Iterative refinement of the minimum norm solution of the bioelectric inverse problem

Functional brain imaging based on the bioelectric scalp field depends on the solution of the inverse problem. The object is to estimate the current distribution in the cortex from a measured noisy scalp potential field. A minimum norm least squares solution is often used for this purpose. Although this approach leads to a unique solution, it represents only one of a set of feasible solutions. In particular, it leads to a solution in which current is found to be generated widely in the cortex. There are other feasible minimum norm solutions for which cortical current is generated only in a restricted region, and it is likely that in many cases, these solutions are of physiological importance. This study presents a method to uncover these solutions. It is based on the idea that a minimum norm solution can be used to define a region of interest, an ellipsoid, within which it is worthwhile to search for another feasible solution. The minimum norm approach is used iteratively and the ellipsoid shrinks. As it shrinks it provides evidence pointing to the location of the active cortical region. The method explicitly recognizes the role of measurement noise in defining feasible solutions. It is tested in a model of the human head that incorporates a realistic cortex in a three-shell sphere. The method improves the localization of cortical activity mimicking physiological processing.