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134 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Rhodin, 1980; Wolinsky & Glagov, 1967). For bovine coronary arteries, previous
studies found SMCs have a longitudinal arrangement in inner and outer layers of
media, whereas the cells in middle layers are arranged along the circumferential
direction of the vessel (Rhodin, 1980). Arrangement of medial collagen is somewhat
controversial. Collagen is commonly described as a meshwork of helically woven
fibers layered around the vessel circumference in some studies (Clark & Glagov,
1985; Rhodin, 1980; Shadwick, 1999; Walker-Caprioglio, Trotter, Mercure, Little, &
McGuffee, 1991) while a later study of 3D microstructure of aortic media suggested
that collagen fiber bundles are parallel within each layer and preferentially oriented in
the circumferential direction as SMCs (O’Connell et al., 2008). Nevertheless, these
studies concur that collagen largely orients towards circumferential direction of
vessels, while elastin presents a complex 3D arrangement, including layered EL,
randomly distributed IL fibrils and radial thick fibers (O’Connell et al., 2008).
3.7.3 Adventitia
The adventitia (outermost layer of an artery) typically consists of dense collagen
fibers, elastin fibers, some fibroblasts, and hydrophilic macromolecules (including
glycosaminoglycans, proteoglycans, and glycoproteins), Fig. 3.18. These constituents contribute to the mecha nical properties mainly by protecting the vessel wall
from overstretch as well as mechanically coupling to the surro unding tissues (Clark
& Glagov, 1985; Zoumi et al., 2004). At physiological pressures, the adventitia is
less stiff than the media and its mechanical function is mainly to support the vessel.
At higher pressures (e.g., in hypertension), however, the collagen fibers reach their
straightened lengths and the adventitia becomes a stiff tube which prevents the artery
form overstretch and rupture (Holzapfel et al., 2000; Humphrey & Na, 2002).
Histological studies show that fibers in adventitia rendered a preferred orientation
in non-coronary arteries (Finlay, McCullough, & Canham, 1995; Haas, Phillips,
Comerota, & White, 1991; Rhodin, 1980 ; Smith, Canham, & Starkey, 1981).
3.7.4 Collagen and Elastin
In general, collagen fibrils are assemblies of sub-fibrils of about 30 nm diameter,
each consisting of microfibrils packed in a tetragonal lattice. The diameter of
collagen fibrils ranges from 50 to 500 nm, depending on tissue type and the age of
the animal (Hiltner, Cassidy, & Baer, 1985), and these fibrils typically run parallel
and gather in large collagen bundles (Birk & Trelstad, 1986; Ottani, Raspanti, &
Ruggeri, 2001). Morphological observations show that collagen fibers have undulated structure and mainly arrange in plane with preferred orientations, which results
in anisotropic properties of blood vessels (Chen, Liu, Slipchenko, Cheng, & Kassab,
2011; Lanir, 1979). The degree of collagen undulation (waviness) is different in soft
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tissues. At lower macroscopic stretch of the tissue, the undulated collagen fibers
contribute little or no effect to the mechanical response. As the macroscopic stretch
increases, collagen bundles become straightened gradually and eventually bear most
of the load to render a highly nonlinear stress–strain relationship (Ottani et al., 2001;
Roach & Bur ton, 1957). It is noted that uncoiled collagen fibrils have a Young’s
modulus of the order of 0.1–1.0 GPa along the fibril direction, whereas the Young’s
modulus of elastin is of the order of 1 00 kPa (Burton, 1954; Gosline et al., 2002;
Gundiah, Ratcliffe, & Pruitt, 2007).
In general, elastin fibers are straight rod-like fibrils composed of a central core
surrounded by microfibrils with a 10 nm diameter (Montes, 1996). Elastin fibers
distribute relatively randomly and form a net-like structure in coronary arteries
(Ottani et al., 2001). Experimental observations show that elastin fibers gradually
extend to take up the load together with cells and ground substance (GS) at very low
strain levels (Ottani et al., 2001; Roach & Burton, 1957), where the stress–strain
behavior of the whole tissue exhibits only weak nonlinearity.
Since the elastin and collagen fibers are the major mechanical microstructural
elements of blood vessel wall, knowledge of their morphometry and deformation are
fundamental to understanding vascular mechanical response. In the adventitia, dense
and wavy collagen fibers form an interwoven network that tangles with elastin fibers
and fibroblasts (Rhodin, 1980). Histologically, a collagen or elastin fiber can be
described as a bundle of loosely bound fibrils (Fratzl et al., 1998; Ottani et al., 2001).
