Biomechanics of Vascular Wall

This thesis contributes to the field of biomechanics of vascular wall. The focus is particularly on the microstructure of vascular elastin and collagen constituents and their contribution to the macroscopic mechanical behavior of the wall. The analysis is done in the framework of continuum mechanics. The work characterizes structural features of elastin and collagen fibers using microscopy techniques and introduces these features to constituent-based constitutive models. The models are applied to the experimental data, derived from inflation-extension tests, to predict the gross mechanical behavior of the tissue. The developed constitutive models could be further used to study in detail the mechanics of vascular tissue in health and disease. The thesis is presented in form of an introduction, four chapters (corresponding to four papers) and a conclusion. The introduction provides the motivation for this thesis as well as the background on vascular wall structure and mechanics. A brief description of the imaging techniques used is presented. Also, structural constitutive modeling of vascular wall is briefly discussed with particular attention to the modeling of elastin and collagen constituents. The first paper focuses on anisotropic properties of elastin in veins. We show that earlier constituent-based strain energy functions (SEFs), where elastin is modeled as an isotropic material, fail in describing accurately the tissue response to inflation-extension loading. We hypothesize that these shortcomings are partly due to unaccounted anisotropic properties of elastin. We extend the previously developed biomechanical model in our laboratory (Zulliger et al., 2004, J. Biomech., 37(7): 989-1000 (2004)) to account for elastin anisotropy and present an anisotropic strain energy function for elastin with one family of fibers in the longitudinal direction. The model is validated using experimental data from inflation-extension tests on rabbit facial veins. The tissue is tested under a fully relaxed smooth muscle state, for longitudinal stretch ratios ranging from 100% to 130% of the in vivo length. The model with the anisotropic elastin fits well the data for a wide range of longitudinal stretch ratios. The main finding of this paper is that the anisotropic description of elastin is required for a full 3-D characterization of the biomechanics of the venous wall. The second paper addresses the role of elastin in anisotropic properties of arteries with particular attention to the structural organization of elastin. A constituent-based model including an anisotropic elastin, with one family of fibers in the circumferential direction, is presented. Micro-structural imaging, based on electron microscopy techniques, is used to support this anisotropy. Inflationˆextension tests, on intact and elastase-treated arteries, provide a data set to validate the model and to study the effect of elastin removal. We show that the SEF, with an anisotropic elastin part, characterizes more accurately the mechanical properties of the arterial wall as compared to models with simply an isotropic elastin. Transmission electron microscopy (TEM) and serial block-face scanning electron microscopy (SBF-SEM) show interlamellar elastin fibers in the circumferential direction and therefore support the nature of the assumed anisotropy. The model predicts an earlier engagement of collagen in elastase-treated arteries compared to the intact arteries and thus suggests a clear functional interaction between the elastin and collagen component that is often neglected in constituent-based SEFs. The third paper presents a structural constitutive model of the vascular wall which integrates both waviness and orientational dispersion of collagen fibers. We extend the model of Zulliger et al., which already accounts for collagen waviness, to include orientational distribution of collagen. We study the effect of parameters related to the orientational distribution on macro-mechanical behavior of the tissue during inflation-extension tests. The model is further applied to the experimental data from rabbit facial veins. The model accurately fits the experimental data of veins, but it does not improve the quality of the fit compared to the one without dispersion. We show that the orientational dispersion of collagen fibers can be compensated by a less abrupt and shifted to higher strain collagen engagement pattern. This should be taken into consideration when the model is used to fit experimental data and model parameters are used to study structural modifications of collagen fiber network in physiology and disease. In the fourth paper, we measure and quantify the waviness and orientational distributions of collagen in rabbit carotids. Quantification of collagen orientation distributions at the zero stress state of arteries is needed to develop realistic and precise biomechanical models. Using the fluorescence collagen marker CNA38-OG488 and confocal laser scanning microscopy, we visualize collagen fibers in adventitia of rabbit common carotids ex vivo. To get the properties related to the zero stress sate, the arteries are cut open along their longitudinal axes. We use semi-automatic and automatic techniques to measure parameters related to the waviness and fiber orientation. We show that the straightness parameter (i.e. the ratio between the distances of endpoints of a fiber to the fiber length) is distributed with a beta distribution. The shape of the probability density distribution does not depend on the mean angle orientation of fibers. In addition, our measurements reveal four axially symmetric families of fibers with mean orientations of 0°, 90°, 43° and -43° and circular standard deviations of 40°, 47°, 37° and 37°, with respect to the axial direction, respectively. To the best of our knowledge, this is the first study focusing on structural properties of collagen in the zero stress state and quantifying fiber waviness. The results of this study can be used to develop more precise structural models of the adventitia including waviness and orientational dispersion of fibers. The conclusion section summarizes the main results of the thesis, presents the improvements made over previous studies, and proposes future perspectives of this work.