A Structural Constitutive Model For Collagenous Cardiovascular Tissues Incorporating the Angular Fiber Distribution (original) (raw)
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Journal of the Mechanical Behavior of Biomedical Materials, 2019
The study proposes a novel theoretical-experimental approach for structure-based constitutive modeling of the passive mechanical properties of arterial tissue. The major novelty is accounting for the existence of individual natural configurations of elastin and collagen and their mechanical interaction in terms of the constituents' individual prestretches in the tissue natural state. The structure-based modeling of collagen allows accounting for effects of change in constituents' prestretch in terms of the change in feasible microstructural parameters, such as range of collagen recruitment stretch, mode of collagen mass fraction intensity function, and fiber directions. The results from an illustrative example for a porcine renal artery show that the model is robust and can adequately describe pressure-radius response and the stress-stretch relationship. The predictive capability of the model is tested in simulations of an isolated change in collagen prestretch and of elastin degradation in an artery kept at constant length. We expect this model to advance understanding about arterial rheology and serve as a useful tool for interpreting experimental data and solving boundary value problems relevant to vascular physiology at normal and pathological states.
Journal of Biomechanics, 2011
A fundamental understanding of the mechanical properties of the extracellular matrix (ECM) is critically important to quantify the amount of macroscopic stress and/or strain transmitted to the cellular level of vascular tissue. Structural constitutive models integrate histological and mechanical information, and hence, allocate stress and strain to the different microstructural components of the vascular wall. The present work proposes a novel multi-scale structural constitutive model of passive vascular tissue, where collagen fibers are assembled by proteoglycan (PG) cross-linked collagen fibrils and reinforce an otherwise isotropic matrix material. Multiplicative kinematics account for the straightening and stretching of collagen fibrils, and an orientation density function captures the spatial organization of collagen fibers in the tissue. Mechanical and structural assumptions at the collagen fibril level define a piece-wise analytical stress-stretch response of collagen fibers, which in turn is integrated over the unit sphere to constitute the tissue's macroscopic mechanical properties. The proposed model displays the salient macroscopic features of vascular tissue, and employs the material and structural parameters of clear physical meaning. Likewise, the constitutive concept renders a highly efficient multi-scale structural approach that allows for the numerical analysis at the organ level. Model parameters were estimated from isotropic mean-population data of the normal and aneurysmatic aortic wall and used to predict in-vivo stress states of patient-specific vascular geometries, thought to demonstrate the robustness of the particular Finite Element (FE) implementation. The collagen fibril level of the multi-scale constitutive formulation provided an interface to integrate vascular wall biology and to account for collagen turnover.
Computational Analyses of Mechanically Induced Collagen Fiber Remodeling in the Aortic Heart Valve
Journal of Biomechanical Engineering-transactions of The Asme, 2003
To optimize the mechanical properties and integrity of tissue-engineered aortic heart valves, it is necessary to gain insight into the effects of mechanical stimuli on the mechanical behavior of the tissue using mathematical models. In this study, a finite-element (FE) model is presented to relate changes in collagen fiber content and orientation to the mechanical loading condition within the engineered construct. We hypothesized that collagen fibers aligned with principal strain directions and that collagen content increased with the fiber stretch. The results indicate that the computed preferred fiber directions run from commissure to commissure and show a strong resemblance to experimental data from native aortic heart valves.
Remodelling of the angular collagen fiber distribution in cardiovascular tissues
Biomechanics and Modeling in Mechanobiology, 2008
Understanding collagen fiber remodelling is desired to optimize the mechanical conditioning protocols in tissue-engineering of load-bearing cardiovascular structures. Mathematical models offer strong possibilities to gain insight into the mechanisms and mechanical stimuli involved in these remodelling processes. In this study, a framework is proposed to investigate remodelling of angular collagen fiber distribution in cardiovascular tissues. A structurally based model for collagenous cardiovascular tissues is extended with remodelling laws for the collagen architecture, and the model is subsequently applied to the arterial wall and aortic valve. For the arterial wall, the model predicts the presence of two helically arranged families of collagen fibers. A branching, diverging hammock-type fiber architecture is predicted for the aortic valve. It is expected that the proposed model may be of great potential for the design of improved tissue engineering protocols and may give further insight into the pathophysiology of cardiovascular diseases.
