A structure-based model of arterial remodeling in response to sustained hypertension

A novel structure-based mathematical model of arterial remodeling in response to a sustained increase in pressure is proposed. The model includes two major aspects of remodeling in a healthy matured vessel. First, the deviation of the wall stress and flow-induced shear stress from their normal physiological values drives the changes in the arterial geometry. Second, the new mass that is produced during remodeling results from an increase in the mass of smooth muscle cells and collagen fibers. The model additionally accounts for the effect of the average pulsatile strain on the recruitment of collagen fibers in load bearing. The model was used to simulate remodeling of a human thoracic aorta, and the results are in good agreement with previously published model predictions and experimental data. The model predicts that the total arterial volume rapidly increases during the early stages of remodeling and remains virtually constant thereafter, despite the continuing stress-driven geometrical remodeling. Moreover, the effects of a perfect or incomplete restoration of the arterial compliance on the remodeling outputs were analyzed. For instance, the model predicts that the pattern of the time course of the opening angle depends on the extent to which the average pulsatile strain is restored at the end of the remodeling process. Future experimental studies on the time course of compliance, opening angle, and mass fractions of collagen, elastin, and smooth muscle cells can validate and improve the introduced hypotheses of the model.

Arterial remodeling using a constituent-based approach

Alkiviadis Tsamis

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.

EPFL2010

Arterial in vitro remodeling

Gabriela Montorzi Thorell

Vascular remodeling is defined as any enduring change in the size and composition of an adult blood vessel, allowing adaptation or repair. The vascular remodeling response has been shown to depend on a variety of endogenous and environmental factors. Physiological remodeling is a tightly regulated process that mainly occurs in response to long-term changes in hemodynamic conditions. The adaptation to these hemodynamic changes implies the production of mediators that influence structure as well as function. A loss of regulation in the adaptive response underlies the pathogenesis of major cardiovascular diseases, including hypertension, atherosclerosis, restenosis and arterial aneurismal dilatation. Specialized enzymes called matrix metalloproteinases (MMPs) have been shown to have a predominant participation in the reorganization of the vessel structure, through the degradation of the extracellular matrix scaffold. The aim of this thesis is to gain insight in the biological and mechanical processes taking place in the vascular wall as an adaptive response to different biomechanical stimuli such as blood pressure and blood flow. This work proposes a new model for the study of vascular remodeling where physical factors acting on the arterial wall can be dissociated and analyzed, individually, in relation to the biological response. The results are presented in form of an introduction, three scientific papers and a conclusion section. The investigation has been designed around three different approaches: adaptation of a non-uniform artery to an in vitro environment, vascular adaptation to steady and pulsatile pressure and vascular adaptation to unidirectional and oscillatory flow. The adaptive response to each one of the variables chosen has been analyzed through biological and biomechanical remodeling indicators of the arterial wall. The introduction is an overview of the biological and biomechanical characteristics of arterial wall in relation to the remodeling process. The contribution of vascular smooth muscle cells and extracellular matrix to physiological and pathological arterial remodeling is discussed. Paper I assesses the relative remodeling of a non-axisymmetric artery in relation to its environment. The study considers the native circumferential asymmetry of the porcine right common carotid, which results from the non-homogenous mechanical and hemodynamic native environment. The adaptive response of the artery to an in vitro perfusion environment is analyzed. The study shows that in vitro perfusion leads, through remodeling, to a circumferentially uniform scleroprotein distribution and to a change in arterial compliance. This study emphasizes the link between structural changes, the biomechanical response and the enzymatic implication in the adaptive response. In paper II we investigate the role of continuous and cyclic stretch, produced by steady or pulsatile pressure acting on the arterial wall, on the remodeling response. The study shows that exposure to continuous and cyclic stretch differentially affects the relative scleroprotein content and leads to a change in arterial wall stiffness. The adaptive outcome is studied through an integrative approach taking into consideration the geometrical and structural adaptation, the biomechanical behavior and the enzymatic agents implicated in extracellular matrix turnover. Paper III analyzes the influence of different flow patterns on the arterial adaptive response. We investigate the differential effects of oscillatory flow, mimicking a plaque-prone hemodynamic environment, and unidirectional flow, to mimicking a physiologically protective (plaquefree) environment. The effect of these hemodynamic forces on the remodeling response are characterized through the study of endothelial and smooth muscle cell function as well as through assessment of agents influencing extracellular matrix turnover. The conclusions section presents a synthesis of the results and contribution of this thesis and proposes perspectives for future studies.

EPFL2004

Geometrical, functional, and histomorphometric adaptation of rat carotid artery in induced hypertension

Nikolaos Stergiopulos, Martin Zulliger

Acute and long-term (up to 56 days) evolution of geometry, structural properties, vascular smooth muscle (VSM) tone and histomorphometric properties of the rat common carotid arteries under induced hypertension were investigated. Hypertension was induced in 8-week old male Wistar rats by total ligation of the aorta between the two kidneys. Rats were sacrificed 2, 4, 8 and 56 days postsurgery. The arterial wall layers thicken non-uniformly during the adaptation process, the inner layers thicken more in the acute phase of hypertension, whereas the outer layers of the wall are thicker than the inner layers at the end of the adaptation phase. Collagen content in the wall media exhibits a non-linear evolution, with a rapid increase in the acute hypertension phase followed by a slower increase at long-term. The elastin content increase is slight and steady, whereas VSM shows a steady but considerable increase which outdoes the collagen increase in long-term phase. VSM tone increases rapidly in the acute phase of remodelling (0-8 days) and this increase in tone contributes to a considerable increase in arterial compliance in the operating pressure range. At long-term (56 days) VSM tone returns to near control level, but compliance is even further increased, which suggests that at long-term the compliance increase is attributed primarily to structural remodelling.