• Duncan Astle

Simulating neurodiversity in the brain using simple computational models

Since the advent of modern neuroscience, neuroscientists have been interested in how our nervous systems – at all levels of analysis – underpin how we think, feel and behave. One way that scientists tend to do this is by linking variation in the brain to variation in behaviour, cognition or clinical outcome.


In our lab, we have done this extensively with large samples of children that are neurodiverse. One of our most significant findings is that there does not seem to be a one-to-one mapping between neurodevelopmental disorders and the brain’s structure. That is, there doesn’t seem to be a single part of the brain that is clearly responsible for any one type of disorder or cognitive difficulty. Why not? We think it is because the brain is so highly connected that developmental differences emerge as brain areas interact, rather than because of the activity of any single area.


But why and how do we get differences in complex brain networks that develop in childhood, at all?


Understanding the mechanisms that drive the developmental trajectories of brain development could help us transition from describing what's really going on, to explaining it. We think this is crucial, as it better enables us to form and build accurate theories of how the brain organises itself over time, and how differences/similarities emerge between people.


This is what we tackled in our latest paper, by bridging computational models with neurodevelopmental questions:

A generative network model of neurodevelopmental diversity of structural brain organization

Danyal Akarca, Petra E Vertes, Edward T Bullmore, The CALM Team & Duncan E Astle

Nature Communications



A generative network model of developmental variability in brain networks


The brain can be thought of as a detailed map of its connections - sometimes called a connectome. Building connectomes for individual participants means that we can study these systematically, something called connectomics. Each node can be thought of as a grey matter region, and the connections between them as white matter bundles. In other words, brain areas connected by fibres.

Here we zoom into the right frontal cortex to show how we can think about the anatomical set-up of that region.


In our paper we ask the fundamental question: Under what conditions could this network have arisen in the first place?


Building on previous fantastic work in this area (e.g. 1, 2), we show that you can actually simulate network development in a really simple way via a wiring equation. This equation balances the “costs” of forming connections (e.g. how far away something is) with how valuable that connection is deemed to be (e.g. via a rule, such as how much connection profiles overlap – termed homophily). What this means is that networks are aiming to be economical in how they are wiring. There is a trade-off between the cost of forming a connection and the potential value of that new connection. This simple economic principle, playing out over development, captures the complexity of the whole network.

Early in development (top), the brain wires with regions that are close to it (2 and 36) but may later shift (bottom) because now there is “value” information (e.g. homophily – overlapping connections) available to the region. For example, 2 will wire with 59, despite it being closer to 27. This is one way in which complex organisation may arise in the brain.


So, what does it all mean?


Whilst this is a really simple idea, it gives us some very elegant insights into how and why the brain may develop as it does.


One is about the governing parameters of the wiring equation. We argue that while we have differences between brains that are important, they are likely dwarfed by our similarities; and that this type of analysis is really nice at teasing these two apart.


In the below image, the dark blue regions are where we find combinations of parameters to the equation that seem to work really well in simulating children’s brains that are neurodiverse. You can see from the left, that the region is pretty narrow – suggesting that only some configurations of simulations are biologically plausible. On the right, we can see each child’s wiring parameters plotted in the space. With each child’s coordinate, you can simulate a representation of their brain with our generative model.


The wiring parameters help tell us how we can condense the brain into the wiring equation, and we find that there is a “sweet spot” of biologically plausible solutions – indicative of there only being a small number of ways the brain can be set up to be sufficiently different to each other (i.e. our differences) while remaining functional (i.e. our similarities).


Not only do parameters show us a way in which variability can be thought of – they can give us much more. We ran further analyses in the paper (amongst much more) about how the wiring parameters are associated with cognitive outcomes:

We ran an analysis which combines wiring parameters to help us predict cognitive outcomes.


Furthermore, when you project the wiring parameters to the brain’s spatial distribution, they overlap with gene-expression in the cortex, including those at the synapse. In the paper, we provide a simple way to run a basic form of our analysis in your web-browser.

We overlapped gene-expression in the cortex with distinct components of the wiring equation, to see what biological/cellular processes may overlap with our modelling.


Future outlooks for computational research in neurodevelopment


Following this work, we have many more questions to answer:


· How can we directly integrate the role of both genetic and environmental influences into our model?

· Do these principles of network development translate across different levels of neuroscience analysis, e.g. single-cell neuronal cultures and 3D cerebral organoids?

· Can our model potentially explain more complex weighted architectures of white matter connectivity, such as fine-tuned details of the brain’s microstructure?


Overall, we think this paper is important because it shifts our focus towards thinking about the mechanisms that shape neurodevelopmental diversity. Fundamentally, we’re passionate about moving from descriptions to explanations of brain-behaviour mechanisms.



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