Medical Engineering & Physics 36 (2014) 1233–1245
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Medical Engineering & Physics
journal homepage: www.elsevier.com/locate/medengphy
In vitro measurements of velocity and wall shear stress in a novel
sequential anastomotic graft design model under pulsatile flow
conditions
Foad Kabinejadian a , Dhanjoo N. Ghista b , Boyang Su c,∗ , Mercedeh Kaabi Nezhadian a,d ,
Leok Poh Chua e , Joon Hock Yeo e , Hwa Liang Leo a
a
Department of Biomedical Engineering, National University of Singapore, Singapore
Education Committee, Southern Ozarks Alliance for Rural Development, Willow Springs, MO, USA
c
Cardiac Mechanics Engineering and Physiology Unit, National Heart Center, Singapore
d
School of Mechanical Engineering, Khaje Nasir Toosi University of Technology, Tehran, Iran
e
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore
b
a r t i c l e
i n f o
Article history:
Received 23 January 2014
Received in revised form 19 June 2014
Accepted 28 June 2014
Keywords:
Particle image velocimetry (PIV)
Coronary artery bypass graft (CABG)
Sequential anastomoses
Hemodynamic
Wall shear stress (WSS)
a b s t r a c t
This study documents the superior hemodynamics of a novel coupled sequential anastomoses (SQA) graft
design in comparison with the routine conventional end-to-side (ETS) anastomoses in coronary artery
bypass grafts (CABG). The flow fields inside three polydimethylsiloxane (PDMS) models of coronary artery
bypass grafts, including the coupled SQA graft design, a conventional ETS anastomosis, and a parallel
side-to-side (STS) anastomosis, are investigated under pulsatile flow conditions using particle image
velocimetry (PIV). The velocity field and distributions of wall shear stress (WSS) in the models are studied
and compared with each other. The measurement results and WSS distributions, computed from the near
wall velocity gradients reveal that the novel coupled SQA design provides: (i) a uniform and smooth flow
at its ETS anastomosis, without any stagnation point on the artery bed and vortex formation in the heel
region of the ETS anastomosis within the coronary artery; (ii) more favorable WSS distribution; and (iii) a
spare route for the blood flow to the coronary artery, to avoid re-operation in case of re-stenosis in either
of the anastomoses. This in vitro investigation complements the previous computational studies of blood
flow in this coupled SQA design, and is another necessary step taken toward the clinical application of
this novel design. At this point and prior to the clinical adoption of this novel design, in vivo animal trials
are warranted, in order to investigate the biological effects and overall performance of this anastomotic
configuration in vivo.
© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
1. Introduction
Coronary artery bypass grafting (CABG), the primary treatment
for coronary artery high-risk patients, has a limited long-term
patency mainly due to anastomotic intimal hyperplasia (IH). Hemodynamics is widely believed to be one of the most important factors
implicated in the initiation and progression of IH [1–4], predominantly at the downstream anastomosis where IH has been found to
be significantly greater [5].
A conventional distal end-to-side (ETS) anastomosis is characterized by abnormal flow conditions, including flow oscillation at
∗ Corresponding author at: 17 Third Hospital Avenue, National Heart Centre, Mistri
Wing, Singapore 168752, Singapore. Tel.: +65 64367782; fax: +65 62230972.
E-mail address: [email protected] (B. Su).
http://dx.doi.org/10.1016/j.medengphy.2014.06.024
1350-4533/© 2014 IPEM. Published by Elsevier Ltd. All rights reserved.
the heel, impact on the artery floor, and flow separation at the toe.
Typically, there is a low-WSS region at the heel, where a vortex
forms due to the interaction of the flow from the graft with the relatively slow flow in the occluded proximal artery. The presence of
a slow recirculation flow (i.e., a vortex) increases the blood nearwall residence time and results in platelet activation [6] and fibrin
thrombus formation [7,8], which leads to IH development [1,9–11].
Along with the vortex, there is a stagnation point on the artery bed,
where the graft flow impinges the arterial floor, whose location
oscillates during the cardiac cycle. This moving stagnation point
provides a low-magnitude-high-oscillatory WSS condition on the
artery bed which has been suggested to enhance atherogenesis [12]
and IH formation [13]. In addition, the flow impact on the artery
floor is known to be injurious to the endothelium and is believed
to be a contributing factor to the graft failure [14]. In a conventional ETS configuration, there is a high spatial gradient of WSS at
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F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
the toe of the anastomosis, which has been postulated as a potential cause of inducing morphological and functional changes in the
endothelium that can contribute to elevated wall permeability and
consequent atherosclerotic lesions [15–17] and IH development
[18].
