Modeling and Identification of Vascular Biomechanical Properties in Large Arteries.

VALDEZ-JASSO, DANIELA. Modeling and Identification of Vascular Biomechanical Properties in Large Arteries. (Under the direction of Dr. Mette S. Olufsen and Dr. Mansoor A. Haider.) In this thesis we focus on developing and evaluating constitutive models of large arteries that describe the dynamic response of cross-sectional vessel area induced by time-varying blood pressure. Using a Kelvin (linear) viscoelastic model and two nonlinear viscoelastic models (an arctangent and a sigmoid), we use an inverse mathematical modeling approach to determine vessel distention as a function of pressure. Each model contains a set of parameters that relate to the mechanical properties of the vessel wall. We apply the models to ex vivo and in vivo data from a total of 21 male Merino sheep as well as ten human subjects. The data are obtained from two anatomical locations, including the thoracic descending aorta and the carotid artery. Sensitivity and statistical analyses are used to compare model predictions, and to choose from the set of candidate models the one that best captures the dynamics present in the experimental data while providing physiologically reasonable parameter estimates. The thesis is motived by two hypotheses: (1) viscoelastic models accounting for linear and nonlinear elastic responses can accurately predict pressure-area dynamics observed in systemic arteries under ex vivo and in vivo experimental conditions, and (2) biomechanical properties of the vasculature can be characterized via model parameter estimates according to anatomical location and experimental conditions (ex vivo and in vivo). Our results show that vascular viscoelasticity is an important feature to include to accurately describe arterial distention. Without incorporating viscoelasticity, our models fail to represent the characteristic pressure-area loops observed experimentally. Vessels closer to the heart (the aorta) show a prominent nonlinearity in their pressurearea dynamics, compared to those located more peripherally (the carotid artery). This nonlinearity necessitates the use of nonlinear models to capture dynamics displayed by the proximal, elastic arteries, while dynamics displayed by the peripheral vessels are better captured using a linear viscoelastic model. The parameter estimates for the two anatomical locations in general exhibit statistically significantly differences, and reflect known physiological differences between anatomical location and experimental conditions. For example, the estimation algorithm consistently produces smaller values for the zero-pressure radius of the carotid artery than for the thoracic descending aorta, and parameters characterizing vessel properties show that vessels ex vivo are stiffer than in vivo. Through the optimal parameter estimates, these models capture the experimental data efficiently and provide insights into the biomechanical properties of the arterial wall. A better understanding of these biomechanical properties provides important insights into arterial vascular biology under normal healthy and pathological conditions. Such insights can be used to aid in vascular graft design and implementation, improve tracking of disease progression, and be incorporated into fluid-dynamic simulations of arterial fluid-structure interaction. Modeling and Identification of Vascular Biomechanical Properties in Large Arteries by Daniela Valdez-Jasso A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fullfillment of the requirements for the Degree of Doctor of Philosophy Biomathematics Raleigh, North Carolina 2010 APPROVED BY: Dr. Stephen L. Campbell Dr. Brooke N. Steele Dr. Mette S. Olufsen Dr. Mansoor A. Haider Chair of Advisory Committee Co-Chair of Advisory Committee ii DEDICATION To Benito and Elizabeth, who taught me how to use my wings to fly and reach my dreams. iii BIOGRAPHY Daniela Valdez-Jasso received her Bachelor of Science and Master of Science degrees in Applied Mathematics from North Carolina State University in 2005 and 2008, respectively. Subsequent to receiving her Masters degree, Daniela joined the Biomathematics program at North Carolina State University, where she pursued her doctoral degree on the topic of soft-tissue biomechanics. iv ACKNOWLEDGEMENTS Gracias, gracias, gracias. O’brigada, o’brigada, o’brigada. Thank you, thank you, thank you. Xie xie, xie xie, xie xie. Merci, merci, merci. Shukran, shukran, shukran. Tak, tak, tak. Danke, danke, danke. v TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Chapter