Constitutive modelling of arteries considering fibre recruitment and three-dimensional fibre distribution

Abstract

Structurally motivated material models may provide increased insights into the underlying mechanics and physics of arteries under physiological loading conditions. We propose a multiscale model for arterial tissue capturing three different scales (i) a single collagen fibre; (ii) bundle of collagen fibres; and (iii) collagen network within the tissue. The waviness of collagen fibres is introduced by a probability density function for the recruitment stretch at which the fibre starts to bear load. The three-dimensional distribution of the collagen fibres is described by an orientation distribution function using the bivariate von Mises distribution, and fitted to experimental data. The strain energy for the tissue is decomposed additively into a part related to the matrix material and a part for the collagen fibres. Volume fractions account for the matrix/fibre constituents. The proposed model only uses two parameters namely a shear modulus of the matrix material and a (stiffness) parameter related to a single collagen fibre. A fit of the multiscale model to representative experimental data obtained from the individual layers of a human thoracic aorta shows that the proposed model is able to adequately capture the nonlinear and anisotropic behaviour of the aortic layers.

Quantification of the regional bioarchitecture in the human aorta

“…Although two families (peaks in probability density histogram) are frequently apparent in the present data, in each case one constitutes a significantly greater area fraction than the other. O'Connell et al (2008), Horny et al (2010), Schriefl et al (2012), Chow et al (2014), Sassani et al (2015), Weisbecker et al (2015) and Sugita & Matsumoto (2018) report that a single family of fibres was evident; however, others have reported two (Schriefl et al 2012;Laksari et al 2016), three (Schriefl et al 2012) and even four (Rezakhaniha et al 2012;Schriefl et al 2012) fibre families, all of which are evident here, further emphasising aortic microarchitectural heterogeneity at a local level. It is shown that a von Mises mixture model is required accurately to fit the complexity of collagen fibre orientations that exist along the aorta, which suggests that common constitutive laws implemented through finite element analysis (Holzapfel et al 2000;Nolan et al 2014) may not be capable of fully capturing the full anisotropy of the vessel.…”

“…(), Weisbecker et al. () and Sugita & Matsumoto () report that a single family of fibres was evident; however, others have reported two (Schriefl et al. ; Laksari et al.…”

Constitutive interpretation of arterial stiffness in clinical studies: a methodological review

“…We submit that the consequent lack of quantitative mechanistic insight limits the field in designing and testing treatment approaches to target the ultrastructural basis of arterial stiffening (15,37,140,159). Motivated by previous work of ours and others (13,23,39,125,142,151), we consider the skillful application of constitutive models to clinical arterial stiffness data of great potential value to close the mentioned gap. Therefore, in the next section, we will discuss the applicability of constitutive modeling and provide some guidance on releasing its potential.…”

Over length quantification of the multiaxial mechanical properties of the ascending, descending and abdominal aorta using Digital Image Correlation

“…The response of fibers are typically assumed to be governed by exponential functions (Holzapfel et al, 2000(Holzapfel et al, , 2005. However, structurally-motivated material models may provide increased insights into the underlying mechanics and physics of arteries and could overcome this drawback (Weisbecker et al, 2015). The work by Gasser et al (2006) included micro-structural information in the model by means of the assumption of a fiber orientation von Mises distribution function.…”