Several studies have been conducted to improve the hemodynamics at the anastomotic junction [4], in order to attain higher
patency rates in bypass grafts. These investigations include studies on the effects of geometrical factors, such as anastomotic angle
[19–22], modified configuration of distal anastomosis [23–26],
graft-to-host artery diameter ratio [27–30], and out-of-plane graft
[31–33], as well as the effects of stenosis severity and proximal
artery flow [34,35], irregularities of venous graft wall due to venous
valve sinus [36], and distance of grafting (distance between anastomosis and stenosis) [37].
Optimization of the abovementioned geometrical factors in
an ETS anastomosis has been shown to somewhat improve the
flow field and distribution of the hemodynamic parameters (HPs).
However, it has not changed the general problematic flow characteristics, such as the vortex formation at the heel or the impact
of the blood on the artery bed. Therefore, in an effort to resolve
the dilemma of an optimal downstream anastomotic geometry,
a novel coupled sequential anastomoses (SQA) configuration has
recently been designed, based on the beneficial flow characteristics
observed in the side-to-side (STS) anastomosis of sequential bypass
grafts [38]. The computational simulations and fluid–structure
interaction (FSI) analyses of this SQA graft design have shown an
improved flow field and advantageous distribution of HPs in the
coupled SQA design, as compared to the conventional ETS anastomosis [38,39].
In this in vitro study, we have investigated the hemodynamics in fabricated polydimethylsiloxane (PDMS) model of the novel
coupled SQA graft design, in comparison with a conventional ETS
anastomosis and a parallel STS anastomosis. These three models
had been labeled as the base models in the previous computational
simulation study [38]. At this stage and prior to the adoption of
this novel SQA graft design for in vivo animal trials and clinical
applications, we have further examined the efficacy of the coupled SQA graft design compared to the existing conventional ETS
anastomosis experimentally, utilizing particle image velocimetry
(PIV) technique. The results of the present in vitro investigation
can complement the earlier computational studies.
2. Materials and methods
The flow field velocity measurement was conducted by PIV in
three life-size PDMS anastomotic models: (i) the novel coupled
sequential anastomoses, (ii) a parallel STS anastomosis, and (iii) a
conventional ETS anastomosis, shown in Fig. 1(a)–(c), respectively.
The latter two were the reference models to be compared, respectively, with the STS and ETS components of the novel SQA graft
design.
2.1. Geometric models
The silicone rubber (i.e., PDMS) models were produced, using
the method introduced by Chong et al. [40]. In the coupled SQA
model, which has been designed based on the beneficial results
of sequential bypass grafting, there is initially a STS anastomosis
distal to the stenosis, and then the graft end is anastomosed to
the same coronary artery further downstream in an ETS fashion,
as shown in Fig. 1(a). The dimensions of the models are listed in
Table 1, where DG , DA , LP , LSTS , LETS , LD , and d stand for the graft
diameter, coronary artery diameter, length of the proximal section
of the host artery, length of the STS anastomosis, length of the ETS
Table 1
Dimensions of the geometric models (mm).
Model
DG
DA
LP
LSTS
LETS
LD
d
Coupled SQA
Conventional ETS
Parallel STS
4
4
4
2
2
2
45
45
45
8
N.A.
8
7
7
N.A.
20
35
30
30
N.A.
N.A.
anastomosis, length of the distal section of the host artery, and the
distance between the two anastomoses in the novel SQA model,
respectively, as shown in Fig. 1. The physical models were bilaterally symmetric with respect to the XZ plane, and the outlet of the
proximal segment of the coronary artery was fully occluded during
the experiments.
