In Diffusion Weighted MR Imaging (DWI), the signal is affected by the biophysical properties of neuronal cells and their relative placement, as well as extra-cellular tissue compartments. Typically, microstructural indices, such as fractional anisotropy (FA) and mean diffusivity (MD), are based on a tensor model that cannot disentangle the influence of these parameters. Recently, Neurite Orientation Dispersion and Density Imaging (NODDI) has exploited multi-shell acquisition protocols to model the diffusion signal as the contribution of three tissue compartments. NODDI microstructural indices, such as intra-cellular volume fraction (ICVF) and orientation dispersion index (ODI) are directly related to neuronal density and orientation dispersion, respectively. One way of examining the neurophysiological role of these microstructural indices across neuronal fibres is to look into how they relate to brain function. Here we exploit a statistical framework based on sparse Canonical Correlation Analysis (sCCA) and randomised Lasso to identify structural connections that are highly correlated with resting-state functional connectivity measured with simultaneous EEG-fMRI. Our results reveal distinct structural fingerprints for each microstructural index that also reflect their inter-relationships.