Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3787_Библиотеки_им_академика_М_И_Перельмана
.pdf
154 3 Mechanical Properties and Microstructure of the Coronary Vasculature
https://t.me/med1917
The volume data are defined similarly where CSA+, CSA, and CSA0are replaced
+
with V
, V, and V0, respectively, with similar definitions (see Table 3.3).
The compliance (C) of the coronary arteries is determined as the change in
luminal dimension (ΔD, ΔCSA, or ΔV) per change in arterial pressure (ΔP
a
external pressure ¼0 mmHg, i.e., ΔP > 0 mmHg. In the negative pressure difference
(ΔP < 0 mmHg) where the vessels are under compression, the compliance is not
defined. The CSA-compliance for the first several generations of the LAD artery is
calculated, as well as, the V-compliance of the total arterial tree (vessels >0.5 mm in
diameter) as summarized in Table 3.4.
Table 3.3 Values for the empirical constants describing the ΔP-CSA relationship (Eq. 3.2) for the
first several generations of the coronary left anterior descending (LAD) arteries
Diameter
range (mm) at
Order
100 mmHg
11 2.03–3.44 2.39 0.9 5.0 1.3 1.99 0.9 34 20 0.989 0.005 27
10 1.03–1.93 1.07 0.3 1.58 0.7 0.53 0.3 47 33 0.988 0.015 23
9 0.73–0.97 0.29 0.1 0.64 0.2 0.23 0.1 33 18 0.967 0.045 10
Data are presented as means SD. R
Hamza et al. (2003) with permission
Table 3.4 Data for cross-sectional area (CSA)-compliance of the three largest orders of the left
anterior descending (LAD) arteries
Diameter range (mm) at
Order
100 mmHg
11 2.03–3.42 4.50 2.2 16.4 18 27
10 1.02–1.97 1.43 0.8 5.2 4.8 23
9 0.67–0.97 0.59 0.02 4.4 4.0 10
Data are presented as means SD. Reproduced from Hamza et al. (2003) with permission
CSA
(mm2)
0
+
CSA
(mm2)
2
represents the goodness-of-curve-fit. Reproduced from
Average CSA
(mm
2
)
CSA
(mm2)
1/2
ΔP
(mmHg) R
Compliance at
100 mmHg
(mm2mmHg1 103) n
2
n
),
Appendix 3: Calculation of Transmural Strain (Guo et al.,
2005)
If the circumference of a deformed vessel in the loaded state is designated by “C”,
the circumferential deformation of a cylindrical can be described by Green strain as
follows:
where λ
i,o
¼ C
the loaded state and C
i,o
=C
1
2
ε
i,o
zs
; C
refers to the inner or outer circumference of the vessel in
i,o
i
,o
zs
refers to the corresponding inner or outer circumference in
i
,o
λ
¼
1
,o
i
2
ð3:4Þ
Appendix 3: Calculation of Transmural Strain (Guo et al., 2005) 155
https://t.me/med1917
the zero-stress state. To assess the degree of non-uniformity of transmural strain, the
ratio of outer to inner strain can be evaluated as:
!
ε
o
ε
i
2
C
C
o
¼
2
C
C
i
2
zs
o
2
zs
i
2
zs
C
i
zs
C
o
ð3:5Þ
Hence, the product of the first and second terms of Eq. (3.5) gives the ratio of outer to
inner Green strain. Equation (3.5) can be simplified if the quotient is considered in
terms stretch ratio, λ, as:
λ
C
o
¼
λ
C
i
zs
C
o
i
zs
C
i
o
ð3:6Þ
The first and second terms become linearized and are easier to interrupt physically.
Theoretically, the intimal strain cannot equal to the adventitial strain when
θ > 180
. This point can be simply illustrated if the deformation is considered in
terms of stretch ratio as given by Eq. (3.6). The first term, ratio of outer to inner
circumference in the loaded state, is physically always >1. The second term, ratio of
inner to outer circumference in the zero-stress state, is <1ifθ < 180
θ > 180
. Hence, when θ < 180the product of the two terms (the first term is >1
and >1if
and the second is <1) can be approximately equal to one and hence implies
uniformity of strain. On the other hand, when θ > 180
both terms are >1 and
hence their product must further deviate from unity. Hence, the strain cannot
theoretically be transmurally uniform when θ > 180
. The experimental evidence
for the non-uniformity is presented in Table 3.5.