In an undulating state, such a fiber can deform under very small load. When
straightened, it can sustain a significant amount of axial stress. Therefore, fibers
are gradually straightened and begin to take up the increasing loads when the artery
is distended (Zoumi et al., 2004). Clearly, the elastin and collagen fibers play a major
role in the mechanical response of blood vessels (Azuma & Hasegawa, 1971; Azuma
& Oka, 1971; Oka, 1972; Oka & Azuma, 1970
; Roach & Burton, 1957).
3.7.5 Ground Substance
Ground substance (GS) is an amorphous gel-like structure that mainly contains
glycosaminoglycans, proteoglycans, and glycoproteins (Eisenstein, Larsson,
Kuettner, Sorgente, & Hascal, 1975; Gogiel & Jaworski, 2000). These hydrophilic
macromolecules create water-filled compartments that maintain turgor pressures
within tissues. In addition, proteoglycans strongly interact with fibers and cells by
forming interfibrillar bridges (Scott & Thomlinson, 1998; Wight, 1996). Enzymatic
degradation of tissues (specific to GS) shows that the gel-like GS has very low
resistance to shear stress and thus has little effect on the mechanical response of
coronary arteries (Chen, Guo, Luo, & Kassab, 2016). Fibroblasts are the most
common cells found in soft tis sues, which synthesize and secrete extracellular matrix
(ECM, denoting fibers and GS here) and play an important role in healing wounds
(McAnulty, 2007; Rhee & Grinnell, 2007). SMCs, on the other hand, are only found
in vasoactive tissue, such as blood vessel, where the structure and function of SMC is
136 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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basically the same. Some studies have shown that cells (fibroblasts and SMCs) have
negligible effects on passive mechanical behaviors of tissues (Cox, 1978; Roach &
Burton, 1957; Thoumine & Ott, 1997; Wolinsky & Glagov, 1964). Other studies,
however, suggest that SMCs have a significant role in transmitting stresses through
serial connections with collagen fibers (Roy, Silac ci, & Stergiopulos, 2005; Roy,
Tsamis, Prod’hom, & Stergiopulos, 2008 ; Silver, Snowhill, & Foran, 2003; Sokolis
et al., 2006). In summary, the wall of coronary arteries is heterogenous with complex
microstructural components. Based on the microstructure, structurally based models
have become state of the art as described in Chap. 4.
3.7.6 Histology
Histology is fundamental to medicine and bioengineering. It is an essential tool to
the cell biologist and pathologist. The pathologist is interested in relative changes
whereas the bioengineer is interested in absolute quantitative measurements to
formulate mathematical models. The predictive power of a mathematical model is
dictated by the accuracy of the histological measurements. The problem lies in the
distortions caused by histological preparation. Since the process of histological
preparation includes fixation, tissue processing, and embedding, it is imperative to
assess the effect of each step. Choy, Mathieu-Costello, and Kassab (2005) analyzed
the effects of a widely used fixation and histological preparation protocol on several
morphometric parameters of the coronary arteries. Over 100 LAD artery segments
obtained swine hearts were fixed in 6.25% glutaraldehyde and embedded in JB-4
solution. The dimensions of the fixed rings in the cast-loaded and no-load states and
histological sections are compared with those of the fresh tissue of various morphometric parameters (inner and outer circumference, and wall thickness and area)
against their means. It is found that (1) Effect of 6.25% glutaraldehyde fixation is
relatively small for the intima-media (<6%) but larger for the adventitia (<13%),
(2) Elastin cannot be fixed and hence retracts after removal of load, and (3) Histological preparations cause small shrinkage (<7%) which is similar for the intimamedia and adventitia. The effect of “result 2” has important implications for vascular
studies after perfusion fixation. The three findings listed above suggest the need for
microscopy approaches that eliminate the need for tissue fixation and processing as
described below.
