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144 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Fig. 3.23 The deformation–loading relations of elastin and collagen fibers. (a, c, e) Fiber
reorientation, presented by normalized orientation angles, at different biaxial loading. (b, d, f)
Change of collagen waviness at different biaxial loading. Each data point presents average
parameter over a specimen. Reproduced from Chen, Slipchenko, et al. (2013) with permission
The relation between axial stretch ratio and fiber reorientation showed that
changes of collagen orientation at three circumferential stretch ratios are similar,
implying that the fibers are sensitive to both circumferential and axial mechanical
loads. Normalized orientation angle of elastin decreased similarly with lower slopes
(Appendix 7) but became highly heterogeneous at higher distensions (Fig. 3.23c, e,
with lower R
2
; Appendix 7). This is the result of elastin gradually forming a netlike
structure in adventitia sublayers and becomes larger than that of collagen at higher
biaxial loading. The change of collagen waviness with an increase of axial strain is
different than that of fiber orientation. At the no-distension state (λ
¼ 1.0), the mean
θ
waviness of collagen decreased rapidly as axial stretch increases (Fig. 3.23b), and
then decreased relatively slowly with an increase of axial stretch while collagen
became straightened gradually to take up the load at the physiological distension
(λ
¼ 1.5, Fig. 3.23d). At λθ¼ 1.8, more collagen fi bers became completely
θ
straightened even at low axial stretch and predominated the mechanical function
of adventitia (Chen, Liu, Slipchenko, et al., 2011; Zoumi et al., 2004). The fibers
aligning in the longitudinal direction remain undulated at high distension with low
3.7 Ultrastructure of Coronary Arteries 145
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axial stretch. These observations reveal microscopic mechanical responses of vascular tissue and are essential to understand tissue mechanical properties and response
at the macroscopic level.
3.7.10 Morphometry of Coronary Media
As demonstrated above, the media plays a major role in load bearing under physiological conditions. In addition to elastin and collagen fibers, the major constituent
of the media is SMC. Elastin fibrils have relatively lower stiffness and support blood
vessels at low pressures while the collagen fibers are much stiffer to protect the artery
from excessive dilation (Zoumi et al., 2004). The SMCs provide negligible contributions to the passive properties of blood vessels (Matsumoto & Nagayama, 2012),
but are the predominate contributors of active behavior (Huo et al., 2012). The
majority of the active blood vessel constitutive models suggest uniaxial length–
tension relationships in the circumferential direction as motivated by the circumferential arrangement of SMC (Clark & Glagov, 1985;O’Connell et al., 2008) albeit the
orientation of SMC has been debated by others (Fujiwara & Uehara, 1992; OsbornePellegrin, 1978; Rhodin, 1980; Wolinsky & Glagov, 1967). Furthe rmore, some
studies observed significant multi-axial responses of blood vessels during vasoconstriction (Gaballa et al., 1998; Hayman, Zhang, Liu, Xiao, & Han, 2013; Huo et al.,
2012; Huo, Zhao, Cheng, Lu, & Kassab, 2013; Lu & Kassab, 2007). A study showed
that the porcine coronary artery displayed significant biaxial vasoconstriction
induced by potassium physiological saline solution (Huo et al., 2012, 2013),
where the active axial stress is more than half the circumferential stress. The
significant axial active response, however, cannot be explained by the obliqueness
of SMC alignment alone. This implies that the biaxial vasoactivity may be induced
by SMC helical orientation as well as multi-axial active responses of individual
SMC. To explain the overall mechanical behavior of coronary arteries (including the
active media layer), the morphology of SMC must be measured and used in a
structure-based model as described in Chap. 4.
