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c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
journal homepage: www.intl.elsevierhealth.com/journals/cmpb
Numerical analysis of coronary artery bypass grafts: An over
view
Amal Ahmed Owida, Hung Do ∗ , Yos S. Morsi
Biomechanics and Tissue Engineering Group, Swinburne University of Technology, Hawthorn, Melbourne, Victoria, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
Arterial bypass grafts tend to fail after some years due to the development of intimal thick-
Received 30 March 2011
ening (restenosis). Non-uniform hemodynamics following a bypass operation contributes
Received in revised form
to restenosis and bypass failure can occur due to the focal development of anastomotic inti-
19 September 2011
mal hyperplasia. Additionally, surgical injury aggravated by compliance mismatch between
Accepted 10 December 2011
the graft and artery has been suggested as an initiating factor for progress of wall thickening along the suture line Vascular grafts that are small in diameter tend to occlude
Keywords:
rapidly. Computational ﬂuid dynamics (CFD) methods have been effectively used to simu-
Coronary artery bypass grafts
late the physical and geometrical parameters characterizing the hemodynamics of various
Numerical simulation
arteries and bypass conﬁgurations. The effects of such changes on the pressure and ﬂow
Wall shear stress
characteristics as well as the wall shear stress during a cardiac cycle can be simulated.
Oscillating shear index
Recently, utilization of ﬂuid and structure interactions have been used to determine ﬂuid
Hemodynamic
ﬂow parameters and structure forces including stress and strains relationships under steady
Intimal hyperplasia
and transient conditions. In parallel to this, experimental diagnostics techniques such as
Laser Doppler Anemometry, Particle Image Velocimetry, Doppler Guide wire and Magnetic
Resonance Imaging have been used to provide essential information and to validate the
numerical results. Moreover, clinical imaging techniques such as magnetic resonance or
computed tomography have assisted considerably in gaining a detailed patient-speciﬁc picture of the blood ﬂow and structure dynamics. This paper gives a review of recent numerical
investigations of various conﬁgurations of coronary artery bypass grafts (CABG). In addition,
the paper ends with a summary of the ﬁndings and the future directions.
© 2011 Elsevier Ireland Ltd. All rights reserved.
1.
Introduction
Our current understanding indicates that the main cause of
the initiation of restenosis is the unfavorable ﬂow conditions
that can occur in and around the anastomosis of coronary
artery bypass grafts (CABG). Moreover, the main factors that
attribute to such adverse hemodynamics conditions include
the geometry of the graft/artery junction, the blood rheology,
graft to artery diameter ratios and the morphology of the graft
∗
surface [1,2]. However, the restenosis formation is normally
characterized by unsteady shear stress, recirculation regions,
pulsatile stress and graft deformations [3]. Moreover, surgical injury is aggravated by compliance mismatch between the
graft and artery which has been suggested as the initiating factor for the progress of intimal thickening around the suture
line of CABG [4,5]. Vascular grafts that are small in diameter tend to occlude rapidly due to the high shear stresses
created on the wall of the arteries; as such high shear conditions may over-stimulate platelet thrombosis, causing a total
Corresponding author. Tel.: +61 3 9214 4336.
E-mail address: [email protected] (H. Do).
0169-2607/$ – see front matter © 2011 Elsevier Ireland Ltd. All rights reserved.
doi:10.1016/j.cmpb.2011.12.005
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Table 1 – Computational ﬂuid dynamic.
Providers
ANSYS
ANSYS
CD-adapco
CD-adapco
COMSOL
Technalysis
Flow Science
Blue Ridge Numerics
OpenCFD
Softswares
CFX
FLUENT
STAR-CCM+
STAR-CD
COMSOL
Passage Software
FLOW-3D
CFdesign
OpenFOAM
occlusion of the artery. Too large diameter vascular grafts, on
the other hand, tend to stimulate abnormally low wall shear
stress which may in return initiate intimal thickening [6].
In recent years, computational ﬂuid dynamics (CFD) has
been widely used as an effective numerical tool to investigate physical and geometrical parameters that characterizing
the hemodynamics of various conﬁgurations of CABG. With
CFD, the pressure and ﬂow characteristics, as well as the
wall shear stress (WSS), for steady and cyclic ﬂows could be
effectively analyzed. Utilization of CFD in biomechanics and
hemodynamic researches is now widely accepted as a better
alternative to in vitro and in vivo measurements which can be
very expensive and time consuming [7]. Still, there is always a
need to obtain a good quantitative experimental data for validation and veriﬁcation of the numerical results. Combining
CFD with experimental and imaging techniques has been used
widely to analyze the hemodynamic of the bypass and graft
junction [2,8,9]. Utilization of these two techniques allows
effective determination of factors such as blood ﬂow ﬁelds,
wall shear stress and gradients, deformation of the artery
and graft junction and the degree of compliance mismatch
[2,10,11].
Although in literature there are numerous publications
related to hemodynamics of CABG and the factors that inﬂuence the development of intimal hyperplasia, there is still
however, a lack of a completed guideline and up-to-date
trend in the ﬁeld of myocardial revascularization. In addition, there is still insufﬁcient knowledge of the ﬂuid structure
interactions and compliance mismatch, particularly for small
diameter arteries [7,8,12–14]. This paper ﬁrst introduces the
numerical analysis techniques that are currently used followed by a discussion of the recent developments of CABG
research and summary of the future areas of research.
2.
Numerical analysis techniques adapted
2.1.
Solution methods for ﬂuid ﬂow
The application of CFD in engineering and hemodynamic
research has been well accepted and used in conjunction with
physical measurements, and pure theoretical approaches. To
meet the increasing demand for CFD various commercial
packages have been introduced in the market and these are
tabulated in Table 1. The choice of any package depends on the
physical problem in hand and the degree of accuracy required.