2.2. Working fluid, flow conditions, and flow circuit
A mixture of 30% glycerin and 70% sodium chloride (NaCl) solution by volume was used as the working fluid in this study (the
NaCl solution was made up of 1 part NaCl and 3 parts water by
weight). This Newtonian mixture’s density was 1156 kg/m3 and its
dynamic viscosity at the working temperature of 25 ◦ C was quantified by a controlled shear rate rheometer (Contraves low rate 40)
to be 0.0054 Pa s (5.4 cP). The refractive index of the mixture was
measured by a commercial refractometer (Atago 3T; High-Precision
Model) to be 1.409, which matches that of the PDMS model.
Each PDMS model was incorporated into the flow circuit, as
shown schematically in Fig. 2, and a computer-controlled gear
pump system (Micropump Inc., Vancouver WA USA), including
one varying flow pump (Model HG0024-N23 PF1SGB1) and one
steady flow pump (Model HG0024-G050), was used to generate
the physiological inlet flow waveform with the time period of 0.9 s,
as demonstrated in Fig. 3 [38]. The flow rate was measured and
monitored by means of an electromagnetic flow meter (Promag
53, Endress + Hauser, Germany) immediately upstream of the test
section.
The peak flow rate during systole was Qmax = 70 ml/min. The
maximum Reynolds and Womersley numbers at the peak systole
were calculated to be Remax = 79 and ˛max = 2.45 respectively, based
on the graft diameter of 4 mm. This suggested that the flow was
laminar, which was further proven by PIV results, as no turbulence
was observed in the flow field.
In the parallel STS model, 15% of the blood flow (on average
within each cardiac cycle) was set to pass through the STS anastomosis into the coronary artery, and the remaining 85% was allowed
to pass through the graft, by adjusting the resistance at the outlets
of the graft and coronary artery of this model. The above flow division was adjusted to make the parallel STS model consistent with
the novel coupled SQA configuration, since the flow was bifurcated
in the same proportion through the coronary artery and the graft
at the STS component of the SQA model (as calculated based on the
PIV results).
In this experiment, hollow glass spheres with mean diameter
of 10 ␮m, density of 1.1 g/cm3 , and refractive index of 1.52 (HGS10, Dantec Dynamics, Denmark) were used as tracer particles and
seeded into the working fluid.
2.3. Particle image velocimetry (PIV) system
The PIV is an optical measurement technique, allowing the
instantaneous acquisition of an entire planar section of a flow
field [41]. The PIV system used in this study, consisted of a
15 Hz Q-switched, double cavity pulsed Nd:YAG laser (Minilase-III,
New Wave Research, USA) with an energy of 150 mJ at a wavelength of 1064 nm, producing a light sheet which was adjusted to
F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
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Fig. 1. Fabricated silicone rubber (PDMS) models of (a) the novel coupled SQA graft design, (b) parallel STS, and (c) conventional ETS anastomosis.
illuminate the tracer particles in the symmetry plane of the models,
as shown schematically in Fig. 2.
The particles’ motion was recorded by means of a synchronized
charge coupled device (CCD) Camera (FlowSense, Dantec Dynamics, Denmark), with a spatial resolution of 1600 × 1200 pixel2 , and
a Nikon lens (AF Micro Nikkor, 60/2.8) positioned normal to the
laser sheet. The image acquisition in this phase-resolved PIV measurement was triggered by a TTL signal (5 V), generated by the gear
pump interface unit, in order to phase-lock the measurements. The
flow data were acquired at different phase points during the cardiac
cycle, and presented for six distinct points as shown in Fig. 3. For
statistical convergence, 100 measurements were found to be sufficient for each time instant, in order to generate a stable velocity
vector map.
2.3.1. Post-processing of the data
2.3.1.1. Image processing. After minimum background subtraction,
Gaussian smoothing, intensity normalization, and masking [41],
the recorded image pairs were analyzed by a two-frame FFT crosscorrelation algorithm (DynamicStudio, Version 2.20.18, Dantec
Dynamics, Denmark) with interrogation areas of 32 × 32 pixel2 ,
overlapped by 50% on each side, to yield the local displacement
vector for each interrogation area [42]. This method provided a total
of 7326 velocity vectors for an area of 13 mm × 9 mm. Validation of
this PIV method is presented in the Appendix.
2.3.1.2. Derivation of WSS. The velocity field obtained by PIV was
used to estimate the rate-of-shear ()
˙ along the wall from the near
wall velocity gradient, and thereby the WSS, using Eq. (1):
WSS = du
d
(1)
where is the dynamic viscosity of the blood analogue, u is the
component of the velocity vector tangential to the wall, and is
the direction normal to the wall. The – coordinate system was
utilized for the ease of calculation and presentation of the results.
