A new constitutive model for multi-layered collagenous tissues

Kroon, Martin; Holzapfel, Gerhard

doi:10.1016/j.jbiomech.2008.05.033

Cited by 60 publications

(51 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Mechanical predictions are thought to be more accurate than those of phenomenological models, as these models account for microstructural features of vessel components, as well as heterogeneity of material properties. The microstructural parameters have been ad hoc rather than based on experimental measurements, due to limited morphological data of the vessel wall (4,17,23,51). The microstructure of the vessel wall, which includes elastin and collagen fibers, smooth muscle cells, and ground substance, is distributed differently in individual vessel layers, i.e., tunica media and adventitia (8,36,43).…”

mentioning

confidence: 99%

A validated 3D microstructure-based constitutive model of coronary artery adventitia

et al. 2016

View full text Add to dashboard Cite

Chen H, Guo X, Luo T, Kassab GS. A validated 3D microstructure-based constitutive model of coronary artery adventitia. J Appl Physiol 121: 333-342, 2016. First published May 12, 2016 doi:10.1152/japplphysiol.00937.2015.-A structure-based model that accurately predicts micro-or macromechanical behavior of blood vessels is necessary to understand vascular physiology. Based on recently measured microstructural data, we propose a three-dimensional microstructural model of coronary adventitia that incorporates the elastin and collagen distributions throughout the wall. The role of ground substance was found to be negligible under physiological axial stretch z ϭ 1.3, based on enzyme degradation of glycosaminoglycans in swine coronary adventitia (n ϭ 5). The thick collagen bundles of outer adventitia (n ϭ 4) were found to be undulated and unengaged at physiological loads, whereas the inner adventitia consisted of multiple sublayers of entangled fibers that bear the majority of load at higher pressures. The microstructural model was validated against biaxial (inflation and extension) experiments of coronary adventitia (n ϭ 5). The model accurately predicted the nonlinear responses of the adventitia, even at high axial force (axial stretch ratio z ϭ 1.5). The model also enabled a reliable estimation of material parameters of individual fibers that were physically reasonable. A sensitivity analysis was performed to assess the effect of using mean values of the distributions for fiber orientation and waviness as opposed to the full distributions. The simplified mean analysis affects the fiber stress-strain relation, resulting in incorrect estimation of mechanical parameters, which underscores the need for measurements of fiber distribution for a rigorous analysis of fiber mechanics. The validated structure-based model of coronary adventitia provides a deeper understanding of vascular mechanics in health and can be extended to disease conditions. constitutive model; collagen; elastin; microstructure; adventitia; material parameters MICROSTRUCTURAL APPROACHES have been advocated for modeling blood vessels to understand better the nonlinear mechanical responses of vessels (7,17,18,25). Mechanical predictions are thought to be more accurate than those of phenomenological models, as these models account for microstructural features of vessel components, as well as heterogeneity of material properties. The microstructural parameters have been ad hoc rather than based on experimental measurements, due to limited morphological data of the vessel wall (4,17,23,51). The microstructure of the vessel wall, which includes elastin and collagen fibers, smooth muscle cells, and ground substance, is distributed differently in individual vessel layers, i.e., tunica media and adventitia (8,36,43). A microstructural constitutive model should be specific for a particular layer based on experimental measurements of microstructure (2).The coronary adventitia consists of three major constituents-elastin, collagen fibers, and ground substance-and...

show abstract

mentioning

confidence: 99%

A validated 3D microstructure-based constitutive model of coronary artery adventitia

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Aneurysms occur primarily in cerebral arteries and the aorta. On the basis of the multi-layer model of Kroon & Holzapfel (2008b), the study by investigated the distribution of the elastic properties of cerebral aneurysm tissue identified by an inverse finite element analysis. The proposed algorithm is able to estimate the distribution and the resulting maximum principal stress at physiological loading with satisfactory accuracy.…”

Section: (A) Arterial Wall Modelling and Its Applicationsmentioning

confidence: 99%

“…An extension to multi-layered structures with the mean fibre alignments distinguishing one layer from another was proposed in Kroon & Holzapfel (2008b). Particular examples of such a structure include artery walls, quadriceps tendons and airway walls.…”

Section: (C) Fibrous Soft Tissues In Generalmentioning

confidence: 99%

Constitutive modelling of arteries

2010

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Therein, we used a rotationally symmetric distribution of collagen fibres. In addition, the model [15] was applied to several other tissues, including the cornea [24] and articular cartilage [25], while, in [26], the constitutive model of [14] was applied with the fibre orientations uniformly distributed over the azimuthal angle. A structure tensor based on a planar counterpart of that in [15] was defined in [27,28] and used in [29].…”

Section: Introductionmentioning

confidence: 99%

Modelling non-symmetric collagen fibre dispersion in arterial walls

Holzapfel

Niestrawska

Ogden

et al. 2015

J. R. Soc. Interface.

Self Cite

208

215

View full text Add to dashboard Cite

New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new nonsymmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15 -35. (doi:10.1098/ rsif.2005). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues.

show abstract

A new constitutive model for multi-layered collagenous tissues

Cited by 60 publications

References 35 publications

A validated 3D microstructure-based constitutive model of coronary artery adventitia

A validated 3D microstructure-based constitutive model of coronary artery adventitia

Constitutive modelling of arteries

Modelling non-symmetric collagen fibre dispersion in arterial walls

Contact Info

Product

Resources

About