Table 3.5 Comparison of inner (εi) and outer (εo) Green strains for the coronary arterial tree for
different order numbers and ranges of opening angles
Order number ε
5 0.37 0.05 0.39 0.05 21 0.252
6 0.41 0.06 0.44 0.06 64 0.006
7 0.48 0.07 0.53 0.07 46 0.007
8 0.55 0.11 0.62 0.10 46 0.004
9 0.62 0.13 0.72 0.14 64 <0.001
10 0.60 0.14 0.78 0.13 66 <0.001
11 0.62 0.12 0.90 0.13 80 <0.001
Opening angle (degrees) ε
45.1–90 0.49 0.12 0.47 0.12 36 0.539
90.1–135 0.49 0.11 0.51 0.11 82 0.067
135.1–180 0.58 0.16 0.68 0.17 125 <0.001
180.1–225 0.59 0.13 0.85 0.15 59 <0.001
225.1–270 0.55 0.12 0.85 0.16 51 <0.001
270.1–315 0.52 0.09 0.85 0.12 14 <0.001
SD εo SD np-value
i
SD εo SD np-value
i
(continued)
156 3 Mechanical Properties and Microstructure of the Coronary Vasculature
https://t.me/med1917
Opening angle (degrees) εi SD εo SD np-value
Reproduced from Guo et al. (2005) with permission
Appendix 4: Time Dependence of Opening Angle (Rehal
et al., 2006)
The Kelvin model is comprised of a combination of linear springs (with spring
constants μ
Fig. 3.29. The stre ss–strain (σ–ε) equation for the Kelvin model can be stated as:
and μ1) and a dashpot (with coefficient of viscosity η1) as shown in
0
¼ E
R
ε þ τ
dε
σ
dt
ð3:7aÞ
σ þ τ
dσ
ε
dt
where μ
¼ ER, μ1¼ (τσ τε)(μ0/τε), and η1¼ τεμ1. The corresponding creep
0
solution of Eq. (3.7a ) can be written as:
ε tðÞ¼
1
E
R
1 1
τ
ε
t=τ
σ
e
τ
σ
HtðÞ ð3:7bÞ
where H(t) is the heavy-side step function. Equation (3.7a) is solved for the creep
recovery response (i.e., σ ¼ 0):
μ0μ
1
1
t
μ0þμ
η
1
1
where ε
ε tðÞ¼ε
is the initial strain. Experimental data of coronary arteries are obtained from
0
e
0
ð3:7cÞ
the zero-stress state (measurements taken within 15–30 s after radial cut from loaded
state, and followed for a period of 6 h). A total of 26 rings are examined from six
hearts (256 27.7 gm).
The material constants for the Kelvin model (E
, τσ, and τε) are determined from a
R
curve fit of the strain or creep data with an equation of the form:
Fig. 3.29 A schematic of
viscoelastic Kelvin model.
F is the force acting in a
spring, u is the
displacement, and u
0
is the
velocity of displacement;
and μ1are spring
μ
0
constants and η
1
is the
coefficient of viscosity of
the dashpot
η
1
u
F
1
μ
1
F
1
u'
1
F
μ
0
u
0
F
Appendix 4: Time Dependence of Opening Angle (Rehal et al., 2006) 157
https://t.me/med1917
ε tðÞ¼A Be
This is analogous to Eq. (3.7b) with A ¼ 1/E
Ct
, B ¼ (τσ τε)/(ERτσ) and C ¼ 1/τσ.A
R
ð3:7dÞ
nonlinear least squares yielded the va lues of the constants A, B, and C which are used
to calculate E
are then used to determine μ
, τσ, and τεas ER¼ 1/A, τσ¼ 1/C, and τε¼ (A B)/CA. These values
R
, μ1, and η1as outlined above. These values are in turn
0
used in Eq. (3.7c) to predict strain which is compared to the experimental data for the
6-h period.
The difference in opening angle for circumferential and axial loading are fitted
with a nonlinear least squares fit of the form analogous to Eq. (3.7d):
ΔOA ¼ α 1 βe
ðÞ ð3:8aÞ
χt
where α, β, and χ are empirical constants obtained from a nonlinear least squares fit.
