Monica K. Hurdal
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SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Monica K. Hurdal Abstract. Cortical folding patterns vary widely across species. A number of biological hypotheses have been proposed to explain cortical morphogenesis and folding but no consensus has been reached. In this presentation I will discuss some of the mathematical models and methods I am using to investigate cortical folding pattern formation in the brain. One class of pattern formation models is based on a Turing reaction-diffusion system. Turing systems have been used to study pattern formation in many biological applications such as animal coat patterns. A Turing system consists of two reaction-diffusion equations representing activator and inhibitor chemical morphogens. I will derive the mathematical equations and conditions needed to construct these Turing system models for cortical folding and present results demonstrating parameters that control domain size and growth rate play a significant role in cortical folding pattern formation. Results using static, dynamically growing, prolate, and oblate spheroid domains will be presented. I will also briefly discuss how conformal invariants may eventually contribute to characterizing folding patterns of the brain. These models offer an explanation as to why certain species may have little or no folding and are able to predict the consistency in pattern formation across species. Additionally, they may help explain lissencephaly, and polymicrogyria, two diseases of cortical folding which affect the number and width of cortical folds. These models represent an important step in improving our understanding of cortical folding pattern formation in the brain and the influence that domain growth and genetic expression can have on cortical folding. |