As shown in Fig. 4, the origins of coordinates 1 to 3 were chosen
on the heel, toe, and artery bed of the anastomosis, respectively.
A computer code, developed in-house, was utilized to interpolate the near-wall velocities within the viscous boundary layer
based on the finite element shape functions [43]. Briefly, the discrete pixel wall location for each data set was extracted (no wall
movement was detected in this study); by marching on these
wall points, the slope of each wall section, located between two
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Gear pump
interface unit
Compliance
chamber
Flow meter
Camera
Calming
chamber
AC
Laser
Computer
st
Te
DC
ct
se
n
io
Needle valve
Fluid circuit
Electrical circuit
Flow direction
Back pressure tank
and reservoir
Fig. 2. Schematic of the mock circulation loop and PIV system.
neighboring wall points, was calculated. Then, on the perpendicular bisector of each wall section, two points with an increment of
0.13 mm (16 pixels) between the subsequent points were located
within the flow boundary layer, and the tangential components
Systolic phase
10
Average velocity (cm/s)
9
Diastolic phase
t2
8
3. Results
7
6
t1
5
3.1. Comparison of the velocity profiles in the anastomotic region
of the models
t3
4
3
2
t4
1
t5
0
0.1
-1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
t6
-2
Time (s)
Fig. 3. The graft velocity waveform; labels indicate the times at which the flow field
and WSS are studied, namely, systolic mid-acceleration (t1 ), peak flow rate (t2 ),
systolic mid-deceleration (t3 ), end systole (t4 ), when the graft average velocity has
just become negative (t5 ), and peak reversed flow (t6 ).
ξ1
η3
of the velocity vectors (with respect to the corresponding wall
section) were interpolated at these points based on the three nearest adjacent velocity vectors, using finite element shape functions.
Subsequently, velocity gradients were calculated from a surface fit
of the velocity using generalized multiquadratic radial basis functions, optimized to minimize the surface roughness of the resultant
fit [44], assuming no-slip condition at the wall. Validation of this
WSS estimation method is presented in the Appendix.
η1
ξ3
η2
ξ2
ξ1
η3
η1
η2
ξ2
ξ3
Fig. 4. The origin and direction of – coordinate system at (1) heel, (2) toe, and (3)
artery bed of anastomosis.
The measured velocity fields in the symmetry plane at the anastomotic region of the models were substantially similar to those
which had been obtained earlier by our computational simulations
[38]; hence, for brevity, the flow fields are not discussed here. However, comprehensive presentation of the velocity vectors (at the six
time points shown in Fig. 3) and discussion of the flow fields are
provided in online Supplementary Material. Accordingly, the very
advantages which had earlier been observed in the flow fields of
the SQA graft design were witnessed in the present experimental
results too. For instance, the flow at the distal ETS anastomosis of
the SQA model during the acceleration phase was smooth, without
any vortex formation or impingement of flow on the artery bed (due
to the partial flow from the STS anastomosis along the coronary
artery changing the velocity components of the ETS anastomosis
flow toward the axis of the coronary artery rather than to the artery
floor), unlike the conventional ETS model, as shown in Fig. 5 for the
peak flow rate (t2 ). Also, the vortices and stagnation point on the
artery bed were eliminated at the STS anastomosis of the SQA model
(due to the flow circulation in the vascular loop of the SQA design)
during deceleration and reversed flow phases, as demonstrated in
Fig. 6 for the time when the net flow rate just became negative (t5 ).
These are positive features of the SQA design, as a stagnation point
is associated with low-magnitude-high-oscillatory WSS condition
F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
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Fig. 5. Measured flow field and velocity vectors in the anastomotic region of the models at the peak flow rate (time t2 ); (a) STS component of the SQA model, (b) ETS
component of the SQA model, (c) parallel STS model, and (d) conventional ETS model. Again, a vortex is present in the heel region of the conventional ETS model with the
blood flow impacting the artery bed, whereas the flow at the ETS component of the SQA model is smooth and devoid of any vortex or impact on the artery floor.
on the artery bed which is prone to enhancement of atherogenesis
[12] and IH formation [13], and elimination of vortices indicates a
higher WSS on the artery bed and lower particle residence time in
the SQA model than those in the parallel STS model. It is to be noted
that enhanced particle residence time may alter the mass transport of atherogenic substances to the vessel wall and increase the
probability of deposition of platelets and macrophages, resulting in
intimal thickening (IT).