Equation (3.8a) can be expressed as:
ln 2
t
t
1=2
ð3:8bÞ
where ΔOA
ΔOA ¼ ΔOA
1
¼ α, ΔOA0¼ α(1 β), and t
1
þ ΔOA0 ΔOA
1
e
¼ ln 2/χ. ΔOA0and ΔOA1represent
1/2
the difference in either opening angle or strain at t ¼ 0 and t ¼1, respectively, and
t
represents the time required for ΔOA to reach 50% of its final value. Table 3.6
1/2
summarizes the curve fit parameters for the c ircumferential and axial data.
Table 3.6 Circumferential and axial loading (difference in opening angle, ΔOA, between loaded
and no-load states): empirical coefficients of nonlinear least squares fit of Eq. (3.7b)
Order number ΔOA
Circumferential
11 2.2 130 1.34 0.971
10 0.74 55.3 0.67 0.931
9 EPCA 0.49 34.2 1.05 0.943
9 IMCA 0.47 13.4 0.82 0.934
Axial
11 3.2 46.8 1.2 0.934
10 1.6 43.1 1.7 0.972
9 EPCA 1.1 33.8 1.4 0.974
9 IMCA 0.13 17.8 0.86 0.957
Data are presented for orders 11, 10, and 9 define EPCA (epicardial coronary arteries) and order
9 IMCA (intramyocardial coronary artery, IMCA). R
Reproduced from Rehal et al. (2006) with permission
ΔOA
1
2
represents the goodness-of-curve-fit.
t
1/2
2
R
158 3 Mechanical Properties and Microstructure of the Coronary Vasculature
https://t.me/med1917
Appendix 5: Morphology of Coronary Arteries and Veins
Table 3.7 Mean morphological measurements at zero-stress state and loaded state of orders 4–11
LAD arterial vessels (a) and orders 12 to 4 of coronary sinus vessels (b)
(a) LAD arterial tree
Zero-stress state Loaded state
Order no.
C
i
4 92.5 112.4 98.5 37.6 4.5 1.01
5 172.9 197.1 108.6 72.5 7.4 1.05
6 352.1 382.3 126.6 150.3 11.2 1.13
7 655.3 700.9 133.2 291.5 18.5 1.21
8 1003.3 1053.5 146.5 459.7 27.3 1.25
9 1562.3 1633.0 155.0 744.6 39.4 1.23
10 3109.1 3109.3 190.0 1449.8 68.5 1.37
11 6498.2 6312.9 223.0 3097.0 129.4 1.45
(b) Coronary sinus vein
Zero-stress state Loaded state
Order no. n
C
mid
4 192.8 28.3 55.8 4.6 1.01
5 308.1 51.2 117.0 7.4 1.02
6 539.6 61.5 199.8 10.0 1.06
7 878.4 74.4 308.5 14.0 1.09
8 1300.0 87.3 468.2 20.1 1.13
9 2200.5 95.0 720.7 28.1 1.15
10 3434.7 104.2 1159.9 43.1 1.18
11 4802.5 112.2 2114.2 67.9 1.20
12 8818.1 131.2 3693.7 97.6 1.23
Reproduced from Guo, Liu and Kassab (2012) with permission
D
: inner diameter, WT (μm): wall thickness, Ciand Co(μm): inner and outer circumferential length;
i
(μm): midwall circumferential length since the vein wall is too thin to discriminate between
C
mid
inner and outer; λ
: axial stretch ratio; ϕ (degree): opening angle
z
C
o
ϕ D
ϕ D
i
i
WT λ
WT λ
z
z
Appendix 6: Isovolumic Myography
The isovolumic system consists of a chamber with two connectors which bridge the
blood vessel and rigid tubes. One tube connected to a 50 mL flask with physiological
saline solution (PSS) and the flask is pressurized with a regulator to inflate the vessel
to the desired pressure. Another tube is connected a solid state pressure transducer
(SPR-524, Microtip catherter transducer, Millar Inc, Texas) to monitor the
transmural pressure and a volume compensator is connected to compensate for
water transport across the vessel wall. The outlet of the tube is blocked to achieve
isovolumic conditions. The PSS aerated with mixed gas (22% O
,5%CO2, balanced
2
Appendix 6: Isovolumic Myography 159
https://t.me/med1917
with 73% N2) filled the chamber and tubes before vessel cannulation. A CCD
(charge-coupled device) camera on a microscop e transfered the image of the vessel
to computer that digitized the external diameter of the vessel. Since the sample rate
of digital conversion (200/s) is higher than the rate of change in the vessel during
vasoreactivity, the diameter is easily tracked. The vessel is inflated to a physiologic
pressure. Since the outlet is closed off, there is no flow in the vessel and the vessel is
merely pressurized. To achieve isovolumic state, a clamp placed on the tube between
the pressurized flask and the connector is closed and the PSS in the lumen of the
vessel and tubes is sealed, i.e., constant volume. The vascular contraction or
relaxation during chemical stimulation is characterized by significant changes of
intraluminal pressure.
