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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3787_Библиотеки_им_академика_М_И_Перельмана
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124 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Order 11
140
120
Order 10
Order 9 EPCA
Order 9 IMCA
100
80
60
40
20
ΔΟpening Angle (Degrees)
0
0123456
Time in No-Load State (hours)
A
70
60
50
40
Order 11
Order 10
Order 9 EPCA
Order 9 IMCA
30
20
10
ΔΟpening Angle (Degrees)
0
0123456
-10
Time in No-Load State (hours)
B
Fig. 3.12 Difference in opening angle (opening angle measured 30 min after radial cut) from the
load state (either circumferentially or axially as shown in Fig. 4.16) to no-load state for different
durations. (a) Circumferential loading.(b) Axial loading. EPCA and IMCA represent epicardial
and intramyocardial coronary arteries, respectively. Reproduced from Rehal et al. (2006) with
permission
future data on the zero-stress state. In summary, these results are important or
understanding the viscoelastic properties of coronary arteries, for interpretation of
the enormous data on the opening angle and strain in the literature, and for standardization of future measurements on the zero-stress state.
3.4 Zero-Stress State 125
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Fig. 3.13 The time course
of the zero-stress state—
opening angle from loaded
state, 1 h in no-load state,
and 3 h in the no-load state.
“*” indicates statistical
significance. Reproduced
from Rehal et al. (2006)
with permission
3.4.5 Effect of Osmolarity on Zero-Stress State
The osmotic pressure plays an important role in controlling the distribution of water
across cell membranes which can intimately regulate the mechanics of the vessel
wall. Lanir et al. (1996) reported the acute effect of swelling on the opening angle of
the ventricle as the heart is perfused with different concentrations of mannitol. Their
experiments showed that opening angle of a rat left ventricle segment decreases with
increases in osmolarity. In a parallel theoretical analysis based on the myocardial
detailed morphology, they reasoned that osmolarity effects on the swelling, and
therefore changes in opening angle could be due to the control of the interstitial fluid
volume and pressure.
Guo, Lanir, and Kassab (2007) have shown that changes in osmolarity also affect
blood vessels in various species. The major findings of their study are that the
opening angle of aorta of mouse, rat and pig increases with a decrease in osmotic
pressure. Low osmolarity (swelling) is associated with larger wall thickness and wall
volume and increased wall stiffness in the vessel. Acute swelling or shrinking causes
immediate mechanical changes in the vessel. The regulation of zero-stress state
through osmotic changes may serve to regulate mechanical homeostasis, i.e.,
through cell volume changes. These changes can be an early and immediate response
to changes in mechanical loading (hyper tension, flo w-overload, etc.) that initiates
growth and remodeling of tissue.
3.4.6 Axial Residual Strain
In vivo, the coronary artery length may change during the cardiovascul ar cycle as the
heart elongates. The existence of pre-stretch and longitudinal tethering is
126 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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documented much earlier than circumferential residual strain (Bergel, 1961; Fuchs,
1900; Hesses, 1926; McDonald, 1974; Patel & Fry, 1966). Numerous studies have
quantified the degree of axial shortening when a blood vessel is excised from the in
situ condition (see Review in Guo and Kassab (2003)), i.e., the in vitro axial length is
significantly shorter than that in the in situ condition under zero pressure. The axial
pre-stretch is typically characterized by the axial stretch ratio, λ
, which is the ratio of
z
the axial length of the vessel in situ to that in vitro. The axial pre-stretch ratio for the
LAD artery is about 1.4 (Lu, Yang, Zhao, Gregersen, & Kassab, 2003). Although the
effect of circumferential residual strain on the in vivo intramural stress distribution
has been thoroughly investigated (see review in Rachev and Greenwald (2003)),
there are fewer studies on the effect of longitudinal pre-stretch (Gleason & Humphrey, 2005; Zhang, Herrera, Atluri, & Kassab, 2005). This topic will be considered
further in Chap. 8.
