Fig. 1: Reconstruction of neocortical activity with geometric eigenmodes.
a, Geometric eigenmodes are derived from the cortical surface mesh by solving the eigenvalue problem, \(\Delta \psi =-\,\lambda \psi \) (equation (1)). The modes \({\psi }_{1},\,{\psi }_{2},{\psi }_{3},\ldots ,\,{\psi }_{N}\) are ordered from low to high spatial frequency (long to short spatial wavelengths). Negative, zero and positive values are coloured blue, white and red, respectively. b, Modal decomposition of brain activity data. The example shows how a spatial map, \(y({\bf{r}}\,,t)\), at a given time, t, can be decomposed as a sum of modes, ψj, weighted by aj. c, Left, we reconstruct task-evoked data using spatial maps of activation for a diverse range of stimulus contrasts. Right, we reconstruct spontaneous activity by decomposing the spatial map at each time frame and generating a region-to-region FC matrix. d, Reconstruction accuracy of seven key HCP task-contrast maps (Supplementary Information 2.1) and resting-state FC as a function of the number of modes. Insets show cortical surface reconstructions, demonstrating the spatial scales relevant to the first 10, 100 and 200 modes corresponding to spatial wavelengths of approximately 120, 40 and 30 mm, respectively. e, Group-averaged empirical task-activation maps and reconstructions (recon.) obtained using 10, 100 and 200 modes of the seven key HCP task contrasts. Black arrowheads indicate localized activation patterns that are more accurately reconstructed when using short-wavelength modes. f, Group-averaged empirical resting-state FC matrices and reconstructions using 10, 100 and 200 modes.
