Characterization of mechanical damage and viscoelasticity on aortas from guinea pigs subjected to hypoxia

Abstract

To reliably assess the rupture risk of the aorta, along with the hazardousness of cardiovascular diseases and other extreme conditions or the effect of possible treatments, it is necessary to understand the influence of damage mechanisms along with the frequency and rate of mechanical loads. In particular, hypobaric hypoxia, an oxygen deficiency in the organism due to its low atmospheric partial pressure, is reported to alter the mechanical properties of blood vessels. In this work, we characterized the passive mechanical response of the aorta, seeking to capture the influence of hypoxia on their elastic, damage, and viscoelastic properties under ex-vivo conditions. The mechanical behavior of the aortic wall is described using an anisotropic hyperelastic model including two fiber families with asymmetric dispersion, along with an anisotropic damage model and an orthotropic viscoelastic model based on a reverse multiplicative decomposition of the deformation gradient. The constitutive model was experimentally calibrated from uniaxial-relaxation and biaxial-tensile test results, previously performed on thoracic aorta samples of guinea pigs. A group of guinea pigs subjected to hypoxia was contrasted with a normoxic (control) group. Cyclic-load stages of uniaxial tests were used to assess dissipation. Once the constitutive model was implemented and calibrated, its performance was evaluated via the numerical simulation of a bulge pressurization test to estimate energy dissipation and pressure associated with the onset of damage. Results indicated that hypoxia does not alter the visco-hyperelastic or damage behavior of the aorta. Besides, the pressure delivered by bulge-test simulations at the onset of damage on collagen fibers was representative of an arterial hypertensive condition.

Keywords: Anisotropic hyperelasticity; Anisotropic mechanical damage; Aortic wall; Non-linear orthotropic viscoelasticity.

Fig. 1

(a) Schematic longitudinal () and circumferential () specimen configurations. (b) Initial dimensions of specimens for biaxial testing. (c) Initial dimensions of specimens for uniaxial testing. (d) Initial thickness of specimens

Fig. 2

Calibration procedure for the constitutive model. Description of the four stages (I to IV), detailing the optimization method and initial, calibrated (free), and fixed sets of constitutive model parameters at each step

Fig. 3

Bulge test simulation. (a) Undeformed configuration and mean fiber directions. (b) Finite element mesh. (c) Typical deformed configuration and analysis point ‘A’. (d) Bulge test experimental setup

Fig. 4

Cauchy stress (in kPa) versus stretch, uniaxial relaxation (a, b) and biaxial (c, d) tensile tests, normoxic group (Nx). Longitudinal (z) and circumferential () directions

Fig. 5

Cauchy stress (in kPa) versus stretch, uniaxial relaxation (a, b) and biaxial (c, d) tensile tests, hypoxic group (Hx). Longitudinal (z) and circumferential () directions

Fig. 6

Constitutive model calibration for a typical animal (Nx-01) of the normoxic group (Nx): Cauchy stress (in kPa) versus stretch of uniaxial relaxation (a,b) and biaxial (c) tensile tests; (d) damage – on matrix (‘m’) or fibers (‘f’) – versus stretch of uniaxial relaxation (Uniax.) and biaxial (Biax.) tensile tests. Longitudinal (z) and circumferential () directions.

Fig. 7

Constitutive model calibration for a typical animal (Hx-02) of the hypoxic group (Hx): Cauchy stress (in kPa) versus stretch of uniaxial relaxation (a,b) and biaxial (c) tensile tests; (d) damage – on matrix (‘m’) or fibers (‘f’) – versus stretch of uniaxial relaxation (Uniax.) and biaxial (Biax.) tensile tests. Longitudinal (z) and circumferential () directions.

Fig. 8

Sensitivity analysis of the constitutive model calibration (5% perturbation) for a typical animal (Nx-01) of the normoxic group (Nx): Mean, 95% confidence interval, and experimental Cauchy stress (in kPa) versus stretch of uniaxial relaxation (a) and biaxial (b) tensile tests; (c-r) First-order sensitivity index of constitutive model parameters. Longitudinal (z) and circumferential () directions.

Fig. 9

Sensitivity analysis of the constitutive model calibration (5% perturbation) for a typical animal (Hx-02) of the hypoxic group (Hx): Mean, 95% confidence interval, and experimental Cauchy stress (in kPa) versus stretch of uniaxial relaxation (a) and biaxial (b) tensile tests; (c-r) First-order sensitivity index of constitutive model parameters. Longitudinal (z) and circumferential () directions.

Fig. 10

Bulge test simulation results at point ‘A’, normoxic group (Nx). Pressure (in kPa) versus: (a) vertical displacement (in mm); (b) maximum Cauchy normal stress (, in kPa); (c) damage to fibers (); (d) energy release rate in fibers (, in ).

Fig. 11

Bulge test simulation results at point ‘A’, hypoxic group (Hx). Pressure (in kPa) versus: (a) vertical displacement (in mm); (b) maximum Cauchy normal stress (, in kPa); (c) damage to fibers (); (d) energy release rate in fibers (, in ).