3.2. Comparison of the WSS distribution in the anastomotic
region of the models
The local WSS was evaluated at the heel, toe, and coronary artery
bed of the anastomosis in all the models at the six time instants, as
shown in Figs. 7–10, wherein the WSS distribution at the heel, toe,
and artery bed of the anastomosis is shown, respectively, in panels
(a), (b), and (c).
3.2.1. WSS distribution in the heel region of the ETS anastomoses
Comparison of the WSS distribution in the heel region of the
ETS component of the SQA design with that of the conventional
ETS model (Figs. 8a and 10a) indicated that the peak value of WSS
was slightly reduced on the graft inner wall ( 1 < 0 mm) of the SQA
design as compared to the conventional ETS model (for instance
from 3 to 2 Pa at t2 ). This was due to the lower flow rate passing through the graft toward ETS anastomosis in the novel design
compared to the conventional ETS model, since part of the flow was
diverted into the coronary artery at the STS anastomosis of the SQA
design. However, the WSS at the heel of the ETS anastomosis of the
SQA model within the coronary artery ( 1 > 0 mm) was considerably
increased in magnitude compared to the conventional ETS model.
This was because in the conventional ETS model, the blood was
almost stagnant in the proximal segment of the coronary artery,
while in the novel SQA design model the partial flow from the STS
component through the coronary artery increased the magnitude
of WSS at this location (note that the change in the sign of the WSS
is due to the definition of the coordinate system and the location
of the origin at the heel region of the models with respect to the
flow directions). It is to be noted that a number of studies have
indicated a strong relationship between the localized distribution
of low-WSS and IT development; as a result, this increase of WSS
magnitude at the heel of the ETS anastomosis is a positive feature
of the SQA design.
3.2.2. WSS distribution in the toe region of the ETS anastomoses
At the toe of the ETS anastomosis of the SQA model and the
conventional ETS model, the qualitative distribution of WSS was
similar, as shown in Figs. 8b and 10b. There was a sharp increase
in the WSS magnitude to its peak at the toe, and then a rapid drop
to form an apex, continued by a slow increase to an asymptotic
value further downstream along the toe within the coronary artery
mainly during the forward flow phases. The peak value of the WSS
at the toe during the peak flow rate (t2 ) was higher in the conventional ETS model (44 Pa) than that in the ETS component of the SQA
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Fig. 6. Measured flow field and velocity vectors in the anastomotic region of the models at time t5 , when the graft average velocity has just become negative; (a) STS
component of the SQA model, (b) ETS component of the SQA model, (c) parallel STS model, and (d) conventional ETS model. There are remarkably larger vortices in the
conventional ETS and parallel STS models, compared to those in the corresponding ETS and STS components of the SQA design model.
model (34 Pa). This represents a more moderate distribution of WSS
(with lower spatial and temporal gradients) at the toe of the ETS
component of the SQA model, which may reduce the probability
of atherosclerotic lesion development, since it has been postulated
that the progress of atherosclerotic lesions and growth of plaque
formation occurs mainly in regions of extreme (either maxima or
minima) WSS [45,46].
velocity profile was skewed toward the artery floor, inducing larger
velocity gradients on the floor side. However, this phenomenon was
less pronounced in the SQA model (Fig. 8) than in the conventional
ETS model (Fig. 10), due to the partial flow from the coronary artery
changing the direction of the graft flow toward the coronary artery
axis and reducing the velocity profile skew toward the artery bed
at the ETS component (as shown earlier in Fig. 5).
