The forward solution¶

Overview¶

This Chapter covers the definitions of different coordinate systems employed in MNE software and FreeSurfer, the details of the computation of the forward solutions, and the associated low-level utilities.

MEG/EEG and MRI coordinate systems¶

The coordinate systems used in MNE software (and FreeSurfer) and their relationships are depicted in MEG/EEG and MRI coordinate systems. Except for the Sensor coordinates, all of the coordinate systems are Cartesian and have the “RAS” (Right-Anterior-Superior) orientation, i.e., the $x$ axis points to the right, the $y$ axis to the front, and the $z$ axis up.

MEG/EEG and MRI coordinate systems

The coordinate transforms present in the fif files in MNE and the FreeSurfer files as well as those set to fixed values are indicated with $T_x$ , where $x$ identifies the transformation.

The coordinate systems related to MEG/EEG data are:

Head coordinates

This is a coordinate system defined with help of the fiducial landmarks (nasion and the two auricular points). In fif files, EEG electrode locations are given in this coordinate system. In addition, the head digitization data acquired in the beginning of an MEG, MEG/EEG, or EEG acquisition are expressed in head coordinates. For details, see MEG/EEG and MRI coordinate systems.

Device coordinates

This is a coordinate system tied to the MEG device. The relationship of the Device and Head coordinates is determined during an MEG measurement by feeding current to three to five head-position indicator (HPI) coils and by determining their locations with respect to the MEG sensor array from the magnetic fields they generate.

Sensor coordinates

Each MEG sensor has a local coordinate system defining the orientation and location of the sensor. With help of this coordinate system, the numerical integration data needed for the computation of the magnetic field can be expressed conveniently as discussed in Coil geometry information. The channel information data in the fif files contain the information to specify the coordinate transformation between the coordinates of each sensor and the MEG device coordinates.

The coordinate systems related to MRI data are:

Surface RAS coordinates

The FreeSurfer surface data are expressed in this coordinate system. The origin of this coordinate system is at the center of the conformed FreeSurfer MRI volumes (usually 256 x 256 x 256 isotropic 1-mm3 voxels) and the axes are oriented along the axes of this volume. The BEM surface and the locations of the sources in the source space are usually expressed in this coordinate system in the fif files. In this manual, the Surface RAS coordinates are usually referred to as MRI coordinates unless there is need to specifically discuss the different MRI-related coordinate systems.

RAS coordinates

This coordinate system has axes identical to the Surface RAS coordinates but the location of the origin is different and defined by the original MRI data, i.e. , the origin is in a scanner-dependent location. There is hardly any need to refer to this coordinate system explicitly in the analysis with the MNE software. However, since the Talairach coordinates, discussed below, are defined with respect to RAS coordinates rather than the Surface RAS coordinates, the RAS coordinate system is implicitly involved in the transformation between Surface RAS coordinates and the two Talairach coordinate systems.

MNI Talairach coordinates

The definition of this coordinate system is discussed, e.g. , in http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach. This transformation is determined during the FreeSurfer reconstruction process.

FreeSurfer Talairach coordinates

The problem with the MNI Talairach coordinates is that the linear MNI Talairach transform does matched the brains completely to the Talairach brain. This is probably because the Talairach atlas brain is a rather odd shape, and as a result, it is difficult to match a standard brain to the atlas brain using an affine transform. As a result, the MNI brains are slightly larger (in particular higher, deeper and longer) than the Talairach brain. The differences are larger as you get further from the middle of the brain, towards the outside. The FreeSurfer Talairach coordinates mitigate this problem by additing a an additional transformation, defined separately for negatice and positive MNI Talairach $z$ coordinates. These two transformations, denoted by $T_-$ and $T_+$ in MEG/EEG and MRI coordinate systems, are fixed as discussed in http://imaging.mrc-cbu.cam.ac.uk/imaging/MniTalairach (Approach 2).

The different coordinate systems are related by coordinate transformations depicted in MEG/EEG and MRI coordinate systems. The arrows and coordinate transformation symbols ( $T_x$ ) indicate the transformations actually present in the FreeSurfer files. Generally,

$\begin{bmatrix} x_2 \\ y_2 \\ z_2 \\ 1 \end{bmatrix} = T_{12} \begin{bmatrix} x_1 \\ y_1 \\ z_1 \\ 1 \end{bmatrix} = \begin{bmatrix} R_{11} & R_{12} & R_{13} & x_0 \\ R_{13} & R_{13} & R_{13} & y_0 \\ R_{13} & R_{13} & R_{13} & z_0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x_1 \\ y_1 \\ z_1 \\ 1 \end{bmatrix}\ ,$

where $x_k$ ,:math:y_k,and $z_k$ are the location coordinates in two coordinate systems, $T_{12}$ is the coordinate transformation from coordinate system “1” to “2”, $x_0$ , $y_0$ ,and $z_0$ is the location of the origin of coordinate system “1” in coordinate system “2”, and $R_{jk}$ are the elements of the rotation matrix relating the two coordinate systems. The coordinate transformations are present in different files produced by FreeSurfer and MNE as summarized in Coordinate transformations in FreeSurfer and MNE software packages. The symbols are defined in CHDFFJIJ. Note: mne_make_cor_set /mne_setup_mri prior to release 2.6 did not include transformations , , , and in the fif files produced.. The fixed transformations $T_-$ and $T_+$ are:

$T_{-} = \begin{bmatrix} 0.99 & 0 & 0 & 0 \\ 0 & 0.9688 & 0.042 & 0 \\ 0 & -0.0485 & 0.839 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$

and

$T_{+} = \begin{bmatrix} 0.99 & 0 & 0 & 0 \\ 0 & 0.9688 & 0.046 & 0 \\ 0 & -0.0485 & 0.9189 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$

Note

This section does not discuss the transformation between the MRI voxel indices and the different MRI coordinates. However, it is important to note that in FreeSurfer, MNE, as well as in Neuromag software an integer voxel coordinate corresponds to the location of the center of a voxel. Detailed information on the FreeSurfer MRI systems can be found at https://surfer.nmr.mgh.harvard.edu/fswiki/CoordinateSystems.

