# Forward computations of the EEG/MEG leadfields

FieldTrip has a consistent set of low-level functions for forward computations of the EEG potential or MEG field. The spatial distribution of a known source in a volume conductor is called a leadfield.

The forward module comprises a complete toolbox of high-quality forward methods, i.e. it contains all functions to set up the volume conduction models of the head and to compute the leadfields. Using the high-level FieldTrip functions and the inverse module, these can be used for reconstructing the sources given real experimental MEG and EEG data.

The objective of supplying these low-level functions as a seperate module/toolbox are to

- facilitate the reuse of these functions in other open-source projects (e.g. EEGLAB, SPM)
- facilitate the implementation and support for new inverse methods, esp. for external users/contributors
- facilitate the implementation of advanced features

The low-level functions for source estimation/reconstruction are contained in the forward and inverse toolboxes, which are released together with FieldTrip. If you are interested in using them seperately from the FieldTrip main functions, you can also download them separately here. For reference: in the past the forward and inverse modules were combined in a single “forwinv” toolbox.

Please note that if you are an end-user interested in analyzing experimental EEG/MEG data, you will probably want to use the high-level FieldTrip functions. The functions such as **ft_preprocessing**, **ft_timelockanalysis** and **ft_sourceanalysis** provide a user-friendly interface that take care of all relevant analysis steps and the data bookkeeping.

## Module layout

The forward module contains functions with a user interface that will be easily understood by experimenced programmers and methods developers and can be considered medium-level functions. They have a clear and consistent programming interface (API) which hides the specific details particular volume conduction models and that allows software developers to write forward methods without having to worry about integrating it with the inverse methods worry about data handling. The low-level functions on which the functions in the forward module depend are located in a private subdirectory which is not accessible from the MATLAB command line.

The forward module is complemented by an inverse module that contains the implementation of various high-quality inverse source estimation algorithms, such as dipole fitting, beamforming and linear estimation using the minimum-norm approach.

Instead of implementing all forward methods completely from scratch, the FieldTrip forward module makes use of some high quality implementations that have been provided by the original method developers. Some of these contributions consist of MATLAB code, some contain MEX files and some are implemented using an external command-line executable that is called from the command-line. All of these external implementations are fully wrapped in the FieldTrip forward module and do not require specific expertise on behalf of the end-user.

## Supported methods for forward computations of the potential or field

The following forward methods are implemented for computing the electric potential (EEG):

- single sphere
- multiple concentric spheres with up to 4 shells
- boundary element model (BEM)
- leadfield interpolation using a precomputed grid
- all forward models supported by the Neuromag meg-calc toolbox

The following forward methods are implemented for computing the magnetic field (MEG):

- single sphere (Cuffin and Cohen, 1977)
- multiple spheres with one sphere per channel (Huang et al, 1999)
- realistic single-shell model based on leadfield expansion (Nolte, 2003)
- leadfield interpolation using a precomputed grid

## Definition of the high-level function-calls (user interface)

Normally, end-users of the FieldTrip toolbox would use the functions in the main FieldTrip directory and not be calling the functions that are part of the forward module directly . The high-level FieldTrip functions characterize themself by having a cfg argument as the first input, doing data handling, conversions of objects and try to support backward-compatibility with older end-user analysis scripts.

Some high-level functions that are of relevance for forward modeling are:

**ft_prepare_headmodel**, this calls ft_headmodel_xxx (see below)**ft_prepare_leadfield**, this calls ft_prepare_vol_sens and ft_compute_leadfield (see below)

These are explained in more detail in the appropriate tutorials.

## Definition of the low-level function-calls (API)

Volume conduction models of the head are represented as a MATLAB structure, which content depends on the model details. In the subsequent documentation the volume conduction model structure is referred to as **vol**. The electrodes in case of EEG, or magnetometers or gradiometers in case of MEG, are described as a MATLAB structure. In the subsequent documentation this is referred to as **elec** for electrodes, **grad** for magmetometers and/or gradiometers, or **sens** to represent either electrodes or gradiometers.

Using the FieldTrip fileio module one can read in volume conduction models and the definition of the sensor array (electrodes or gradiometers) from file by using the **ft_read_vol** and/or **ft_read_sens** functions:

[vol] = ft_read_vol(filename) [sens] = ft_read_sens(filename)

This assumes that the volume conduction model was created in external software (e.g. CTF, Neuromag, or ASA) and that the sensor description is stored in an external acquisition-specific file format.

Alternative to reading the volume conduction model from an external file, you can of course also generate a volume conduction model based on a geometrical description of the head. For example, you can fit a single or multiple spheres to a set of points that describes the head surface. FieldTrip provides a separate function for the constructing of a head model for each of the EEG/MEG computational forward methods:

[vol] = ft_headmodel_asa(filename, ...) [vol] = ft_headmodel_bem_cp(geom, ...) [vol] = ft_headmodel_concentricspheres(geom, ...) [vol] = ft_headmodel_dipoli(geom, ...) [vol] = ft_headmodel_halfspace(location, orientation, ...) [vol] = ft_headmodel_infinite(...) [vol] = ft_headmodel_localspheres(geom, grad, ...) [vol] = ft_headmodel_openmeeg(geom, ...) [vol] = ft_headmodel_singleshell(geom, sens, ...) [vol] = ft_headmodel_singlesphere(pnt, ...)

