Multiscale Elastic Models of Collagen Bio-structures: From Cross-Linked Molecules to Soft Tissues - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 78

direction, and their geometric features depend on the animal species. For instance,
addressing rat tail tendons, collagen fiber crimp period and amplitude are in the
order of 200 and 10 lm, respectively [ 27 , 28 ], and fiber radius varies between 2
and 15 lm[ 29 ] (while in humans it can be as high as 300 lm). Finally, collagen
volume fraction has been reported to be about 50 % [ 30 ], with a little variability
depending on tendon location and on physiological conditions.
Due to collagen content and organization, uni-axial tendon stress/strain curves
are J-shaped, exhibiting the highly non-linear mechanical response that has been
previously described (Fig. 2 ).
2.2.2 Aortic Wall
The aorta is the largest artery in the body, and its structure and mechanical response
have a crucial role in the fluid-structure interaction mechanisms relevant to the
cardiovascular system. The walls of the aorta are made up of three different tissue
layers: a thin inner layer (intima), a thick elastic middle layer (media), and a thin outer
layer (adventitia). Among these layers, the media is the most important from the
mechanical point of view, as a result of its thickness and stiffness. Histologically, the
tunica media is made up of concentric layers consisting in smooth muscle cells
embedded in an organized network of loose connective tissue. Many authors (e.g.,
[ 31 , 32 ]) describe the media tissue as a thick cylinder comprising different layers,
usually denoted as medial lamellar units (MLUs), that have practically the same
structural arrangement.
Geometrical features of the aortic media are extremely variable among different
living species, depending on the animal size and weight, as well as on the location
along the vessel length (e.g., in the thoracic—T—or abdominal—A—zones).
Referring to humans, many authors (e.g., [ 31 , 33 - 35 ]) indicate that the aortic
radius at zero pressure is about 6-9 mm (T) or 5-8 mm (A), that the media
thickness-to-radius ratio is about 0.1-0.2, and that the MLU number is about 60
(T) or 30 (A). The three-dimensional histological structure of a single MLU has
been recently investigated [ 36 ] and described as a thick sub-layer of elastin sided
by an interlamellar substance made up of water, elastin, smooth muscle cells and
collagen. Collagen results in about 20-30 % of the aortic wall dry-weight [ 37 ] and
is organized in crimped fibrils with radius varying from 25 to 50 nm [ 38 ]. Fibrils
are in turn arranged in both thick and thin bundles (namely, fibers). Analysis by
means of scanning electron microscopy reveals fiber period in the order of 5 lm
and fiber amplitude-to-period ratio about 0.2-0.5 [ 36 ]. Fibers are organized in such
a way that no complex mesh within each interlamellar layer appears, but they are
disposed to realize sub-layers with a uni-directional regular character. In other
words, fibers are arranged in circumferential laminae with the fiber axis helically
wrapped around the vessel direction, with the wrapping angle (i.e., the angular
deflection of the fiber axis with respect to the vessel axis) varying across the MLU
thickness, in agreement with a multi-directional tissue structure. Histological
evidences [ 36 ] confirmed that the wrapping angle exhibits a symmetric uni-modal