In general, development of computational numerical techniques is based on the application of three fundamental
principles: (1) conservation of mass, (2) Newton’s second law,
(rate change of momentum =
of forces) and (3) conservation of energy. These fundamental principles can then be
expressed in terms of mathematical equations which can be
calculated and described as numbers and the ﬁnal numerical
results are then obtained in space (two and three dimensional
co-ordinations) and time [15].
2.1.1.
Governing equations
Generally, a simpliﬁed mathematical model is used by
researchers for both steady and/or pulsatile ﬂows where some
or all of the following assumptions are adopted:
• The blood is homogeneous, non-deformable, and does not
interact chemically with the ﬂuid.
• The blood is Newtonian; its density does not depend on
pressure variations, but only on the variations of temperature.
• The temperatures of the artery and the blood are assumed
to be identical with a thermodynamic equilibrium.
• No heat sources or sinks exist in the ﬂuid; thermal radiation
and Rayleigh dissipation are negligible.
• The natural convection effect is considered by using the
Boussinesq approximation, where the temperature inﬂuence on the density is considered only in the term
describing the body force, while in all the other terms the
density is assumed to be constant.
Taking these assumptions into consideration, the
Navier–Stokes equations for time dependent incompressible
viscous ﬂuid are given by [16]:
Continuity equation :
∇ ·u=0
Momentum equations :
∂u
+ u · ∇u
∂t
(1)
= −∇p + ∇ 2 u
(2)
where is the ﬂuid density [kg/m3 ], is the viscosity [kg/m s],
u is the ﬂuid velocity vector in three dimensions [m/s], and p
is the pressure [N/m2 ].
2.1.2.
Boundary conditions
Although in literature there are numerous investigations dealing with steady and pulsatile ﬂows simulations using various
waveforms as input conditions [7,8,12], an exact comparison of the ﬁndings of these studies is difﬁcult as there is
no consistency in the input parameters and the physiological
anastomosis geometries used by each investigation. Table 2
shows the list of boundary conditions used by various authors.
The effects of non-Newtonian assumption on the accuracy
of the results of steady and unsteady ﬂows were found to be
negligible [17–19]. In any case, most researchers used the blood
ﬂow velocity waveform taken from in vivo measurements as
input boundary conditions. Generally, Magnetic Resonance
Imaging and Doppler ultrasound method are the most common techniques used in obtaining in vivo blood ﬂow data
[20–23]. These experimental data are then used for validation
of numerical analysis and quantiﬁcations of the hemodynamics of various CABG. For example, Bertolotti et al. [24] applied
the instantaneous velocities data obtained from patients to
691
x
NonNewtonian
material
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Constant
outlet
pressure
analyze the ﬂow in two different arteries geometries. Similarly,
Sankaranarayanan et al. [25] studied an out-of-plane CABG
model and used CT data obtained from the aorta and from left
anterior descending coronary as input boundary conditions.
Reynolds number is used to determine the effect of turbulence of the blood ﬂow inside an artery. The general consensus
is that for a pipe ﬂow turbulence occurs at Reynolds number
equal to or higher than 2000. However, Young and Tsai [26]
observed a transition to turbulent at Reynolds number around
140. In addition, Ku [6] pointed out that the pulsatile blood ﬂow
inside the body from higher to lower pressure was not fully
developed at some regions of arteries. Still, the recent numerical and experimental study by Zhang et al. [9], demonstrated
that the effect of turbulence is quite small and as such the
laminar ﬂow assumption is valid.
Beside Reynolds number, nondimensional parameter
Womersley number (˛) is normally used to correlate between
the unsteady and viscous forces [21]. Based on the value of
Womersley number one can determine whether the viscous
forces are dominant i.e. the velocity proﬁles are parabolic or
less viscous forces are dominant i.e. the proﬁle is ﬂat. Note as
reported by Ku et al. that the role of non Newtonian of blood is
important to factor in and could not be neglected [21]. In addition, Ku [6] also mentioned that for medium sized artery, with a
range of Reynolds numbers between 100 and 1000 or Womersley numbers between 1 and 10 respectively, the assumption of
rigid artery wall is acceptable as the role of elasticity in artery
is known to be very small.
Since blood’s rheological properties could vary from one
person to another, it is impossible to consider the effects of all
parameters involved in one model. Normally, however, only
the shear rate is incorporated in the analysis as the main factor
of the blood’s viscosity [18].
Generally, the following correlations are normally used:
For pulsatile ﬂows, Womersley velocity proﬁles are computed and imposed at the inlets where ˛ is deﬁned as:
˛=
x
x
x
x
x
Transient
x
x
x
x
x
x
x
x
Womersley parameter :
D
2
ω
(3)
and
C=
x
x
x
Do et al. [7]
Freshwater et al. [2]
Qiao et al. [27]
Fan et al. [28]
Sankaranarayanan et al. [25]
Vimmr and Jonasova [18]
Chen et al. [29]
Kouhi and Morsi et al.
Kim et al. [30]
Bertolotti and Deplano [17]
Lee et al. [19]
Zhang and Chua et al. [9]
Politis et al. [31]
Politis et al. [32]
x
x
Compliance :
x
Re =
VDH
(4)
x
x
x
x
x
x
Reynolds number :
Steady
Authors
Table 2 – Different types of boundary conditions for CFD simulation.
Newtonian
ﬂuid
x
x
Power Law, Carreau,
Walburn–Schenck,
Casson, Generalized
Power Law model
Non-Newtonian
ﬂuid (shear
thinning ﬂuid)
x
x
x
x
x
x
x
x
x
x
x
x
x
x
No-slip
condition
x
x
x
x
x
x
x
Rigid
artery
wall
x
Young
Modulus
Fluid structure
interaction (FSI)
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D
P×D
(5)
where C is compliance, D is step change in diameter, P is
step change in pressure, D is the diastolic diameter recorded
for each pressure step.