3.2.3. WSS distribution on the coronary artery bed of the ETS
anastomoses
On the coronary artery bed opposite to the heel of the ETS
anastomosis (−2 ≤ 3 ≤ 3 mm), the WSS was slightly higher in magnitude in the SQA model than that in the conventional ETS model,
as shown in Figs. 8c and 10c, respectively. This is due to the fluid
flowing through the coronary artery segment between the two
anastomoses of the novel SQA model (contrasted with the flow circulation in the conventional ETS model). This moderate increase in
the WSS magnitude, conjugated by the absence of the stagnation
point on the artery bed in the ETS anastomosis of the SQA model
(as mentioned earlier) can reduce the risk of IT and atherosclerosis development at this critical location. On moving downstream
along the artery bed, the WSS magnitude was increased, reaching its peak value opposite to the toe of the ETS anastomosis, as
shown in Figs. 8c and 10c, and then, was reduced to an asymptotic
value in both models (not shown here). These values of WSS at the
downstream of the artery bed in the ETS anastomosis of the conventional ETS model ( 3 ≥ 6.5 mm) were higher than those along
the toe of the anastomosis within the coronary artery ( 2 ≥ 1 mm in
Figs. 8b and 10b) during the forward flow phases, indicating that the
3.2.4. WSS distribution in the heel region of the STS anastomoses
Upon comparing the distribution of WSS in the STS anastomosis of the SQA model and the parallel STS model, shown in
Figs. 7a and 9a respectively, the qualitative distribution of the WSS
was mostly similar in the heel region of the STS anastomosis of
the two models. However, at time t5 the WSS in the graft over the
heel region ( 1 ≤ 0) was positive (with respect to 1 coordinate at
the heel, shown in Fig. 4) in the parallel STS model, while it had
negative values in the STS component of the SQA model. This was
consistent with the opposing flow directions over the heel region
in the two models at this time instant (as shown in Fig. 6).
3.2.5. WSS distribution in the toe region of the STS anastomoses
At the toe of the STS anastomosis of the two models, the distribution of WSS was about the same. However, at times t4 and t5 ,
the magnitude of WSS on the graft and the coronary artery walls
had different distributions in the two models, as demonstrated in
Figs. 7b and 9b. In the STS component of the novel SQA model, due
to the strong backflow through the coronary artery at these time
instants, the WSS magnitude was higher on the coronary artery
wall at the toe of the anastomosis ( 2 ≥ 0) than on the graft wall
F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
(a)
1239
4
3.5
WSS (Pa)
3
2.5
t1
2
t2
1.5
t3
1
t4
0.5
t5
0
t6
-0.5
-1
-1.5
-2
-1.5
-1
-0.5
0
ξ1
(b)
0.5
1
1.5
(mm)
3
WSS (Pa)
2
1
t1
0
t2
t3
-1
t4
-2
t5
-3
t6
-4
-5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
ξ2 (mm)
(c)
2.5
2
1.5
t1
t2
WSS (Pa)
1
t3
0.5
t4
0
t5
-0.5
t6
-1
-1.5
-2
0
2
4
ξ3
6
8
10
(mm)
Fig. 7. WSS distribution in the STS component of the SQA model, along the (a) heel, (b) toe, and (c) artery bed.
at the toe ( 2 ≤ 0), where a small recirculation zone resulted in a
low WSS magnitude at time t5 (as shown in Fig. 6). However, in the
parallel STS model, owing to the large vortices within the coronary
artery, the WSS magnitude was lower on the artery wall at the toe
( 2 ≥ 0) than on the graft wall ( 2 ≤ 0) on account of the higher flow
rate in the graft (than in the coronary artery).
3.2.6. WSS distribution on the coronary artery bed of the STS
anastomoses
On the coronary artery bed, during the acceleration phase and
the peak flow, the magnitude of WSS was higher in the parallel STS
model than that in the STS anastomosis of the SQA model (e.g., 5
versus 2 Pa at 3 = 8.8 mm at time t2 ), as shown in Figs. 9c and 7c,
respectively. During the deceleration phase (t3 ), in the parallel
STS model (Fig. 9c), the WSS magnitude was generally low, with
a region of negative values at the middle of the bed opposite to
the anastomosis junction (−0.9 ≤ 3 ≤ 6.2 mm), indicating that the
shear was directed proximally. This was due to the large vortex, formed in the coronary artery at this time instant (see the
online Supplementary Material). The zero value of WSS at point
3 = 6.2 mm corresponded to the stagnation point, created just distal to the vortex. However, in the STS anastomosis of the SQA model
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Fig. 8. WSS distribution in the ETS component of the SQA model, along the (a) heel, (b) toe, and (c) artery bed.