Chen, Luo, et al. (2013) determined the morphology and orientation of coronary
SMC using confocal microscopy. Samples of porcine coronary arteries are considered under one of six loading conditions: (1) ZSS; (2) No-load state (0 mmHg
distension); (3) 40 mmHg distension; (4) 80 mmHg distension; (5) 120 mmHg
distension; and (6) 160 mmHg distension. The pressurized states are made under
perfusion fixation using the minimal shrinkage protocol described above (Choy
et al., 2005). The orientation of the SMC is measured using an automated algorithm
as described below. Manual measurements are made for dimensions of SMC where
the length and width are determined by the major and minor axes of each cell,
respectively. The aspect ratio, featuring the cell shape, is identified by the ratio of
length to width of a given cell. Additionally, the orientation angle θ
defined as the angle between the direction of major axis and circumferential direction
of cell. The stained image of the nucleus is first converted to a binary image, where
VSMC
of SMC is
146 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Fig. 3.24 Distribution of smooth muscle cells (SMCs) geometrical parameters at zero-stress state
(ZSS). (a) Probability density functions (PDFs) of the lengths of SMC and the nucleus; (b) PDFs of
the widths of SMC and the nucleus; (c) PDFs of the aspect ratios of SMC and the nucleus; (d) PDFs
of the orientation angles of SMC and the nucleus. Columns present experimental measurements,
and solid and dashed lines present normal distributions of geometrical parameters of SMC and the
nucleus, respectively. Reproduced from Chen, Luo, et al. (2013) with permission
the nucleus-containing pixels are clearly distinguished from the background by
median filtering. The MATLAB library function “BWLABEL” is implemented to
count and record connected components (the nuclei) and the function
“REGIONPROPS” is used to calculate the properties (e.g., orientation angle, length,
and width).
At ZSS, the histograms of geometrical parameters of SMC and nuclei are shown
in Fig. 3.24, and their probability distribution functions are fitted to continuous
normal distributions (Appendix 8, Table 3.11). The length of individual SMC is
56.0 10.3 μm which is larger than that of the nuclei (15.0 4.7 μm) while their
widths are similar (3.9 0.7 μm vs. 3.4 0.8 μm) (Fig. 3.24a, b). The means of
aspect ratio of the SMC and the nuclei are 14.7 3.5 and 4.6 1.7, respectively, as
plotted in Fig. 3.24c. SMC aligned off the circumferential direction of the vessel
with a bimodal distribution with a mean angle of 18.7 10.9
consistent with the angle of the nucleus, 19.9 10.7
. The length and width of
(Fig. 3.24d),
SMC followed a normal distribution in coronary media, while the orientation angle
3.7 Ultrastructure of Coronary Arteries 147
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Fig. 3.25 The deformed smooth muscle cells (SMCs) of coronary media under various distention
pressures: The loading pressures in (a–e) are: 0 mmHg, 40 mmHg, 80 mmHg, 120 mmHg,
160 mmHg, respectively. Reproduced from Chen, Luo, et al. (2013) with permission
showed a bimodal normal distribution, in line with observations of SMC helical
arrangement in vessels. The SMC orientation and distribution implies that SMC
constriction generates not only circumferential active stress, but also axial active
responses in coronary arteries as will be demonstrated below.
The SMC of passive coronary media deformed signi ficantly with an increase in
distention pressure (Fig. 3.25). The cells gradually shifted in the circumferential
direction at elevated pressure, i.e., reorienting to the loading direction. The SMCs are
significantly stretched in the axial direction and became more spindled with longer
tails (Fig. 3.25d, e) than those in the no-load state (Fig. 3.25a), while the nuclei did
not significantly deform. Changes of geometries of SMC and nuclei are quantified
and plotted in Fig. 3.26, and the correspondi ng nonlinear dependency on distension
pressure is tabulated (Table 3.12, Appendix 8). The length of SMC increased
significantly until distension pressure reached 80 mmHg, while the length of the
nuclei increased relatively slightly as shown in Fig. 3.26a. The widths of SMC and
the nuclei did not change significantly under all pressures. Accordingly, the aspect
ratio of SMC increased significantly at lower pressures and plateaued at higher
pressures, while that of the nuclei did not change significantly as shown in
Fig. 3.26b. The orientation angles of SMC and the nuclei decreased significantly
from the no-load state to 40 mmHg distension, while smaller changes are observed in
a pressure range of 40–160 mmHg (Fig. 3.26a). The mean orientation angle of SMC
became 13.0 2.6
at 80 mmHg and 11.9 3.0at 160 mmHg pressure. There is no
significant difference between the orientation of SMC and the nuclei at each load.
148 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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Fig. 3.26 The nonlinear
parameter–pressure
relations of smooth muscle
cells (SMCs) and the
nucleus of coronary media.
With the increase of
distension pressure: (a)
Changes of the length and
with; (b) Change of the
aspect ratio; (c) Changes of
the orientation angle.