Guo, Liu, and Kassab (2012) provided a complete set of physiological axial
stretch data through the coronary arterial and venous trees. The longitudinal variations along both the arterial tree and venous tree and between the arteries and veins
of the same size are evaluated. Casts of the coronary arteries and veins are made
using silicone elastomer as described in Chap. 2. The coronary artery inlet perfusion
pressure is maintained at 100 mmHg while the venous outlet pressure is 5–6 mmHg
(approximately equivalent to right atrial pressure). Each labeled segment is
photographed to obtain axial length in the loaded state with the hardened elastomer
maintained in the lumen. The vessels are then cut perpendicular to the longitudinal
axis into segments. The elastomer is then pushed out of each segment, and a radial
cut is made to reveal the zero-stress state (ZSS) after about 30 min. The morphological data of coronary arterial (Table 3.7a) and venous (Table 3.7b) trees are
summarized in Appendix 5 for diameters, wall thicknesses, circumferences, opening
angles, and axial stretch ratios. The arterial wall is generally thicker than the venous
wall of the same order by ~50%. The wall thickness-to-radius ratio (WTRR),
however, increases towards the smaller diameter ( p < 0.01), for both arteries and
veins. This ratio is significantly higher for the arteries than the veins of the same
order ( p < 0.01), and the difference is more obvious for the larger veins. The
opening angle decreases towards the smaller veins ( p < 0.05). In comparison with
the LAD arterial vessels, the veins have smaller opening angles that suggest lower
residual deformation in the vessel wall.
Figure 3.14 shows the relation between the physiological axial stretch ratio, λ
and the logarithm of the inner diameter D
(Fig. 3.14a) and order number
in
n (Fig. 3.14b) for the LAD artery and coronary sinus vein. In general, the axial
stretch ratio of LAD is significantly larger than that of vein. There is also a significant
increase of λ
shown in Fig. 3.14b, λ
with the vessel diameter for both coronary arteries and veins. As
z
increases from a mean value of 1.01 for order 4 arteries to 1.5
z
for order 11, and from 1.01 for order 4 veins to 1.23 for order 12 veins; orders 4 and
4 vessels are nearly not axially stretched (λ
with vessel diameter, it is observed that λ
~ 1) in vivo. Given this and that λzdrops
z
¼ 1 for smaller vessels (order 3–3), as
z
shown by a dashed line in Fig. 3.14b.
,
z
3.5 Triaxial Testing of Coronary Arteries 127
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Fig. 3.14 (a) Relation between axial stretch ratio λzand the logarithm of inner diameter Din(μm)
along LAD arterial and coronary venous tree. (b) Variation of λ
order number, n. Solid line, least squares fit of the following form: LAD, λ
2
¼ 0.99); Vein, λz¼ 0.029n + 0.89 (R2¼ 0.99). Note that λz¼ 1 for smaller vessels (order 3–3),
(R
as shown by a dashed line. Reproduced from Guo et al. (2012) with permission
3.5 Triaxial Testing of Coronary Arteries
The coronary arteries are mechanically unique in that they are embedded in a
constantly deforming heart that undergoes circumferential, axial, and torsional
deformation and motion. Hence, in addition to the intravascular pulse pressure that
can induce circumferential deformation of the coronary artery wall, the vessels are
of the LAD artery and vein with
z
¼ 0.062n + 0.75
z
128 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Fig. 3.15 A schematic of triaxial machine that allows pressure inflation, axial extension, and
torsion of a coronary vessel mounted in a physiological solution. The deformations (outer diameter,
axial stretch, and twist) are noted along with the loads (pressure, axial force, and torque).
Reproduced from Lu et al. (2003) by permission
also subjected to axial and tors ional deformation from the myocardium. Therefore,
mechanical testing that involves all three modes of deformation is necessary. To
address the various modes of deformation and stresses, a triaxial testing apparatus
and method is devised as described below.
Figure 3.15 shows a schematic of the triaxial machine that allows coronary vessel
segments to be inflated, axially stretched, and twisted. An arterial specimen is
mounted on the cannula horizontally on both ends in an organ bath to maintain
immersion of the vessel specimen in physiological solution. A pressure regulator is
used to control the luminal pressure in the arterial specimen. The cannula is mounted
on a linear stage where the motor drives the stage and records the axial force by a
load cell. The load cell is calibrated with a series of weights and a linear relation in
the range of interest is confirmed. The cannula on the left is connected to the torque
transducer as shown in Fig. 3.15. The right cannula is connected to a load cell and the
load cell is fixed with a servo motor that twists the speci men at given angle. The
torque transducer is made of a flexure pivot bearing and an encoder which are fixed
on a pivot connected to the left cannula. The flexure pivot bearing shows a linear
relation between twist angle and applied torque.
