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Self-similar correlation function in brain resting-state fMRI

Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain’s 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e., they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatiotemporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state fMRI data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behavior of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being both in health and disease. It is increasingly evident that brain regions are continuously interacting even when the brain is “at rest” and, more importantly, that the functional networks uncovered from resting data closely matches those derived from a wide variety of different activation conditions [1, 2]. Starting with the uncovering of coherent fluctuations of functional magnetic resonance imaging (fMRI) in time series of motor cortex [3], many other findings have validated the notion of correlated networks as a dynamical substrate of the resting brain. It has been established that these networks, which can be separated on the basis of their temporal features [4–6], are located at consistent locations across subjects and are equally detectable even during sleep [7] and anesthesia [8]. These exciting findings provide a novel window to observe the brain at work and, at the same time, highlight our limited understanding of the functional organization of the brain at large scales [9], compared with the, often precise, knowledge we have of the small (neural circuit level) scale. In particular, little is known on how the cortex is able to solve the conflicting dynamical demands imposed by the functional segregation of local areas differing in their anatomy and physiology on one side and on the other their global integration shown during perception and behavior. This riddle is clearly pointed out by Tononi [10]: “traditionally, localizationist and holist views of brain function have exclusively emphasized evidence for either functional segregation or for