Reproduced from Chen,
Luo, et al. (2013) with
permission
3.7 Ultrastructure of Coronary Arteries 149
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The morphological-pressure relations of SMC and nuclei are obtained for the
length and orientation angle. The change of SMC length increased sharply from the
no-load state to 80 mmHg distention and became plateaued at higher pressure,
consistent with that of the outer diameter of vessels. This suggests that recruited
collagen fibers either in media or adventitia prevent the intact vessel as well as SMC
from overstretch at high pressure. The reorientation of SMC displayed similar
nonlinear dependency on distention pressure (Fig. 3.26c), gradually orienting
towards the circumferential direction of the vessels with an increase in pressure.
The orientation angle of the SMC is about 13.0 2.6
at 80 mmHg pressure,
suggesting that SMC align slightly off the circumferential direction of vessels at
physiological pressure. It should be noted that the physiological axial stretch ratio
(about 1.3 for coronary arteries) leads to a large oblique arrangement of the SMC
from the vessel circumferential direction.
In blood vessels, SMCs connect with the extracellular matrix (ECM) via focal
adhesion and the deformation thus strongly depends on ECM deformation as well as
the macroscopic deformation of blood vessels. It is likely that flexible actin filaments
deform with ECM through dense bodies in passive tissue such that collagen and
elastin fibers follow affine deformation (Sacks, 2003; Stella et al., 2008) as described
in Chap. 4. A previous study showed that SMCs depend nonlinearly on fiber
deformation, based on changes in the aspect ratios of the nuclei under various biaxial
loading conditions (Stella et al., 2008 ). This conclusion, however, may be questionable since deformation of the nucleus is different from that of the cellular cytoskeleton, as shown in Fig. 3.26a. The deformation of the nuclei is not affine with tissue
level deformation.
3.7.10.1 Automation of Smooth Muscle Cell Measurements
To reduce labor and eliminate human error, Luo, Chen, and Kassab (2016) developed a 3D segmentation algorithm to determine SM C morphology and orientation of
the data presented above. A 3D semi-automatic segmentation method is developed
to reconstruct individual SMCs from cell clumps as well as to extract the 3D
geometry of SMCs. A new edge blocking model is introduced to recognize cell
boundary while an edge growing model is developed for optimal interpolation and
edge verification. The proposed methods are designed based on region of interest
selected by the user and interactive responses of limited key edges. Enhanced cell
boundary features are used to construct the cell’s initial boundary for further edge
growing. A unified framework of morphological parameters (dimensions and orientations) is proposed for the 3D volume data. Virtual phantom is designed to validate
the tilt angle measurements, while other parameters extracted from 3D segmentations are compared with manual measurements to assess the accuracy of the algorithm. The mean length, width, and thickness of SMCs in the media are
62.9 14.9 μm, 4.6 0.6 μm, and 6.2 1.8 μm (mean SD). In the longitudinal–
circumferential plane of the blood vessel, SMCs align off the circumferential
150 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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direction with two mean angles of 19.4 9.3and 10.9 4.7, while an out-ofplane angle (i.e., radial tilt angle) is found to be 8 7.6
with a median of 5.7. The
obtained 3D geometries will be utilized in mathematical models as described in
Chap. 4.
3.7.10.2 In Situ Deformat ion of Smooth Muscle Cells
Although the data above on the SMC morphology is informative, it is obtained
statistically across different specimens because of the need for different deformation
conditions and fixation. An ideal approach would allow real-time imaging of fresh
specimens similar to that of elastin and collagen using TPEF and SHG, respectively,
as described above. To address this issue, Zhang et al. (2018) introduced an
epi-stimulated Raman scattering (epi-SRS) imaging platform for in situ functional
imaging of SMC in fresh coronary arteries. For the first time, the pressure-induced
morphological deformation of fresh SMCs is imaged with no fixation and in a labelfree manner.
A balloon catheter connected to a pressure gauge system is inserted into the artery
tube to control the pressure applied to the coronary vessel segment. The balloon is
made from a soft and flexible thin polymer film with circumference sufficiently
larger than that of the artery. Hence, the pressure is applied completely and uniformly to the whole artery for homogeneous expansion with no tension taken up by
the balloon at the distension pressures used. The segment with the internal balloon is
mounted on microscope stage. To elucidate the pressure-induced structural variation
of SMCs, epi-SRS imaging of SMCs at various loading pressures (0, 20, 40, 80,
120, 160 mmHg) are performed in the same location of the sample, as shown in
Fig. 3.27a–f. Clearly, the SMCs showed deformation with an increase in distention
pressure (Fig. 3.27g). At elevated loading pressure, SMCs reoriented towards the
circumferential direction and are significantly stretched in the major axial direction,
i.e., became more spindled (Fig. 3.27g). The data on orientation, length, and width of
SMC in fresh specimens shown in Fig. 3.27g are generally in agreement with those
of fixed specimens in Fig. 3.26. Finally, the cell length, width, and orientation angle
are changed back to the initial values when the pressure is reduced to the baseline
value, indicating reversible elastic deformation.