3.5.1 Two-Layer Model
Classically, the vessel wall has been considered as a homogeneous material. The
homogenous model of the vessel wall persisted until the 1990s with the exception of
the studies by Von Maltzahn et al. (Von Maltzahn, Besdo, & Wiemer, 1981; Von
Maltzahn, Warriyar, & Keitzer, 1984). In the past two decades, however, the vessel
has been modeled as a shell of several layers each of which has its own elasticity
3.6 Active Mechanical Properties 129
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constants and its own state of zero-stress resultants and zero-stress moments (Berry,
Rachev, Moore, & Meister, 1992; Demiray & Vito, 1991; Holzapfel, Gasser, &
Ogden, 2000; Rachev, 1997; Xie, Zhou, & Fung, 1995; Yu, Zhou, & Fung, 1993).
The coronary blood vessel wall can be considered as a two-layer composite
(intima-medial and adventitial layers) in swine since the intima is very thin unlike
humans. Each layer has its own zero-stress state and its own elastic constants. The
coronary arter y can be tested as an intact vessel followed by dissection of either the
adventitia or the media. Experimentally, this is feasible as the vessel can be dissected
at the cleavage plane that separates intima-media from adventitia at the external
elastic lamina. An intact coronary artery segment is initially mechanically tested in
the triaxial machine (Fig. 3.15) under various modes of deformation (inflation, axial
extension, and twist). Subsequently, the segment is removed from the triaxial
machine and in some coronary arteries, the adventitia of the arterial segments is
carefully dissected away from the media at the external elastic laminae with the aid
of a stereomicroscope. The intima-medial layer of the arterial segments remained
intact and is tested in the triaxial machine according to the same protocol used for the
intact wall. In additional coronary arteries, the vessel segment is inverted inside-out
and the media is dissected away leaving the adventitia intact. The adventitia is then
re-inverted and tested in the triaxial machine using the same testing protocol.
3.6 Active Mechanical Properties
Although the passive mechanical properties of coronary arteries have been extensively studied as demonstrated above, the active mechanical properties of coronary
arteries are much less known. Most of our current knowledge stems from uniaxial
active constitutive length–tension relationships in the circumferential direction
(Carlson & Secomb, 2005; Cornelissen, Dankelman, VanBavel, & Spaan, 2002;
Rachev & Hayashi, 1999; Yang, Clark, Bryan, & Robertson, 2003). To fill in the
gap, Huo, Cheng, Lu, Liu, and Kassab (2012) tested the biaxial material properties of
RCA under potassium (K
active properties of coronary arteries is described in Chap. 4.
+
) contraction. The constitutive formulation of passive and
3.6.1 Isovolumic Myography
Wire and pressure myographs are widely used to study the vasoactivity of large and
small blood vessels (Kuo, Chilian, & Davis, 1990; Mulvany & Halpern, 1976). In the
wire myograph, the blood vessel is cut into rings and each ring is mounted by two
hooks in an isometric myograph. Typically, one of the hooks is fixed while the other is
connected to a force transducer (Mulvany & Halpern, 1976). The length of the ring is
maintained constant (isometric) while the force is recorded during contraction or
relaxation. The strengths of this method are that it yields the isometric properties of
130 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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the blood vessels, and that the tension measurements are very sensitive. The weaknesses of this method are that the geometry and loading deviate significantly from
physiological conditions, and that the cutting of vessel rings induces injury. Furthermore, the wire myograph is less sensitive for small vessels (<0.5 mm in diameter)
(Dunn, Wellman, & Bevan, 1994; Falloon, Stephens, Tulip, & Heagerty, 1995).
To remedy the weaknesses of the wire myograph, the pressure myograph is
developed, for which the blood vessel is cannulated to a perfusion system and
connected to a pressurized container which regulates the pressure (Davis & Gore,
1989; Halpern, Osol, & Coy, 1984). A microscope with charge-coupled device
(CCD) camera is used to monitor the diameter of the vessel. The increase or decrease
of the diameter of the vessel reflects vasodilation or vasoconstriction, respectively.
The sensitivity to detect vasoactivity in pressure myograph is high for small arteries
because of the large dimensional change of arterioles. Since the pressure is typically
maintained constant and the diameter changes during contraction , the method is
isobaric.