3.7.7 Multi-Photon Microscopy
The development of nonlinear imaging modality (multi-photon microscopy, MPM)
has enabled noninvasive measurements of biological tissues and cells without
fixation or staining. MPM imaging is driven by two primary types of nonlinear
interaction between ultra-fast laser light and biological tissues: two-photon excited
3.7 Ultrastructure of Coronary Arteries 137
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fluorescence (TPEF) for elastin and second-harmonic generation (SHG) for collagen. MPM is well developed and widely implemented for imaging cells
(Campagnola, Clark, Mohler, Lewis, & Loew, 2001; Gauderon, Lukins, &
Sheppard, 2001; Mansfield et al., 2009 ), thin tissue sections (Campagnola et al.,
2002; Garcia & Kassab, 2009), thick unstained biological specimens (Arkill, Moger,
& Winlove, 2010; Zoumi et al., 2004), and engineered tissues (Raub et al., 2008;
Zoumi, Yeh, & Tromberg, 2002).
MPM enables the study of simultaneous mechanical loading-imaging of fresh,
unfixed, and unstained elastin and collagen fibril bundles to understand the relation
between macro-mechanical response and microstructure. Some studies, based on the
use of the custom planar mechanical devices (Hu, Humphrey, & Yeh, 2009; Keyes,
Borowicz, et al., 2011; Timmins, Wu, Yeh, Moore, & Greenwald, 2010), required
splaying a vessel open which introduces artificial stresses in the specimens. Others
used simultaneous mechanical loading-imaging on a fresh unfixed, unstained lymphatic vessel segment to investigate the microstructure and their response to external
mechanical loading (Arkill et al., 2010; Keyes, Haskett, Utzinger, Azhar, & Geest,
2011). These studies investigated the reorientation of collagen and elastin fibers
under pressurized conditions and provided the corresponding statistical data. Chen,
Liu, Slipchenko, et al. (2011) used fluorescent microspheres as markers to track the
scan area as well as deformation of individual fibers. This study quantified the
geometrical data of collagen and elastin fibers as well as their loading–deformation
behavior on unstained fresh coronary adventitia in a cylindrical specimen as
described below.
3.7.8 Morphometry of Coronary Adventitia
In order to quantify the geometrical features of fibers under deformation, unstained
fresh adventitia specimens of arteries are imaged simultaneously under various
mechanical loading (Fig. 3.19), and the in situ deformation of elastin and collagen
fibers are measured for a given fiber. To image the adventitia, the intima-media
layers are removed (Chen, Liu, Slipchenko, et al., 2011). Since the penetration depth
of the MPM is limited and the loose tissue on the external adventitia layer cannot be
removed thoroughly, an inverted adventitia segment is scanned. The adventitia at
no-load state is rather loose and the opening angle is relatively small as described in
earlier section, so the mechanical deformation is not significantly altered by the
inversion.
3.7.8.1 Simultaneous Mechanical Loading-Imaging
MPM images (Z-stack) from the adventitia specimen are obtained using a combined
second harmonic generation/two-photon excited fluorescence (SHG/TPEF) setup
138 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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(Chen, Liu, Slipchenko, et al., 2011). The specimen is first mounted on a custommade organ bath chamber, and an elastic balloon is inserted to conduct distension
and extension testing for vessel segments. The specimen is preconditioned several
times before testing. Diameter of a segment is recorded by a commercial camera, and
fluorescent microspheres (excitation/emission wavelength: 540/584 nm) are dispersed on the outer surface of specimen to track the scan area as well as the
deformation of individual fiber during loading (Fig. 3.19). When increasing distension load, the elastic balloon is inflated slowly to track the same scan area during the
imaging. Five loading conditions are considered as λ
¼ 1.0, 1.2, 1.4, 1.6, and 1.8.
θ
The elastin and collagen are found to form multiple concentric densely packed
fiber sheets, with a thickness of 3–7 μm and alternating principal directions. MPM
images of the first five layers of specimens are collected (total average thickness of
30 μm) due to penetration limitation of MPM (Fig. 3.20). Image processing is then
implemented on selected MPM images (Chen, Liu, Slipchenko, et al., 2011). Four
geometrical parameters are measured: (1) Orientation angle θ (circumferential direction θ ¼ 0
), (2) Waviness λ0, (3) Width D of a single fiber, and (4) Are a fractions of
fibers in images as described below.
3.7.8.2 Morphometry of Elastin and Collagen Fibers at No-Distension
State
Both elastin and collagen fibers in the inner adventitia formed layered structures
(Finlay et al., 1995; Haas et al., 1991), where orientation, width, and area fraction of
fibers revealed significant transmural variation as shown in Fig. 3.20. This sublayer
structure is about 3–7 μm thick and occupied 30–40% of the total adventitial
thickness. This structure is not present towards the exterior adventitia where collagen
fibers are highly random and elastin fi bers are largely absent.
