Parametric Surface-Source Modeling and Estimation With Electroencephalography

Electroencephalography (EEG) is an important tool for studying the brain functions and is becoming popular in clinical practice. In this paper, we develop four parametric EEG models to estimate current sources that are spatially distributed on a surface. Our models approximate the source shape and extent explicitly and can be applied to localize extended sources which are often encountered, e.g., in epilepsy diagnosis. We assume a realistic head model and solve the EEG forward problem using the boundary element method. We present the source models with increasing degrees of freedom, provide the forward solutions, and derive the maximum-likelihood estimates as well as Cramér-Rao bounds of the unknown source parameters. In order to evaluate the applicability of the proposed models, we first compare their estimation performances with the dipole model's using several known source distributions. We then discuss the conditions under which we can distinguish between the proposed extended sources and the focal dipole using the generalized likelihood ratio test. We also apply our models to the electric measurements obtained from a phantom body in which an extended electric source is imbedded. We observe that the proposed model can capture the source extent information satisfactorily and the localization accuracy is better than the dipole model.