Although a fairly constant volume of the solution can be achieved in the lumen of
vessel, it is not strictly constant since the PSS may be transported cross the vessel
wall (water flux) driven by the transmural pressure. Although the rate of water flux is
very small (<1 nL/min) and no visible reduction of diameter is seen during the
duration of experiment (<1 h), a pressure drop (drop in baseline pressure) is still
measurable (~0.6–3 mmHg/min). In order to stabilize the baseline pressure, a
volume compensator is connected in parallel with the pressure transducer. The
volume compensator is comprised of a gastight connector, a microsyrange (maximum volume: 25 μL), a microsyringe pump, and a microsyringe pump controller.
The critera for the compensatory rate of the microsyringe pump controller is to
maintain the transmural pressure at the desired baseline value (variation
< 0.2 mmHg/min). The re is no measurable change of vessel diameter during
compansation. If the leak rate is >1 μL/min, the specimen is discarded as the vessel
wall is damaged.
The circumferential tension (T) and stress (a) are computed based on the
following:
and
where P is intraluminal pressure measured by a pressure transducer and r
internal radius of blood vessel computed by the incompressibility assumption
(Eq. 3.9c) from the external radius which is measured by diameter tracking system.
h is wall thickness which is computed as the difference between r
cross-sectional wall area of the vessel at the no-load state (zero intraluminal pressure) which is measured from the images of the arterial cross-sectional view. Finally,
λ is the axial stretch ratio which is determined by the measurem ent of the comparison
T ¼ P r
σ ¼
r
¼
int
P r
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
2
r
ext
int
int
h
A
0
πλ
and r
ext
ð3:9aÞ
ð3:9bÞ
ð3:9cÞ
. A0is the
int
is
int
160 3 Mechanical Properties and Microstructure of the Coronary Vasculature
https://t.me/med1917
between the in vivo and ex vivo length between two markers on the outer
vessel wall.
Dose–response vasoconstriction and vasodilatation in response to vasoconstrictors and vasodilators are carried out under isovolumic conditions. Phenylephrine
(PE) is the vasoconstrictor and acetylcholine (ACh) is the vasodilator used for the
arteries except for coronary artery. ACh is the vasoconstrictor and bradykinin
(BK) is the vasodilator for the coronary artery. Briefly, the artery is stimulated to
contract with a vasoconstrictor from 10
10
to 105mole/L to determine the maximal
dose at maximal contraction. Then, the artery is rinsed and equilibrated for 30 min.
The artery is contracted with submaximal doses of the vasoconstrictor and relaxed
with the vasodilator by a series of doses: 10
10
to 105mole/L in the PSS. The
relaxation resulted in the reduction of intraluminal pressure and circumferential
tension which is computed using Eqs. (3.9a, 3.9b, and 3.9c). The calculation of
percent relaxation (%R) is based on both intraluminal pressure ( %R
R
) for comparsion:
T
%R
¼ Pd P
%R
ðÞ= P
P
¼ Td T
ðÞ= T
T
i
i
P
ðÞ100 ð3:10aÞ
max
i
T
ðÞ100 ð3:10bÞ
max
i
) and tension (%
P
and
%R
¼ σd σ
ðÞ= σ
σ
i
σ
ðÞ100 ð3:10cÞ
max
i
where P
pressure (P
(σd), Ti(σi), and T
(T
, Pi, and P
d
), and maximum pressure (P
i
or σd), physiological level (Tior σi), and maximum tension (T
d
are the intraluminal pressures at each dose (Pd), inflation
max
) at 0 mole/L of ACh, respectively. T
max
max(σmax
) are the circumferential tension (or stress) at every dose
max
or σ
max
)at
0 mole/L of ACh, respectively. To show the differences in various arteries,
mid-tension and mid-stress are computed during vasorelaxation as the averages of
maximal and minimal tension and stress, respectively.
