Is there a mathematician in the house?


In a nutshell: No computer on earth is powerful enough to analyse the raw data on how each of the brain’s 86 billion neurons interact. This review article describes a workaround: using maths to pull out the salient features of those interactions to predict the brain’s response to disease or injury.

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Is there a mathematician in the house?

The big picture:

The connectome, or how the brain’s 86 billion neurons connect to each other, is core to brain function. But interpreting this vast sea of data is challenging, even at the limits of detail imposed by current imaging technology.

In this review, Alex Fornito, a CIBF associate investigator at Monash University, Andrew Zalesky of University of Melbourne, and Michael Breakspear, CIBF partner investigator at the University of Queensland, show how neuroscientists are using the mathematics of networks to mine and interpret these data.

The brain is a highly interconnected system — witness how disease affecting one part of the brain can spread to other, some times distant areas, in stroke or epilepsy. Doctors often have no way of predicting these patterns of spread. But mathematical modelling could ultimately help, playing a key role in the diagnosis and treatment of brain disorders, says Fornito.

“Understanding how connections are organized in the brain allows us to identify points of vulnerability, where damage will have a widespread effect on the brain’s performance,” he says.

Or predict the pattern of disease spread: One mathematical model discussed in the review predicted how grey matter atrophies in Alzheimer’s disease over time, matching very well with brain images of what actually happens to people with Alzheimer’s.


The review also describes how mathematics can be used to identify and understand hub regions — areas in the brain that connect systems with different functions. These are likely to play an important role in the brain’s ability to provide a coherent experience of the world. The idea — borne out by brain imaging studies of disorders such as schizophrenia — is that damage to these hubs will have the most profound and widespread impact on brain function.

The paper also describes some proof-of-principle studies in which mathematical models of the connectome, combined with brain imaging data, predicted when the damaged brain will fail, and when it will adapt by making use of alternative pathways to the damaged ones.

Fornito and his colleagues propose that damage to hub regions will severely limit the brain’s capacity to adapt because it disrupts both main and alternative pathways.

Next steps:
Mapping the human connectome and refining mathematical models of brain network organization will ultimately lead to better understanding, diagnosis and treatment of brain disease and injury.

Fornito, A., Zalesky, A., & Breakspear, M. (2015). The connectomics of brain disorders. Nature Reviews Neuroscience, 16(3), 159-172.

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