Wall Shear Stress (WSS) :
w
=
du
dy
(6)
Time Average Wall Shear Stress (TAWSS):
TAWSS =
1
T
T
w
0
dt
(7)
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Table 3 – Meshing technique [33].
Shape of element
Types of meshing
2D
Triangle
Quadrilateral
Tetrahedral
Hexahedral
Surface meshing
3D
2D, 3D
⎛
Oscillating shear index (OSI) :
OSI = 0.5 ⎝1 −
T
0
T
0
w dt
w
⎞
⎠ (8)
dt
where
•
, are the dynamic viscosity [kg/m s] and density [kg/m3 ]
of the ﬂuid respectively;
• DH is the hydraulic diameter [m2 ];
• ω is the pulse rate [rad/s]
Depending on the problem in hand all or some are used to
examine the hemodynamics and structure forces.
Fig. 1 – Flow chart of the ﬂuid structure interaction analysis.
2.1.3.
Mesh generation
In CFD analysis, it is well recognized that the accuracy of
numerical results are directly related to the quality of mesh
adopted. In fact, mesh independent test is regularly used to
verify the accuracy of the numerical results. There are many
methods of meshing available in literature to optimize the
number of elements, accuracy and time required for the simulation [33].
Although there are several types and shape of meshing elements (illustrated in Table 3), the shape and distribution of the
elements automatically follow meshing algorithms. In addition, the process of meshing can be deﬁned either by surface
or volumes mapping which are in turn subdivided into triangle, quadrilateral, tetrahedral and hexahedral shapes, etc.
[33].
2.2.
Solution methods for ﬂuid structure interaction
In the last few decades the numerical computations of ﬂuid
structure interaction (FSI) approach as illustrated by Fig. 1,
have gained considerable popularity and have been applied
to various types of cardiovascular hemodynamics problems
[14,34,35]. In cardiovascular ﬁelds typical compliant structures
like blood vessels, artery junctions, heart and heart valves
present a huge challenge in analyzing the structure deformation and the blood ﬂuid ﬂow inside them as the heart beats.
For bypass grafts and arteries the determination of the geometry, behavior of the tissue, as it is tethered to and supported
by surrounding tissue and organs as well as the determination
of the correct input boundary conditions are challenging
Until recently most researchers avoided the above mentioned complexity, and a rigid artery wall assumption was
adopted. However, this was an unjustiﬁed assumption since
under pulsatile conditions, the structure and deformation of
artery wall is affected by the cyclic hemodynamics forces.
However„ rigid artery assumption maybe valid to a certain
degree for small arteries (<6 mm) but not for larger arteries
such as the aorta as the degree of deformation and adaptations of these vessels are signiﬁcant. Hence accurate analysis
should incorporates structure forces as well as the hemodynamic forces. In addition, even after few decades of research,
there is a need and high demand to demonstrate the clinical
relevance of the full hemodynamics and the structure interactions [36].
Traditionally ALE (Arbitrarily Lagrangian–Eulerian) formulation is the better-known method for FSI problems [37]. Such
method requires continuous updating of the ﬂuid mesh to
account for the motion of the structural domain. In general,
the standard practice for this type of problem is to formulate the geometrically non-linear structure in a Lagrangian
description, while the ﬂuid is expressed in an Eulerian way
due to the presence of convective terms. Note that the presence of convective terms in the case of moving boundary
ﬂow problem increases the numerical sophistication in the
Eulerian description, whereas the Lagrangian description for
the moving structural boundary is straightforward. Although
ALE formulations are shown as an expensive technique and
has limited coupling when used with large vascular models,
that require continues updating of the geometry, signiﬁcant
progress has been made in recent years in solving coupling
blood ﬂow problems in deformable domains using ALE. Still,
other formulation techniques have been developed for FSI
such as: the immersed boundary method which based on the
wall deformability and transpiration techniques based on linearization principles [36].
In a study of Figueroa et al. [36], a coupled momentum
method and a modiﬁed Navier–Stokes equations have been
used for investigating the deformability of the wall domain
surrounding the ﬂuid. However, it was stated that in order
to further improve the simulation of wave propagation in
three-dimensional models of the vasculature, Womerseley’s
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
elastic wave theory and traction conditions need to be used as
input boundary conditions.
To determine the effect of the structure domination on
the hemodynamics results, Valencia and Villanueva [38] have
carried out a FSI investigation in a non-symmetric stenotic
arteries and in eight stenotic artery models with rigid walls.
The authors reported that effects of the inlet boundary condition of pressure were found to be critical. However, the
assumption of rigid walls stenotic artery was found to be unrealistic, as the artery is considerably dilated and compressed in
one cardiac cycle. Moreover, the authors found that the geometry and severity of the stenosis had signiﬁcant effects on the
recirculation length, wall displacement, effective wall stress,
and distribution of low-density lipoprotein (LDL) concentration.
Donea et al. [37] argued that the use of ALE technique can
be justiﬁed for those simulations that involve mesh generation within a considerable time span. However, in the case
of large deﬂection problem, some interpolation techniques to
update the variables for newly generated mesh are needed.
However, the updated mesh may introduce an artiﬁcial diffusivity, which is a major concern regarding the applicability
of ALE in these type of circumstances. Therefore a ﬁctitious
domain (FD)/mortar element (ME) technique has been proposed [39], where ﬂuid motion is structured using a ﬁxed mesh
in an Eulerian setting and a Lagrangian formulation for the
solid wall. In FD method, the velocity constraint associated
with the rigid internal boundaries is imposed by means of the
Lagrange multiplier, while the ME method allows coupling of
domains with dissimilar element distributions [40]. The major
advantage of FD/ME method is that it does not require any
updating of the mesh of the ﬂuid domain. However, updating
of mesh becomes inevitable for very large deﬂection problem
[41].
