Date of Award

December 2019

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical and Aerospace Engineering

Advisor(s)

Alan J. Levy

Keywords

Homeostasis, Homeostatic elastic states, Mechanical stability of elastic arteries

Subject Categories

Engineering

Abstract

Vascular mechanics has undergone significant growth within the last 50 years owing to the rapid development of nonlinear continuum mechanics occurring roughly within the same period and motivated primarily by rubber materials. However, one important distinction of blood vessels, in contrast to typical engineering materials is that, through a variety of physiological mechanisms, they seek to maintain constant a preferred mechanical state (mechanical homeostasis) thereby exhibiting a remarkable mechanical stability in response to temporal evolution and alterations in blood pressure, vessel tethering forces and geometry and material properties. The mechanical state experienced by blood vessels plays a critical role in mechanical homeostasis and mechanical stability, and there remains a pressing need for mechanical/mathematical analysis to i) understand/predict the stretch/stress states within vessels and how they evolve with increasing blood pressure and tethering forces, ii) understand/predict the mechanical stability of arteries in response to diverse stimuli such as inhomogeneities in geometry and material properties. This dissertation seeks to add to this vibrant field by conducting a rigorous analysis of i) the mechanics of the homeostatic states of uniform circumferential stress and uniform stretch in an N-layer cylindrical artery subject to circumferential prestress, axial tethering force and the pressure of blood and ii) the local mechanical stability by imperfection growth in a solid body subject to inhomogeneities in geometry and material properties. In order to make these results relevant to a blood vessel, a micromechanics based constitutive relation is proposed based on the more or less regular architecture of a large elastic artery composed of collagen, elastin and vascular smooth muscle. Although the primary focus of the work is on the healthy artery, the effect on imperfection growth of diseased tissue constituents is accounted for in a simple model of damaged elastin and collagen.

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Open Access

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