The orientation angle of SMCs decreased significantly with pressure changing
from no load state (19.8 3.5
) to 80 mmHg (10.5 2.6) and became plateaued
when the pressure is higher than 80 mmHg. This demonstrates that SMCs align
slightly off the circumferential direction of vessels at physiological pressure. The
length of SMCs also increased from 46.5 4.4 to 55.2 4.2 μm with pressure from
0 to 80 mmHg and plateaued thereafter. Conversely, the width of SMCs showed a
decrease from 3.6 0.7 to 2.7 0.3 μm. These results suggest that the SMCs are
protected from overstretch at high pressure, most likely by the adjoining collagen
fibers in the media.
The deformation of individual SMC follows that of blood vessel since SMCs
connect with the extracellular matrix of blood vessels via focal adhesion. The pliable
3.7 Ultrastructure of Coronary Arteries 151
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(a) (b) (c)
y
z
x
(d) (e) (f)
25
(g)
20
15
10
Orientation (Degree)
-20 0 20 40 60 80 100 120 140 160 180
65
60
m)
μ
55
50
Length (
45
-20 0 20 40 60 80 100 120 140 160 180
4.5
4.0
μm)
3.5
Width (
3.0
2.5
-20 0 20 40 60 80 100 120 140 160 180
Pressure (mmHg)
Angle
Length
Width
Fig. 3.27 Deformation of living SMCs under various distension pressures: (a–f) 3D reconstructed
images of SMCs at the pressure of 0 mmHg, 20 mmHg, 40 mmHg, 80 mmHg, 120 mmHg, and
160 mmHg, respectively. The directions of x- and y-axis are indicated in (a), and z-axis represents
depth. Stack size: 35 μm 80 μm 10 μm. (g) Geometric responses of fresh SMCs to distension
pressure (average of 10 cells). Reproduced from Zhang et al. (2018) with permission
actin filaments in SMCs are the predominant constituents of cellular cytoskeleton,
and thus likely contribute to SMC deformation through dense bodies in passive
tissue. Similarly, the collagen and elastin fibers also follow affine deformation as
described in Chap. 4.
To further validate the feasibility of this epi-SRS imaging plat form for functional
imaging of active SMCs, the morphological responses of SMCs to drug treatment
are also investigated. Fresh SMC in media layer is treated with 0.2 mM isosorbide
dinitrate as a vasodilator. Time-course SRS imaging of VMSCs is then recorded, and
the results are shown in Fig. 3.28a. Deformation of SMC in response to vasodilation
is observed. SMC is reori ented away from the circumferential direction, and the
length of SMC is decreased transiently. The SMC’s width increased from 2.8 0.4
to 3.8 0.5 μm, indicating relaxation of cells. Changes of geometries of SMC versus
time are quantified Fig. 3.28b. The most significant change occurred within 20 min
after the drug is added. During drug treatment, the values for orientation angle and
length change are 7.7
and 8.2 μm, respectively, as deduced from Fig. 3.28b. The
values are similar to the geometric differences at no load state and at 80 mmHg,
suggesting significant relaxation of SMC after drug treatment. No significant
changes are observed in the control group where no drug is added in the medium
(Fig. 3.28c).
152 3 Mechanical Properties and Microstructure of the Coronary Vasculature
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0 min 5 min 10 min 20 min
30 min 40 min 50 min 60 min
y
z
x
25
20
15
10
Orientation (Degree)
0 102030405060
65
m)
60
55
Length (μ
0 102030405060
4.5
4.0
3.5
3.0
Width (μm)
2.5
0 102030405060
Time (min)
25
20
15
10
Orientation (Degree)
0 102030405060
65
60
55
Length (μm)
0 102030405060
4.5
4.0
3.5
3.0
Width (μm)
2.5
0 102030405060
Time (min)
Fig. 3.28 Real-time responses of SMCs to drug treatment. (a) Time-course imaging of the
deformation of fresh SMCs after addition of 0.2 mM isosorbide dinitrate. The time points are
indicated in each image. (b) Corresponding angle and length changes (average of 10 cells). (c)
Control. Loading pressure: 80 mmHg. The directions of x- and y-axis are the axial and circumferential directions of the vessel, respectively. z-axis represents depth. Size: 35 μm 80 μm 10 μm.