Modelling the mechanical response of elastin for arterial tissue
Journal of biomechanics, 2009
We compare two constitutive models proposed to model the elastinous constituents of an artery. Holzapfel and Weizsäcker [1998. Biomechanical behavior of the arterial wall and its numerical characterization. Comput. Biol. Med. 28, 377-392] attribute a neo-Hookean response, i.e. Psi=c(I(1)-3)), to the elastin whilst Zulliger et al. [2004a. A strain energy function for arteries accounting for wall composition and structure. J. Biomech. 37, 989-1000] propose Psi=c(I(1)-3)(3/2). We analyse these constitutive models for two specific cases: (i) uniaxial extension of an elastinous sheet; (ii) inflation of a cylindrical elastinous membrane. For case (i) we illustrate the functional relationships between: (a) the Cauchy stress (CS) and the Green-Lagrange (GL) strain; (b) the tangent modulus (gradient of the CS-GL strain curve) and linearised strain. The predicted mechanical responses are compared with recent uniaxial extension tests on elastin [Gundiah, N., Ratcliffe, M.B., Pruitt, L.A., 2007...
Role of elastin anisotropy in structural strain energy functions of arterial tissue
Biomechanics and Modeling in Mechanobiology, 2011
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 inflationextension 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.
Improved Prediction of the Collagen Fiber Architecture in the Aortic Heart Valve
Journal of Biomechanical Engineering, 2004
Living tissues show an adaptive response to mechanical loading by changing their internal structure and morphology. Understanding this response is essential for successful tissue engineering of load-bearing structures, such as the aortic valve. In this study, mechanically induced remodeling of the collagen architecture in the aortic valve was investigated. It was hypothesized that, in uniaxially loaded regions, the fibers aligned with the tensile principal stretch direction. For biaxial loading conditions, on the other hand, it was assumed that the collagen fibers aligned with directions situated between the principal stretch directions. This hypothesis has already been applied successfully to study collagen remodeling in arteries. The predicted fiber architecture represented a branching network and resembled the macroscopically visible collagen bundles in the native leaflet. In addition, the complex biaxial mechanical behavior of the native valve could be simulated qualitatively wi...
Journal of biomechanics, 2015
A key element of the cardiac cycle of the human heart is the opening and closing of the four valves. However, the material properties of the leaflet tissues, which fundamentally contribute to determine the mechanical response of the valves, are still an open field of research. The main contribution of the present study is to provide a complete experimental data set for porcine heart valve samples spanning all valve and leaflet types under tensile loading. The tests show a fair degree of reproducibility and are clearly indicative of a number of fundamental tissue properties, including a progressively stiffening response with increasing elongation. We then propose a simple anisotropic constitutive model, which is fitted to the experimental data set, showing a reasonable interspecimen variability. Furthermore, we present a dynamic finite element analysis of the aortic valve to show the direct usability of the obtained material parameters in computational simulations.
A new constitutive model for multi-layered collagenous tissues
Journal of Biomechanics, 2008
Collagenous tissues such as the aneurysmal wall or the aorta are multi-layered structures with the mean fibre alignments distinguishing one layer from another. A constitutive representation of the multiple collagen layers is not yet developed, and hence the aim of the present study. The proposed model is based on the constitutive theory of finite elasticity and is characterized by an anisotropic strain-energy function which takes the material structure into account. The passive tissue behaviour is modelled and the related mechanical response is assumed to be dominated by elastin and collagen. While elastin is modelled by the neo-Hookean material the constitutive response of collagen is assumed to be transversely isotropic for each individual layer and based on an exponential function. The proposed constitutive function is polyconvex which ensures material stability. The model has five independent material parameters, each of which has a clear physical interpretation: the initial stiffnesses of the collagen fabric in the two principal directions, the shear modulus pertaining to the non-collagenous matrix material, a parameter describing the level of nonlinearity of the collagen fabric, and the angle between the principal directions of the collagen fabric and the reference coordinate system. An extension-inflation test of the adventitia of a human femoral artery is simulated by means of the finite element method and an error function is minimized by adjusting the material parameters yielding a good agreement between the model and the experimental data.
Biomechanics and Modeling in Mechanobiology, 2011
A patient-specific mechanical description of the coronary arterial wall is indispensable for individualized diagnosis and treatment of coronary artery disease. A way to determine the artery's mechanical properties is to fit the parameters of a constitutive model to patient-specific experimental data. Clinical data, however, essentially lack information about the stress-free geometry of an artery, which is necessary for constitutive modeling. In previous research, it has been shown that a way to circumvent this problem is to impose extra modeling constraints on the parameter estimation procedure. In this study, we propose a new modeling constraint concerning the in-situ fiber orientation (β phys). β phys , which is a major contributor to the arterial stress-strain behavior, was determined for porcine and human coronary arteries using a mixed numerical-experimental method. The in-situ situation was mimicked using in-vitro experiments at a physiological axial pre-stretch, in which pressure-radius and pressure-axial force were measured. A single-layered, hyperelastic, thick-walled, two-fiber material model was accurately fitted to the experimental data, enabling the computation of stress, strain, and fiber orientation. β phys was found to be almost equal for all vessels measured (36.4 ± 0.3) • , which theoretically can be explained using netting analysis. In further research, this finding can be used as an extra modeling constraint in parameter estimation from clinical data.