Voxel-based dipole orientation constraints for distributed current estimation

Abstract

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.

Fig. 1. Anisotropic Conductivity Tensors

Fiber orientation is denoted by color, with red denoting left-right, green marking anterior-posterior, and blue being superior-inferior.

Fig. 2. Sulci Identification Procedure

a) Original segmentation showing white matter (white), grey matter (grey), and CSF (black). b) First layer of cortex added to white matter (light grey). No thickness violations c) Second layer of cortex added. Voxel in red show high thickness and is labeled as sulcus. d) Third layer added. All voxels in red subsequently labelled as sulci.

Fig. 3. Brain Segmentation Before/After Model Based Sulci Extraction

a) Axial slice of collected T1 data used for segmentation. b) Original segmentation obtained using automated procedure. c) Segmentation following model based sulci extraction.

Fig. 4. MAG and RDM Distributions with Changing Measurement SNR

In all box plots, the box denotes the median, and the 25th and 75th percentiles. The whiskers show total signal range, and outliers are plotted with +’s. a) Box plots of RDM values for measurements SNR levels of 0–15dB. Results with unconstrained dipole orientations are on the left (in red), and results with dipole orientations constraints are on the right (in blue). b) Corresponding MAG plots.

Fig. 5. MAG and RDM Distributions with Changing Number of Active Regions

a) Box plots of RDM values for 1–3 target regions. Results with unconstrained dipole orientations are on the left (in red), and results with dipole orientations constraints are on the right (in blue). b) Corresponding MAG plots. c) Percentage improvement in RDM d) Percentage improvement in MAG

Fig. 6. MAG and RDM Distributions with Changing Image Noise Levels

a) Box plots of RDM values for image noise levels of 5–25%. Results with unconstrained dipole orientations are on the left (in red), and results with dipole orientations constraints are on the right (in blue). b) Corresponding MAG plots. c) Percentage Improvement in RDM d) Percentage Improvement in MAG

Fig. 7. Simulation Results - One Active Region

Reconstruction results for activity simulated within the right superior parietal lobule. (a, d, g, j) show true region of activity in Patients #1–4. (b, e, h, k) show reconstructions with unconstrained dipoles within each voxel. (c, f, i, l) are reconstructions with constrained dipole orientations. Each reconstruction (in color) is overlaid on a slice from the T1 MRI located approximately through the midpoint of the true activity region.

Fig. 8. Simulation Results - Two Active Regions

Reconstruction results for activity simulated within two regions: the right anterior supra marginal gyrus and the right posterior middle temporal gyrus. (a, d, g, j) show true region of activity in Patients #1–4. (b, e, h, k) show reconstructions with unconstrained dipoles within each voxel. (c, f, i, l) are reconstructions with constrained dipole orientations. Each reconstruction (in color) is overlaid on a slice from the T1 MRI located approximately through the midpoint of the true activity region.

Fig. 9. Simulation Results - Three Active Regions

Reconstruction results for activity simulated within the left angular gyrus, posterior aspect of the right inferior temporal gyrus, and the right anterior supra marginal gyrus. (a, g, m, s) show true region of right hemisphere activity in Patients #1–4. (b, h, n, t) show reconstructions in the right hemisphere with unconstrained dipoles within each voxel. (c, i, o, l) are right hemisphere reconstructions with constrained dipole orientations. (d, j, p, v) show the true activity within the left hemisphere. (e, k, q, w) are left hemisphere reconstructions with unconstrained dipoles. (f, l, r, x) are right hemisphere reconstructions with constrained dipole orientations. Each reconstruction (in color) is overlaid on a slice from the T1 MRI located approximately through the midpoint of the true activity region.

Fig. 10. Reconstructions of Interictal Spike Data

Reconstruction images with and without dipole orientation constraints for four patients.