Limiting extensibility constitutive model with distributed fibre orientations and ageing of abdominal aorta

Abstract

The abdominal aorta is susceptible to age-related pathological changes (arteriosclerosis, atherosclerosis, aneurysm, and tortuosity). Computational biomechanics and mechanobiology provide models capable of predicting mutual interactions between a changing mechanical environment and patho-physiological processes in ageing. However, a key factor is a constitutive equation which should reflect the internal tissue architecture. Our study investigates three microstructurally-motivated invariant-based hyperelastic anisotropic models suitable for description of the passive mechanical behaviour of the human abdominal aorta at a multiaxial state of stress known from recent literature. The three adopted models have also been supplemented with a newly proposed constitutive model (limiting extensibility with fibre dispersion). All models additively decouple the mechanical response of the isotropic (elastin and smooth muscle cells represented by the neo-Hookean term) and the anisotropic (collagen) parts. Two models use exponential functions to capture large strain stiffening ascribed to the engagement of collagen fibres into the load-bearing process. The other two models are based on the concept of limiting extensibility. Perfect alignment of reinforcing fibres with two preferred directions as well as fibre dispersion are considered. Constitutive models are calibrated to the inflation-extension response adopted from the literature based on the computational model of the residually-stressed thick-walled tube. A correlation analysis of determined material parameters was performed to reveal dependence on the age. The results of the nonlinear regression suggest that limiting fibre extensibility is the concept which is suitable to be used for the constitutive description of the aorta at multiaxial stress states and is highly sensitive to ageing-induced changes in mechanical response.

Segmental and age differences in the elastin network, collagen, and smooth muscle phenotype in the tunica media of the porcine aorta

“…The data provided in the Supplement 1 can be directly used in biomechanical models of the porcine aorta that are based on histological findings (Sokolis, 2010;Horný et al, 2014aHorný et al, , 2014b. According to the Delesse principle (Howard and Reed, 1998), the area fractions occupied by the components are consistent estimates of the corresponding volume fractions of these components.…”

Effect of Perivascular Tissue on Inflation-Extension Behavior of Abdominal Aorta

“…In what follows, constitutive model and geometrical data characterizing abdominal aorta of 38 years old male donor are adopted from Horny et al (2014). They used results, originally published by Labrosse et al (2013), to determine material parameters of the human abdominal aorta defined in the constitutive model suggested by Gasser et al (2006).…”

“…v V = 78.488 v w is a stress-like material parameter and v + = 4.911 is a dimensionless parameter. The material parameters were adopted from Horny et al (2014). g e and g f are generalised invariants related to imperfect fiber alignment.…”

“…indicates internal pressure and P QR is the reduced axial (prestretching) force acting on the closed end of the tube additionally to the force generated by the pressure acting on the end (Horny et al, 2013;Horny et al, 2014;Matsumuto and Hayashi, 1996). The distributions of the principal Cauchy stress components , and across the deformed wall thickness (aorta and perivascular tissue layers) are given equations (17), (18) where…”

“…In the present study, the analytical model of bilayer thick-walled closed tube (the human abdominal aorta and perivascular adipose tissue as outer layer) has been created as a subject of the inflation-extension test, by using geometrical data of human abdominal aorta from Labrosse et al (2012), material parameters of aorta from Horny et al (2014) and material parameters of human perivascular tissue from Vonavkova et al (2015). To the authors knowledge, this is the first study where the analytical model with individual layers (abdominal aorta and fat tissue) is studied.…”