Stable Identification of Sources Associated with Epileptic Focus on the Cerebral Cortex

Abstract

Objective: To present a stable algorithm that determines, from electroencephalographic measurements, the para-meters of dipolar sources associated with epileptic foci located on the cerebral cortex. Methodology: A boundary value problem is used to establish correlations between the sources and the measurements. The problem is divided into two linear subproblems and in each one, the method of Minimum Square and the Tikhonov regularization are used for finding stables solutions. These subproblems are an ill-posed problem in the Hadamard sense, which is due to the numerical instability, that is, small changes in the data can produce substantial variations in the solution of each problem. The Tikhonov regularization parameter was chosen using the L curve method. To find the solution of the boundary value problem are used the Fourier series method and the Finite Element Method. Results: A type of source that represents the epileptic foci on the cerebral cortex and a stable algorithm for finding the parameter of these sources were proposed. Synthetics examples and MATLAB programs were developed for the case of bidi-mensional geometry. Originality: The separation of the original problem into two subproblems and the synthetics examples are a product of this research. Conclusion: A stable algorithm was proposed for determining the parame-ters of the dipolar current defined on the cerebral cortex.