Reproduced from Zhang et al. (2018) with permission
Appendix 1: Compliance and Distensibility
Table 3.1 Data on the diameter-compliance of the first several generations of the coronary arteries
(c)(b)(a)
D (mm) Order α + SD (mm/mmHg) 10
3
β + SD (mm) R
2.01–3.5 11 1.8 0.54 2.4 0.34 0.93 0.042 17
1.01–2.0 10 1.4 0.33 1.1 0.26 0.90 0.049 14
0.51–1.0 9 1.2 0.23 0.65 0.18 0.87 0.052 8
2
The constants α and β and the goodness-of-curve-fit, R
, are for the linear fit described by the
equation D ¼ αP + β. Reproduced from Kassab and Molloi (2001)with permission
2
n
Table 3.2 Comparison of diameter (D) distensibility data of various species
Species D (mm)
Human 4.9 0.3 2.2 0.53 70–110 In vitro, Caliper Gow and Hadfield
Dog 3.6 0.69 60–140 In vivo,
Dog 3.1 0.68 60–140 In vitro, Caliper Gow and Hadfield
Dog 2.6 0.77 107–135 In vitro,
Pig 2.6 0.34 0.68 0.21 60–140 In situ,
Pig 1.3 0.24 1.2 0.39 60–140 In situ,
Distensibility
(1/mmHg) 10
Pressure
3
(mmHg) Method Reference
Ultrasonic
Microscopy
Angiography
Angiography
(1979)
Patel and Janicki
(1970)
(1979)
Tomoike et al.
(1981)
Kassab and Molloi
(2001)
Kassab and Molloi
(2001)
(continued)
Appendix 2: Transmural Pressure–CSA Relation (Hamza et al., 2003) 153
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Species D (mm)
Pig 0.79 0.20 1.6 0.73 60–140 In situ,
Reproduced from Kassab and Molloi (2001) with permission
Distensibility
(1/mmHg) 10
Pressure
3
(mmHg) Method Reference
Angiography
Kassab and Molloi
(2001)
Appendix 2: Transmural Pressure–CSA Relation (Hamza
et al., 2003)
The ΔP-CSA relationship for various vessels with diameter >0.5 mm is determined.
The vessels are grouped in the following diameter ranges: 0.5–1.0 mm, 1.01–2.0 mm,
and 2.01–3.5 mm, which roughly correspond to orders 9, 10, and 11, respectively.
For each experiment, the ΔP-CSA measurements are taken for seven segments along
the main LAD trunk and three segments along the side branches. The ΔP-CSA
relationship in the range of 150 to +150 mmHg pressure difference are curve fitted
using nonlinear regression, according to the following relationship:
CSA ¼
where CSA is the cross-sectional area of the vessel at a given pressure difference
(ΔP ¼ intravascular pressure box pressure) and α, β, γ, and δ are curve fit
constants. Equation (3.1) can be expressed in terms of four physical constants as:
1 þ e
α
þ δ ð3:1Þ
βγΔPðÞ
CSA ¼
+
where CSA
is the asymptotic value of CSA in the positive ΔP direction (below
yield pressure where vessel may undergo plastic deformation and rupture); CSA
the asymptotic value of the CSA in the negative ΔP direction; CSA
value at ΔP ¼ 0; and ΔP
+
and CSA(i.e.
CSA
related to the physical constants (CSA
CSAþ CSA
1 þ
1/2
CSAþþCSA
ðÞ
CSAþCSA
CSA0CSA
is the pressure difference corresponding to the average of
2
0
e
). The empirical curve fit constants (α, β, γ, δ) are
+
þ
CSA
CSA
0
CSA
1=2
ΔP
ln
CSAþCSA
CSA0CSA
0
and CSA, CSA0, ΔP
ΔP
ΔP
1=2
þ CSA
1/2
) as follows:
¼ α þ δ
¼ δ
¼
α þ δ 1 þ e
1 þ e
βγ
βγ
¼ γ ð3:3Þ
0
is the CSA
ð3:2Þ
is
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