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

支撑大脑形成的发育计划是在细胞尺度上对复杂的时空过程进行精细调控的结果。这一方案的变异会导致物种形成，但也会带来精神分裂症、癫痫和小头畸形等畸形。到目前为止，人们通过分析稀疏的时间数据来研究大脑发育，这些数据可能会遗漏关键信息。这个项目旨在通过开发、分析和数值模拟作为偏积分-微分方程组的确定性模型，以及对应的基于个体的复杂时空细胞过程模型来填补我们知识中的这一空白，这些模型是我们在不同动物物种中观察到的各种脑结构、形状和大小的基础。预计将设计和研究的数学模型将补充经验研究，使其能够超越可以通过实验进行研究的情景，并揭示否则将保持未被观察到的紧急现象。此外，它们将构成一系列的分析和数值挑战，这将使它们本身成为有趣的数学对象。

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.