As in any other inverse method, source estimation with the help of LORETA also requires several sophisticated steps, grouped into the forward and inverse problem. No worries, all these steps are implicitly taken care of in the implementation of LORETA in Analyzer 2. Thus, what is expected from you are mainly two things:
- Valid head coordinates. If your data does not contain valid head coordinates (standard or realistic), you can adopt the default coordinates as defined internally in Analyzer 2, as long as your channel names match the international 10-20 electrode system and its derivatives (i.e., 10-10 and 10-5 systems). Moreover, it is also recommended to have a uniform distribution of the electrodes throughout the scalp with the number of electrodes being at least 64 or higher (Michel CM et al., 2004). The coordinate system used by Analyzer 2 is illustrated in the User Manual (Appendix C Electrode coordinate system).
- Voltage measurements (EEG data). The most important pre-requisite which is highly specific to Analyzer’s LORETA is that only time-domain voltage values are valid input for the algorithm. Moreover, as in any kind of scalp-level analyses, for e.g., ERP analysis, source analysis also benefits from a high signal-to-noise ratio, which can be achieved by having well pre-processed data.
This is the only prior information that is required from your side. However, if you are curious to know more about the implicit mechanisms of the forward and inverse problem, we will provide you with the basic ingredients without going too deeply into the mathematics behind it. To start with, consider that you have two domains: one being the electrode space where you have the voltage measurements and the second one being the source space, where the neuronal current sources are confined inside the brain. As mentioned above, the forward problem computes the electrical potentials based on the information about channel coordinates from the electrode space and the source parameters (position, orientation and magnitude of the neuronal current sources) from the source space. This computation entails modeling of 1) the neuronal current sources and its spatial distribution within the brain as well as 2) the volume conductor medium.
- Source model: a pre-defined source space is important to model sources. In Analyzer 2, the source space is restricted to the regions of the cortical gray matter and hippocampus in the Talairach atlas, discretized into a total of 2394 voxels at 7 mm spatial resolution. These sources are then modeled using equivalent current dipoles.
- Volume conductor model (anatomical and head models): it describes the geometrical and conductive properties of the head. In Analyzer 2, we offer a standard brain which is based on the MNI-305 brain template. The MNI images are co-registered to the Talairach brain atlas to map the detailed brain structures into the MNI space. Moreover, our LORETA implementation is based on a 3-shell spherical head model. This head model is fitted to the MNI brain template, which has already been co-registered to the Talairach brain atlas.
In addition, the electrodes shall be projected to the co-registered spherical head model. Once all these ingredients are brought to the same coordinate system, the lead-field matrix, [Nelectrodes x 3Msources] (3 represents the X, Y and Z components of the sources), is computed. This matrix serves as a mapping mechanism from the neuronal current sources within the brain to the electrical potentials on the head surface.
All of the above steps are necessary pre-requisites for solving the inverse problem. The inverse problem aims to minimize the difference between the true voltage measurements and the calculated electrical potentials, as provided by the forward solution. Strikingly, there is an infinite number of source spatial configurations giving rise to the same voltage distribution. Therefore, the inverse problem in general does not have a unique solution, unless certain assumptions and mathematical constraints are imposed. In the case of LORETA, a unique inverse solution is achieved by imposing a constraint on the spatial configurations of the neuronal current sources, i.e., LORETA aims to find the smoothest spatial distributon within the source space. (Pascual-Marqui et al., 1994 and Pascual-Marqui et al., 1999). Finally, the unique inverse matrix, [3Msources x Nelectrodes], fulfills all the conditions mentioned above, which relates the true voltage measurements to the estimated neuronal current sources.