In each adventitia layer, there is a major orientation of collagen and elastin fibers,
and a seconda ry principal direction for elastin fibers as shown in Fig. 3.20. The
orientation angles of collagen fibers followed a bell-shaped distribution (truncated
normal distribution) in each layer. Furthermore, the main orientation angles varied in
subsequent layers randomly as shown in Fig. 3.20. The orientation distribution of
collagen fibers is shown in Fig. 3.21a, which demonstrates that most of collagen
fibers aligned at about 60
in the no-distension state. The main orientation angles of
elastin fibers are parallel with collagen fibers but with secondary principal directions.
As a result, elastin fibers form a net-like structure and collagen fibers tend to
uniformly align in a layer, which confirms that isotropic mechanical response of
vessel wall predominates by non-collagenous matrix material (mainly elastin fibers)
while anisotropic deformation is almost entirely due to collagen fibers in most models
(Chen, Liu, Zhao, Lanir, & Kassab, 2011; Holzapfel et al., 2000; Kroon & Holzapfel,
2008; Li & Robertson, 2009; Zulliger, Fridez, Hayashi, & Stergiopulos, 2004).
The waviness of the collagen fibril bundle is also found to follow a bell-shaped
distribution as shown in Fig. 3.21b (mean waviness is about 1.24). The morphometric features of elastin fiber differed signi ficantly from collagen where elastin is
3.7 Ultrastructure of Coronary Arteries 139
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Fig. 3.19 Multi-photon microscopy (MPM) images of collagen and elastin fibers under different
mechanical loading. Fluorescent microspheres are used to track the scan area and deformation of
individual fibers. (a–c) Photos of the specimen with the scaling marker in sub-chamber are taken to
record the specimen diameters at (a) no-distension state λ
respectively; (d–f) two photon emission florescence (TPEF) images with lower magnification are
captured first to track the scan area at corresponding loads; (g–i) TPEF images (for elastin fiber)
with appropriate magnification and resolution are collected at corresponding loads; (j–i) SHG
(second harmonic generation) images (for collagen fiber) are collected simultaneously with TPEF
images. Reproduced from Chen, Liu, Slipchenko, et al. (2011) with permission
¼ 1.0; (b) λθ¼ 1.63; (c) λθ¼ 1.92
θ
140 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Fig. 3.20 Collagen and elastin fibers in the inner adventitia form layered structures. Images (a–e)
are five collagen layers at different depth Z, and images (f–j) are five elastin layers at the exactly
same depth as the collagen layers in (a–e). In each layer, white arrow indicates the main orientation
of fibers and yellow arrow indicates the second principal direction for elastin (X, Y, Z: axial,
circumferential, and radial directions). Reproduced from Chen, Liu, Slipchenko, et al. (2011)
rod-like rather than a spiral, and more than 80% of elastin fiber is straight (waviness
λ
1.0) at no-distension state (Fig. 3.20f–j). Collagen fibers became thicker
0
towards the exterior of adventitia, while elastin fibers became thinner as shown in
Fig. 3.22c. The width–layer relationships of fibers are curve fitted using linear
regression (solid line in Fig. 3.21c, Table 3.8 in Appendix 7). The width of collagen
changed more than that of elastin in inner adventitia. The average width of collagen
fibers of all layers is about 2.8 μm, and that of elastin fibers is 2.0 μm. Similarly, the
area fraction of collagen fibers is found to increase significantly in deeper layers
while that of elastin fibers decreased moderately as shown in Fig. 3.20d and
Table 3.8 (Appendix 7). The average area fraction of collagen and elastin over all
layers are 33% and 22%, respectively.
The elastin fibers are rarely found in exterior adventitia wher e collagen fibers
become much thicker and orient randomly. The outer adventitia occupies about
60–70% of adventitia thickness and the main function of thicker collagen fibers is to
support the vessel and connect with surrounding tissue rather than to resist the
transmural pressure. On the other hand, the inner adventitia which consists of
alternating elastin and collagen fiber layers plays an important role in opposing the
transmural pressure and prevents over-distension of vessel at high loading. The
aforementioned microstructure-based model (Chen, Liu, Zhao, et al., 2011) can
consider the protective function of the adventitia of coronary arteries with the present
measured geometry and deformation of microstructures, to accurately predict both
macroscopic responses and microenvironment of blood vessel.
