fMRI evidence that human brain has (functional) small world properties
A study on network properties of the whole brain (functional connectivity data from fMRI)… interesting to see this type of work published in J. Neurosci. Building on previous fMRI/whole brain connectivity studies, the authors use a set of wavelet basis functions to estimate the correlations between different anatomical regions.
Also includes some analyses on resiliency of the system (via a metric like “largest connected cluster”) to random and targeted attack (ie. node deletion). It would be neat if they also did some analysis of common stroke damage. I would think that a stroke probably doesn’t qualify as a “targeted attack”, in the traditional sense, but, due to the predefined structure of the major circulatory structures (eg. circle of Willis), there are likely regions that are near the most commonly blocked arteries, etc. Perhaps someone with some medical qualifications could weigh in here?
There is also a nice discussion of why the human brain does not appear to be a scale-free network: That nodes do not seem to follow the “rich-get-richer” rule of preferential attachment. Evolutionarily recent structures like prefrontal seem to be among the hubs of the system and older structures like limbic regions do not dominate. Here’s a picture of the connectivity map from the paper:
Full abstract after the jump.
Small-world properties have been demonstrated for many complex networks. Here, we applied the discrete wavelet transform to functional magnetic resonance imaging (fMRI) time series, acquired from healthy volunteers in the resting state, to estimate frequency-dependent correlation matrices characterizing functional connectivity between 90 cortical and subcortical regions. After thresholding the wavelet correlation matrices to create undirected graphs of brain functional networks, we found a small-world topology of sparse connections most salient in the low-frequency interval 0.03–0.06 Hz. Global mean path length (2.49) was approximately equivalent to a comparable random network, whereas clustering (0.53) was two times greater; similar parameters have been reported for the network of anatomical connections in the macaque cortex. The human functional network was dominated by a neocortical core of highly connected hubs and had an exponentially truncated power law degree distribution. Hubs included recently evolved regions of the heteromodal association cortex, with long-distance connections to other regions, and more cliquishly connected regions of the unimodal association and primary cortices; paralimbic and limbic regions were topologically more peripheral. The network was more resilient to targeted attack on its hubs than a comparable scale-free network, but about equally resilient to random error. We conclude that correlated, low-frequency oscillations in human fMRI data have a small-world architecture that probably reflects underlying anatomical connectivity of the cortex. Because the major hubs of this network are critical for cognition, its slow dynamics could provide a physiological substrate for segregated and distributed information processing.
January 11th, 2006 at 1:00 pm
Very interesting - thanks. This reminds me of work done by Olaf Sporns, specifically a paper called “The small world of the cerebral cortex” (available at http://www.indiana.edu/%7Ecortex/NI2004.pdf) where they also look at clustering and average path length.
I am a little surprised by what they say about the brain not showing scale-free properties, though not for any good reason. I guess I’m just attached to the idea of preferential attachment
Perhaps the cortex overall does not show preferential attachement, but individual regions might? Or perhaps the brain isn’t scale free since the neurons at the “tail end” of the connectivity distribution would be eliminated via pruning?