Date of Award

2014

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Liu, Liping Dr.

Abstract

Sickle cell anemia is an abnormality that causes a deformation in the shape of the red blood cell that hinders the circulation of the red blood cell through the blood vessel. The deformation is caused by the association of monomers to each other to form polymers (polymerization). The oxygenation of the sickle cell may lead to the melting of polymers (depolymerization). Many studies have been conducted to understand the dynamics of depolymerization. This study focuses on the impact of various parameters over the output values in the system of de-polymerization. Both mathematical and statistical approaches for the sensitivity analysis of the parameters are developed and conducted on the carbon monoxide (CO) mediated sickle cell hemoglobin (HbS) de-polymerization. The sensitivity analysis measures how sensitive the model output is with respect to the changes of the model input parameters and which input parameters are key factors that affect the model output. There are many approaches in the parameter sensitivity analysis. This study focuses on two: the traditional sensitivity analysis (TSA) that utilizes the traditional sensitivity functions (TSFs) and the multi-parameter sensitivity analysis (MPSA). The TSA is a local sensitivity analysis that computes the first-order partial derivatives of the system output with respect to the input parameters, i.e. the TSFs. The TSFs are obtained numerically by the Runge- Kutta method on the sensitivity equations. The MPSA is a global sensitivity analysis that enumerates the overall effect of the model input parameters on the output by perturbing the model input parameters within large ranges. The MPSA is implemented by employing a Monte Carlo method over a broad range of parameters values and comparing the cumulative distribution functions of the acceptance and unacceptance groups of the parameters. All four concentrations as model outputs and four binding/melting rates as input parameters are considered in this study. The sensitivity results from TSA and MPSA are essentially consistent. For the model output de-oxygenated monomers, the most sensitive parameter is the CO-binding rate of monomers, while the most insensitive parameter is the CObinding rate of polymers being that it does not affect the de-oxygenated monomers at all. For the model output CO-bound monomers, the most sensitive parameter is the melting rate of the deoxygenated polymers, while both CO-binding rate of polymers and melting rate of polymers are insensitive. For the model output de-oxygenated polymers, the most sensitive parameter is the melting rate of de-oxygenated polymers, while the other three parameters are insensitive. For the model output CO-bound polymers, the most sensitive parameter is the CO-binding rate on polymers, while the most insensitive parameter is the melting rate of CO-bound polymers.

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