Coordinate transformations in FreeSurfer and MNE software packages. The symbols $T_x$ are defined in *MEG/EEG and MRI coordinate systems*. Note: mne_make_cor_set /mne_setup_mri prior to release 2.6 did not include transformations $T_3$ , $T_4$ , $T_-$ , and $T_+$ in the fif files produced.
Transformation	FreeSurfer	MNE
$T_1$	Not present	Measurement data files Forward solution files (fwd.fif) Inverse operator files (inv.fif)
$T_{s_1}\dots T_{s_n}$	Not present	Channel information in files containing $T_1$ .
$T_2$	Not present	MRI description files Separate coordinate transformation files saved from mne_analyze Forward solution files Inverse operator files
$T_3$	mri/*mgz files	MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
$T_4$	mri/transforms/talairach.xfm	MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
$T_-$	Hardcoded in software	MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.
$T_+$	Hardcoded in software	MRI description files saved with mne_make_cor_set if the input is in mgz or mgh format.

The head and device coordinate systems¶

The head coordinate system

The MEG/EEG head coordinate system employed in the MNE software is a right-handed Cartesian coordinate system. The direction of $x$ axis is from left to right, that of $y$ axis to the front, and the $z$ axis thus points up.

The $x$ axis of the head coordinate system passes through the two periauricular or preauricular points digitized before acquiring the data with positive direction to the right. The $y$ axis passes through the nasion and is normal to the $x$ axis. The $z$ axis points up according to the right-hand rule and is normal to the $xy$ plane.

The origin of the MEG device coordinate system is device dependent. Its origin is located approximately at the center of a sphere which fits the occipital section of the MEG helmet best with $x$ axis axis going from left to right and $y$ axis pointing front. The $z$ axis is, again, normal to the $xy$ plane with positive direction up.

Note

The above definition is identical to that of the Neuromag MEG/EEG (head) coordinate system. However, in 4-D Neuroimaging and CTF MEG systems the head coordinate frame definition is different. The origin of the coordinate system is at the midpoint of the left and right auricular points. The $x$ axis passes through the nasion and the origin with positive direction to the front. The $y$ axis is perpendicular to the $x$ axis on the and lies in the plane defined by the three fiducial landmarks, positive direction from right to left. The $z$ axis is normal to the plane of the landmarks, pointing up. Note that in this convention the auricular points are not necessarily located on $y$ coordinate axis. The file conversion utilities (see Importing data from other MEG/EEG systems) take care of these idiosyncrasies and convert all coordinate information to the MNE software head coordinate frame.

Creating a surface-based source space¶

The fif format source space files containing the dipole locations and orientations are created with the utility mne_make_source_space . This utility is usually invoked by the convenience script mne_setup_source_space , see Setting up the source space.

The command-line options are:

—version

Show the program version and compilation date.

—help

List the command-line options.

—subject <*name*>

Name of the subject in SUBJECTS_DIR. In the absense of this option, the SUBJECT environment variable will be consulted. If it is not defined, mne_setup_source_space exits with an error.

—morph <*name*>

Name of a subject in SUBJECTS_DIR. If this option is present, the source space will be first constructed for the subject defined by the –subject option or the SUBJECT environment variable and then morphed to this subject. This option is useful if you want to create a source spaces for several subjects and want to directly compare the data across subjects at the source space vertices without any morphing procedure afterwards. The drawback of this approach is that the spacing between source locations in the “morph” subject is not going to be as uniform as it would be without morphing.

—surf <*name1*>: <*name2*>:...

FreeSurfer surface file names specifying the source surfaces, separated by colons.

—spacing <*spacing/mm*>

Specifies the approximate grid spacing of the source space in mm.

—ico <*number*>

Instead of using the traditional method for cortical surface decimation it is possible to create the source space using the topology of a recursively subdivided icosahedron ( <number> > 0) or an octahedron ( <number> < 0). This method uses the cortical surface inflated to a sphere as a tool to find the appropriate vertices for the source space. The benefit of the --ico option is that the source space will have triangulation information between the decimated vertices included, which some future versions of MNE software may be able to utilize. The number of triangles increases by a factor of four in each subdivision, starting from 20 triangles in an icosahedron and 8 triangles in an octahedron. Since the number of vertices on a closed surface is $n_{vert} = (n_{tri} + 4) / 2$ , the number of vertices in the k th subdivision of an icosahedron and an octahedron are $10 \cdot 4^k +2$ and $4_{k + 1} + 2$ , respectively. The recommended values for <number> and the corresponding number of source space locations are listed in Table 3.1.

