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Mechanical and Microstructural

Behavior of Vascular Tissue

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Estefanı ´a Pen ˜a* ,†,‡ , Alberto Garcı ´a , Pablo Sa ´ez , Juan A. Pen ˜a* ,
Myriam Cilla* ,‡,j , Miguel Angel Martı ´nez* ,†,‡
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*Arago ´n Institute of Engineering Research (I3A), University of Zaragoza, Zaragoza, Spain Department of Mechanical
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Engineering, University of Zaragoza, Zaragoza, Spain Centro de Investigacio ´n en Red en Bioingenierı ´a, Biomaterialesy
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Nanomedicina, CIBER-BBN, Zaragoza, Spain Laboratori de Calcul Numeric, Universitat Politecnica de Catalunya,
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Barcelona, Spain Department of Management and Manufacturing Engineering, University of Zaragoza, Zaragoza, Spain
Centro Universitario de la Defensa, Academia General Militar, Zaragoza, Spain
j

4.1 INTRODUCTION

The study of the mechanical factors that induce vascular pathologies, especially in arteries, has been one of the main
research lines in biomechanics. This is not surprising because according to the World Health Organization (WHO),
cardiovascular chronic diseases are the leading cause of death. In this regard, a wide number of constitutive relations
describing the mechanical response have been proposed for cardiovascular tissue. Therefore, the mechanical variables
that strongly influence the mechanobiology on the vascular tissue may be computed [1]. Accurate mechanical models
and appropriate numerical approaches can be an asset in the study of cardiovascular dysfunctions and the simulation
of surgical interventions, for example, carotid stenting.
The arterial wall is composed of three distinct elements: the vascular smooth muscles (VSMs) that form the cellular
part of the vessel, and the extracellular matrix major components elastin and collagen. Collagen is the main load-
bearing component within the tissue while the elastin provides elasticity to the tissue. The mechanical behavior of
an arterial wall is governed mainly by smooth muscle cells (SMC), the matrix material (consisting mainly of water,
elastin, and proteoglycans), and the collagen fibers. Their three-dimensional (3D) organization is vital to accomplish
proper physiological functions. The combined contribution of these constituents determines the mechanical response
of the tissue, described as highly nonlinear and anisotropic, due to the existence of clear preferential orientations of the
fiber bundles. The microstructural composition and thus the mechanical properties of the arterial wall vary along the
cardiovascular tree and also for different species [2–6]. García et al. [3] found differences in the stress-strain curves for
the circumferentially oriented swine carotid samples depending on the longitudinal position, becoming stiffer when
increasing the distance from the aorta. This finding was directly correlated with a significant variation on the tissue
composition and the presence of the different microconstituents. Peña et al. [4] compared ascending thoracic aorta,
descending thoracic aorta (DTA), and infrarenal abdominal aorta. Abdominal tissues were found to be stiffer and
highly anisotropic. They found that the aorta changed from a more isotropic to a more anisotropic tissue and became
progressively less compliant and stiffer with the distance to the heart. They also observed substantial differences in the
anisotropy parameter between aortic samples where abdominal samples were more anisotropic and nonlinear than
the thoracic samples.
Numerous constitutive models have been proposed to describe the arterial mechanical response. The preferred
methodology to describe and reproduce its complex mechanical response is the definition of a strain energy function
(SEF) from which the stress response is derived; see, for example, Refs. [7–12] and references therein. Although phe-
nomenological models (PMs) may reproduce the biomechanical properties of the vascular tissue, their material

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