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4.3 MECHANICAL CHARACTERIZATION AND MODELING OF THE AORTA 73
(A) (B) (C)
FIG. 4.6 Hematoxylin-and-eosin-stained sections 5 μm from DTA. (A) Intima; (B) media; (C) adventitia.
FIG. 4.7 Collagen fibers in the intima, the media, and the adventitia of the DTA. The longitudinal and circumferential directions are along hor-
izontal and vertical directions and the artery radius is along the perpendicular one. Image extracted from an acquired image stack and corresponding
to a thickness of 15 μm. (A) Intima DTA; (B) media DTA; (C) and adventitia DTA.
images that reveals that the collagen orientation distribution changed significantly across the wall thickness. In the
intima, the collagen fiber shows a practically isotropic distribution. In the media, collagen fibers are dominantly
aligned along the circumferential direction (vertical orientation in the images) and the dispersion of the orientation
gradually increases toward the adventitia.
4.3.2 Material Models for the Porcine Aorta
Stress-stretch curves resulting from the tensile tests were used to fit several constitutive models. The fitted data were
restricted to the elastic range, so data acquired after noticeable variations in the curve slope were neglected for the
fitting procedure. Arterial tissue subject to loading exhibits strong nonlinearity, large strains, and anisotropy,
so the SEF is used to reproduce the mechanical behavior of the aortas. In order to generate constitutive mechanical
parameters that could be used on computational simulations, each of the biaxial specimens tested was fitted to four
constitutive models proposed in the literature.
4.3.3 Phenomenological Model
The strong nonlinearity motivated the use of an exponential function for describing the strain energy stored in the
collagen fibers that was previously proposed by Holzapfel et al. [9]. The main hypothesis was that each family of fibers
represents the main direction of collagen bundles that are orientated in a helicoidal manner. Both families of fibers were
assumed to have the same mechanical response and the anisotropy directions were assumed to be helically oriented at
θ degrees relative to circumferential direction [9]. Here, θ is treated as a phenomenological variable. The SEF
proposed by the authors was
k 1 2
X
Ψ ¼ μðI 1 3Þ + expðk 2 ½I i 1 Þ 1 , (4.17)
2k 2
i¼4,6
where
2
2
2
2
2
2
2
2
I 4 ¼ λ cos θ 1 + λ sin θ 1 , I 6 ¼ λ cos θ 2 + λ sin θ 2 : (4.18)
θ
θ
z
z
I. BIOMECHANICS
