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4.3 MECHANICAL CHARACTERIZATION AND MODELING OF THE AORTA 71

approaches (MM and CMM) are reproduced better than the distal one. The material parameter values better fit to the
stress-stretch curve around the medium stress zone 60 140 [kPa] that corresponds to the estimated physiological
stress state for an artery.
The mechanical response of arteries depends significantly on the tissue structure, in particular on the percentage
of their microconstituents and the fiber distribution. Oneofthe maingoalsofour previous work wastodetermine
and model the passive mechanical properties of the swine carotid artery in both the proximal and distal regions [3,
27, 35], but only from a phenomenological perspective. However, until now, we did not include the information
concerning the amount of microconstituents in the constitutive equations. This missing piece of the puzzle motivates
thestudy of thevolumefractions ϕ elas , ϕ vsmc ,and ϕ coll to introduce them into all these models along with the fiber
orientation (in the CLPM, MM, and CLMM) and dispersion (in the MM and CLMM) retrieved by experimental
analysis [3, 27].
Therefore, the final goal of this work was: (i) to investigate the capabilities of the phenomenological [34] and micro-
structural approaches [27, 35, 36], including experimental information of the collagen fiber distribution [3, 27] and the
volume fractions of the arterial constituents; and (ii) to compare these models between each other. In this regard, we
not only propose a new, highly accurate constitutive model for the artery, but also look at the big picture comparing the
performance of different constitutive models in the literature.

The more accurate fitting was achieved by the phenomenological (ε p ¼ 0.0526 and ε d ¼ 0.1199) and the CLPM (ε p ¼
0.0862 and ε d ¼ 0.125). The MM did not capture the proximal and distal behavior at the same time, producing the worst
results (ε p ¼ 0.74) for the longitudinal direction of the proximal samples. The CLMM captured better the behavior on
both directions and positions (ε p ¼ 0.36 and ε d ¼ 0.20), but was still far from the errors reached by the PM.
However, despite the error results, it is worth mentioning the fundamental fact of physically motivated results. In
this regard, the PM predicted a fiber orientation of θ prox ¼ 43.42 degrees and θ dist ¼ 89.99 degrees. This fiber orien-
tation does not match with the experimental observations in Sáez et al. [27], where collagen fibers were observed
mainly along the circumferential direction with very low dispersion for both distal and proximal locations. Addi-
tionally, the measure of the fiber dispersion, ρ, is not in agreement with the highly concentrated distribution
obtained in our experimental results. Including the experimental observations explicitly into the PM conducted
to complete useless results since the longitudinal compliance was extremely low. This can be observed in the
MM where this approach gives very high fitting errors. Although the model also includes information on collagen
dispersion, the imposition of the angle of the collagen bundles invalidates the predictability features of this model.
The CLPM overcomes the limitations observed in the PM by including the collagen cross-links that are attached
among the main fibers. However, the collagen fibers did not gather information on the collagen fiber dispersion.
The CLMM improved the fitting outcome at the low and large strain regimes, considering both the real distribution
and orientation of the collagen fibers. It also predicts mechanical parameters that are in agreement with the com-
pliance reported in the literature.
The PM, with a larger number of parameters, was unable to reproduce the mechanical tests when microstructural
information of the tissue was included in the model, although the best results were obtained when the parameters were
considered as free variables to fit. The constitutive models described in Sáez et al. [27, 35] were able to reproduce the
mechanical test by physical motivated data, even after including microstructure information from experimental
results. Concerning this, we conclude that the CLMM, even though it does not produce the best results in terms of
residual errors, was the only model capable of appropriately reproducing the mechanical test comprising the actual
orientation and distribution of the experimental results.

4.3 MECHANICAL CHARACTERIZATION AND MODELING OF THE AORTA

The prevalence of aortic disease in the worldwide population has led to much research into computational model-
ing of cardiovascular interventions. Noninvasive techniques and especially stenting for endovascular thoracic or
abdominal aneurysm repair are increasingly relevant due to the numerous advantages they offer. Before the final
human clinical trials, research has been conducted on animal models, with swine the most common due to the sim-
ilarities between the human and swine cardiovascular systems.

4.3.1 Experimental Findings for the Porcine Aorta
To analyze the microstructure of the descending thoracic and abdominal aorta, we used two kinds of experimental
data of the swine aortic tree obtained previously in our group [4, 5]. Porcine aortas (n ¼ 7) were harvested postmortem

I. BIOMECHANICS