The Mathematical Modelling of Various Problems arising in the Biomedical Sciences

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Quantitative models are playing an increasingly central role in the biological sciences and are rapidly becoming an indispensable tool for discoveries of the future in these fields. The development of an accurate, quantitative model suitable for simulating the response of soft biological tissues under different scenarios will be an important milestone in the applied biological sciences. Whilst conventional experimental approaches have contributed to major advances in the biological sciences, there is room for significant improvement. Fresh approaches are needed to gain a deeper understanding of the principles underlying the development and function of biological systems and how these may go awry.Clearly the application areas in the biosciences for appropriate mathematical/computational frameworks are manifold. These range from conditions such as hydrocephalus (a clinical condition frequently encountered by neurosurgeons) to the treatment and control of tumours in clinical oncology. Half a century of biomedical research has produced very modest improvements in the treatment and management of such conditions and diseases. Mathematical models, computer simulations and engineering technologies have also contributed to translational research that has revolutionized clinical management and treatment, resulting in decreased mortality and healthcare costs. My long term research program is focussed on the development of a comprehensive quantitative model, coupled with experimentally informed computer simulations to develop a more fundamental understanding of the response of biological tissues in vastly different loading situations. The careful coupling of mathematical modelling and well designed experiments will result in a deeper understanding of the underlying mechanisms that give rise to many long standing medical conditions and diseases and provide rational guidance in the search for appropriate therapies.