"Vascular systems in the human blood circulation regulate their environment when there are alterations of hemodynamic loading from homeostatic levels, depending on the magnitude and the duration of the changes. The main focus of this work is to develop a bio-chemo-mechanical model of arterial growth and remodeling wherein changes in blood pressure and flow are sustained over weeks or months. Using a two-step kinetic reaction model of collagen, which is the dominant structural protein in arteries, as a function of arterial wall stress changes, we track and evaluate the temporal change in mass deposition and degradation of extracellular matrix. We employ a constrained mixture model to capture the response of the artery to hemodynamic loadings, leading to strain energy changes that depend on the stiffness and relative mass ratio of the constituents of the artery. In so doing, we investigate the temporal changes of the geometry of the artery over weeks and months. We also explore the possible ranges of the collagen turnover rates, the coupling between collagen turnover and stresses, and the length of time it takes for the vascular stresses to return back to the steady homeostatic states while the artery is still under sustained loadings. The developed mathematical models are verified by previously published mathematical models and validated by comparing the mathematical result with animal experiments. Using reported experimental data, we inversely compute the arterial constituent mass turnover. After minimizing the total error between the simulated and experimental arterial thickness values, parameters such as collagen and smooth muscles degradation rates are estimated. The efficiency of computation is improved by singular value decomposition and regularization. We also study a lumped whole body model in the cardiovascular system with baroreflex. In this model, we incorporate the effect of arteriovenous fistula and can get verifiable results as per reported vascular maturation data."--Pages ii-iii.
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