Theory of small on large: Potential utility in computations of fluid–solid interactions in arteries

Baek, Seungik; Gleason, Rudolph L.; Rajagopal, Κ. R.; Humphrey, Jay D.

doi:10.1016/j.cma.2006.06.018

Cited by 252 publications

(236 citation statements)

References 30 publications

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“…In Rachev & Hayashi (1999) the passive state was described by A = 0, the basal state by A ≈ 50 kPa and the fully activated state by A ≈ 100 kPa. The same activation was used in the study by Baek et al (2007a) in conjunction with a constitutive law of the type (2.29). They developed a theory of small deformations superimposed on a large deformation in the context of fluid-solid interactions, and they showed that the theory predicts that the stiffness of the wall decreases with increasing vasoconstriction.…”

Section: Active Response Of Artery Wallsmentioning

confidence: 99%

“…An engagement strain was also discussed by Speirs et al (2008), who used a finite element implementation to analyse the inflation and extension of a thick-walled tube by using the models (2.21) and (2.22) and compared the results with those from the engagement model of Zulliger et al (2004a). Baek et al (2007a), Hu et al (2007) and Zeinali-Davarani et al (2009) considered a model of the form of equation (2.29) but with four families of fibres instead of two. This model is motivated by microscopic data on the arterial collagen organization obtained from multi-photon microscopy (Wicker et al 2008).…”

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

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Constitutive modelling of arteries

2010

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This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thickwalled circular cylindrical tube in order to illustrate its extension-inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.

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Section: Active Response Of Artery Wallsmentioning

confidence: 99%

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

Constitutive modelling of arteries

2010

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“…41 The Neo-Hookean model C iso D C(I 1 -3)/2 for the isotropic contribution has been suggested with the stress-like material parameter C > 0 (the shear modulus). 42 The strain energy function can be expressed as following by considering the 4-fiber family of collagen: 20,24,43 …”

Section: Constitutive Modelmentioning

confidence: 99%

“…17,18 Many works either chose a purely phenomenological approach like the Fung-type model, or consider histostructural information, such as the Holzapfel-Gasser-Ogden constitutive model 19 or fiber family model [20][21][22] to capture the nonlinear hyperelastic mechanical behavior of the soft biological tissues, especially the arterial wall. Since the fiber family constitutive based material model has the potential ability to address the mechanical properties of the skin tissue better than that of phenomenological model, [23][24][25] it would be useful and practically valuable to determine the material coefficients of the rat and mice skins in different anatomical locations, including the abdomen and back, from uniaxial data with the previously proposed model by Holzapfel. Therefore, the objective of this study is to experimentally and numerically determine the anisotropic mechanical properties of the rat and mice skin tissues using histostructural and uniaxial test data.…”

Section: Introductionmentioning

confidence: 99%

Mechanical characterization of the rat and mice skin tissues using histostructural and uniaxial data

2015

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The skin tissue has been shown to behave like a nonlinear anisotropic material. This study was aimed to employ a constitutive fiber family equation to characterize the nonlinear anisotropic mechanical behavior of the rat and mice skin tissues in different anatomical locations, including the abdomen and back, using histostructural and uniaxial data. The rat and mice skin tissues were excised from the animals' body and then the histological analyses were performed on each skin type to determine the mean fiber orientation angle. Afterward, the preconditioned skin tissues were subjected to a series of quasi-static axial and circumferential loads until the incidence of failure. The crucial role of fiber orientation was explicitly added into a proposed strain energy density function. The material coefficients were determined using the constrained nonlinear optimization method based on the axial and circumferential extension data of the rat and mice samples at different anatomical locations. The material coefficients of the skins were given with R 2 0.998. The results revealed a significant load-bearing capacity and stiffness of the rat abdomen compared to the rat back tissues. In addition, the mice abdomen showed a higher stiffness in the axial direction in comparison with circumferential one, while the mice back displayed its highest stiffness in the circumferential direction. The material coefficients of the rat and mice skin tissues were determined and well compared to the experimental data. The optimized fiber angles were also compared to the experimental histological data, and in all cases less than 11.85% differences were observed in both the skin tissues.

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“…This presents some difficulty, because arterial tissue is anisotropic and nonlinear in the stressstretch relationship, displays pseudo-elastic behavior, and changes material properties with age due to structural change and remodeling. The aim of this work is to implement the structurally-motivated phenomenological "four fiber family" model introduced by Baek et al [1] for simulation of biomechanical properties in the human aorta with and without aneurysms. As a first step, a 2D finite element model (FEM) implementation is presented and used as a benchmark to numerically reproduce the stress-strain relations obtained in biaxial stress-strain experiments [2,3].…”

Section: Introductionmentioning

confidence: 99%