Source Localization

The existence ofdetectable magnetic fields and electric potential distributions at the head surface is a consequence of the physics of electromagnetism. Given an adequate description of the source currents and the conductivity properties of the medium, it is possible to compute the anticipated field topographies. Calculations to solve this so-called forward problem can employ models of greater or lesser detail, depending on the complexity of the system and the required degree of accuracy. Computation of the forward problem for more complex source distributions—extended regions of activation or multiple active sources—is more time-consuming, but not significantly more difficult. The principle of superposition tells us that the contributions for multiple source currents will sum linearly.

In principle, it may be feasible to invert the process—to compute the currents that give rise to an observed field or potential distribution at the head surface. Unfortunately, this inverse problem is not well-behaved. In general, many different current distributions can produce the same set of surface measure ments. To appreciate the problem intuitively, consider a homogeneous spherical volume that is conductive. It is possible to account for any given potential or magnetic field distribution measured at or above the surface, with a suitable collection of currents limited to the surface of the sphere. However, we can define another spherical shell 1 cm below the surface and derive another current distribution to account for the same set of observations. Given this fundamental ambiguity, how can we hope to reconstruct the proper set of current sources buried deep in the brain from the data available at the head surface?

The general strategy is to build a model of the sources that might produce the observed responses. The source model defines the structure of the solution. Model parameters define the details. In some cases, source models are very restrictive, so that a single, best-fitting set of model parameters can be found. In such cases, the accuracy of the solution depends on the applicability of the source model. As the complexity of the source model increases, generally the number of parameters also increases. This allows more complex source distributions to be modeled, but tends to increase the ambiguity of the reconstruction problem. By defining the criteria that we prefer in an acceptable solution it is generally possible to find a solution, but again, the accuracy of the solution depends on the validity of the assumptions.

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