How does the human brain work? It depends on who you ask.

At school, you were likely taught that our brains contain billions of neurons that process inputs and help us form thoughts, emotions and movements. Ask imaging specialists, and you’ll learn about how we can see the brain in different ways using a variety of imaging techniques and about what we can learn from each image. Neuroscientists also will tell you about the interactions between neurons and related chemicals, such as dopamine and serotonin.

If you ask a subgroup of neuroscientists who focus on mathematical frameworks for how the brain’s shape influences its activity – an area of mathematical neuroscience called neural field theory – you’ll begin to understand the relationship between brain shape, structure and function in yet another way.

Neural field theory builds upon our conventional understanding of how the brain works. It uses the brain’s physical shape – the size, length and curvature of the cortex, and the three-dimensional shape of the subcortex – as a scaffold upon which brain activity happens over time and space. Scientists then model the brain’s macroscopic electrical activity using the brain’s geometry to impose constraints. Electrical activity along the cortex, for example, might be modelled as a superposition of travelling waves propagating through a sheet of neural tissue.

“The idea that the geometry of the brain can influence or constrain whatever activity happens inside is not a conventional neuroscience question, right? It’s a very esoteric question…There’s been decades of work in trying to map the intricate wiring of the brain, and we’ve thought that all the activity that comes out of the brain is driven by this intricate wiring,” says James Pang, a research fellow at Monash University’s Turner Institute for Brain and Mental Health.

In a study published in Nature, Pang and his colleagues have challenged this prevailing understanding by identifying a strong relationship between brain shape and functional MRI (fMRI) activity.

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