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

Arterial remodeling in response to increased blood flow using a constituent-based model

Previous theoretical models of arterial remodeling in response to changes in blood flow were based on the assumption that material properties of the arterial wall remain unchanged during the remodeling process. According to experimental findings, however, remodeling due to increased flow is accompanied by alteration in the structural properties of elastin, which results in a decrease in its effective elastic stiffness. To account for these effects, we propose a predictive model of arterial remodeling hypothesizing that the variation in mechanical properties of elastin is initiated and driven by the deviation of the intimal shear stress from its baseline value. Geometrical remodeling restores the wall stress distribution as it was under normal flow conditions. A constrained mixture approach is followed. Artery is modeled as a thick-walled cylindrical tube made of non-linear, elastic, anisotropic and incompressible material. Data for a rabbit thoracic aorta have been employed. At the final adapted state, the model predicts a non-monotonic dependence of arterial compliance on the magnitude of flow. This result is in agreement with available experimental data in the literature

Arterial remodeling in response to hypertension using a constituent-based model

Hypertension-induced arterial remodeling has been previously modeled using stress-driven remodeling rate equations in terms of global geometrical adaptation (Rachev A, Stergiopulos N, Meister JJ. Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J Biomech 29: 635-642, 1996) and was extended later to include adaptation of material properties (Rachev A, Stergiopulos N, Meister JJ. A model for geometric and mechanical adaptation of arteries to sustained hypertension. J Biomech Eng 120: 9-17, 1998). These models, however, used 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. (1998) by applying similar remodeling rate equations to a constituent-based SEF. The new SEF includes a statistical description for collagen engagement, and remodeling now affects material properties only through changes in the collagen engagement probability density function. The model predicts asymptotic wall thickening and unchanged deformed inner radius as to conserve hoop stress and intimal shear stress, respectively, at the final adapted hypertensive state. Mechanical adaptation serves to restore arterial compliance to control levels. Average circumferential stress-strain curves show that the material at the final adapted hypertensive state is softer than its normotensive counterpart. These findings as well as the predicted pressure-diameter curves 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

A RealTime Graphic Environment for a Urological Operation Training Simulator

of a training simulator for urological operations, is presented. The graphic environment simulates endoscope insertion in a small diameter deformable tube and is used with a low-force 5-dof force-feedback haptic mechanism. Piecewise Bezier interpolations are used for smooth urethra deformations. A novel particle-based model computes the forces and torques fed to the haptics. Realistic textures from medical databases are employed and a 25 fps refresh rate is achieved using the Rendering Thread method. The overall simulator software is made of three processes running on two distinct platforms, communicating via Ethernet and TCP/IP. Keywords_Graphical training simulator, force model, haptics. I

A constituent-based model of age-related changes in conduit arteries

Tsamis A, Rachev A, Stergiopulos N. A constituent-based model of age-related changes in conduit arteries. Am J Physiol Heart Circ Physiol 301: H1286-H1301, 2011. First published July 1, 2011; doi: 10.1152/ajpheart.00570.2010.-In the present report, a constituent-based theoretical model of age-related changes in geometry and mechanical properties of conduit arteries is proposed. The model was based on the premise that given the time course of the load on an artery and the accumulation of advanced glycation end-products in the arterial tissue, the initial geometric dimensions and properties of the arterial tissue can be predicted by a solution of a boundary value problem for the governing equations that follow from finite elasticity, structure-based constitutive modeling within the constrained mixture theory, continuum damage theory, and global growth approach for stress-induced structure-based remodeling. An illustrative example of the age-related changes in geometry, structure, composition, and mechanical properties of a human thoracic aorta is considered. Model predictions were in good qualitative agreement with available experimental data in the literature. Limitations and perspectives for refining the model are discussed

Development of a Real-time Visual and Force Environment for a Haptic Medical Training Simulator

Submitted as a full paper to Artificial Life and Robotic

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