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Boamah, Edward Kwasi

Mathematics

2005

Ph. D.

Hemodialysis (HD) is one type of procedure for eliminating toxic chemicals and infusing bicarbonate in people whose kidneys do not function properly. Research and development in the hemodialyzer industry have, hitherto, depended mostly on empirical evidence to optimize HD therapy. This is often costly and involves numerous clinical trials. In search for optimal HD, researchers have used 'black box' input-output ordinary differential equation models to study the dynamic exchange of solutes during HD. In the era of advances in contemporary HD therapy, these models are oversimplistic. In collaboration with Nephrologists and HD centers, we have developed a comprehensive mathematical model to describe the dynamic exchange process of solutes in the hemodialyzer. We have developed the models to determine the steady state and the time-dependent patterns of the solute changes in the hemodialyzer unit. The model, which is represented by a coupled set of transport equations, delineates the blood and dialyzate compartments of the hemodialyzer, and includes bicarbonate buffering reaction in the blood channel and bicarbonate replenishment mechanism in the dialyzate. A numerical solution of the model using finite difference schemes give solute concentrations at various distances along the blood and dialyzate channels at different times. This modeling exercise has allowed us to examine some physical mechanisms of the hemodialyzer, some of which include key fiber properties, ultrafiltration rate, blood and dialyzate flow rates, duration of HD, and their affects on the dynamic exchange of solutes during HD therapy.