3.7 Ultrastructure of Coronary Arteries 141
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20
a
Collagen
15
Elastin
10
% of population
5
0
-90 -60
-30 0
30 60 90 1.0 1.1 1.2 1.3 1.4 1.5
Orientation angle
20
b
Collagen
15
10
% of population
5
0
Waviness
550
cd
4
Collagen
Elastin
40
Collagen
Elastin
30
3
20
2
Mean width (µm)
1
123
45
10
Mean of area fraction
0
12345
Layer Number Layer Number
Fig. 3.21 Statistical data of microstructure of collagen and elastin fibers. (a) The orientation
distribution of fibers of all specimen layers; (b) The bell-shaped distribution of the collagen fiber
waviness of all layers; (c) Layer-to-layer heterogeneity of the fiber width; (d) Layer-to-layer
heterogeneity of area fraction of fiber. Reproduced from Chen, Liu, Slipchenko, et al. (2011)
with permission
1.5 1.4
a
1
0.5
Normalized orientation angle
0
1 1.2 1.4 1.6 1.8
Circumferential strectch ratio
Elastin
λ
θ
bc
1.2
1
Mean waviness
0.8
1 1.2 1.4 1.6 1.8
Circumferential strectch ratio
Elastin
λ
θ
1.2
1
0.8
Normalized width
0.6
1 1.2 1.4 1.6 1.8
Circumferential strectch ratio
Collagen
Elastin
λ
θ
Fig. 3.22 In situ deformation of collagen and elastin fibers. (a) Change of mean orientation angle
normalized by initial orientation angle for collagen and elastin; (b) Change of mean waviness for
collagen and waviness of elastin fibers is about 1.0 constantly; (c) Change of mean width
normalized by initial width for collagen and elastin. Reproduced from Chen, Liu, Slipchenko,
et al. (2011) with permission
142 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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3.7.9 In Situ Deformation of Elastin and Collagen Fibers
In situ deformation of individual fibers under various mechanical loading is tracked
in reference to the fluorescent microspheres and the extent of fiber deformation
depended on the initial orientation angle at no-distension state (Chen, Liu,
Slipchenko, et al., 2011). Fibers oriented towards the circumferential direction
(distension direction) are stretched much more than those aligned more axially,
such that the former became straightened or thinner earlier than the latter. For
collagen fibers, the orientation angle and the waviness are approximately uniform
in a layer so that fiber deformation tended to be homogeneous while elastin fiber
deformation is much more heterogeneous due to the various fiber orientations.
Both collagen and elastin fibers gradually oriented towards the circumfer ential
direction (Fig. 3.22a). The orientation–distension relationships of collagen and
elastin are curve fitted by linear least squares method in Appendix 7, Table 3.9
(solid line in Fig. 3.22a). Since collagen fibers aligned uniformly in a layer, the
change of their mean orientation angles is more homogeneous. The orientation
angles of elastin are heterogeneous with multiple directions as shown in
Fig. 3.22a, i.e., the orientation of collagen shifted towards the circumferential
direction more gradually than the elastin fibers. Furthermore, collagen fibers in a
layer tended to align towards the principal direction so that the bell-shaped distribution of orientation angles became narrower (Chen, Liu, Slipchenko, et al., 2011).
In Fig. 3.22b, a linear least squares fit is used to describe the waviness–distension
relation of collagen (Appendix 7, Table 3.9), which shows that the collagen fibers are
stretched gradually at elevated distension and became completely straightened
(λ
1.0) to take up loads at λθ 1.8. Although the initial waviness of collagen
0
fiber slightly varied in different layers, the waviness became uniform under higher
loads. As shown in Fig. 3.22b, the relative dispersion (RD ¼ SD/mean) of waviness
of collagen fibers decreased gradually with increase of loading conditions (i.e.,
RD ¼ 6.0 2.9λ
has heterogeneous mechanical response to loads given the observed significant
transmural heterogeneity. It should be noted that the RDs of orientation angle and
width of fibers are independent of circumferential loads.
