By modeling the trade-off between two competing ways of making useful connections, a team of UK and US scientists has created a remarkably complete statistical picture of the human brain’s complex network. They suggest the simple mathematical model not only helps us better understand healthy brains, but also offers unique insights into schizophrenia and similar disorders.
The scientists report their work in a recently published issue of the Proceedings of the National Academy of Sciences (PNAS), and comment on it in a press statement released on 12 April.
The lead author of the study is Ed Bullmore, a professor in the Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, at the University of Cambridge in the UK.
In the way it makes connections, the “wiring” of the human brain appears similar to other complex networks such as social networks and the world wide web.
However, until this study, we knew little about the rules involved in the shaping of the human brain network, as the authors explain in their background information:
“Although a sophisticated set of measures is available to describe the topology of brain networks, the selection pressures that drive their formation remain largely unknown.”
Bullmore and colleagues found they could produce a good model from two competing pressures: a “distance penalty” for maintaining long-range connections, and a preference to link regions (including those quite far apart), that share similar input. At first they just had the first one, but then when they introduced the second one, the model greatly improved, as Bullmore himself explains:
“There is a huge amount of evidence that the wiring of brain networks tends to minimize connection costs. Less costly, short-distance connections are much more numerous than more costly, long-distance connections. So our model realistically includes a distance penalty on long-distance connections, which will tend to keep connection costs low.”
“However”, he adds, “we found that cost control alone was not enough to reproduce a wide range of network properties. To do that, we had to model an economical trade-off between cost control and another term which favoured new, direct connections between regions that shared similar input or were otherwise already indirectly linked.”
The team writes that, together, these two “biologically plausible factors” were enough to represent an “impressive range of topological properties of functional brain networks”.
They calibrated the model using functional magnetic resonance imaging (fMRI) data from one set of healthy volunteers, and then showed it provided a good fit to networks estimated in a second independent data set.
Furthermore, by slightly “detuning” the model so it favored more connections between distant brain regions, they found it “generated a reasonable simulation of the abnormal properties of brain functional networks in people with schizophrenia”.
Co-author Dr Petra E Vértes, also of the University of Cambridge, says:
“This result echoes some prior neuroimaging results which suggest that brain networks in schizophrenia may be associated with an abnormal trade-off between connection costs and other topological properties of brain networks.”
The authors suggest simple models like this, based on trade-off rules about connectivity between different brain areas, may help explain many aspects of brain network organization, both in health and disease.
Written by Catharine Paddock PhD