Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to external inputs. Here, we consider two measures of phase synchronization: the phase-lock interval, or duration of coupling between a pair of (neurophysiological) processes, and the lability of global synchronization of a (brain functional) network. Using computational simulations of two mechanistically distinct systems displaying complex dynamics, the Ising model and the Kuramoto model, we show that both synchronization metrics have power law probability distributions specifically when these systems are in a critical state. We then demonstrate power law scaling of both pairwise and global synchronization metrics in functional MRI and magnetoencephalographic data recorded from normal volunteers under resting conditions. These results strongly suggest that human brain functional systems exist in an endogenous state of dynamical criticality, characterized by a greater than random probability of both prolonged periods of phase-locking and occurrence of large rapid changes in the state of global synchronization, analogous to the neuronal “avalanches” previously described in cellular systems. Moreover, evidence for critical dynamics was identified consistently in neurophysiological systems operating at frequency intervals ranging from 0.05–0.11 to 62.5–125 Hz, confirming that criticality is a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth.

Graph theory provides many metrics of complex network organization that can be applied to analysis of brain networks derived from neuroimaging data. Here we investigated the test-retest reliability of graph metrics of functional networks derived from magnetoencephalography (MEG) data recorded in two sessions from 16 healthy volunteers who were studied at rest and during performance of the n-back working memory task in each session. For each subject's data at each session, we used a wavelet filter to estimate the mutual information (MI) between each pair of MEG sensors in each of the classical frequency intervals from gamma to low delta in the overall range 1-60 Hz. Undirected binary graphs were generated by thresholding the MI matrix and 8 global network metrics were estimated: the clustering coefficient, path length, small-worldness, efficiency, cost-efficiency, assortativity, hierarchy, and synchronizability. Reliability of each graph metric was assessed using the intraclass correlation (ICC). Good reliability was demonstrated for most metrics applied to the n-back data (mean ICC=0.62). Reliability was greater for metrics in lower frequency networks. Higher frequency gamma- and beta-band networks were less reliable at a global level but demonstrated high reliability of nodal metrics in frontal and parietal regions. Performance of the n-back task was associated with greater reliability than measurements on resting state data. Task practice was also associated with greater reliability. Collectively these results suggest that graph metrics are sufficiently reliable to be considered for future longitudinal studies of functional brain network changes.

Figure 1. Action potential firing is independent of dI/dt in Purkinje neuronsA, somatic whole-cell recording of action potential firing elicited by slow (2.5 s) ramp currents in a Purkinje neuron (top panel; ramp peak 0.9 nA), and a layer 5 pyramidal neuron (bottom panel; ramp peak 2.0 nA). Prior to the ramp the Purkinje neuron was hyperpolarized to _65 mV by the injection of a negative holding current, whereas the pyramidal neuron was resting at _65 mV. B, plot of the instantaneous firing frequency during the ramp currents shown in A. Note that the onset frequency (indicated by an arrow) is very different for the Purkinje and pyramidal neurons. C, relationship between the slope of injected current and the onset frequency for different ramps. Lines represent linear (top) or polynomial (bottom) fits.

The hyperpolarization-activated cation current I h exhibits a steep gradient of channel density in dendrites of pyramidal neurons, which is associated with location independence of temporal summation of EPSPs at the soma. In striking contrast, here we show by using dendritic patch-clamp recordings that in cerebellar Purkinje cells, the principal neurons of the cerebellar cortex, I h exhibits a uniform dendritic density, while location independence of EPSP summation is observed. Using compartmental modeling in realistic and simplified dendritic geometries, we demonstrate that the dendritic distribution of I h only weakly affects the degree of temporal summation at the soma, while having an impact at the dendritic input location. We further analyze the effect of I h on temporal summation using cable theory and derive bounds for temporal summation for any spatial distribution of I h . We show that the total number of I h channels, not their distribution, governs the degree of temporal summation of EPSPs. Our findings explain the effect of I h on EPSP shape and temporal summation, and suggest that neurons are provided with two independent degrees of freedom for different functions: the total amount of I h (controlling the degree of temporal summation of dendritic inputs at the soma) and the dendritic spatial distribution of I h (regulating local dendritic processing).