Modelling non-symmetric collagen fibre dispersion in arterial walls

Abstract

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.

On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube

“…7 considers and discusses the aforementioned case of particular practical interest [1][2][3][4][5][6][7][8][9][10][11], where fibres grow with and within the tube in a helical manner. A similar kind of interest is shown afterwards for the families of plane fibres considered in Sect.…”

“…These investigations focus attention on the material anisotropy caused in different layers of the arterial vessel by the dispersion and the mean alignment of collagen fibres. It has become, for instance, understood [5] that two families of fibres are present in the intima, media and adventitia of human aortas, and these are helically arranged with respect to the cylinder axis. Often a third and sometimes a fourth fibre family is present in the intima along the respective axial and circumferential directions [5].…”

“…It has become, for instance, understood [5] that two families of fibres are present in the intima, media and adventitia of human aortas, and these are helically arranged with respect to the cylinder axis. Often a third and sometimes a fourth fibre family is present in the intima along the respective axial and circumferential directions [5]. However, there exist also artery wall layers, such as the medial layer of human common iliac arteries, which have only a single preferred fibre direction [6,7].…”

“…[10,11]). In this context, particular mention is made of a set of experimental and theoretical investigations that aim to clarify the role of collagen fibre reinforcement as well as its influence on the mechanical behaviour of arterial wall (see [5][6][7] and relevant references therein). These investigations focus attention on the material anisotropy caused in different layers of the arterial vessel by the dispersion and the mean alignment of collagen fibres.…”

“…The latter include arteries and veins (e.g. [4][5][6][7]), muscles (e.g. [8]) and even living creatures of tubular shape [9].…”