—all

Include all nodes to the output. The active dipole nodes are identified in the fif file by a separate tag. If tri files were used as input the output file will also contain information about the surface triangulation. This option is always recommended to include complete information.

—src <*name*>

Output file name. Use a name <dir>/<name>-src.fif

Note

If both --ico and --spacing options are present the later one on the command line takes precedence.

Note

Due to the differences between the FreeSurfer and MNE libraries, the number of source space points generated with the --spacing option may be different between the current version of MNE and versions 2.5 or earlier (using --spacing option to mne_setup_source_space ) if the FreeSurfer surfaces employ the (old) quadrangle format or if there are topological defects on the surfaces. All new FreeSurfer surfaces are specified as triangular tessellations and are e of defects.

Creating a volumetric or discrete source space¶

In addition to source spaces confined to a surface, the MNE software provides some support for three-dimensional source spaces bounded by a surface as well as source spaces comprised of discrete, arbitrarily located source points. The mne_volume_source_space utility assists in generating such source spaces.

The command-line options are:

—version

Show the program version and compilation date.

—help

List the command-line options.

—surf <*name*>

Specifies a FreeSurfer surface file containing the surface which will be used as the boundary for the source space.

—bem <*name*>

Specifies a BEM file (ending in -bem.fif ). The inner skull surface will be used as the boundary for the source space.

—origin <*x/mm*> : <*y/mm*> : <*z/mm*>

If neither of the two surface options described above is present, the source space will be spherical with the origin at this location, given in MRI (RAS) coordinates.

—rad <*radius/mm*>

Specifies the radius of a spherical source space. Default value = 90 mm

—grid <*spacing/mm*>

Specifies the grid spacing in the source space.

—mindist <*distance/mm*>

Only points which are further than this distance from the bounding surface are included. Default value = 5 mm.

—exclude <*distance/mm*>

Exclude points that are closer than this distance to the center of mass of the bounding surface. By default, there will be no exclusion.

—mri <*name*>

Specifies a MRI volume (in mgz or mgh format). If this argument is present the output source space file will contain a (sparse) interpolation matrix which allows mne_volume_data2mri to create an MRI overlay file, see Converting volumetric data into an MRI overlay.

—pos <*name*>

Specifies a name of a text file containing the source locations and, optionally, orientations. Each line of the file should contain 3 or 6 values. If the number of values is 3, they indicate the source location, in millimeters. The orientation of the sources will be set to the z-direction. If the number of values is 6, the source orientation will be parallel to the vector defined by the remaining 3 numbers on each line. With --pos , all of the options defined above will be ignored. By default, the source position and orientation data are assumed to be given in MRI coordinates.

—head

If this option is present, the source locations and orientations in the file specified with the --pos option are assumed to be given in the MEG head coordinates.

—meters

Indicates that the source locations in the file defined with the --pos option are give in meters instead of millimeters.

—src <*name*>

Specifies the output file name. Use a name * <dir>/ <name>*-src.fif

—all

Include all vertices in the output file, not just those in use. This option is implied when the --mri option is present. Even with the --all option, only those vertices actually selected will be marked to be “in use” in the output source space file.

Creating the BEM meshes¶

The mne_surf2bem utility converts surface triangle meshes from ASCII and FreeSurfer binary file formats to the fif format. The resulting fiff file also contains conductivity information so that it can be employed in the BEM calculations.

Note

The utility mne_tri2fiff previously used for this task has been replaced by mne_surf2bem .

Note

The convenience script mne_setup_forward_model described in Setting up the boundary-element model calls mne_surf2bem with the appropriate options.

Note

The vertices of all surfaces should be given in the MRI coordinate system.

Command-line options¶

This program has the following command-line options:

—version

Show the program version and compilation date.

—help

List the command-line options.

—surf <*name*>

Specifies a FreeSurfer binary format surface file. Before specifying the next surface (--surf or --tri options) details of the surface specification can be given with the options listed in Surface options.

—tri <*name*>

Specifies a text format surface file. Before specifying the next surface (--surf or --tri options) details of the surface specification can be given with the options listed in Surface options. The format of these files is described in Tessellation file format.

—check

Check that the surfaces are complete and that they do not intersect. This is a recommended option. For more information, see Topology checks.

—checkmore

In addition to the checks implied by the --check option, check skull and skull thicknesses. For more information, see Topology checks.

—fif <*name*>

The output fif file containing the BEM. These files normally reside in the bem subdirectory under the subject’s mri data. A name ending with -bem.fif is recommended.

Surface options¶

These options can be specified after each --surf or --tri option to define details for the corresponding surface.

—swap

Swap the ordering or the triangle vertices. The standard convention in the MNE software is to have the vertices ordered so that the vector cross product of the vectors from vertex 1 to 2 and 1 to 3 gives the direction of the outward surface normal. Text format triangle files produced by the some software packages have an opposite order. For these files, the --swap . option is required. This option does not have any effect on the interpretation of the FreeSurfer surface files specified with the --surf option.

—sigma <*value*>

The conductivity of the compartment inside this surface in S/m.

—shift <*value/mm*>

Shift the vertices of this surface by this amount, given in mm, in the outward direction, i.e., in the positive vertex normal direction.

—meters

The vertex coordinates of this surface are given in meters instead of millimeters. This option applies to text format files only. This definition does not affect the units of the shift option.

—id <*number*>

Identification number to assign to this surface. (1 = inner skull, 3 = outer skull, 4 = scalp).

