BIOMATHTECH 07-10 · Mathematical modeling of human physiological systems with biomedical applications

Final Activity Report Summary - BIOMATHTECH 07-10 (Mathematical Modeling of Human Physiological Systems with Biomedical Applications)

The primary scientific reason for the events in BIOMATHTECH 07-10 was to introduce potential new researchers to key issues and techniques needed for carrying out research in mathematical modelling of physiological systems. Training introduced participants to important mathematical and statistical techniques needed for such research. Each event sought to integrate methods and applications and provide understanding and insight into methodological problems and clinical applications in four fundamental areas of physiological research. Each event included a summer school followed by a workshop. The school provided participants with an introduction to mathematical, physiological, and modelling tools unified around a specific fundamental topic in modelling and a specific physiological focus. In this way, a frame of reference was established for participants to integrate methods with applications. Tools developed in the events were chosen to allow for more individually focused study after the events. The associated workshop was designed as if it could be a standalone scientific event in the same area of the school focus with presentations by current top researchers. The school participants attended the workshop which reinforced the ideas presented to the school participants while also providing a high level scientific meeting for students, workshop presenters, and teachers. The workshops also provided opportunities to establish collaborative relationships between students, workshop presenters, and school teachers. School participants were also encouraged to give contributions to the workshop. Event 1. The first event focused on principles of modelling and applications of control theory to physiological systems with application to the cardiovascular and respiratory systems. Clinical applications included sleep apnoea, congestive heart failure, blood pressure control and the interaction of these and other conditions. Several school and workshop lectures focused on physiology and problems with experimental design. The role of time delay in feedback control was also examined theoretically and in terms of clinical manifestations of instabilities induced by delay. Event 2. The second event extended the mathematical treatment of the first event to include stochastic effects and the application of stochastic differential equations in modelling physiological systems. Applications were given in neuronal firing and the insulin glucose control system. Clinical conditions included diabetes, diagnosis of diabetes, and the control of glucose levels through insulin treatment design. Event 3. Having considered principles of modelling and model development using ordinary and stochastic differential equations, the third event made an in depth study of model validation with the focus on both parameter estimation and experimental design. This is a key issue in current work especially in regards to fitting models to individual patient's assessment of system function and diagnosis. Clinical assessment often involves limited data from minimally invasive tests on first screening and this represents special challenges to model design and validation, where the model must be rich enough to reflect dynamics of interest, but the parameter set simple enough to be robustly identified with limited data. Hence the clinical application reflects this issue with special examples drawn from the metabolic control system. Event 4. Having examined the cardiovascular, respiratory, and metabolic control systems (in particular glucose control) and neuronal function, a key as intermediary in physiological control, the fourth event considered issues at the cellular level by focusing on cancer growth and treatment. In this treatment, both normal cellular activities and cancer mechanisms were studied and modelled. Mathematical modelling included ordinary and delay differential equations and the extension to partial differential equation models.

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