Most of these functions take a geometrical description of the head, skull and/or brain surface as input. These geometrical descriptions of the shape of the head can for example be derived from an anatomical MRI, from a CT scan, or from a Polhemus measurement of the outside of the scalp. In most cases the geometrical model consists of a Nx3 matrix with surface points, which is sometimes accompanied with a description of the triangles that form the surface. The processing of the anatomical data such as MRIs to construct a geometrical model is not part of the forward module and is described elsewhere specifically for MEG and EEG.

Detailed information for each of the functions that creates a head model can be found in the respective reference documentation: **ft_headmodel_asa**,
**ft_headmodel_bemcp**,
**ft_headmodel_concentricspheres**,
**ft_headmodel_dipoli**,
**ft_headmodel_halfspace**,
**ft_headmodel_infinite**,
**ft_headmodel_localspheres**,
**ft_headmodel_openmeeg**,
**ft_headmodel_singleshell**,
**ft_headmodel_singlesphere**.

If desired the volume conduction model and the sensor array can be spatially transformed using a 4×4 homogenous transformation matrix. E.g. the electrodes can be translated and rotated to align them with head coordinate system, or they can be translated and rotated to switch to another coordinate system.

[vol] = ft_transform_vol(transform, vol) [sens] = ft_transform_sens(transform, sens)

The reason for using the **ft_transform_sens** and **ft_transform_vol** functions is that they allow you to transform any sensor type (EEG and/or MEG) and any volume conduction model without you having to manipulate the elements within the sens or vol structure.

Up to here the head model only depends on the geometrical description of the volume conductor and is independent of the data, with exception of the MEG localspheres model. The consequence is that the head model can be used for multiple experimental sessions, multiple electrode or gradiometer placements, or different selections of channels for a single session. The head model, i.e. the **vol** structure, can be saved to disk and re-used in an analysis on the next day.

Following the initial set-up of the head model, but prior to the actual forward computations, the **ft_prepare_vol_sens** function should be called to link the head model and the sensors and make a data dependent forward model (consisting of the vol and sens).

[vol, sens] = ft_prepare_vol_sens(vol, sens, ...)

The **ft_prepare_vol_sens** function does a variety of things, depending on the peculiarities of the sensors and head model. It can be used for channel selection, which sometimes involves both the sensors and volume conduction model (e.g. in case of a localspheres MEG model). It will project EEG electrodes (which are described as a Nx3 set of points) onto the scalp surface. It will provide an interpolation of the BEM potential (which is usually computed at the vertices) onto the electrodes. In general the **ft_prepare_vol_sens** function tries to carry out as many preparations as possible, so that subsequently the leadfields can be computed as efficiently as possible.

Finally the subsequent computation of the EEG potential or MEG field distribution is done with the **ft_compute_leadfield** function:

[lf] = ft_compute_leadfield(pos, sens, vol, ...)

Most functions have additional optional input arguments that are specified as key-value pairs.

## Boundary element method (BEM) implementations

FieldTrip relies on external contributed software for the low-level computations of the BEM system matrix. The external software is included in the standard FieldTrip release in the external directory.

### fieldtrip/external/openmeeg

The OpenMEEG software is developed within the Athena project-team at INRIA Sophia-Antipolis and was initiated in 2006 by the Odyssee Project Team (INRIA/ENPC/ENS Ulm). OpenMEEG solves forward problems related to Magneto- and Electro-encephalography (MEG and EEG) using the symmetric Boundary Element Method, providing excellent accuracy.

The MATLAB interface to the OpenMEEG implementation is kindly provided by Maureen Clerc, Alexandre Gramfort, and co-workers.

### fieldtrip/external/bemcp

The bemcp implementation is kindly provided by Christophe Phillips, hence the “CP” in the name.

### fieldtrip/external/dipoli

The dipoli implementation is kindly provided by Thom Oostendorp.

## Finite element method (FEM) implementation

FieldTrip makes use of external contributed software for the low-level computations of the finite element method, which is included in the standard FieldTrip release in the external directory.

### fieldtrip/external/simbio

The simbio implementation is kindly provided by Carsten Wolters and colleagues. More information can be found here.

## Standard International Units

MATLAB allows the representation of any data in arrays, but does not have an explicit mechanism for dealing with the representation of physical properties of the numbers in those arrays. The FieldTrip data structures provide slightly more information on the units of the numbers represented in the arrays and considers:

- the geometrical properties of the volume conduction model
- the conductive properties of the volume conduction model
- the geometrical properties of the sensor description
- the geometrical properties of the source model
- the units of the channel level values (e.g. T, uV or fT/cm)
- the units of of dipole strength

The forward module functions are written such that they operate correctly if all input data to the functions is specified according to the International System of Units, i.e. in meter, Volt, Tesla, Ohm, Ampere, etc. The high-level FieldTrip code or any other code that calls the forward module functions (e.g. EEGLAB) is responsible for data handling and bookkeeping and for converting MATLAB arrays and structures that represent units into SI units prior to passing the arrays and structures to the forward code.

# Related documentation

The literature references to the implemented methods are given here.

Frequently asked questions about forward and inverse modeling:

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