The Mathematical and Computational Modelling of Various Problems in the Life Sciences

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Many processes in the Life Sciences involve a complex interplay between a multi-scale cascade of physiological processes and pathways. In humans, these result in function/dysfunction of organs and other crucial processes, and lead in particular to the manifestation of particular medical conditions or diseases. Whilst enormous amounts of experimental and clinical data are being continuously generated, one of the crucial challenges facing researchers currently, is how to organize and extract useful knowledge from the vast array of information gathered from experiments and clinical trials. My proposed research is directed at using mathematical/computational modeling to study problems arising in the life sciences in order to develop models that reveal underlying mechanisms driving processes that lead to dysfunction, and hence suggest possible disruptive strategies. This research attempts to understand and model clinical conditions and diseases (including hydrocephalus and tumor growth) through a synergistic combination of experimental data and theoretical and computational methods. The term hydrocephalus represents a family of disorders characterized by expansion of the ventricles within the brain. Genetic factors are believed to contribute to the development of congenital hydrocephalus; in contrast, acquired hydrocephalus occurs after development of the brain and can be due to many causes such as trauma, hemorrhage, infection, tumors. The increasing numbers of aging patients with Normal Pressure Hydrocephalus (NPH), further substantiates the need for a deeper understanding of this disorder. The development of an accurate, quantitative model for simulating the mechanical behavior of brain tissue, will be an important milestone in the clinical neurosciences since it will help in predicting the damage sustained by the brain in a variety of circumstances and guide treatment decisions. In addition, the identification of major factors that influence treatment response in brain tumors and other cancerous tumors has been a problem of longstanding interest and relevance to clinical oncology. Fresh approaches are needed to understand the causes and therapeutic potential of this deadly disease, of hydrocephalus and other conditions. The biomechanical behavior of biological tissues is one of the most demanding and complicated to model. The main thrust of my research program here, is to develop a comprehensive quantitative model, coupled with carefully designed interlocking sequence of computational simulations based on experimental data, to predict the response of brain tissue in vastly different loading situations as regularly facing the neurosurgeon. The careful coupling of mathematical modeling, well designed experiments and the use of novel technologies will lead to a deeper understanding of the underlying mechanisms that give rise to long standing puzzles such as “normal pressure” hydrocephalus, growth and control of tumors and various other conditions.