—ico <*number*>

Downsample the surface to the designated subdivision of an icosahedron. This option is relevant (and required) only if the triangulation is isomorphic with a recursively subdivided icosahedron. For example, the surfaces produced by with mri_watershed are isomorphic with the 5th subdivision of a an icosahedron thus containing 20480 triangles. However, this number of triangles is too large for present computers. Therefore, the triangulations have to be decimated. Specifying --ico 4 yields 5120 triangles per surface while --ico 3 results in 1280 triangles. The recommended choice is --ico 4 .

Tessellation file format¶

The format of the text format surface files is the following:

<nvert>

<vertex 1>

<vertex 2>

...

<vertex nvert>

<ntri>

<triangle 1>

<triangle 2>

...

<triangle ntri> ,

where <nvert> and <ntri> are the number of vertices and number of triangles in the tessellation, respectively.

The format of a vertex entry is one of the following:

x y z

The x, y, and z coordinates of the vertex location are given in mm.

number x y z

A running number and the x, y, and z coordinates are given. The running number is not considered by mne_tri2fiff. The nodes must be thus listed in the correct consecutive order.

x y z nx ny nz

The x, y, and z coordinates as well as the approximate vertex normal direction cosines are given.

number x y z nx ny nz

A running number is given in addition to the vertex location and vertex normal.

Each triangle entry consists of the numbers of the vertices belonging to a triangle. The vertex numbering starts from one. The triangle list may also contain running numbers on each line describing a triangle.

Topology checks¶

If the --check option is specified, the following topology checks are performed:

The completeness of each surface is confirmed by calculating the total solid angle subtended by all triangles from a point inside the triangulation. The result should be very close to $4 \pi$ . If the result is $-4 \pi$ instead, it is conceivable that the ordering of the triangle vertices is incorrect and the --swap option should be specified.
The correct ordering of the surfaces is verified by checking that the surfaces are inside each other as expected. This is accomplished by checking that the sum solid angles subtended by triangles of a surface $S_k$ at all vertices of another surface $S_p$ which is supposed to be inside it equals $4 \pi$ . Naturally, this check is applied only if the model has more than one surface. Since the surface relations are transitive, it is enough to check that the outer skull surface is inside the skin surface and that the inner skull surface is inside the outer skull one.
The extent of each of the triangulated volumes is checked. If the extent is smaller than 50mm, an error is reported. This may indicate that the vertex coordinates have been specified in meters instead of millimeters.

Computing the BEM geometry data¶

The utility mne_prepare_bem_model computes the geometry information for BEM. This utility is usually invoked by the convenience script mne_setup_forward_model , see Setting up the boundary-element model. The command-line options are:

—bem <*name*>

Specify the name of the file containing the triangulations of the BEM surfaces and the conductivities of the compartments. The standard ending for this file is -bem.fif and it is produced either with the utility mne_surf2bem (Creating the BEM meshes) or the convenience script mne_setup_forward_model , see Setting up the boundary-element model.

—sol <*name*>

Specify the name of the file containing the triangulation and conductivity information together with the BEM geometry matrix computed by mne_prepare_bem_model . The standard ending for this file is -bem-sol.fif .

—method <*approximation method*>

Select the BEM approach. If <approximation method> is constant , the BEM basis functions are constant functions on each triangle and the collocation points are the midpoints of the triangles. With linear , the BEM basis functions are linear functions on each triangle and the collocation points are the vertices of the triangulation. This is the preferred method to use. The accuracy will be the same or better than in the constant collocation approach with about half the number of unknowns in the BEM equations.

Coil geometry information¶

This Section explains the presentation of MEG detection coil geometry information the approximations used for different detection coils in MNE software. Two pieces of information are needed to characterize the detectors:

The location and orientation a local coordinate system for each detector.
A unique identifier, which has an one-to-one correspondence to the geometrical description of the coil.

The sensor coordinate system¶

The sensor coordinate system is completely characterized by the location of its origin and the direction cosines of three orthogonal unit vectors pointing to the directions of the x, y, and z axis. In fact, the unit vectors contain redundant information because the orientation can be uniquely defined with three angles. The measurement fif files list these data in MEG device coordinates. Transformation to the MEG head coordinate frame can be easily accomplished by applying the device-to-head coordinate transformation matrix available in the data files provided that the head-position indicator was used. Optionally, the MNE software forward calculation applies another coordinate transformation to the head-coordinate data to bring the coil locations and orientations to the MRI coordinate system.

If $r_0$ is a row vector for the origin of the local sensor coordinate system and $e_x$ , $e_y$ , and $e_z$ are the row vectors for the three orthogonal unit vectors, all given in device coordinates, a location of a point $r_C$ in sensor coordinates is transformed to device coordinates ( $r_D$ ) by

$[r_D 1] = [r_C 1] T_{CD}\ ,$

where

$T = \begin{bmatrix} e_x & 0 \\ e_y & 0 \\ e_z & 0 \\ r_{0D} & 1 \end{bmatrix}\ .$

Calculation of the magnetic field¶

The forward calculation in the MNE software computes the signals detected by each MEG sensor for three orthogonal dipoles at each source space location. This requires specification of the conductor model, the location and orientation of the dipoles, and the location and orientation of each MEG sensor as well as its coil geometry.