The change of collagen width is more homogeneous than that of elastin fiber
(Fig. 3.22c), consistent with the change of fiber orientation angle. The width change
of coll agen fibers is insignificant at lower loading (λ
decreased at λ
width–distension relationship of collagen fibers (Appendix 7, Table 3.9). On the
other hand, elastin fibers became thinner continuously and gradually at higher
loading as shown in Fig. 3.22c.
The nearly uniform alignment of collagen fibers makes their deformation more
homogeneous than elastin fibers which have multiple directions in each layer. As a
result, collagen fibers are uniformly stretched and shifted towards the circumferential
direction of the adventitia and elastin fibers gradually resembled a network Additionally, change of the fiber orientation and waviness depends on both the
; R ¼ 0.78). This suggests that the layered structure of adventitia
θ
¼ 1.0, 1.2, and 1.4), but
θ
> 1.4. Hence, a piecewise linear function is used to describe the
θ
3.7 Ultrastructure of Coronary Arteries 143
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longitudinal stretch and luminal pressure. The statistical data (Fig. 3.21a) showed
that most of elastin and collagen fibers oriented towards the axial direction rather
than the circumferential direction at no-distension state with physiological axial
stretch ratio λ
¼ 1.3. When the specimens are returned to their relaxed axial
axial
length with luminal pressure remaining zero, elastin and collagen fibers re-oriented
and aligned in the circumferential direction (Arkill et al., 2010), and collagen fibers
became slightly more undulated.
The collagen fibers thinned down significantly (Fig. 3.22c)atλ
1.4, albeit they
θ
are not completely straightened at this state. This is consistent with the diameter–
pressure curve of coronary adventitia that shows the adventitia becomes stiffer after
λ
1.4 (Chen, Liu, Slipchenko, et al., 2011). In other words, collagen fibers in
θ
adventitia are gradually recruited after λ
1.4 to take up loads, and then gradually
θ
predominate in the mechanical function of adventitia and became completely
straightened when loaded at λ
1.8. This finding suggests that collagen contributes
θ
mainly to the flat region of the nonlinear stress–strain curve whereas elastin mainly
contributes to the toe portion of the stress–strain curve (Roach & Burton, 1957;
Zoumi et al., 2004). This underscores the function of the adventitia in a normal
vessel (with physiological blood pressure λ
1.5) is to support the vessel rather
θ
than to take up loads.
All the deformation patterns are described by linear least squares fit as shown in
Table 3.9 (Appendix 7). These linear relationships are, however, only determined
between distension loading λ
loading beyond λ
¼1.8, these relationships may become nonlinear. In future studies,
θ
¼ 1.0 to λθ¼ 1.8. When considering distension
θ
a larger range of loading should be considered to determine the extent of linearity.
The uniaxial (vessel distension) experiments discussed above are extended to
biaxial (combination of vessel inflation and axial extension loading) studies. Figure 3.23 shows quantitative data of in situ biaxial deformation of fibers. Fiber
reorientations of 5 specimens varying with an axial stretch ratio λ
ferential stretch ratio λ
( p < 0.05 be tween λz¼1.0 and 1.5), are plotted in Fig. 3.23a,
θ
, at each circum-
z
c, e . The fiber reorientation is normalized in reference to initial orientation angle of
each sample at zero-stress state (ZSS). The correlations between normalized orientation angle and axial stretch ratio λ
are summarized in Table 3.10 (Appendix 7). The
z
slopes of three correlations of collagen are nearly the same (α 0.41), suggesting that
changes of collagen orientation are similar at the three distension loads. It is also
found that elastin shifted towards the axial direction more gradually (α 0.34) at each
distention load. The change of elastin orientation angle, however, is more random as
compared with that of collagen fiber, especially at higher loads. At circumferential
stretch ratio λ
¼ 1.0 and 1.5, the change of elastin orientation is significant under
θ
elevated axial stretch ratio ( p < 0.05) but became insignificant ( p > 0.05) at higher
load λ
¼1.8. The changes of the waviness of collagen fibers are plotted in Fig. 3.23b,
θ
d, f. The waviness of collagen fibers decreased rapidly with an increase of λ
λ
¼1.0 ( p < 0.05) as shown in Fig. 3.23b, but decreased relatively slowly at λθ¼1.5
θ
( p < 0.05, Fig. 3.23d). At λ
¼ 1.8, most of collagen fibers became completely
θ
z
straightened as shown in Fig. 3.23f.
at
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