Linking human brain local activity fluctuations to structural and functional network architectures

Abstract

Activity of cortical local neuronal populations fluctuates continuously, and a large proportion of these fluctuations are shared across populations of neurons. Here we seek organizational rules that link these two phenomena. Using neuronal activity, as identified by functional MRI (fMRI) and for a given voxel or brain region, we derive a single measure of full bandwidth brain-oxygenation-level-dependent (BOLD) fluctuations by calculating the slope, α, for the log-linear power spectrum. For the same voxel or region, we also measure the temporal coherence of its fluctuations to other voxels or regions, based on exceeding a given threshold, Θ, for zero lag correlation, establishing functional connectivity between pairs of neuronal populations. From resting state fMRI, we calculated whole-brain group-averaged maps for α and for functional connectivity. Both maps showed similar spatial organization, with a correlation coefficient of 0.75 between the two parameters across all brain voxels, as well as variability with hodology. A computational model replicated the main results, suggesting that synaptic low-pass filtering can account for these interrelationships. We also investigated the relationship between α and structural connectivity, as determined by diffusion tensor imaging-based tractography. We observe that the correlation between α and connectivity depends on attentional state; specifically, α correlated more highly to structural connectivity during rest than while attending to a task. Overall, these results provide global rules for the dynamics between frequency characteristics of local brain activity and the architecture of underlying brain networks.

Introduction

Relating structure and function is fundamental to understanding the mechanisms of information processing in the brain. Non-invasive functional brain imaging, specifically MRI/fMRI, has played a pivotal role in demonstrating structure–function rules due to its capability to localize activity and relate it to structural features across the whole brain, on the scale of millimeters. Recent studies examining brain activity during rest demonstrate large-scale functional organizational rules, thus revealing intrinsic dynamical properties of the brain (Fox and Raichle, 2007). Likewise, functional connectivity (FC) of the brain during rest shows correspondences to structural connectivity (SC), although this relationship is intricate and not reciprocal — i.e., SC is highly indicative of FC, but not vice versa (Adachi et al., 2012, Greicius et al., 2009, Honey et al., 2009, Vincent et al., 2007). Still, rules with which structural and functional networks shape and constrain each other remain fundamental, unanswered questions in the field.

The power spectrum of brain activity signals is related to various network properties. This relationship has been captured across many studies using multiple methods such as fMRI (Ding et al., 2011, Tomasi and Volkow, 2011), EEG (von Stein et al., 1999), cultured neuronal networks (Jia et al., 2004, Muramoto et al., 1993), multi-unit activity (Konig et al., 1995), simultaneous single-unit recording and optical imaging (Tsodyks et al., 1999), and computational models (Steinke and Galan, 2011). These results have highlighted the central role of the spectral profile in understanding the structure–function interactions in the brain. However, most fMRI research has utilized only the low frequency component of the BOLD signal, assuming that frequencies above 0.1 Hz are contaminated with noise. On the other hand, BOLD frequencies above 0.1 Hz exhibit coherent patterns of activity (Niazy et al., 2011) and show an anatomically constrained distribution of power as a function of BOLD frequency (Baria et al., 2011). Therefore, it remains largely unknown how the full bandwidth properties of the BOLD signal relate to brain network properties. Here we aim to show that the architecture of synchronous brain networks and white matter networks (structure) is tightly related to the fluctuations of local BOLD activity (function).

In the frequency domain, the full bandwidth power spectrum of fMRI BOLD signal (approximately 0–0.24 Hz) roughly follows a straight line when viewed in log power versus frequency: log (P) = − α(f). The value (α) offers a glimpse of the distribution of power across frequencies, and in a sense it provides some information about the heterogeneity of the informational content that is observed locally. The larger the absolute value of α, the higher the relative power at lower frequencies in the signal, whereas smaller values suggest that the fluctuations are more random, with less temporal redundancy, and are therefore more efficient in online information processing (He, 2011, Mandelbrot and Van Ness, 1968). Here we examine the relationship between α and FC, i.e., the presence of temporal coherence of BOLD activity, as well as α and SC, i.e., the presence of anatomical connectivity based on diffusion tensor imaging probabilistic tractography, for fMRI activity during either resting state or during a visual-motor attention task. We assess this relationship at different spatial resolutions and as a function of its underlying regional synaptic wiring. First, we test the hypothesis that the distribution of power in local fluctuations, at a per voxel basis, is related to the number of functionally connected voxels across the whole brain. Second, we parcel the brain into 3 anatomical regions of differing hodology that correspond to synaptic wiring and functional complexity (including unimodal, heteromodal, and limbic–paralimbic regions (Mesulam, 1998)), and we examine differential relations between the power of local fluctuations and FC. Third, to our knowledge, the MRI structure–function studies have solely relied on resting scan conditions, perhaps due to the growing evidence that functional networks during rest and task are spatially (Greicius et al., 2004, Smith et al., 2009) and dynamically (Tagliazucchi et al., 2011) similar. Previous work from our lab, however, counters this notion by demonstrating widespread shifts in BOLD frequency power between rest and task conditions (Baria et al., 2011). Here we demonstrate that BOLD power is differentially related to network architecture according to brain state, i.e., during rest versus attending to task. The significance of such an investigation lies in its potential to provide global rules for the dynamics between the spectral characteristics of local brain activity in relation to the architecture of underlying brain networks, as well as in relation to brain state.