In our recent work, we have used ALE technique to
simulate the valve deformation that arises from FSI. The analysis was carried out at various initial steps for a range of
Reynolds numbers and the results so far are promising. In
addition, a 3D transient FSI has been developed by using
the ALE kinematical description together with an appropriate ﬂuid grid. The analysis was carried out at various initial
steps for a range of Reynolds numbers and physiological
conditions [35].
The numerical solution of FSI problems is a challenging one, especially when system under consideration is 3D
with large degree of deformation. CABG junction is a typical
example, where the motion of thin-walled, artery structure is
maneuvered by the motion of a ﬂuid. The large deformation
of the physical (structural) boundary due to the ﬂuid forces
and material non-linearity increases the numerical difﬁculty
to many folds. The geometrically non-linear structure is usually formulated in a Lagrangian description, while the ﬂuid
is often expressed in an Eulerian way due to the presence
of convective terms. The presence of convective terms in the
case of moving boundary ﬂow problem increases the numerical sophistication in the Eulerian description, whereas the
Lagrangian description for the structural moving boundary is
straight forward. However, due to the large ﬂow distortions
and structural deformations, element entanglement supports
the use of the ALE technique.
2.3.
693
Validations of numerical simulations
As pointed out above, it is well recognized now that the ﬂow
properties play a signiﬁcant role in understanding the cause of
bypass failure. In addition, the contribution of CFD in understanding the hemodynamics of various arteries conﬁgurations
cannot be ignored. Various researchers have investigated the
accuracy of CFD results and the factors that may affect the
numerical predications [8,9,42]. The standard methods cover
in vitro or in vivo data that are obtained from an experimental set up or from patients. Experimentally, Laser Doppler
Anemometry and Particle Image Velocimetry (PIV) as well
as MRI techniques have been widely used for validations
of numerical results [8,9,42]. Those techniques allow capturing the instantaneous ﬂow ﬁelds with high resolution, blood
velocity data and relevant calculated parameters of the hemodynamics of ﬂuid dynamics. According to Owida et al. [8], for
bypass graft research, it is difﬁcult to have a good agreement
between the experimental and numerical data and in some
cases the degree of discrepancy can be in the range of 30–40%.
Researchers argued that these differences could be attributed
to various factors related to the experimental set up and the
approximation of the numerical solution.
For FSI however, various researchers have carried out
a number of experimental investigations to validate the
results of the numerical predictions. [14,34,35]. For example,
Kanyanta et al. [14] carried out a study using analytical and
in vitro analysis of transient ﬂow inside a specially designed
polyurethane mock artery and found good agreement (over
95%), between the numerical stimulations and experimental
data.
3.
Anastomosis types
In artery bypass various conﬁgurations of anastomosis are
implemented (anastomosis is deﬁned as the surgical connection between the host artery and the graft) and these
have been extensively investigated to determine their hemodynamic performance and functionality under different
physiological conditions. Generally, as shown in Fig. 2 there are
three types of anastomosis, namely, end-to-end, end-to-side
and side-to-side conﬁgurations. These are discussed below in
a systematic way.
3.1.
End-to-end anastomosis
In end-to-end anastomosis, the arteries are sutured along
their transversal diameter. In other word, the affected section of artery is removed and replaced with graft. In 1978,
Pietsch et al. [43] compared the results of two operative procedures end-to-end and end-to-side anastomosis on 52 cases
and reported that both end-to-end and end-to-side repairs
were similar in performance and there was no signiﬁcant
difference in the incidence of anastomotic leak or recanalization of the ﬁstula. However, the rate of anastomotic stricture
in the end-to-end group was signiﬁcantly higher than that
in the end-to-side group. Nabuchi et al. [44] found that the
percentage of angiographical occlusion at end-to-end anastomosis was around 3.6%. Furthermore, it was reported the
694
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
Fig. 2 – Schematic representation of the classiﬁcation of anastomosis: end-to-end (a), end-to-side (b), and side-to-side (c).
occlusion could not be found in 100% of patients involved
in the survey over a period of 12 months. In the same year
Hoedt et al. [45] reported the results of clinical investigation
of 204 bypass operations from which 118 end-to-side and 86
end-to-end anastomoses conﬁgurations. The authors pointed
out that implementing end-to-side bypass operation could
improve femoropopliteal bypass patency.
Dobrin et al. [46] investigated the clinical impacts and
hemodynamics of end-to-end artery to polytetraﬂuoroethylene graft and recommended the use of a larger diameter graft
than host artery in order to provide less restrictive anastomosis compared with size-matched graft. The ﬁndings from this
study also highlighted the importance of the rigidity of the
grafts and the degree of compliance mismatch between the
graft and the artery which could produce an adverse effect on
the blood ﬂow passing from the compliant artery into the rigid
conduit. Moreover, it has been proposed that compliance mismatch may inﬂuence graft patency and the development of
intimal hyperplasia. Nevertheless, it is likely that the thrombogenicity of the ﬂow surface of the graft is more important
than the effect of compliance on short-term patency.
Baumgartner et al. [47] investigated the inﬂuence of suture
technique and suture materials selection (6-0 polypropylene
and 6-0 polybutester) on the mechanics of end-to-end and
end-to-side anastomosis under various operating conditions.
They stated that although the surgeons construct end-to-side
or end-to-end anastomosis in a speciﬁc way depending up
on the experience and the skill of the clinician, the selected
suture materials could inﬂuence the distensibility and size
of anastomotic lumen. In addition, the type of interrupted
sutures could initiate turbulence ﬂow and might decrease the
blood ﬂow provided to the distal vascular bed in severe cases.
