Applications of mathematics in medicine

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Medical healthcare is clearly becoming a priority on many government agendas. One of the enormous challenges facing the medical community is how to organise and extract useful knowledge from the enormous amount of information gathered from basic science experiments and clinical trials. Mathematical models are playing an increasingly central role in this endeavour and will therefore be an integral part of biomedical discoveries of the future. New research paradigms for the modelling of physiological events and the development of computer simulations have enabled theoretical concepts to become practical medical tools. Some of these mathematically-based tools, such as surgical training simulators, have revolutionised clinical management and treatment, and have led to decreased mortality and healthcare costs. Brain injury, is a frequent outcome in a range of disease processes and leads to disabilities that are emotionally devastating and costly from a societal viewpoint. The development of an accurate mathematical model suitable for the simulation of the mechanical behaviour of the brain, will be an important milestone in the clinical neurosciences because it will help to predict the damage sustained by the brain in a variety of circumstances and aid in treatment decisions. The identification of major factors that influence treatment response in brain and other cancerous tumours has been a problem of longstanding interest and relevance to clinical oncology. Whilst conventional treatments like radiotherapy and chemotherapy have contributed to major advances in the management and control of cancer, there is still room for significant further improvement. Thus the combination of mathematical modelling and novel computational methods, validated using experimental and clinical data, provides a powerful new tool in biomedical research. My research program is directed at using mathematical/computational modelling to study problems arising in medicine with a view to developing models of clinical relevance and use. I attempt to understand and model clinical conditions such as hydrocephalus, as well as tumour growth and control at a more fundamental level using continuum mechanics.