The output of each SQUID sensor is a weighted sum of the magnetic fluxes threading the loops comprising the detection coil. Since the flux threading a coil loop is an integral of the magnetic field component normal to the coil plane, the output of the k ^th MEG channel, $b_k$ can be approximated by:

$b_k = \sum_{p = 1}^{N_k} {w_{kp} B(r_{kp}) \cdot n_{kp}}$

where $r_{kp}$ are a set of $N_k$ integration points covering the pickup coil loops of the sensor, $B(r_{kp})$ is the magnetic field due to the current sources calculated at $r_{kp}$ , $n_{kp}$ are the coil normal directions at these points, and $w_{kp}$ are the weights associated to the integration points. This formula essentially presents numerical integration of the magnetic field over the pickup loops of sensor $k$ .

There are three accuracy levels for the numerical integration expressed above. The simple accuracy means the simplest description of the coil. This accuracy is not used in the MNE forward calculations. The normal or recommended accuracy typically uses two integration points for planar gradiometers, one in each half of the pickup coil and four evenly distributed integration points for magnetometers. This is the default accuracy used by MNE. If the --accurate option is specified, the forward calculation typically employs a total of eight integration points for planar gradiometers and sixteen for magnetometers. Detailed information about the integration points is given in the next section.

Implemented coil geometries¶

This section describes the coil geometries currently implemented in Neuromag software. The coil types fall in two general categories:

Axial gradiometers and planar gradiometers and
Planar gradiometers.

For axial sensors, the z axis of the local coordinate system is parallel to the field component detected, i.e., normal to the coil plane.For circular coils, the orientation of the x and y axes on the plane normal to the z axis is irrelevant. In the square coils employed in the Vectorview (TM) system the x axis is chosen to be parallel to one of the sides of the magnetometer coil. For planar sensors, the z axis is likewise normal to the coil plane and the x axis passes through the centerpoints of the two coil loops so that the detector gives a positive signal when the normal field component increases along the x axis.

Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included. lists the parameters of the normal coil geometry descriptions Accurate coil descriptions lists the accurate descriptions. For simple accuracy, please consult the coil definition file, see The coil definition file. The columns of the tables contain the following data:

The number identifying the coil id. This number is used in the coil descriptions found in the FIF files.
Description of the coil.
Number of integration points used
The locations of the integration points in sensor coordinates.
Weights assigned to the field values at the integration points. Some formulas are listed instead of the numerical values to demonstrate the principle of the calculation. For example, in the normal coil descriptions of the planar gradiometers the weights are inverses of the baseline of the gradiometer to show that the output is in T/m.

Note

The coil geometry information is stored in the file $MNE_ROOT/share/mne/coil_def.dat, which is automatically created by the utility mne_list_coil_def , see Creating the coil definition file.

Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included.
Id	Description	n	r/mm	w
2	Neuromag-122 planar gradiometer	2	(+/-8.1, 0, 0) mm	+/-1 ⁄ 16.2mm
2000	A point magnetometer	1	(0, 0, 0)mm	1
3012	Vectorview type 1 planar gradiometer	2	(+/-8.4, 0, 0.3) mm	+/-1 ⁄ 16.8mm
3013	Vectorview type 2 planar gradiometer	2	(+/-8.4, 0, 0.3) mm	+/-1 ⁄ 16.8mm
3022	Vectorview type 1 magnetometer	4	(+/-6.45, +/-6.45, 0.3)mm	1/4
3023	Vectorview type 2 magnetometer	4	(+/-6.45, +/-6.45, 0.3)mm	1/4
3024	Vectorview type 3 magnetometer	4	(+/-5.25, +/-5.25, 0.3)mm	1/4
2000	An ideal point magnetometer	1	(0.0, 0.0, 0.0)mm	1
4001	Magnes WH magnetometer	4	(+/-5.75, +/-5.75, 0.0)mm	1/4
4002	Magnes WH 3600 axial gradiometer	8	(+/-4.5, +/-4.5, 0.0)mm (+/-4.5, +/-4.5, 50.0)mm	1/4 -1/4
4003	Magnes reference magnetometer	4	(+/-7.5, +/-7.5, 0.0)mm	1/4
4004	Magnes reference gradiometer measuring diagonal gradients	8	(+/-20, +/-20, 0.0)mm (+/-20, +/-20, 135)mm	1/4 -1/4
4005	Magnes reference gradiometer measuring off-diagonal gradients	8	(87.5, +/-20, 0.0)mm (47.5, +/-20, 0.0)mm (-87.5, +/-20, 0.0)mm (-47.5, +/-20, 0.0)mm	1/4 -1/4 1/4 -1/4
5001	CTF 275 axial gradiometer	8	(+/-4.5, +/-4.5, 0.0)mm (+/-4.5, +/-4.5, 50.0)mm	1/4 -1/4
5002	CTF reference magnetometer	4	(+/-4, +/-4, 0.0)mm	1/4
5003	CTF reference gradiometer measuring diagonal gradients	8	(+/-8.6, +/-8.6, 0.0)mm (+/-8.6, +/-8.6, 78.6)mm	1/4 -1/4