Appendix 7: Morphology of Adventitia Fibers
Table 3.8 The layer-to-layer heterogeneity of mean width and area fraction of collagen and elastin
fibers assumed as a linear function: P ¼ αN + β, where N is the layer order and α and β are empirical
curve fit parameters
Collagen Elastin
Geometric parameter
Width 0.34 1.76 0.97 -0.05 2.20 0.92
Area fraction 2.38 25.8 0.97 1.73 27.0 0.95
This function is determined by least squares method, and R
between predicted data value and experimental measurement. Reproduced from Chen, Liu,
Slipchenko, et al. (2011) with permission
αβ R αβ R
2
represents the goodness-of-curve-fit
2
d
Appendix 8: Morphology of Media Smooth Muscle Cells 161
https://t.me/med1917
Table 3.9 The mechanical loading–deformation relation of fiber (collagen and elastin) geometrical
parameter is assumed as linear function: P ¼ αλ
+ β, where λθis circumferential stretch ratio of
θ
vessels
Collagen Elastin
Geometric parameter
αβR αβR
2
Orientation 0.34 1.35 0.94 0.58 1.56 0.78
Waviness 0.22 1.43 0.95 NA
a
Width 1.0 λθ< 1.4 0.10 1.11 0.70 0.33 1.32 0.87
2
represents the goodness-of-curve-fit between pressure and stretch ratio. Reproduced from Chen,
R
Liu, Slipchenko, et al. (2011) with permission
a
NA Not applicable. There is no waviness for elastin because the fibers are straight
Table 3.10 The relations between axial stretch ratio λ
1.4 λ
< 1.8 0.40 1.51 0.88
θ
and fiber (collagen and elastin) geometric
z
parameters (the orientation angle and waviness) are assumed as linear function: y ¼ αx + β,
determined by least squares method
Collagen Elastin
Α Β R
2
αβR
2
Geometric parameter
Normalized orientation
angle
Circumferential stretch
ratio
1.0 0.41 0.61 0.81 0.36 0.65 0.73
1.5 0.41 0.46 0.65 0.31 0.63 0.47
1.8 0.42 0.27 0.50 0.34 0.49 0.27
Waviness 1.0 0.38 1.59 0.88
1.5 0.21 1.38 0.66
1.8 0.02 1.03 0.02
a
R2represents the goodness-of-curve-fit. Reproduced from Chen, Liu, Slipchenko, et al. (2011) with
permission
a
At circumferential stretch ratio λθ¼ 1.8, most collagen fibers become straightened and fiber
waviness remains as 1.0
Appendix 8: Morphology of Media Smooth Muscle Cells
Table 3.11 The distribution of geometrical parameters of the nucleus and vascular smooth muscle
cells (VSMCs) of the media are fitted to a continuous normal distribution (or a bimodal normal
distribution) fxðÞ¼
2
represents goodness of fit
R
Parameters μσR
Length (μm) 15.0 4.7 0.96 56.0 10.3 0.98
Width (μm) 3.4 0.8 0.85 3.9 0.7 0.93
Aspect ratio 4.6 1.7 0.80 14.7 3.5 0.88
Orientation (
) 19.9 10.7 0.98 18.7 10. 9 0.92
Aspect ratio is defined as cell length divided by width. Reproduced from Chen, Luo, et al. (2013)
with permission
2
xμðÞ
1
2
p
ffiffiffiffi
2σ
e
σ
2π
, where μ is the mean of the distribution, σ is standard deviation, and
Nucleus VSMC
2
μσR
2
162 3 Mechanical Properties and Microstructure of the Coronary Vasculature
https://t.me/med1917
Table 3.12 Nonlinear relations between geometrical parameters and distension pressures for
smooth muscle cells (SMCs) and the nucleus obtained by curve fitting to a logarithmic function:
+ a2Log(x)
y ¼ a
1
Parameters a
1
a
2
2
R
SMC Length (μm) 60.2 7.7 0.95
Aspect ratio 17.4 1.8 0.90
Orientation (
) 18.2 2.9 0.99
Stretch ratio 1.1 0.1 0.95
Nucleus Length (μm) 16.1 0.9 0.81
Orientation (
) 17.2 2.5 0.99
Aspect ratio is length divided by width. Aspect ratio is defined as cell length divided by width. R
represents the goodness-of-curve-fit. Reproduced from Chen, Luo, et al. (2013) with permission
References
Arkill, K. P., Moger, J., & Winlove, C. P. (2010). The structure and mechanical properties of
collecting lymphatic vessels: An investigation using multimodal nonlinear microscopy. Journal
of Anatomy, 216, 547–555. https://doi.org/10.1111/j.1469-7580.2010.01215.x
Azuma, T., & Hasegawa, M. (1971). A rheological approach to the architecture of arterial walls.