However, it must be stated that very limited research has been
reported on the effect of the sutures on the ﬂuid ﬂow and
structure deformation.
Kim et al. [48] have carried out a numerical simulation of
ﬂow through an anastomosis end-to-end model and compared the results with experimental data. At higher pressure
difference between inside and outside the artery (transmural
pressure), the authors observed a region of ﬂow separation
of 2 mm distal to the artery junction. In addition, the observations of law shear stress near the anastomosis junction in
ﬂow from the tubing to the graft were reported. Moreover, a
correlation between regions of low wall shear stress and the
development of anastomotic intimal hyperplasia was found.
However, it must be pointed out that this study was carried
out under various simpliﬁed assumptions, such as steady
ﬂow conditions, Newtonian ﬂuid, axisymmetric geometry,
and rigid wall at each pressure level which do not reﬂect the
correct physiological conditions.
Qiu and Tarbell [49] used a ﬁnite element model with transient ﬂow and moving boundaries to simulate the oscillatory
ﬂow in the anastomotic region of vascular grafts. The study
focused on the effects of radial artery wall motion and phase
angle between pressure and ﬂow waves and the behavior of
near end-to-end vascular graft anastomoses models. The ﬁnding showed a signiﬁcant decrease of the minimum distal mean
wall shear rate on the deformable model with oscillatory ﬂow
compared with the rigid and steady ﬂow. These results suggest the compliance mismatch induces lower mean WSR and
more oscillatory WSR that could contribute to the initiation of
intimal hyperplasia.
In other investigation by Weston et al. [50] the degree of
compliance mismatch, diameter mismatch, and impedance
phase angle effect on the wall shear rate distributions in
end-to-end anastomosis models under sinusoidal ﬂow conditions, were studied. The authors highlighted the importance of
degree of compliance mismatch on the patency rate. Moreover,
Rory et al. [51] investigated the effect of the size discrepancy
of micro arterial anastomosis (small-to-large) on the functionality of the grafts and reported that the vessel size mismatch
was found to be a major cause for anastomotic failure in micro
vascular surgery. Moreover, it was noted that the end-to-end
conﬁguration should be used only when the option of endto-side anastomosis is unavailable. However, an early clinical
study demonstrated a low arterial patency rate when using
an end-to-end technique where a size mismatch of 3:1 or 4:1
was present. Indeed, end-to-side technique was proposed to
overcome size mismatch.
Moreover, it should be noted that the geometry of anastomosis might inﬂuence its patency. However, as shown in
Fig. 3, the size discrepancy can be maneuvered by the surgeon by either increasing the circumference of the cut end or
decreasing the cut end of larger vessel. In addition, as reported
by Rickard et al. [13], the excision of a wedge of the larger
vessel could have better hemodynamics. However, the literature also suggests that the ﬂow separation could be observed
as vessel ratio increased from 1 to 3 in wedge technique. It
should also be noted that an abrupt change may cause ﬂow
separation and vortex formation as well as turbulence which
almost certainly never occurs in natural artery. In addition, the
occurrence of endotheliocytes might act as transducers of wall
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
695
Fig. 3 – Schematic representation of the end-to-end
techniques for managing size discrepancy (small-to-big)
[13].
shear stress and systematize vessel wall remodeling and as a
result the presence of shear stresses changes. However, more
recent study by Schouten et al. [52] found no signiﬁcant difference in patency rates between end-to-end and end-to-side
anastomosis bypass grafts.
3.2.
End-to-side anastomosis
The end-to-side conﬁguration, due to its simplicity, is the most
common and researched anastomosis junctions. The general
idea of end-to-side anastomosis is redirecting the blood ﬂow
into another alternative way around the blocked artery by
putting bypass graft over the blockage. Basically, the distal
segment of end-to-side anastomosis can be divided into three
types as shown in Fig. 4.
Taylor’s patch conﬁguration utilizes a vein patch at the distal anastomosis that gives more tapered funnel shape and is
known to decrease turbulence and circulation ﬂows in anastomosis junction. Furthermore, it is also known to prevent the
development of intimal hyperplasia and improve the hemodynamics characteristics [54]. Miller cuff technique, on the other
hand, uses a segment of vein sutured to the circumference
of arteriotomy and this prosthetic graft is then sewn into the
venous cuff.
The hemodynamics investigations of these types of anastomoses have focused on the factors that may initiate the
development of intimal hyperplasia in coronary revascularization. These factors include anastomosis angles (Fig. 5),
ratios of graft–host diameter and out of plane anastomosis
[2,7,8,55–57]. In addition, it is well recognized that the ﬂow
within end-to-side anastomosis is three dimensional and the
development of ﬂow in various regions around the junctions
is highly depended on the input boundary conditions. These
authors reported the effect of boundary conditions and geometry conﬁgurations on the development of IH, endothelial
rupture and degree of compliance associated with disturbed
ﬂows of low and high WSS, WSS gradient as well as oscillating shear index (OSI) [2,49,58]. With respect to the effect of
angle, it was reported that a low angle of 18◦ minimized WSSG
and therefore reduced the development of intimal hyperplasia
(MIH) [59]. Other ﬁndings suggest that the highest ﬂuid velocity was found in 30◦ of anstomosis while the lowest velocity
Fig. 4 – (A) Schematic representation of the conventional
end-to-side anastomosis, (B) Taylor-patch and (C)
Miller-cuff [53].
was found in 60◦ . Moreover, the larger the anastomosis angle,
the thicker intimal hyperplasia at the ﬂoor of host artery.