Accurate coil descriptions
Id	Description	n	r/mm	w
2	Neuromag-122 planar gradiometer	8	+/-(8.1, 0, 0) mm	+/-1 ⁄ 16.2mm
2000	A point magnetometer	1	(0, 0, 0) mm	1
3012	Vectorview type 1 planar gradiometer	2	(+/-8.4, 0, 0.3) mm	+/-1 ⁄ 16.8mm
3013	Vectorview type 2 planar gradiometer	2	(+/-8.4, 0, 0.3) mm	+/-1 ⁄ 16.8mm
3022	Vectorview type 1 magnetometer	4	(+/-6.45, +/-6.45, 0.3)mm	1/4
3023	Vectorview type 2 magnetometer	4	(+/-6.45, +/-6.45, 0.3)mm	1/4
3024	Vectorview type 3 magnetometer	4	(+/-5.25, +/-5.25, 0.3)mm	1/4
4001	Magnes WH magnetometer	4	(+/-5.75, +/-5.75, 0.0)mm	1/4
4002	Magnes WH 3600 axial gradiometer	4	(+/-4.5, +/-4.5, 0.0)mm (+/-4.5, +/-4.5, 0.0)mm	1/4 -1/4
4004	Magnes reference gradiometer measuring diagonal gradients	8	(+/-20, +/-20, 0.0)mm (+/-20, +/-20, 135)mm	1/4 -1/4
4005	Magnes reference gradiometer measuring off-diagonal gradients	8	(87.5, +/-20, 0.0)mm (47.5, +/-20, 0.0)mm (-87.5, +/-20, 0.0)mm (-47.5, +/-20, 0.0)mm	1/4 -1/4 1/4 -1/4
5001	CTF 275 axial gradiometer	8	(+/-4.5, +/-4.5, 0.0)mm (+/-4.5, +/-4.5, 50.0)mm	1/4 -1/4
5002	CTF reference magnetometer	4	(+/-4, +/-4, 0.0)mm	1/4
5003	CTF 275 reference gradiometer measuring diagonal gradients	8	(+/-8.6, +/-8.6, 0.0)mm (+/-8.6, +/-8.6, 78.6)mm	1/4 -1/4
5004	CTF 275 reference gradiometer measuring off-diagonal gradients	8	(47.8, +/-8.5, 0.0)mm (30.8, +/-8.5, 0.0)mm (-47.8, +/-8.5, 0.0)mm (-30.8, +/-8.5, 0.0)mm	1/4 -1/4 1/4 -1/4
6001	MIT KIT system axial gradiometer	8	(+/-3.875, +/-3.875, 0.0)mm (+/-3.875, +/-3.875, 0.0)mm	1/4 -1/4

The coil definition file¶

The coil geometry information is stored in the text file $MNE_ROOT/share/mne/coil_def.dat. In this file, any lines starting with the pound sign (#) are comments. A coil definition starts with a description line containing the following fields:

** <class>**

This is a number indicating class of this coil. Possible values are listed in Coil class values.

** <id>**

Coil id value. This value is listed in the first column of Tables Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included. and Accurate coil descriptions.

** <accuracy>**

The coil representation accuracy. Possible values and their meanings are listed in Coil representation accuracies..

** <np>**

Number of integration points in this representation.

** <size/m>**

The size of the coil. For circular coils this is the diameter of the coil and for square ones the side length of the square. This information is mainly included to facilitate drawing of the coil geometry. It should not be employed to infer a coil approximation for the forward calculations.

** <baseline/m>**

The baseline of a this kind of a coil. This will be zero for magnetometer coils. This information is mainly included to facilitate drawing of the coil geometry. It should not be employed to infer a coil approximation for the forward calculations.

** <description>**

Short description of this kind of a coil. If the description contains several words, it is enclosed in quotes.

Coil class values
Value	Meaning
1	magnetometer
2	first-order axial gradiometer
3	planar gradiometer
4	second-order axial gradiometer
1000	an EEG electrode (used internally in software only).

Coil representation accuracies.
Value	Meaning
1	The simplest representation available
2	The standard or normal representation (see Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included.)
3	The most accurate representation available (see Accurate coil descriptions)

Each coil description line is followed by one or more integration point lines, consisting of seven numbers:

** <weight>**

Gives the weight for this integration point (last column in Tables Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included. and Accurate coil descriptions).

** <x/m> <y/m> <z/m>**

Indicates the location of the integration point (fourth column in Tables Normal coil descriptions. Note: If a plus-minus sign occurs in several coordinates, all possible combinations have to be included. and Accurate coil descriptions).

** <nx> <ny> <nz>**

Components of a unit vector indicating the field component to be selected. Note that listing a separate unit vector for each integration points allows the implementation of curved coils and coils with the gradiometer loops tilted with respect to each other.

Creating the coil definition file¶

The standard coil definition file $MNE_ROOT/share/mne/coil_def.dat is included with the MNE software package. The coil definition file can be recreated with the utility mne_list_coil_def as follows:

mne_list_coil_def –out $MNE_ROOT/share/mne/coil_def.dat

Computing the forward solution¶

Purpose¶

Instead of using the convenience script mne_do_forward_solution it is also possible to invoke the forward solution computation program mne_forward_solution directly. In this approach, the convenience of the automatic file naming conventions present in mne_do_forward_solution are lost. However, there are some special-purpose options available in mne_forward_solution only. Please refer to Computing the forward solution for information on mne_do_forward_solution.

Command line options¶

mne_forward_solution accepts the following command-line options:

—src <*name*>

Source space name to use. The name of the file must be specified exactly, including the directory. Typically, the source space files reside in $SUBJECTS_DIR/$SUBJECT/bem.

