Arterial remodeling using a constituent-based approach

This thesis is intended to contribute to the field of biomechanics of growth and remodeling of arteries. The work focuses particularly on growth and remodeling caused by sustained hypertension, increased blood flow, and ageing. A structure-based constitutive law is employed, which accounts for the elastic and structural properties of the components of the vascular tissue. Analysis of the biomechanical properties of the arterial wall allows for quantification of the developed wall stresses and strains. The dynamics of arterial growth and remodeling is described by appropriate remodeling rate equations. The corner-stone of this theoretical project is, of course, the development of physiologically relevant evolution laws describing the shear stress- and wall stress-induced growth and remodeling of the arterial wall. The model predictions are presented in the form of an introduction, four chapters (four papers) and a conclusion. The introduction begins with the motivation for this project. The link between mechanical load and remodeling in blood vessels follows. The state of the art on theoretical models of arterial remodeling in response to hypertension, changed flow, and ageing is also presented. The first paper presents a novel theoretical model of hypertension-induced arterial remodeling using a structure-based constitutive law. Arterial remodeling in response to sustained hypertension has been previously modeled using a phenomenological strain energy function (SEF), the parameters of which do not bear a clear physiological meaning. Here, we extend the work of Rachev et al. by applying similar evolution laws to a constituent-based SEF, which includes a statistical description for collagen recruitment in load bearing. Remodeling affects the material properties only through changes in the probability density function of collagen engagement. The model simulates the remodeling of a rabbit thoracic aorta and predicts that, at the final adapted hypertensive state, the wall thickness is increased to conserve the baseline value of hoop stress and the lumen radius remains unchanged to preserve the normotensive levels of intimal shear stress. Furthermore, the remodeling of material properties serves to restore the arterial compliance to control levels. The material at the final adapted state is softer than its normotensive counterpart as indicated by the average circumferential stress-strain curves. Model predictions are in good qualitative agreement with experimental data. The novelty in our findings is that biomechanical adaptation leading to maintenance of compliance at the hypertensive state can be perfectly achieved by appropriate readjustment of the collagen engagement profile alone. The second paper addresses a predictive model of arterial remodeling in response to increased flow using a constituent-based SEF. Prior theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the vascular tissue remain unchanged during the remodeling process. Experimental findings show, however, that increased flow causes structural alterations in the elastin resulting in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling in response to increased flow hypothesizing that the deviation of the intimal shear stress from its baseline value initiates and drives the variation in the mechanical properties of elastin. The mismatch in wall stresses with respect to baseline values drives the changes in the geometrical parameters of the stress-free configuration. A constrained mixture approach is followed and the artery is modeled as a thick-walled cylindrical tube made of nonlinear, elastic, anisotropic and incompressible material. We make use of literature data for a rabbit thoracic aorta. The model predicts that, at the final adapted state, the arterial compliance depends non-monotonically on the magnitude of the flow, which is in agreement with available experimental data in the literature. The third paper expands the model of the first paper in order to include another major aspect of remodeling in a healthy matured vessel: the new mass that is produced during remodeling results from an increase in the mass of smooth muscle cells and collagen fibers. The model also takes into consideration the effect of the average pulsatile strain on collagen fiber engagement in load bearing. Remodeling of a human thoracic aorta was simulated by the model and the results agree well with published model predictions and experimental data. According to the model, the total arterial mass increases fast in the early stages of remodeling and does not vary thereafter, despite any further geometrical changes as well as structural reorganization of the collagen fibers. Furthermore, the perfect or incomplete restoration of the average pulsatile strain at the end of the remodeling process has an impact on the time course of certain parameters of the model such as the opening angle. Future experimental studies on the time variation of compliance, opening angle and mass fractions will validate and improve the introduced hypotheses of the model. In the fourth paper we perform a theoretical study of aortic remodeling in ageing using a constituent-based modeling approach. The model is based on two major hypotheses. First, mechanical fatigue failure in the elastin structure is caused by the pulsatile wall strain and the number of cardiac cycles. The fragmentation of elastin results in an increase in the inner radius at the zero-load state. Second, the accumulation of advanced glycation end products (AGEs) over time increases the cross-linking of collagen fibers making the recruitment of the fibers occur at lower strains and more abruptly. This raises the stiffness of the collagen fiber network. Furthermore, the geometrical remodeling follows the increase in the lumen radius at the load-free configuration and preserves the baseline level of circumferential stress at the inner and outer surface under mean pressure. Additionally, the geometrical changes lead to an increase in the content of collagen fibers, affecting accordingly the mass fractions of elastin and smooth muscle cells. We employ the constituent-based SEF of Zulliger and Stergiopulos in order to verify the results of their curve-fitting study on the elastic and structural properties of the human thoracic aorta. We further monitor the time variation of certain geometrical characteristics. Model results agree well with published experimental data. According to the model, the fragmentation of elastin only affects the geometrical remodeling, with the total arterial mass being increased with increased damage of elastin. With progressed age, elastin contributes less in bearing load, allowing the stiff collagen to lower the arterial compliance and cause a monotonic decrease in the pulsatile strain. Also, the accumulation of AGEs over time impacts on both the material and the geometrical parameters, with the latter being affected at high ages. The net effect is a decrease in the arterial dimensions and mass at high ages due to an increased accumulation of AGEs. Surprisingly, the time course of the mass fractions of the wall components is not affected by the increase or decrease of AGEs, indicating that the geometrical and structural reorganization of the vascular tissue is done in such a way in order to preserve the relative content of the wall constituents. There is a need for more experimental data to support the conclusions of the parametric analysis. The concluding section summarizes the main results of the thesis, presents the improvements made over previous theoretical investigations, emphasizes the need for more experimental data in order to validate and improve the models, and proposes future extensions of the work.