In 2001, the method of using CFD to determine the inﬂuence of proximal artery conditions on the ﬂuid ﬂow was ﬁrst
attempted by of Kute and Vorp [60]. Although the ﬁnding indicated that the proximal artery was an important determinant
of the hemodynamics at the distal anastomosis of end-to-side,
the study had several limitations when looking at the end-toside conﬁgurations such as: only one anastomosis angle and
steady boundary conditions were used.
Lei et al. [61] have carried out a comprehensive study with
the aim of analyzing the distribution of distal anastomotic
wall shear stress gradients for conventional geometries, so an
optimum anastomosis junction with minimum or low myointimal hyperplasia, atheroma could be determined. The results
Fig. 5 – Illustration of the range of anastomosis angles of
conventional end-to-side anastomosis.
696
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
showed both the standard and Taylor patch anastomoses
geometries have relatively high wall shear stress gradients in
the regions of the toe and heel of the artery graft. Moreover,
the optimized design proposed by the authors in comparison
with Taylor patch geometries showed a reduction by almost
50% of wall shear stress gradients. The authors came up with
a recommendation of a 10-degree to 15-degree of heel angle
and a cuff-type anastomosis to achieve an appropriate small
bevel angle, in order to minimize wall shear stress gradients
at the distal end of a carotid endarterectomy patch. Moreover, Heise et al. [62] investigated the hemodynamics of bypass
anastomoses for three different conﬁgurations of anastomosis such as: Taylor patch, Miller cuff and femoro-crural patch
prosthesis. The authors found that the ﬂow patterns inside
the junction of Taylor patch, Millar cuff contained large ﬂow
separation zones that are known to initiate intimal hyperplasia development. The femoro-crural patch prosthesis on the
other hand provided a better result and no vortices creation
were found.
Leuprecht et al. [63] on the other hand investigated
experimentally the hemodynamics and the wall structure of
anatomically correct two conﬁgurations, conventional and
Miller-cuff ones. The effects of geometric conditions, degree
of compliance of various synthetic materials, and the incorporated venous cuff on general ﬂuid ﬂows and shear stress under
various operating conditions were investigated. The authors
observed a very complex vortex ﬂows, circulation regions,
and separation zones around the junction area. It was also
noted that an increase of compliance mismatch led to large
increase of the intramural stresses. This phenomenon can
have an adverse effect on suture line hyperplasia which is
in line with the in vivo observation. Furthermore, the authors
observed a progress of distal anastomotic intimal hyperplasia appearing to be promoted by altered ﬂow conditions and
intramural stress distributions at the region of the artery–graft
junction anastomosis. It was also noted that high patency of
the Miller-cuff prosthesis reported in vivo, maybe attributed
to the larger space within junction would slow the progress
of the IH. The same group, Perktold et al. [53] studied three
types of distal end-to-side anastomoses using expanded polytetraﬂuoroethylene (PTFE) prostheses. The study also applied
weak coupling of ﬂuid and structure to calculate mechanical
stresses on the deformable vessel walls as well as the inﬂuence
of the suture material on the connection area. In comparing
with in vivo results, the results demonstrated the correlations of intimal hyperplasia development in the graft–artery
junctions with the compliance mismatch of the geometries.
However, the authors stated that to improve the long term
function of the prosthesis reconstructions with venous grafts,
a reduction of compliance mismatch should be implemented.
Such action will not adversely affect the local blood ﬂow within
the modiﬁed model.
Our group on the other hand [2,7], showed that higher
anastomotic angle gave higher WSS values and these values changed remarkably around the toe and along the
bed of the host artery and with the anastomotic angles
and the host–graft ratios. Moreover, the results also indicated that the idealistic anastomosis angle was found to
be 20◦ . Also, the OSI values at the heel showed similar characteristics though the TAWSS values along the
Fig. 6 – Schematic representation of the composite coronary
artery bypass grafts [31].
graft at the heel demonstrated a signiﬁcant increase
[2].
Politis et al. [31] used CFD method to examine a steady state
of blood ﬂow inside four different composite coronary bypass
and sequential graft (Fig. 6).
conﬁgurations, namely, T, Y,
The ﬁndings found that the effect of local geometry on the
local hemodynamics, especially at the anastomosis sites, to be
quite signiﬁcant and observed the lowest shear stress regions
on the lateral walls of bifurcations. Later, the same group [32]
investigated the effect of different degrees of stenosis on the
transient ﬂow inside T-graft and -graft respectively. Again,
the signiﬁcance of graft conﬁgurations was highlighted and it
was reported that oscillating shear stresses was evident even
in a moderate degree of stenosis.
Sherwin et al. [64] argued that in the majority of the published researches, the center-lines of the graft and the host
vessel lie within the same plane, therefore forming planar
conﬁgurations. The authors examined the effect of “in and
out of plane” of the anastomosis grafts, of a solid geometry of
end-to-side anastomosis model under steady ﬂow conditions.
Later, the same group Papaharilaou et al. [55] investigated the
inﬂuence of out-of-plane geometry on pulsatile ﬂow within
a model of speciﬁcally structured distal end-to-side anastomosis. They found that the anastomosis bed was inﬂuenced
mostly by the reduced peak wall shear stress (WSS) values in
comparison to previous similar planar models. Additionally,
the mean oscillatory WSS magnitude in this model was shown
to decrease.
In order to examine the whole ﬂow patterns in both the
proximal and the distal anastomosis, Chua et al. [65] carried
out a numerical analysis of the hemodynamics of the steady
blood ﬂow inside of a completed anastomosis (Fig. 7). Typical physiological ﬂow conditions inputs were incorporated
into the model and particular attention was given to the factors that inﬂuence the phenomena of intimal hyperplasia (IH).