Lu and Kassab (2007, 2011) introduced a modification of the pressure myograph,
called isovolumic myograph, to study vasoreactivity in vascular segments. This
approach retains the sensitivity to contractile force of a wire myograph, while
providing a physiologic geometry and loading like pressure myograph. The principle
of the isovolumic myograph (Fig. 3.16) is based on the utility of a hydraulically
closed system with low compliance such that contraction against an
incompressibility fluid increases the pressure with the closed system while dilatation
decreases it. This method maintains a constant volume of fluid in the lumen of the
vessel during contraction and relaxation which are characterized by increase (contraction of vessel) and decrease (dilatation) of pressure, respectively. The detailed
protocol for isovolumic myography is outlined in Appendix 6.
Isovolumic myography is used to assess vasoreactivity in a wide range of arteries
(elastic and muscular ranging from 300 μm up to over 5 mm in diameter), which
would have previously required pressure myography for smaller vessels and wire
myography for larger vessels and result in data that cannot be directly compared
(Lu & Kassab, 2011). Figure 3.17 shows large vascular reactive circumferential
tension in large diameter arteries since tension is proportional to vessel diameter
(Appendix 6). Since the intraluminal pressure of large arteries is similar to that of
small arteries during vascular reactivity, the variation of over tenfold is observed in
circumferential tension from large to small arteries (Fig. 3.17a). The circumferential
stress, which is tension normalized by wall thickness, showed a much smaller
variation in the same range of vessels (Fig. 3.17b). Furthermore, the changes of
stress during dose–response vascular relaxation are similar in all arteries
(Fig. 3.17b). The percent relaxations of the stress (Appendix 6) of the arteries are
shown in Fig. 3.17c which appear similar to vascular relaxation curves. The percent
relaxation of the tension and intraluminal pressure are approximately identical to that
of the stress.
It is interesting that circumferential stress varies relatively little from large to
small arteries (Fig. 3.17b) in comparison with the large (an order of magnitude)
change of circumferential tension (Fig. 3.17a). The stress reflects the vascular
3.6 Active Mechanical Properties 131
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+5%CO
95%O
Gas Tank
2
2
CCD
Camera
95%O
Gas Tank
+5%CO
2
2
Pressure
Regulator
Microscope
Pressure
Regulator
Micromanipulator
Pressure
8
Fresh
Fresh
Fresh
Fresh
Flask
Stopcock
Transducer
FT
FT
4
4
vessel
Stopcock
Stopcock
9
Ach
Ach
Ach
Ach
Flask
Fig. 3.16 A schematic of the isovolumic myograph setup. FT Axial force transducer. Reproduced
from Lu and Kassab (2007) with permission
A
55
45
35
.
25
15
-11 -10 -9 -8 -7 -6 -5
\\
12
Circ. Tension (mN/mm)
8
4
0
-10-9-8-7-6-5
ACh/BK log [M]
Femoral, Rat
Carotid, Mouse
Mesente ric, Rat
Carotid, Pig
Aorta, Rat
Coronary, Pig
B
280
E
230
180
M
130
Circ. Stress (kPa)
80
-10-9-8-7-6-5
ACh/BK log [M]
C
0
20
40
60
80
% Relaxation
100
120
-10-9-8-7-6-5
ACh/BK log [ M]
Fig. 3.17 The dose–response vasorelaxation of circumferential tensions, stresses, and percentage.
(a) Circumferential tension decreased stepwise during dose–response vasorelaxation in all arterial
segments. The values of the tension showed over tenfold difference from large (carotid artery of pig)
to small (mesenteric artery of rat) diameter segments. (b) Circumferential stress decreased stepwise
during dose–response vasorelaxation. The values of the stresses are narrowed in onefold range from
large to small diameter segments. Especially, values of elastic arteries are higher than that of
muscular arteries. E elastic arteries, M muscular arteries. (c) The percent relaxations are calculated
as the ratio of the tensions of arteries, which are the same as the ratio of the stresses (data not
shown). Ach and BK represent acetylcholine and bradykinin, respectively. Reproduced from Lu
and Kassab (2011) with permission
132 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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relaxation in unit-wall thickness as it normalizes the tension. Results show that
circumferential stresses are relatively similar in various arteries (Fig. 3.17b), which
implies that a single vascular smooth muscle layer has similar vasoreactive property.