(Fig. 7c) at this time (t3 ), the results showed fluctuations in the
WSS values on the artery bed. This could possibly be due to the
inaccuracy inducted into the PIV results, caused by scattering of
the laser light sheet due to the unevenness of the inner surfaces
of this fabricated model at this particular region. Another possible
reason for this inaccuracy can be the accumulation of some seeding particles in this low-velocity region, which would induce errors
into the velocity measurement, and consequently, the WSS calculation. These oscillations also resulted in fluctuations in the sign
of WSS, due to the very small (nearly zero) velocity magnitude at
this time (t3 ). Some fluctuations in the magnitude of WSS could
also be observed in this model at other time instants. At time t5 ,
the WSS magnitude on the artery bed of the parallel STS model
(Fig. 9c) was much lower than that in the STS anastomosis of the
novel SQA model (Fig. 7c), due to the recirculation zones and low
velocity regions created within the coronary artery in the parallel STS model (as shown in Fig. 6c). However, during the backflow
phase (t6 ), both models showed similar WSS distributions.
F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
1241
Fig. 9. WSS distribution in the parallel STS model, along the (a) heel, (b) toe, and (c) artery bed.
4. Discussion
A novel CABG coupled SQA model has been designed and
fabricated, and its flow fields and WSS distributions were studied and compared to those of the conventional ETS and parallel
STS anastomoses. PIV measurements were utilized in this investigation to complement the previous computational modeling of
the blood flow through this novel CABG design [38,39], from
which more complex HPs had been derived to quantify hemodynamics in the novel CABG coupled SQA design models with
a variety of the design parameters, including the anastomotic
angle at the ETS component of the SQA design, the distance
between the two (STS and ETS) anastomoses, and the out-of-plane
grafting.
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F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
Fig. 10. WSS distribution in the conventional ETS model, along the (a) heel, (b) toe, and (c) artery bed.
4.1. Features of the coupled SQA graft design
(i) During the acceleration and early deceleration phases the flow
at the ETS anastomosis is smooth as part of the graft flow
(which is diverted into the coronary artery at the STS anastomosis of the SQA model) lifts up the flow coming from the
graft at the ETS anastomosis and directs it smoothly into the
coronary artery. By this means, there is no impact on the
artery bed and no flow recirculation at the heel. It is to be
noted that the flow impact on the artery floor is believed
to be injurious to the endothelium and a contributing factor to graft failure [14], and a stagnation point is always
associated with a low WSS and high spatial WSS gradient
region, which may contribute to IT and atherosclerosis development, and may increase the risk of aggregation of red blood
cells [12,13].
F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
1243
Experiment
1.0
Theory
t/T=0.133
V (m/s)
0.8
t/T=1
0.6
0.4
0.2
0.0
0.001 5
t/T=0.856
t/T=0.75
0.001 0
0.000 5
0.000 0
0.000 5
0.001 0
0.001 5
0.000 5
0.001 0
0.001 5
r (m)
0.00 8
V (m/s)
0.00 6
t/T=0.75
0.00 4
0.00 2
0.00 0
0.00 2
0.00 4
0.001 5
0.001 0
0.000 5
0.000 0
r (m)
Fig. 11. Comparison of the PIV measurement results with the analytical Womersley solution for a sinusoidal flow in a straight tube for different phases of the flow cycle.
Lower panel shows the up-scaled graph at t/T = 0.75 for a better illustration of the velocity profile.
(ii) During the late deceleration phase at the distal anastomosis,
part of the flow goes back to the STS anastomosis through
the coronary artery. There, it lifts up the flow coming into the
STS anastomosis junction from the graft, and directs the flow
smoothly back into the graft, thereby, avoiding the formation
of stagnation point and vortex in the STS anastomosis region,
as demonstrated in Fig. 6. It is to be kept in mind that a vortex
is always associated with low WSS and high particle residence
time which result in platelet activation and IT [10,11,47,48].
(iii) WSS distribution is more moderate in the novel SQA model,
especially at the ETS anastomosis, as compared with the
conventional ETS model; this can reduce the chance of IH
development.
(iv) Moreover, this novel coupled STS-ETS SQA design provides a
spare route for the blood flow to the coronary artery, in order
to avoid re-operation in case of re-stenosis in either of the
anastomoses.