Moreover, the authors reported that under the typical physiological conditions, high gradients of velocity and wall shear
stress were observed in the vicinity of the distal part. It was
reported that these phenomena could inﬂuence the response
of vascular endothelial cell and the blood ﬂow which in turn
could affect the initiation of IH and long-term graft patency
rate. Later on, Shankarnarayanan et al. [66] looked at the effect
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
Fig. 7 – Schematic representation of the complete
anastomosis model [65].
of pulsatile ﬂow on the completed anastomosis and demonstrated that the intimal hyperplasia occurred in regions of ﬂow
separation zones at the toe and the heel, and that the ﬂow
stagnation was observed at the ﬂoor of the anastomosis. Moreover, in other investigation by the same group [25], the focus
was given on the inﬂuence of the out-of-plane geometry of the
graft. They reported that the CABG geometry has a signiﬁcant
effect on the velocity distributions and the secondary ﬂow and
vortex structures were seen in the in-plane velocity patterns.
It was then concluded that non-planarity of the blood vessel
along with the inﬂow conditions displayed a substantial effect
on the hemodynamics of CABG which could inﬂuence the long
term patency of graft.
Iudicello et al. [67] stated that the ﬂow in end-to-side
anastomosis is complex, three dimensional, and contains
areas with long residence times. In addition, various simulations have modeled steady state mean ﬂow and pulsatile
ﬂows of various waveforms [24,68]. However, applying nonphysiological anastomosis geometry and non-uniform initial
boundary conditions makes a quantitative comparison of the
arteries difﬁcult. Kute and Vorp [60] analyzed the effect of
proximal artery ﬂow on the hemodynamics at the distal anastomosis of a vascular bypass graft and reported that the
velocity vectors for all the proximal arterial ﬂow conditions
showed swirl ﬂows toward the ﬂoor of the artery, and their
distribution varied with the ﬂow conditions in the proximal
artery.
3.3.
Side-to-side CABG anastomosis
Bonert et al. [69,70] numerically investigated the ﬂuid ﬂow and
shear stress of side-to-side CABG in typically solid geometric models. The authors also compared the hemodynamics
of end-to-side with side-to-side conﬁgurations and indicated
that the parallel form of side-to-side anastomosis gave a
hemodynamics better than that of non-parallel one and the
hemodynamics of side-to-side was found to be inferior to endto-side anastomosis. They also compared the hemodynamics
of two conﬁgurations, diamond and parallel conﬁgurations
and found that diamond conﬁguration had larger area of WSS
as well as higher spatial WSS gradient compared with parallel
conﬁguration. The authors concluded that the parallel conﬁguration should be preferred over the diamond one. However,
literatures suggest that there are differences in the patency
rates of the two types of anastomosis namely end-to-side or
a side-to-side anastomosis. Conversely, according to Niinami
697
and Takeuchi [71], the side-to-side anastomosis conﬁguration has four advantages:(1), easy to apply perfect sutures
(2) Straightforward method to open id need arises via distal end of the graft (3) distal end of the graft could be held
beyond the surgical clip by forceps without damaging the arterial graft. Moreover, the degree of successful of side-to-side
anastomosis can be effortless checked by a probe. Moreover,
it has been found that the side-to-side CABG gives better
hemodynamic performance that end-to-side CABG. Moreover,
Sottiurai [72,73] has carried out an animal model to examine the development of neointimal hyperplasia in end-to-side
versus side-to-side anastomoses and found neointimal hyperplasia to be present at the heel, toe, and ﬂoor of the end-to-side
but not in the side-to-side anastomoses.
With the emphasis of constructing clinically based models,
various researchers have combined the advantages of CAD,
MRI and Computed Tomography (CT) scans to construct realistic models of anastomosis. Jin et al. [74] have used (CT)
slices to construct vascular model and used MRI data as input
boundary conditions. The authors demonstrated the link of
low and oscillating WSS area with clinical observations of the
atherosclerotic-prone sites in the left coronary artery. Similarly, Boutsianis et al. [75] investigated the whole coronary
arteries domain with high temporal and spatial resolution
of CT scans and constructed the effects of stenosis on distal hemodynamics on the investigated model. Moreover, the
authors also suggested that the computational results can
support and contribute for surgeons in precise surgical or
interventional planning.
In 2004, Ramaswamy et al. [76] applied the advantage of
intravascular ultrasound (IVUS) and bi-plane angiographic
fusion images together with CFD to present and describe local
ﬂow dynamics in both 3-D spatial and 4-D spatial and temporal model of left anterior descending (LAD) coronary artery. In
this study, the motion of the geometry was accurately captured, reconstructed and incorporated into the CFD model.
The numerical results presented the distribution of the velocity proﬁles in the region of the stenosis. The ﬁndings of the
study also showed that the circumferential distribution of
the axial wall shear stress (WSS) patterns in the vessel is
altered with the wall motion. In addition, the results showed a
decrease of magnitudes of time-averaged axial WSS between
the arterial motion and rigid model which might provide more
realistic predictions on the progression of atherosclerotic disease. Furthermore, Ku et al. [21] compared and validated the
CFD and MRI ﬂow in an in vitro large artery bypass graft model.
They reported an excellent qualitative agreement with a maximum 6% error of volume ﬂow rates.
Latter in 2007, Frauenfelder et al. [77], used 16-detector
row computed tomography (CT) to construct realistic geometric models of coronary arteries and bypasses for CFD
analysis. They investigated the inﬂuence of patient-speciﬁc
geometry of end-to-side and side-to-side anastomosis on perianastomotic hemodynamics to identify geometrically driven
ﬂow features that might increase the tendency of venous
graft failure. The numerical results showed that there were
differences found between the two types of anastomosis. In
addition, some limitations of applying CT scan technology for
CFD analysis within authors’ investigation have been identiﬁed and these include:
698
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
Fig. 8 – Schematic representation of the two-way coronary
artery bypass graft [27].
