Mathematical Modelling of Brain Morphogenesis, Organoids, and Neurological Disorders

This project falls within the EPSRC Mathematical Biology research area
The aim of this research project is to study the mechanisms involved in brain morphogenesis and to clarify the possible causal relationships between cortical folding and neurological disorders. The novelty of our research methodology is to use a combination of both solid and fluid mechanics to model active forces and diffusion mechanisms which the brain is subjected to.
Due to ethical concerns, there is a limitation on how much data one can acquire regarding in-vivo brains, with an even smaller number of experiments that can be performed on them. This has led many researchers to turn their attention to human brain organoids, artificially grown in-vitro miniature organs having features that are similar to the brain. Understanding this simplified system is crucial before moving on to studying the adult human brain.
As a first step my aim is to combine fluid and solid mechanics to model the growth and development of brain organoids. Currently, the structure of brain organoids across different cultures has been found variable, and there is no standardized method to ensure uniformity of organoid cultures. A central question is to understand the mechanisms and factors responsible for such variations . A quantitative study of organoid structure and growth using our research methodology will be instrumental in answering such questions, with a potentially huge impact.
In previous work, human brain organoids were modelled as two dimensional continuum morphoelastic structures. The study found that organoids with a stiff cortex will buckle earlier than those with a soft cortex. These results agree with experimental findings and the model gives new insights on the role played by the microstructural remodeling of the cortex in determining the lissencephaly pathology, a mutation associated with a smoother cortex. Part of my research is to extend the analysis to three dimensional morphoelastic structures and to add additional diffusive processes to model nutrient uptake by the organoid and how this affects growth. This will help elucidate the mechanisms that contribute to the variability in shape and features observed during the production and culturing of the organoids.
Another project concerns the role of mechanical effects in axon growth. Recent works have demonstrated the role of durotaxis, the directed response to variations in substrate rigidity, on axon guidance and development. It has been shown that bundle migration follows rigidity gradients by using the theory of morphoelastic rods. Although durotaxis by itself may not be sufficient to establish a functional network, the authors note that the prepatterning of tissues with different stiffnesses in the nervous system may be a crucial factor in guiding axons to their designated locations in addition to known guidance cues such as chemotaxis. I plan to study the role of combined durotaxis and chemotaxis in axon guidance during brain morphogenesis. In particular, I will investigate how the prepatterning of tissues with different stiffnesses might arise during the development of the brain or be the result of folding and see if it agrees with the experimental evidence. Such a study would significantly further our understanding of how the neural networks of the brain form during development, something that should shed light on the development of neurological disorders.