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Research Projects: Overview: The biomedical science disciplines are witnessing a profound shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex properties and phenomena are required. I am an interdisciplinary mathematician whose current research interest is predominantly focused at the interface of applied mathematics and its application to the biomedical sciences. This is the area of research that has come to be known as mathematical biology or biomathematics. Mathematical biology is a fast growing subject, which has gained significant attention and importance in recent years and it is, arguably, one of the most exciting application-oriented sub-disciplines of mathematics. My research work, to date, is in four (4) areas of mathematical biology: (i) Muscle Physiology, (ii) Lung Physiology, (iii) Renal Physiology, and (iv) Developmental Biology. Muscle Physiology: Molecular Muscle Mechanics: A new generation of optical trapping techniques, namely laser tweezers, are currently being used to measure forces and displacements of individual myosin molecules. Results from these studies have hitherto attracted different models of data analysis and interpretation. As a result, differing estimates of the myosin working stroke or step size have been postulated. These differences could stem from complicating factors such as Brownian (thermal) noise acting on the laser trap assay. My main objective in these studies is to develop mathematical models for actomyosin interaction at the molecular level, which incorporate strain-dependent displacements, ATP hydrolysis, viscosity and Brownian noise acting on the actomyosin system. I have developed new mathematical models, based on stochastic Langevin dynamics, coupled with the kinetics for actomyosin interaction. Renal Physiology: Hemodialysis Therapy: This modeling challenge is to construct realistic model mechanisms that capture key physiological processes that may be involved in acid-base homeostasis associated with end-stage renal diseases (ESRD), and show how they are orchestrated. Metabolic acidosis, for example, in patients with ESRD still remains a problem despite major technical advances in alkali delivery during hemodialysis treatment. The proposed work aims to gain insight into the factors regulating body bicarbonate stores in patients receiving hemodialysis treatment, and to use this knowledge to construct testable mathematical models that will allow us to study, in more detail, (i) the overall nature of solute transfer across dialysis membranes, (ii) the body's response to this rapid alkalinization during the dialysis (intradialytic) period, (iii) the events influencing body alkali stores during the post-dialysis (interdialytic) period, and (iv) the overall variation in solute exchange between dialysate, blood and the body compartments. The long-term objective is to couple our model mechanisms, their refinements, and computations to direct clinical measurements in order to acquire the information needed to determine the most appropriate approach to rectify the metabolic acidosis in patients receiving hemodialysis treatment. Lung Physiology: Aerosol Deposition in the Acinus: This long-term study will focus on the development of new mathematical models for the interaction, transport, deposition, and elimination of aerosol particles in the acinus. Specific problems to be studied will include particle size analysis and modeling; deposition, translocation, and clearance in the lungs. Of particular interest to us, and alongside some of the activities of NASA, is the role that gravity plays in the deposition of inhaled aerosol particles in the respiratory tract and in the acinus, and how extended periods of microgravity and the hazards of closed space environment affect pulmonary function. Aerosol studies in microgravity have shown unexpectedly high deposition. Factors attributing to this observation are yet to be known. Thus, studies of this nature will be extremely useful in understanding the factors that cause inhaled particulate matter to have high deposition rate, and adverse health consequences that are both prevalent on the ground and in space flights. The experience on Mir space station with frequent fires and the release of toxic gases is testament to the fact that the lung is one of the most vulnerable organs in the body in terms of space travel.