The Japanese Journal of Physiology, 21,37–47. https://doi.org/10.2170/jjphysiol.21.27
Azuma, T., & Oka, S. (1971). Mechanical equilibrium of blood vessel walls. American Journal of
Physiology, 221, 1310–1318. https://doi.org/10.1152/ajplegacy.1971.221.5.1310
Bergel, D. H. (1961). The static elastic properties of the arterial wall. The Journal of Physiology,
156, 445–457. https://doi.org/10.1113/jphysiol.1961.sp006686
Berry, J., Rachev, A., Moore, J. E., & Meister, J. J.. (1992). Analysis of the effect of a non-circular
two layer stress-free state on arterial wall stresses. In Proceedings of the 14th Annual Interna-
tional Conference of the IEEE (pp. 65–66). https://doi.org/10.1109/IEMBS.1992.5760860
Birk, D. E., & Trelstad, R. L. (1986). Extracellular compartments in tendon morphogenesis:
Collagen fibril, bundle, and macroaggregate formation. The Journal of Cell Biology, 103,
231–240. https://doi.org/10.1083/jcb.103.1.231
Borg, T. K., & Caulfield, J. B. (1980). Morphology of connective tissue in skeletal muscle. Tissue &
Cell, 12, 197–207. https://doi.org/10.1016/0040-8166(80)90061-0
Borg, T. K., & Caulfield, J. B. (1981). The collagen matrix of the heart. Federation Proceedings,
40, 2037–2041.
Borg, T. K., Sullivan, T., & Ivy, J. (1982). Functional arrangement of connective tissue in striated
muscle with emphasis of cardiac muscle. Scanning Electron Microscopy, 4, 1775–1784.
Boulesteix, T., Pena, A.-M., Pagès, N., Godeau, G., Sauviat, M.-P., Beaurepaire, E., & Schanne-
Klein, M.-C. (2006). Micrometer scale ex vivo multiphoton imaging of unstained arterial wall
structure. Cytometry Part A: Journal of Quantitative Cell Science, 69A(1), 20–26. https://doi.
org/10.1002/cyto.a.20196
Burton, A. C. (1954). Relation of structure to function of the tissues of the wall of blood vessels.
Physiological Reviews, 34, 619–642. https://doi.org/10.1152/physrev.1954.34.4.619
Campagnola, P. J., Clark, H. A., Mohler, W. A., Lewis, A., & Loew, L. M. (2001). Second-
harmonic imaging microscopy of living cells. Journal of Biomedical Optics, 6, 277–286. https://
doi.org/10.1117/1.1383294
Campagnola, P. J., Millard, A. C., Terasaki, M., Hoppe, P. E., Malone, C. J., & Mohler, W. A.
(2002). Three-dimensional high-resolution second-harmonic generation imaging of endogenous
structural proteins in biological tissues. Biophysical Journal, 82, 493–508. https://doi.org/10.
1016/S0006-3495(02)75414-3
2
References 163
https://t.me/med1917
Carlson, B. E., & Secomb, T. W. (2005). A theoretical model for the myogenic response based on
the length–tension characteristics of vascular smooth muscle. Microcirculation, 12(4), 327–338.
https://doi.org/10.1080/10739680590934745
Caulfield, J. B., & Borg, T. K. (1979). The collagen network of the heart. Laboratory Investigation,
40(3), 364–372.
