Mathematical modelling of brain formation to map species variation and developmental malformations.

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The developmental programme underpinning the formation of the brain results from the delicate regulation of complex spatio-temporal processes at the cellular scale. Variations of this programme lead to speciation, but they can also bring about malformations such as schizophrenia, epilepsy, and microcephaly. To date, brain development has been studied through analysis of sparse temporal data that may miss crucial information. This project aims to fill this gap in our knowledge via the development, analysis and numerical simulation of deterministic models formulated as partial integro-differential equations, and corresponding stochastic individual-based models for the complex spatio-temporal cellular processes underlying the variety of brain architectures, shapes and sizes that we observe in different animal species. The mathematical models that will be designed and studied are expected to complement empirical research by enabling extrapolation beyond scenarios which can be investigated through experiments and by revealing emergent phenomena that would otherwise remain unobserved. Moreover, they will pose a series of analytical and numerical challenges which will make them interesting mathematical objects per se.