—bem <*name*>

Specifies the BEM to be used. These files end with bem.fif or bem-sol.fif and reside in $SUBJECTS_DIR/$SUBJECT/bem. The former file contains only the BEM surface information while the latter files contain the geometry information precomputed with mne_prepare_bem_model , see Computing the BEM geometry data. If precomputed geometry is not available, the linear collocation solution will be computed by mne_forward_solution .

—origin <*x/mm*> : <*x/mm*> : <*z/mm*>

Indicates that the sphere model should be used in the forward calculations. The origin is specified in MEG head coordinates unless the --mricoord option is present. The MEG sphere model solution computed using the analytical Sarvas formula. For EEG, an approximative solution described in

—eegmodels <*name*>

This option is significant only if the sphere model is used and EEG channels are present. The specified file contains specifications of the EEG sphere model layer structures as detailed in The EEG sphere model definition file. If this option is absent the file $HOME/.mne/EEG_models will be consulted if it exists.

—eegmodel <*model name*>

Specifies the name of the sphere model to be used for EEG. If this option is missing, the model Default will be employed, see The EEG sphere model definition file.

—eegrad <*radius/mm*>

Specifies the radius of the outermost surface (scalp) of the EEG sphere model, see The EEG sphere model definition file. The default value is 90 mm.

—eegscalp

Scale the EEG electrode locations to the surface of the outermost sphere when using the sphere model.

—accurate

Use accurate MEG sensor coil descriptions. This is the recommended choice. More information

—fixed

Compute the solution for sources normal to the cortical mantle only. This option should be used only for surface-based and discrete source spaces.

—all

Compute the forward solution for all vertices on the source space.

—label <*name*>

Compute the solution only for points within the specified label. Multiple labels can be present. The label files should end with -lh.label or -rh.label for left and right hemisphere label files, respectively. If --all flag is present, all surface points falling within the labels are included. Otherwise, only decimated points with in the label are selected.

—mindist <*dist/mm*>

Omit source space points closer than this value to the inner skull surface. Any source space points outside the inner skull surface are automatically omitted. The use of this option ensures that numerical inaccuracies for very superficial sources do not cause unexpected effects in the final current estimates. Suitable value for this parameter is of the order of the size of the triangles on the inner skull surface. If you employ the seglab software to create the triangulations, this value should be about equal to the wish for the side length of the triangles.

—mindistout <*name*>

Specifies a file name to contain the coordinates of source space points omitted due to the --mindist option.

—mri <*name*>

The name of the MRI description file containing the MEG/MRI coordinate transformation. This file was saved as part of the alignment procedure outlined in Aligning the coordinate frames. These files typically reside in $SUBJECTS_DIR/$SUBJECT/mri/T1-neuromag/sets .

—trans <*name*>

The name of a text file containing the 4 x 4 matrix for the coordinate transformation from head to mri coordinates. With --trans, --mri option is not required.

—notrans

The MEG/MRI coordinate transformation is taken as the identity transformation, i.e., the two coordinate systems are the same. This option is useful only in special circumstances. If more than one of the --mri , --trans , and --notrans options are specified, the last one remains in effect.

—mricoord

Do all computations in the MRI coordinate system. The forward solution matrix is not affected by this option if the source orientations are fixed to be normal to the cortical mantle. If all three source components are included, the forward three source orientations parallel to the coordinate axes is computed. If --mricoord is present, these axes correspond to MRI coordinate system rather than the default MEG head coordinate system. This option is useful only in special circumstances.

—meas <*name*>

This file is the measurement fif file or an off-line average file produced thereof. It is recommended that the average file is employed for evoked-response data and the original raw data file otherwise. This file provides the MEG sensor locations and orientations as well as EEG electrode locations as well as the coordinate transformation between the MEG device coordinates and MEG head-based coordinates.

—fwd <*name*>

This file will contain the forward solution as well as the coordinate transformations, sensor and electrode location information, and the source space data. A name of the form <name>-fwd.fif is recommended.

—meg

Compute the MEG forward solution.

—eeg

Compute the EEG forward solution.

—grad

Include the derivatives of the fields with respect to the dipole position coordinates to the output, see Field derivatives.

Implementation of software gradient compensation¶

As described in Applying software gradient compensation the CTF and 4D Neuroimaging data may have been subjected to noise cancellation employing the data from the reference sensor array. Even though these sensor are rather far away from the brain sources, mne_forward_solution takes them into account in the computations. If the data file specified with the --meas option has software gradient compensation activated, mne_forward_solution computes the field of at the reference sensors in addition to the main MEG sensor array and computes a compensated forward solution using the methods descibed in Applying software gradient compensation.

Warning

If a data file specified with the --meas option and that used in the actual inverse computations with mne_analyze and mne_make_movie have different software gradient compensation states., the forward solution will be in mismatch with the data to be analyzed and the current estimates will be slightly erroneous.

The EEG sphere model definition file¶

For the computation of the electric potential distribution on the surface of the head (EEG) it is necessary to define the conductivities ( $\sigma$ ) and radiuses of the spherically symmetric layers. Different sphere models can be specified with the --eegmodels option.

The EEG sphere model definition files may contain comment lines starting with a # and model definition lines in the following format:

<name>: <radius1>: <conductivity1>: <radius2>: <conductivity2>:...

