Voxel-Based Dipole Orientation Constraints for Distributed Current Estimation

Distributed electroencephalography source localization is a highly ill-posed problem. With measurements on the order of 10
²
, and unknowns in the range of 10
⁴
-10
⁵
, the range of feasible solutions is quite large. One approach to reducing ill-posedness is to intelligently reduce the number of unknowns. Restricting solutions to gray matter is one approach. A further step is to use the anatomy of each patient to identify and constrain the orientation of the dipole within each voxel. While dipole orientation constraints for cortical patch-based approaches have been proposed, to our knowledge, no solutions for full volumetric localizations have been presented. Patch techniques account for patch surface area, but place dipoles only on the surface, rather than throughout the cortex. Variability in human cortical thickness means that thicker regions of cortex will potentially contribute more to the EEG signal, and should be accounted for in modeling. Additionally, patch models require cortical surface identification techniques, which can separate them from the extensive literature on voxel-based MR image processing, and require additional adaptation to incorporate more complex information. We present a volumetric approach for computing voxel-based distributed estimates of cortical activity with constrained dipole orientations. Using a tissue thickness estimation approach, we obtain estimates of the cortical surface normal at each voxel. These let us constrain the inverse problem, and yield localizations with reduced spatial blurring and better identification of signal magnitude within the cortex. This is demonstrated for a series of simulated and experimental data using patient-specific bioelectric models.