# Source localisation methods

Source localization methods rely on mathematical models of the bio-electrical generators and the volume conductors within which they lie.

The forward problem consists in modeling the scalp electromagnetic fields produced by a known source configuration. This modeling requires knowledge of the complex geometry and the different conduction properties of cerebral tissues constituting the brain and its envelopes. Several head models have been proposed. The earliest models consider the head as a series of concentric spheres, each layer corresponding to a different tissue whose conductivity is assumed to be homogeneous. The most used model is constituted of three layers (skin, skull, and an inner medium encompassing all intracranial content). A four-layer model which includes a thin intermediate layer modeling cerebro-spinal fluid is sometimes used. Recently, more realistic surface head models have been proposed. These models are based on the segmentation of anatomical images obtained using magnetic resonance imaging (MRI). The construction of these models relies on the ability of segmentation algorithms to separate the different tissues of the head. These models offer the advantage of taking into account the complex geometry as well as the significant inter-subject variability of the conductor volume. However, as these models are difficult to implement and computationally consuming, spherical head models are still the most used models to solve the forward problem.

The inverse problem consists in finding the source configuration whichcould explain the electromagnetic activity recorded at the scalp. The difficulty in solving the inverse problem is that an infinite number of source configurations can produce equal results at the scalp. Dipolar modeling techniques assume that the event-related electrical brain activity is concentrated in areas whose sizes are small as compared to their distance from the recording electrodes. Indeed, under these conditions, activity within these areas can be assimilated to a single equivalent dipole. Spatio-temporal dipolar-modeling algorithms, introduced by Scherg and Von Cramon (1986), assume that the position (and sometimes the orientation) of equivalent dipoles stay constant within an arbitrarily defined temporal window. The temporal sequence of activity is then explained by a variation in strength (and orientation) of these dipoles. The location, magnitude, and orientation of dipolar sources are then iteratively optimized until the scalp distribution of electromagnetic fields produced by the given configuration best coincides with the actual scalp recording. The key limitation of these methods is the necessity to predefine the number of active sources. This a priori assumption is crucial as it will determine whether a given solution actually provides neurophysiological information about where the recorded signals are generated in the brain. Recent methods have attempted to circumvent the important problem related to arbitrarily defining the number of sources. These methods are based on a ‘distributed source’ model (Dale and Sereno 1993; Pascual-Marqui et al. 1994; Baillet and Garnero 1997). Distributed source models consist in the reconstruction of the brain electrical activity in each point of a three-dimensional mesh. As each point of the mesh is considered a possible location of a current source, no a priori assumption as to the number of dipoles is required. However, as an infinite number of current source distributions can produce the exact same scalp potentials, different constraints are required to identify the most physiologically acceptable solution. The space within which sources are allowed is another important constraint defined by the investigator. For dipole-based algorithms, this constraint is defined by the space that is included in the search procedure. For distributed source algorithms, this constraint is defined by the location of the points constituting the three-dimensional solution mesh. As a-priori assumptions are required to define these constraints, the validity of a given source configuration is conditioned by the validity of these assumptions. Therefore, use of prior experimental results to constrain solutions should be used with caution as this could lead to the introduction of systematic errors or bias.