Dynamical Regulation in Physiological Systems

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Many physiological phenomena show complex fluctuations. This variability can be an index of the***health of the individual, as in the case of the heart rate, fluctuations in sleep-wake cycle or smooth muscle***contractions in the gastro-intestinal track. In recent years, research combining experimental studies of***physiological systems with theoretical models of physiological dynamics has provided new insight into the mechanisms responsible for some cardiac and hematological disorders. Carrying out the appropriate experiments requires***great care and precision in order to obtain data sufficiently detailed to be compared with theoretical observations***which in turn suggest new theoretical (modeling) approaches.***For the following systems, we will be developing mathematical models thriving for a***representation that is simplified enough to allow for significant understanding of the system as a***whole, yet is complex enough to incorporate all the fundamental components of the physiology.***1) The regulation of the circulating blood cells is a complex biochemical system. We study the***influence of the main regulatory protein, erythropoietin (EPO), in the feedback mechanism maintaining the number of red blood cells (which carry oxygen to all tissues and organs) at an appropriate level; we also explore the interactions of these cells with systems predominantly controlling the regulation of the other types of circulating blood cells (mainly platelets, which are responsible for the prevention of bleeding).***2) Emerging zoonotic diseases are defined by the World Health Organization (WHO) as diseases transmitted from animals to men "that are newly recognized or newly evolved, or that have occurred previously but show an increase in incidence or expansion in geographical, host or vector range". With modifications in the habitat of a number of species involved in the transmission of these diseases, there is renewed interest in understanding their propagation mechanisms. We shall investigate mathematical models for such a mosquito-borne disease, Dengue Fever (DF), trying to understand the dynamics of multiple expositions to different strains of DF.