Encoding cortical dynamics in sparse features

Abstract

Distributed cortical solutions of magnetoencephalography (MEG) and electroencephalography (EEG) exhibit complex spatial and temporal dynamics. The extraction of patterns of interest and dynamic features from these cortical signals has so far relied on the expertise of investigators. There is a definite need in both clinical and neuroscience research for a method that will extract critical features from high-dimensional neuroimaging data in an automatic fashion. We have previously demonstrated the use of optical flow techniques for evaluating the kinematic properties of motion field projected on non-flat manifolds like in a cortical surface. We have further extended this framework to automatically detect features in the optical flow vector field by using the modified and extended 2-Riemannian Helmholtz-Hodge decomposition (HHD). Here, we applied these mathematical models on simulation and MEG data recorded from a healthy individual during a somatosensory experiment and an epilepsy pediatric patient during sleep. We tested whether our technique can automatically extract salient dynamical features of cortical activity. Simulation results indicated that we can precisely reproduce the simulated cortical dynamics with HHD; encode them in sparse features and represent the propagation of brain activity between distinct cortical areas. Using HHD, we decoded the somatosensory N20 component into two HHD features and represented the dynamics of brain activity as a traveling source between two primary somatosensory regions. In the epilepsy patient, we displayed the propagation of the epileptic activity around the margins of a brain lesion. Our findings indicate that HHD measures computed from cortical dynamics can: (i) quantitatively access the cortical dynamics in both healthy and disease brain in terms of sparse features and dynamic brain activity propagation between distinct cortical areas, and (ii) facilitate a reproducible, automated analysis of experimental and clinical MEG/EEG source imaging data.

Keywords: Helmholtz–Hodge decomposition; MEG source imaging; epilepsy; motion field; optical flow.

Figure 1

Examples of different types of vector fields (green arrows) and their corresponding U and (H) HHD components. (A) Emerging source represented by a minima in the scalar potential U. (B) Traveling source detected by (H). (C) Receding source represented by a maxima in the scalar potential U.

Figure 2

Decomposition of cortical activity in a series of dynamic features. Response to median nerve stimulation of the right wrist. Upper panel shows the butterfly plot of somatosensory evoked fields (SEFs). Two features identified by HHD are shown in the middle panel. Bottom panel shows zoom view of the detected features.

Figure 3

Lesion is shown on T2 (left) and T1 (right) with red outline. Epileptic activity emerging from the edge of the lesion is shown as texture map.

Figure 4

Encoding of epileptic spike in diverging features. (A) MEG traces with epileptic spike marked. (B) MRI with MEG activity represented as the color texture. (C) Average MEG activity during the spike. (D) U HHD scalar potential is mapped onto the cortical surface using textured colors. The divergence part of vector flow of MEG sources is represented by green arrows at each vertex location. Critical points in the U map (shown with magenta sphere) reveal sources shown in dark blue and sink in red.