Registering imaged ECoG electrodes to human cortex: A geometry-based technique

Abstract

Background: The accurate localization of implanted ECoG electrodes over the brain is of critical importance to invasive diagnostic work-up for the surgical treatment of intractable epileptic seizures. The implantation of subdural electrodes is an invasive procedure which typically introduces non-uniform deformations of a subject's brain, increasing the difficulty of determining the precise location of the electrodes vis-à-vis cortex. Formalization of this problem is used to define a novel solution for the optimal localization of subdural electrodes.

New method: We demonstrate that nonlinear transformation is required to accurately register the implanted electrodes to the non-deformed pre-surgical cortical surface, and that this problem is accommodated by utilizing known features of electrode geometry. Techniques to register chronically implanted subdural electrodes to the undistorted brain image are described and evaluated using simulated and clinical data.

Results: Principal Axis, our novel analysis method that estimates an electrode's orientation by the moment of inertia of the solid electrode volume, proved to be the most reliable measure in both the simulated and clinical datasets.

Comparison with existing methods: This method of electrode translation along its principal axis is an improvement over other techniques, such as the limited view provided by intraoperative photography, and the image degradation inherent in post-operative MRI.

Conclusions: This technique compensates for alterations due to post-operative brain edema, and translates subdural electrodes to their original location on pre-operative MRI 3D models. This is helpful in the correct localization of seizure foci and functional mapping of epilepsy patients.

Keywords: Brain deformation; Electrocorticography (ECoG); Electrode registration; Epilepsy surgery; Geometric modeling; Subdural electrodes.

Figure 1

Two examples of how electrodes (yellow) shift in axial slices of post-operative CT (red) co-registered to pre-operative MRI (grey). a) (patient 4) A typical patient with a moderate (1 cm) medial shift of right frontal and parietal electrodes. b) (patient 1) A patient with occipital electrodes showing anterior shift of left occipital electrodes. These shifts reflect the underlying brain deformation.

Figure 2

An S² manifold C deforms into another S² manifold C′ by homeomorphism s. electrodes E are mapped to E′ by s.

Figure 3

3D rendered ECoG electrodes from a CT scan. The electrodes as imaged in high resolution CT exhibit disk-like geometry as they progressively wrap around the cortex (blue: electrodes, green: translation to the dura).

Figure 4

Simulated electrodes (radius = 2.5 mm, thickness = 2.5 mm) digitized in the same anisotropic CT voxels (0.5 × 0.5 × 0.5 mm resolution), but at different orientations to the voxel plane (left column in-plane, center and right columns out-of-plane) and shown from different angles (rows). The true orientation of the electrode is represented by the black line and the three colored lines represent the orientation calculated by each of the three measures: Best-Fitting Plane (BFP; yellow), RANSAC (R; blue), and Principal Axis (PA; red). The angular displacement between the true and calculated electrode orientation increases when the orientation of the electrode does not match the voxel slice orientation. Nevertheless, the Principal Axis method significantly outperformed the other two measures regardless of electrode orientation. Some overlapping axes are not visible.

Figure 5

Histograms showing the results of the accuracy in degrees between the true orientation and the orientations estimated by the three proposed methods. The Principal Axis method shows the lowest angular displacement highlighting it as the most robust and reliable method.

Figure 6

Histograms showing the results of the accuracy in degrees between the true orientation and the orientations estimated by Principal Axis at voxel resolutions varying from 0.2 mm isotropic to 1.5 mm isotropic. Mean accuracy decreases linearly with cubic voxel size.

Figure 7

(patient 1) An electrode (marked with cursors and arrow) segmented from CT, and registered to the presurgical MRI, floating in space over a sulcus.

Figure 8

Electrodes registered to the cortical surface for three representative patients. Electrodes registered using Principal Axis are marked red, Manually marked cyan, and Nearest Neighbor Approximation marked yellow. White electrodes denote electrodes not registered due to poor signal quality or merged contacts. Pink electrodes highlight errors in registration that led to the placement onto an incorrect gyral surface.

Figure 9

Individual electrode histograms reflecting the difference in mislocalization errors in mm between Nearest Neighbor and Principal Axis methods, presented for each of the 10 patients. Positive values on the x-axis reflect the number of individual electrodes that were better localized with Principal Axis, and negative numbers on the x-axis reflect the number of individual electrodes that were better localized with Nearest Neighbor.