Reference: Please review the complete publlication: [Kitzbichler MG, Smith ML, Christensen SR, Bullmore E (2009) Broadband Criticality of Human Brain Network Synchronization. PLoS Comput Biol 5(3): e1000314. https://doi.org/10.1371/journal.pcbi.1000314]
Introduction: Critical dynamics are recognized as typical of many different physical systems including piles of rice or sand, earthquakes and mountain avalanches.
Critical dynamics: Dynamic systems in a critical state will generally demonstrate scale-invariant organization in space and/or time, meaning that there will be similar fluctuations occurring at all time and length scales in the system.
In other words, there is no characteristic scale to critical dynamics, which will be optimally described byscale-invariant or fractal metrics.
Thus, power law or fractal scaling has been widely accepted as a typical empirical signature of non-equilibrium systems in a self-organized critical state [1], although the existence of power law scaling does not by itself prove that the system is self-organized critical (SOC).
For example, turbulence is a conceptually distinct class of dynamics, which is also characterized by self-similar or scale-invariant energy cascades, that can be empirically disambiguated from criticality (Defined as not critical) [2],[3].
The existence of power laws for the spatial and temporal statistics of critical systems is compatible with the related observations that the dynamics of individual units or components of such systems will show long-range correlations in space and time, and change in state of a single unit can rapidly trigger macroscopic reconfiguration of the system.
Many of these phenomena can be studied using computational models of dynamic systems such as the Ising model of magnetization (see Figure 1) and the Kuramoto model of phase coupled oscillators (see Figure 2). In both these models, the dynamics can be controlled by continuous manipulation of a single parameter. For the Ising model, this control parameter is the temperature; whereas for the Kuramoto model it is the strength of coupling between oscillators.
In both cases, as the control parameter is gradually increased (or decreased), the dynamics of the systems will pass through a phase transition, from an ordered to a random state (or vice versa), at which point the emergence of power law scaling and other fractal phenomena will be observed at the so-called critical value of the control parameter.
Self-organized critical systems differ from these computational models in the sense that they are not driven to the cusp of a phase transition by external manipulation of an control parameter but instead spontaneously evolve to exist dynamically at that point.
Self-organized criticalityis 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 2 measures of phase synchronization:
- 1 the phase-lock interval, or duration of phase synchronization coupling between a pair of (neurophysiological) processes
- 2 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 1 and 2 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 datarecorded from normal volunteers under resting conditions.
- These results strongly suggest that human brain functional systems exist in an endogenous state of critical dynamics,
- characterized by a greater than random probability of both
- 1 prolonged periods of phase-locking
- 2 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 critical dynamicsis a property of human brain functional network organization at all frequency intervals in the brain's physiological bandwidth. {{{ Like a dog-whistle that sends-out an alarm to the rest of the Brain, and maybe body, alerting the brain, and maybe body, to potential global environmental or other changes. i.e. Dangers or other criticalities mbm}}}
Author Summary
Systems in a critical state are poised on the cusp of a transition between ordered and random behavior. At this point, they demonstrate complex patterning of fluctuations at all scales of space and time.
- Criticality is an attractive model for brain dynamics
- because it optimizes information transfer
- storage capacity
- and sensitivity to external stimuli in computational models.
However, to date there has been little direct experimental evidence for critical dynamics of human brain networks.
Here, we considered two measures of functional coupling or phase synchronization between components of a dynamic system: the phase lock interval or duration of synchronization between a specific pair of time series or processes in the system and the lability of global synchronization among all pairs of processes.
We confirmed that both synchronization metrics demonstrated scale invariant behaviors (objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality) in two computational models of critical dynamics as well as in human brain functional systems oscillating at low frequencies (<0.5 Hz, measured using functional MRI)
and at higher frequencies (1–125 Hz, measured using magnetoencephalography).
We conclude that human brain functional NeuroNetworks demonstrate dynamic critical scale invariant oscillating synchronization states in all frequency intervals, a phenomenon we have named as ‘Broadband Criticality’.
[Kitzbichler MG, Smith ML, Christensen SR, Bullmore E (2009) Broadband Criticality of Human Brain Network Synchronization. PLoS Comput Biol 5(3): e1000314. https://doi.org/10.1371/journal.pcbi.1000314