Page 69 - Advances in Biomechanics and Tissue Regeneration

64 4. MECHANICAL AND MICROSTRUCTURAL BEHAVIOR OF VASCULAR TISSUE

parameters lack a clear physical meaning. Moreover, these models are unreliable for predictions beyond the strain
range used in parameter estimation [13]. However, structurally motivated material models may provide increased
insights into the underlying mechanics and physics of arteries and could overcome this drawback [14].
Identification of an appropriate SEF is the preferred method to describe the complex nonlinear elastic properties of
vascular tissues [15]. An ideal SEF should be based on histological analysis to provide a better description of wall
deformation under load [11, 16]. Early SEFs were purely phenomenological functions where parameters involved
in the mathematical expression have not physiological meaning [17, 18]. Later, structure-based or constituent-based
SEF was developed, where the parameters mean some physical and structural properties of the different components
of the vessel wall [9, 12]. In several tissues, there is a strong alignment of the collagen fibers with little dispersion in their
orientation. In other cases, such as the artery wall, there is significant dispersion in the orientation, which has a
significant influence on the mechanical response. Proposed structure-based models were used by taking into account
the spatial dispersion or distribution or waviness of collagen fiber directions [7, 8, 16, 19, 20].
In this chapter, we study some constitutive models, some with a phenomenological approach and others micro-
structurally and physically oriented, that describe more accurately the features of the arterial wall. The mechanical
behavior and structural organization of the DTA and the carotid artery are studied together in order to overcome some
limitations of previous models. We aim to examine the advantages and limitations of phenomenological versus more
microstructural-oriented approaches.

4.2 MICROSTRUCTURAL MODELING OF THE CAROTID ARTERY

The carotid artery has been widely studied because it is prone to develop atherosclerosis, stenosis, collagen
remodeling, etc. An extensive range of experimental results for the carotid artery can be found in the literature.
Experimental procedures such as inflation tests on animals [6, 21, 22] and humans [23, 24], simple tension tests
[3, 25], and nano-indentation tests [26] have been used to determine the mechanical properties of carotids. However,
these studies are usually fitted with phenomenological and microstructure-based SEFs without taking into account the
histological data from different regions. Therefore, the constitutive laws commonly consider independent material
parameters for each position.

4.2.1 Experimental Findings for the Porcine Carotid Artery
To analyze the microstructure of the porcine carotid artery, we used three kinds of experimental data of a swine
carotid artery obtained previously in our group [3, 27]. Tissue samples from 14 specimens were processed in a histo-
logical laboratory and images were used to quantify their microconstituents [3]. We also analyzed the collagen bundle
distribution means of using polarized light microscopy techniques [27]. We used the average collagen distribution to
calibrate the presented microstructural model (MM) in order to obtain general constitutive parameters for the porcine
carotid. Finally, we also carried out several cyclic uniaxial tension tests [3] on swine carotid tissue. The details are illus-
trated in the following sections.

4.2.1.1 Histological Analysis
García et al. [3] reported the composition of the porcine carotid depending on the location of the sample by image
analysis techniques. In order to quantify the percentage areas of elastin fibers and SMC, a segmentation procedure was
followed by means of Software ImageJ. Several histologies of different samples were analyzed. The samples were
grouped depending on the type of stain (Orcein’s elastin, Masson’s trichrome, and antismooth muscle actin immuno-
histochemical study) and the elastin, collagen, and muscular tissue composition were determined (Fig. 4.1). Quanti-
fication of elastin areas for distal and proximal locations was, respectively, 19.6 4.1 and 52.6 6.7. The area
percentages of SMC achieved by means of the antismooth muscle actin stains were 44.3 4.2 and 31.0 3.3 for distal
and proximal samples. Finally, collagen quantification by using Masson’s trichrome stain reported 23.5 3.9 and
14.9 2.3 for swine samples in the two different locations, respectively [3].
Regarding the collagen fiber distribution, segments of each vessel were fixed and prepared for histological analysis.
Slides were stained for birefringence enhancement with a Picrosirius Red stain, which causes collagen to appear in a brighter
orange-yellow when viewed through polarized light [28–30]. Samples were analyzed in a BX50 microscope (Olympus,
Melville, NY) equipped with an Achromat UD 16/0.17 objective and a CMEX-1300x camera (Euromex microscopen
B.V., Arnhem, The Netherlands) equipped with a Universal Rotary Stage (Carl Zeiss GmbH, Jena, Germany) [30].

I. BIOMECHANICS