4_prepare.m eeg_leadfieldb.m halfspace_medium_leadfield.m inf_medium_leadfield.m leadfield_fns.m eeg_strip_monopole.m inf_medium_leadfield.m meg_forward.m meg_ini.m

ama2vol.m fitsphere.m headcoordinates.m transfer_elec.m

Examples of volumetric functions are:

ana2ana functions:
ft_read_mri
ft_volumereslice
ft_volumerealign
ft_volumenormalise
ft_volumesmooth

ana2seg functions:
ft_volumesegment
ft_volumethreshold
Morphology operators

seg2seg functions:
e.g. the functions from the image processing toolbox

seg2mesh functions:
ft_prepare_mesh
ft_surface_extract

mesh2mesh functions:
ft_read_headshape
ft_read_sens
ft_electroderealign
ft_prepare_mesh gone into:

ft_surfaceextract
ft_surfacerefine
ft_surfacedownsample

ft_surfacesmooth
ft_surfacecheck, like closed? outward pointing? etc

mesh2vol functions:
ft_prepare_headmodel

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This function performs a set of sanity checks on the triangulated surfaces which allow to generate quantitative indexes.

We want to check:

1. the area of the entire surface
2. the intersection of two surfaces
3. the orientation of the triangles (outwards/inwards)
4. the presence of disconnected triangles
5. the presence of redundant vertices
6. the surface represents a closed area (i.e. the brain)

The reason for this function to exist is to understand if the mesh represents a regular and correct triangulation (e.g. the area is in cm2 and not km2). These checks are required in order to generate a correct forward model and are model dependent. Some of the steps might require direct interaction with the operator for a further visual inspection.

The routines that handle voxel based volumes can be described as functions that go from an anatomical input to segmented binary images (ana2seg routines), from anatomy to processed anatomy (ana2ana routines) and from segmented volumes into segmented volumes (seg2seg routines). The characteristic of voxel based routines is that the volumes are regular (cubic voxels upon reslicing).

Alternatively the routines that deal with geometric information other that voxel-based are handling the following geometrical objects:

- 0d : a point
- 1d : a line
- 2d : a plane/triangle/surface
- 3d : tetrahedra or hexahedra (irregular volume information, non voxel based)

(they might belong to the mesh2mesh routines class)

All routines that create head models must allow the transition from all objects to all others (if possible), and from voxel based images to geometrical objects. For example the routine prepare_mesh_manual segments boundaries directly from the MRI scans and generates connected lines (if goes from ana to 1d objects).