Although this novel design does involve one additional anastomosis (and prolonged operation time), the distinct advantages
observed in the flow field and WSS distribution in this coupled SQA
design may motivate the use of this novel design over conventional
ETS anastomosis.
Also, a recent study on topology optimization with application
to bypass graft geometries [49] has shown that among the different investigated geometric models, the optimized bypass graft
has two outlet channels, resembling our proposed novel sequential anastomoses design. This optimized model has shown the best
performance among the studied models in terms of WSS, with a relatively uniform WSS distribution and the smallest maximum value
of WSS. The study has referred to our proposed novel sequential
anastomoses design and concluded that their topology optimization method leads to this sequential anastomotic design too.
5. Conclusion
A novel CABG anastomotic configuration has been designed, and
its flow fields and WSS distributions were investigated by utilizing
PIV method. This in vitro investigation complements the previous computational studies, and constitutes another necessary step
toward the clinical application of this novel coupled SQA design.
So far, an innovative CABG design has been provided and its hemodynamic benefits have been validated (by this in vitro experiment
and the earlier computational studies [38,39], as well as by some
topology optimizations [49]). At this point and prior to the clinical
adoption of this novel design, in vivo animal trials are warranted, in
order to investigate the biological effects and overall performance
of this anastomotic configuration in vivo.
Funding
None.
Ethical approval
None.
Conflict of interest
The authors affirm that there are no financial and personal relationships or involvement with any commercial organization that
could inappropriately influence or bias the present manuscript.
Appendix.
A.1. Validation of PIV method
In order to validate the accuracy and precision of the PIV measurements, a comparison was conducted between the PIV results
for a fully developed sinusoidal flow (Q = 140(1 + Sin (4.2t) ml/min)
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F. Kabinejadian et al. / Medical Engineering & Physics 36 (2014) 1233–1245
Table 2
Comparison of the WSS values obtained by different methods.
t/T
0.2
0.75
0.856
1
Theory
Estimation (based on experimental PIV data)
Estimation (based on theoretical data points)
8.56
12.73
7.79
−0.03
−0.04
−0.02
1.25
1.94
1.09
5.15
6.98
4.59
in a straight tube (with an inner diameter of 3 mm) and the corresponding Womersley solution [50].
As shown in Fig. 11, a good qualitative match was observed
between the experimentally obtained and analytical velocity
profiles at different phases of the flow cycle. The quantitative comparison of the results revealed an average relative difference of 8.6%
in the velocity magnitude between the two sets of data. This reasonable discrepancy confirmed that the accuracy of the PIV results
was acceptable.
A.2. Validation of the WSS estimation method
In order to validate the accuracy of the WSS estimation method,
a comparison was conducted between the WSS values estimated
from PIV results for the abovementioned fully developed sinusoidal
flow in a straight tube (with an inner diameter of 3 mm) and the
corresponding analytically calculated WSS values obtained from
the Womersley solution at the very time instants for which the PIV
results were validated (i.e., t/T = 0.2, 0.75, 0.856, and 1, as shown in
Fig. 11).
Moreover, the WSS calculation method was applied to data
points obtained from the analytical solution (rather than the PIV
data) at the abovementioned time points, and compared with
those obtained from the analytical solution and from the PIV data
(Table 2). The WSS values obtained from the analytical data points
do not include (and are not influenced by) the PIV measurement
error; hence, they can indicate the accuracy/error of the WSS calculation method. Whereas the WSS values obtained from the PIV
results are highly influenced by the near-wall error of the PIV measurement results.As shown in Table 2, the WSS values estimated
based on the analytical data points showed a good agreement with
the analytically calculated WSS values with an error of <13% (except
for t/T = 0.75 with an error of <33%, which was mainly due to the
small magnitude of the WSS at this time point, resulting in higher
percentage of error even for small differences between the two sets
of data). However, the WSS values estimated based on the PIV data
(which include the near-wall PIV measurement errors) had relative
errors of up to about 55% with respect to the analytically calculated
WSS values. Nevertheless, the trend of the WSS variations was identical among the different sets of data which made the comparison
of the WSS variation among different geometric models valid in the
present study.
Appendix B. Supplementary data
Supplementary data associated with this article can be found,
in the online version, at http://dx.doi.org/10.1016/j.medengphy.
2014.06.024.
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