When the file is loaded the layers are sorted so that the radiuses will be in ascending order and the radius of the outermost layer is scaled to 1.0. The scalp radius specified with the --eegrad option is then consulted to scale the model to the correct dimensions. Even if the model setup file is not present, a model called Default is always provided. This model has the structure given in Structure of the default EEG model

Structure of the default EEG model
Layer	Relative outer radius	$\sigma$ (S/m)
Head	1.0	0.33
Skull	0.97	0.04
CSF	0.92	1.0
Brain	0.90	0.33

EEG forward solution in the sphere model¶

When the sphere model is employed, the computation of the EEG solution can be substantially accelerated by using approximation methods described by Mosher, Zhang, and Berg, see Forward modeling (Mosher et al. and references therein). mne_forward_solution approximates the solution with three dipoles in a homogeneous sphere whose locations and amplitudes are determined by minimizing the cost function:

$S(r_1,\dotsc,r_m\ ,\ \mu_1,\dotsc,\mu_m) = \int_{scalp} {(V_{true} - V_{approx})}\,dS$

where $r_1,\dotsc,r_m$ and $\mu_1,\dotsc,\mu_m$ are the locations and amplitudes of the approximating dipoles and $V_{true}$ and $V_{approx}$ are the potential distributions given by the true and approximative formulas, respectively. It can be shown that this integral can be expressed in closed form using an expansion of the potentials in spherical harmonics. The formula is evaluated for the most superficial dipoles, i.e., those lying just inside the inner skull surface.

Field derivatives¶

If the --grad option is specified, mne_forward_solution includes the derivatives of the forward solution with respect to the dipole location coordinates to the output file. Let

$G_k = [g_{xk} g_{yk} g_{zk}]$

be the $N_{chan} \times 3$ matrix containing the signals produced by three orthogonal dipoles at location $r_k$ making up $N_{chan} \times 3N_{source}$ the gain matrix

$G = [G_1 \dotso G_{N_{source}}]\ .$

With the --grad option, the output from mne_forward_solution also contains the $N_{chan} \times 9N_{source}$ derivative matrix

$D = [D_1 \dotso D_{N_{source}}]\ ,$

where

$D_k = [\frac{\delta g_{xk}}{\delta x_k} \frac{\delta g_{xk}}{\delta y_k} \frac{\delta g_{xk}}{\delta z_k} \frac{\delta g_{yk}}{\delta x_k} \frac{\delta g_{yk}}{\delta y_k} \frac{\delta g_{yk}}{\delta z_k} \frac{\delta g_{zk}}{\delta x_k} \frac{\delta g_{zk}}{\delta y_k} \frac{\delta g_{zk}}{\delta z_k}]\ ,$

where $x_k$ , $y_k$ , and $z_k$ are the location coordinates of the $k^{th}$ dipole. If the dipole orientations are to the cortical normal with the --fixed option, the dimensions of $G$ and $D$ are $N_{chan} \times N_{source}$ and $N_{chan} \times 3N_{source}$ , respectively. Both $G$ and $D$ can be read with the mne_read_forward_solution Matlab function, see Table 10.1.

Averaging forward solutions¶

Purpose¶

One possibility to make a grand average over several runs of a experiment is to average the data across runs and average the forward solutions accordingly. For this purpose, mne_average_forward_solutions computes a weighted average of several forward solutions. The program averages both MEG and EEG forward solutions. Usually the EEG forward solution is identical across runs because the electrode locations do not change.

Command line options¶

mne_average_forward_solutions accepts the following command-line options:

—version

Show the program version and compilation date.

—help

List the command-line options.

—fwd <*name*> :[ <*weight*> ]

Specifies a forward solution to include. If no weight is specified, 1.0 is assumed. In the averaging process the weights are divided by their sum. For example, if two forward solutions are averaged and their specified weights are 2 and 3, the average is formed with a weight of 2/5 for the first solution and 3/5 for the second one.

—out <*name*>

Specifies the output file which will contain the averaged forward solution.

Table Of Contents

Previous topic

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The forward solution¶

Overview¶

MEG/EEG and MRI coordinate systems¶

The head and device coordinate systems¶

Creating a surface-based source space¶

Creating a volumetric or discrete source space¶

Creating the BEM meshes¶

Command-line options¶

Surface options¶

Tessellation file format¶

Topology checks¶

Computing the BEM geometry data¶

Coil geometry information¶

The sensor coordinate system¶

Calculation of the magnetic field¶

Implemented coil geometries¶

The coil definition file¶

Creating the coil definition file¶

Computing the forward solution¶

Purpose¶

Command line options¶

Implementation of software gradient compensation¶

The EEG sphere model definition file¶

EEG forward solution in the sphere model¶

Field derivatives¶

Averaging forward solutions¶

Purpose¶

Command line options¶

Navigation

Table Of Contents

Previous topic

Next topic

Quick search

The forward solution¶

Overview¶

MEG/EEG and MRI coordinate systems¶

The head and device coordinate systems¶

Creating a surface-based source space¶

Creating a volumetric or discrete source space¶

Creating the BEM meshes¶

Command-line options¶

Surface options¶

Tessellation file format¶

Topology checks¶

Computing the BEM geometry data¶

Coil geometry information¶

The sensor coordinate system¶

Calculation of the magnetic field¶

Implemented coil geometries¶

The coil definition file¶

Creating the coil definition file¶

Computing the forward solution¶

Purpose¶

Command line options¶

Implementation of software gradient compensation¶

The EEG sphere model definition file¶

EEG forward solution in the sphere model¶

Field derivatives¶

Averaging forward solutions¶

Purpose¶

Command line options¶