Cebova, M., & Kristek, F. (2011). Age-dependent ultrastructural changes of coronary artery in
spontaneously hypertensive rats. General Physiology and Biophysics, 30, 364–372. https://doi.
org/10.4149/gpb_2011_04_364
Chen, H., Guo, X., Luo, T., & Kassab, G. S. (2016). A validated 3D microstructure-based
constitutive model of coronary artery adventitia. Journal of Applied Physiology, 121(1),
333–342. https://doi.org/10.1152/japplphysiol.00937.2015
Chen, H., Liu, Y., Slipchenko, M. N., Cheng, J.-X., & Kassab, G. S. (2011). The layered structure
of coronary adventitia under mechanical load. Biophysical Journal, 101, 2555–2562. https://doi.
org/10.1016/j.bpj.2011.10.043
Chen, H., Liu, Y., Zhao, X., Lanir, Y., & Kassab, G. S. (2011). A micromechanics finite-strain
constitutive model of fibrous tissue. Journal of the Mechanics and Physics of Solids, 59,
1823–1837. https://doi.org/10.1016/j.jmps.2011.05.012
Chen, H., Luo, T., Zhao, X., Lu, X., Huo, Y., & Kassab, G. S. (2013). Microstructural constitutive
model of active coronary artery media. Biomaterials, 34(31), 7575–7583. https://doi.org/10.
1016/j.biomaterials.2013.06.035
Chen, H., Slipchenko, M. N., Liu, Y., Zhao, X., Cheng, J.-X., Lanir, Y., & Kassab, G. S. (2013).
Biaxial deformation of collagen and elastin fibers in coronary adventitia. Journal of Applied
Physiology (1985), 115(11), 1683–1693. https://doi.org/10.1152/japplphysiol.00601.2013
Choy, J. S., Mathieu-Costello, O., & Kassab, G. S. (2005). Effect of fixation and histological
preparation on coronary artery dimensions. Annals of Biomedical Engineering, 33(8),
1027–1033. https://doi.org/10.1007/s10439-005-4854-4
Chuong, C. J., & Fung, Y. C. (1983). Three-dimensional stress distribution in arteries. Journal of
Biomechanical Engineering, 105(3), 268–274. https://doi.org/10.1115/1.3138417
Chuong, C. J., & Fung, Y. C. (1986). On residual stresses in arteries. Journal of Biomechanical
Engineering, 108, 189–192. https://doi.org/10.1115/1.3138600
Cinthio, M., Ahlgren, Å. R., Bergkvist, J., Jansson, T., Persson, H. W., & Lindström, K. (2006).
Longitudinal movements and resulting shear strain of the arterial wall. American Journal of
Physiology-Heart and Circulatory Physiology, 291, H394–
ajpheart.00988.2005
Clark, J. M., & Glagov, S. (1985). Transmural organization of the arterial media. The lamellar unit
revisited. Arteriosclerosis, 5,19–34. https://doi.org/10.1161/01.ATV.5.1.19
Cornelissen, A. J. M., Dankelman, J., VanBavel, E., & Spaan, J. A. E. (2002). Balance between
myogenic, flow-dependent, and metabolic flow control in coronary arterial tree: A model study.
American Journal of Physiology-Heart and Circulatory Physiology, 282(6), H2224–H2237.
https://doi.org/10.1152/ajpheart.00491.2001
Cox, R. H. (1978). Passive mechanics and connective tissue composition of canine arteries.
American Journal of Physiology-Heart and Circulatory Physiology, 234, 533–541. https://
doi.org/10.1152/ajpheart.1978.234.5.H533
Davis, M. J. (1988). Microvascular control of capillary pressure during increases in local arterial
and venous pressure. American Journal of Physiology-Heart and Circulatory Physiology, 254,
H772–H784. https://doi.org/10.1152/ajpheart.1988.254.4.H772
Davis, M. J., & Gore, R. W. (1989). Length-tension relationship of vascular smooth muscle in
single arterioles. American Journal of Physiology-Heart and Circulatory Physiology, 256(3),
H630–H640. https://doi.org/10.1152/ajpheart.1989.256.3.H630
Demiray, H., & Vito, R. P. (1991). A layered cylindrical shell model for an aorta. International
Journal of Engineering Science, 29(1), 47–54. https://doi.org/10.1016/0020-7225(91)90075-E
Dobrin, P. B. (1984). Mechanical behavior of vascular smooth muscle in cylindrical segments of
arteries in vitro. Annals of Biomedical Engineering, 12, 497–510. https://doi.org/10.1007/
BF02363919
H402. https://doi.org/10.1152/
Соседние файлы в папке Библиотека им академика М.И. Перельмана