Mathematical Models of Brain Morphogenesis

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Despite many speculative papers on the topics of brain morphogenesis, particularly cortical folding, the biomechanical factors that are responsible for normal and abnormal brain development are largely unknown. The general objective of this research is to develop quantitative biomechanical models for brain morphogenesis. The mathematical models will be based on fundamental mechanical principles and state-of-the-art experimental measurements of structure, microstructure, and mechanical properties, combined with precise, quantitative descriptions of growth and remodeling. In conjunction with experiments, these models will be used to test the hypothesis that spatial and temporal variations in mechanical stress, viscoelastic properties, and growth of the developing brain produce observed changes in shape. This project focuses on two specific periods of brain development where dramatic changes in form are apparent: (1) the early period of expansion and differentiation of the neural tube into the primary vesicles of the brain (forebrain, midbrain, and hindbrain); and (2) the later period of folding of the cerebral cortex (gyrogenesis). Mathematical and computational modeling of the nonlinear, three-dimensional continuum mechanics of brain formation is a necessary complement to classical biological approaches to this basic problem in neurobiology. The results from this project will provide fundamental new insight into the biomechanical mechanisms of brain development.In this project, mathematical models for growth and development of the brain will be built and tested. The brain's form is closely related to its function, but the mechanisms that drive the brain into its final shape are poorly understood. The project focuses on two stages that appear particularly important: (1) the stage of early development when three primary segments of the brain emerge; (2) the stage of later development when the outer surface of the brain folds into a convoluted pattern. Many educated guesses about the process of brain development have been proposed, but none have been supported by convincing evidence. Hypothesized mechanisms will be described in quantitative, precise, computer simulations, and the results will be assessed objectively. New experimental studies will provide physical parameters for these computer models. The objective is a coherent, physically plausible, understanding of the form-function relationship that drives brain development. This information is of fundamental importance to understanding the normal brain. In addition, many disabilities and diseases of the brain, such as schizophrenia, epilepsy, and mental retardation are associated with abnormal brain shape. This project will address important gaps in the fundamental knowledge of brain development needed to address these problems.