A Network Inversion Technique for Estimating Equivalent Dipole Description of Visual Evoked Potential

Estimation of intra-cranial neural activities by means of regularized neural-network-based inversion techniques

Artificial neural networks can be exploited to solve inverse problems arising from the estimation of neural activities in the brain. In this paper, we review the network inversion techniques for solving inverse problems with special attention directed towards electroencephalographic dipole localization and the improvement of positron emission tomography. In our regularized network inversion technique, for stabilizing the solution, we explicitly include the a priori knowledge by adding penalty terms to the energy function and/or build this knowledge into the architecture of the multi-layered neural networks that are used as an inverse problem solver. In the electroencephalogram analysis, the consensus term added to the energy function facilitated 3-dipole localization for visually evoked potentials. Effectiveness of our regularization is shown in improving the positron emission tomographic images and for generating metabolic images of the brain, under the constraints given by the a priori knowledge inherent to the measurement systems and physiological rules.

EEG source localization: a neural network approach

Functional activity in the brain is associated with the generation of currents and resultant voltages which may be observed on the scalp as the electroencephelogram. The current sources may be modeled as dipoles. The properties of the current dipole sources may be studied by solving either the forward or inverse problems. The forward problem utilizes a volume conductor model for the head, in which the potentials on the conductor surface are computed based on an assumed current dipole at an arbitrary location, orientation, and strength. In the inverse problem, on the other hand, a current dipole, or a group of dipoles, is identified based on the observed EEG. Both the forward and inverse problems are typically solved by numerical procedures, such as a boundary element method and an optimization algorithm. These approaches are highly time-consuming and unsuitable for the rapid evaluation of brain function. In this paper we present a different approach to these problems based on machine learning. We solve both problems using artificial neural networks which are trained off-line using back-propagation techniques to learn the complex source-potential relationships of head volume conduction. Once trained, these networks are able to generalize their knowledge to localize functional activity within the brain in a computationally efficient manner.