Self-organized Criticality of the Brain in Functional MRI

Self-organized criticality is a concept which was first proposed by Bak et al. (1988) in the field of physics. What is the critical state of a dynamical system? Simply describing, it can be regarded as a critical point of phase transition. You can imagine the zero degree as a critical boundary between water and ice. In this critical state, water is in the form of snowflakes, and is known to have fractal structure and self-similarity. In general, any system in the critical state exhibits fractal scaling properties. Indeed, Bak et al. proposed that the 1/f noise is a temporal sign of self-organized criticality.

The concept is useful to investigate any natural or spontaneous system without any external stimulation or behavior. Let us think of the brain in resting state. If we observe the spontaneous activity of the brain in resting state, does the brain exhibit any fingerprint of self-organized criticality? The answer is 'yes'. Plenz and Thiagarajan (2007) showed spatiotemporal patterns of spontaneous neuronal activity in the brain cortex, and they call such a phenomenon 'neuronal avalanche'. Such patterns have fractal scaling properties in terms of probability density distribution of delay duration of consecutive active neurons.

Measuring neuronal activity through local field potential (LFP)
and the groups of consecutive active neurons
(TRENDS in Neurosciences)

The self-organized criticality is consistently observed not only in micro-scale recordings but also the macro-scale neuroimaging data. Kitzbichler et al. (2009) observed the criticality properties both in MEG and in functional MRI data by using newly defined measurements such as the phase locking interval (PLI) and the global lability of synchronization. The probability density distribution of phase locking intervals has power-law scaling, i.e., linear relationship in logarithmic scales.

The probability distribution of phase locking interval of functional MRI data
(Ed Bullmore et al. 2009)

Self-organized criticality is a very promising concept for resting state brain analysis since it is dedicated to analyze spontaneous dynamic systems. Recently, some scientists are investigating the relationship between self-organized criticality and fractal behavior of the brain.


References

P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality, Physical Review A. 38 (1988).
D. Plenz, T.C. Thiagarajan, The organizing principles of neuronal avalanches: cell assemblies in the cortex?, Trends In Neurosciences. 30 (2007) 101-10.
M.G. Kitzbichler, M.L. Smith, S.R. Christensen, E. Bullmore, Broadband criticality of human brain network synchronization., PLoS Computational Biology. 5 (2009) e1000314.
E. Bullmore, A. Barnes, D.S. Bassett, A. Fornito, M. Kitzbichler, D. Meunier, et al., Generic aspects of complexity in brain imaging data and other biological systems., NeuroImage. 47 (2009) 1125-34.