The Instantaneous And Dynamical EEG Inverse Problem Under The State Space Model

The EEG(electroencephalographic) inverse problem should be considered as a system which has known the output in order to find the input. There are more and more application about this technology in the field of clinical diagnosis of brain and cognitive science. In our case, we take the system output as measurement, and the corresponding input is treated as the state parameters, what should we do next is to solve the state space model. In this thesis, we firstly take a brief introduction about the existing methods of this research, and then the new method is showed.The difficulty of inverse problem which use the distributed sources as the source model is that the solution is non-unique, because in the inverse problem, the number of unknowns is much larger than the number of effective equations. The traditional methods put some mathematic and physical constraint to the problem in order to obtain the optimal solution, and they all ignore the electrophysiological nature of EEG. We use the Kalman Filter to solve the state space problem which contains a electrophysiological equation in the state space model. It is happy to see that our method has some advantages in the source localization.The Jansen's Neural Mass Model can represent the dynamics of neural activity, we have done some work to diagnose the Alzheimer Disease by analyzing the parameters of the model and find their differences between the patients and the healthy people. For the dynamical EEG inverse problem, we add this model to the state space, in other words, we use the Jansen's Neural Mass Model to describe the dipoles. As this problem is nonlinear now, so we use the unscented Kalman Filter to solve the problem, and the results show that this method can respond the dynamical property of the EEG inverse problem.