Hence, the vascular reactivity can be standardized and is comparable from large to
small arteries. An additional interesting observation is that the circumferential
stresses in either elastic arteries (aorta and carotid artery) or muscular arteries
(coronary, femoral, and mesenteric arteries) are relatively similar (Fig. 3.17b) and
the stresses in elastic arteries are larger than those in muscular arteries despite the
order of magnitude difference in diameter of either elastic or muscular arteries,
respectively. Given the significant structural differences between elastic and muscular arteries, this finding implies that vascular structure may contribute to vascular
reactivity. In summary, the isovolumic myograph has equivalent sensitivities in
various arteries and provides an approach to unify measurement of all size of arteries
under the same conditions. This novel methodology should advance our understanding of active properties of coronary arteries and other vessels.
3.7 Ultrastructure of Coronary Arteries
3.7.1 Intima
The coronary artery wall is composed of the intima, media, and adventitia
(Fig. 3.18a, b). The intima (innermost layer of an artery) consists of endothelial
cells, a few collagen bundles, and basal lamina. Rhodin (1980) found that the
subendothelial area contains bundles of longitudinally arranged smooth muscle
cells (SMCs), which is consistent with the longitudinal arrangement of inner
media SMCs. In most vessels, the intima is normally very thin and does not
contribute to the mechanical properties of the vessel wall in normal animals
(Wagenseil & Mecham, 2009; Zoumi, Lu, Kassab, & Tromberg, 2004). It should
be noted that in intimal hyperplasia the contribution of the intima may be significant
depending on the degree of disease. Interestingly, Velican and Velican (1985)
pointed out that a healthy human coronary artery has a thick intimal layer which
develops rapidly in early years and continues to grow throughout life. Holzapfel,
Sommer, Gasser, and Regitnig (2005) reported the ratio of thickness of adventitia,
media, intima, and the total wall of non-atherosclerotic aged human coronary arteries
as 0.4 0.03, 0.36 0.03, and 0.27 0.02, respectively.
3.7.2 Media
The media layer serves as the most important mechanical layer, i.e., under normal
hemodynamic loadings Rhodin (1980) as it bears the majority of the load at
physiological loadings (Lu, Pandit, & Kas sab, 2004). The media consists of three
3.7 Ultrastructure of Coronary Arteries 133
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Fig. 3.18 Histology of the coronary artery wall (a) Two-dimensional image sections of the
coronary artery recorded at different x-positions for λ
adventitia, the adventitia-media border, and the media. (b) Emission spectra corresponding to the
adventitia-media border and the media are shown on bottom and top, respectively. Modified from
Zoumi et al. (2004) with permission
¼800 nm and P ¼ 60.2 mW for the
ex
mechanically significant constituents, i.e., SMCs, elastin fibrils, and collagen fibers
(Fig. 3.18). The smooth muscles, when activated, achieve active response to physiological loads by altering the circumferential mechanical properties (Dobrin, 1984;
Tanaka & Yamada, 1990). Elastin fibrils have relatively lower stiffness and larger
deformability, which helps to maintain blood flow through Windkessel-type effect in
elastin vessels. For most arteries, elastic lamellae (EL) are thick continuous sheets of
elastin with periodic pores, and SMCs fill within inter-lamellae (IL) space and
connect to dense and intricately organized IL elastin fibers, while collagen bundles
intersperse between EL and enveloped SMCs (Clark & Glagov, 1985;O’Connell
et al., 2008). Coronary media EL is composed of narrower and more widely spaced
elastin fibers (Clark & Glagov, 1985) and thus presents a thin and porous structure
compared to aorta. Moreover, the IL space becomes wider and may contain more
than one layer of SMCs (Clark & Glagov, 1985; Zoumi et al., 2004). A later study of
Boulesteix et al. (2006) found that murine coronary arteries do not contain many
elastin laminae as found in aorta and carotid arteries. It is reported that the volume
density of SMC is 74% while that of extracellular matrix (i.e., collagen and elastin
fibers, extracellular matrix (ECM) is 17% for adult murine coronary media (Cebova
& Kristek, 2011). The ratio of collagen to elast in content is 3.7 in media layer of
porcine RCA (Garcia & Kassab, 2009) which is slightly larger than that of intact
coronary arteries (e.g., ratio of intact canine coronary arteries is reported as 3.1 by
Fischer and Llaurado (1966) likely due to the lower ratio of collagen to elastin in
adventitia.
The arrangement and orientation of SMCs in the media show variations depending
on types of arteries and species (Clark & Glagov, 1985; Fujiwara & Uehara, 1992 ;
Hansen, Dineen, & Pullen, 1980;O’Conn ell et al., 2008; Osborne-Pellegrin, 1978;
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