• The geometric data for CFD is depended on the reconstruction time point and might change at different
reconstruction time points.
• The realistic in-ﬂow and out-ﬂow velocity proﬁles could not
be used as the boundary conditions.
• The effect of the heart movement and changing pressure at
the outer wall of the vessels due to the myocardium contraction was not included in the numerical analysis.
• The degree of compliance mismatch between the host and
graft of coronary artery bypass graft, effect of the pressure
and WSS distribution near the anastomosis were not investigated and might be different in elastic model.
3.4.
Alternative conﬁgurations of CABG
More recently, Qiao and Liu [56] have carried out an investigation related to the effect of graft–host diameter ratios
on the ﬂow patterns and the wall shear stress in coronary
artery bypass graft (CABG). Using ﬁnite element techniques,
the authors investigated the pulsatile blood ﬂows in three
CABG models namely graft diameter larger than, equal to and
smaller than that of the coronary artery. The ﬁndings from this
study indicated that out of the three models evaluated, large
model can bring about better hemodynamics to some extent
with relatively large positive longitudinal velocity, uniform
and large WSS, and small WSSG. Furthermore, the authors
found that larger or isodiametric graft is favorable, but no distinct difference of WSS based temporal parameters was found
between all the three models, suggesting alternative anastomotic designs are necessary for the improvement of CABG
patency rates.
Fig. 10 – Schematic representation of the A new design
model [12].
Similarly, Qiao et al. [27] also used ﬁnite element technique
to examine the inﬂuence of graft diameter on the wall shear
stress in a femoral two-way bypass graft (Fig. 8), simulating
the pulsatile blood ﬂows in two models. Both models were
constructed with different diameters of grafts. The authors
applied the same geometric structure and the boundary conditions for both models and found that femoral artery bypassed
with a large graft demonstrated relatively uniform wall shear
stress and small wall shear stress gradients. Moreover, the
large model exhibited better and more regular hemodynamic
phenomena which could be effective in decreasing the probability of the initiation and development of postoperative
intimal hyperplasia and restenosis. Again, this study showed
that large grafts maybe more suitable in the clinical practice
of femoral two-way bypass operation.
Later, Fan et al. [28] examined the hemodynamics inside a
modiﬁed 45◦ of S-type bypass (Fig. 9). The authors observed
an improvement of ﬂow patterns and WSS distributions in
comparison with different angle of conventional bypass grafts.
The authors observed a signiﬁcant difference in the ﬂow patterns of conventional bypass and the S-type bypass model. A
clear swirling ﬂow near the distal part of the S-type bypass
was observed which could eliminate the low WSS along the
host ﬂoor.
Recently, Kabinejadian et al. [12] proposed a new CABG
coupled-sequential anastomosis conﬁguration (Fig. 10) to
optimize the ﬂow ﬁelds and distributions of various WSS
parameters on coronary bypass graft. Based on the traditional
end-to-side and side-to-side conﬁgurations, the authors combined both methods in a single narrowing host in order to
provide more uniform and smooth ﬂow at the end-to-side
anastomosis. This study was initiated to develop another
alternative for the blood ﬂow to the host artery so that
an improved hemodynamics at the coronary artery bed,
Fig. 9 – Schematic representation of the S-type artery bypass graft [28].
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
especially in the heel region of the end-to-side anastomosis,
with more moderate shear stress indices can be achieved.
3.5.
Clinical implications
In general, when the coronary artery bypass graft is performed, the local hemodynamic of the native arteries will
change. Several physiologies will be responded by arteries
to resist the sudden change of the new ﬂow conditions.
These adaption of arteries to the new hemodynamic conditions may constitute pathological disease [6]. Kassab and
Navia [78] have proposed the hypothesis that the underlying mechanism of graft failure and large perturbations could
lead to non-physiological condition and result in re-modeling
procedure. Conversely, other studies of wall mechanics and
ﬂuid dynamics in distal anastomoses pointed toward localized development of intimal hyperplasia as a consequence of
physiological re-modeling in response to abnormal conditions
of ﬂow and/or wall stresses [63,79]. Indeed, Sankaranarayanan
et al. [25] pointed out that wall shear stress, oscillating shear
index, ﬂow separation and secondary ﬂow are critical to intimal hyperplasia and atherogenesis. This might be explained
by the collagen and tissue factor in the blood can be damaged when exposed under high value of shear stress. Thus, the
process of platelet activation and adherence will trigger the
formation of blood clotting. In contrast, it is reported that the
early atherosclerotic lesions and atheroma in coronary artery
are correlated with low wall shear stress and ﬂow recirculation
areas [6].
According to Cavalcanti and Tura [80], endothelial cell proliferation and permeability are enhanced by blood pressure,
and in the presence of arterial injury, hypertension causes a
signiﬁcant increase of the intimal smooth muscle cell replication rate. Moreover, the shape and orientation of endothelial
cells are sensitive to blood ﬂow, and align themselves with the
direction of ﬂow and the formation of an endothelial cell layer
on the inner surface of a synthetic graft in the healing process
is undoubtedly a critical issue for the success of implantation
as it prevents platelet aggregation.
Moreover, Bernad et al. [81] used CFD to assess the hemodynamics of venous bypass graft using patient-speciﬁc data
from computed tomography (CT) angiography. In addition,
to understand the detailed ﬂow physics of transition to turbulence downstream of the graft curvature, the 3D model
was assumed as rigid wall which simulate blood ﬂow in narrowed venous bypass graft. The study was concentrated on
the implemented new methods that will enable the creation
of postoperative vascular models using simulation based medical planning system.
4.
Conclusion and ﬁnal remarks
Arterial bypass grafts tend to fail after some years due to
the development of intimal thickening (restenosis). It is well
recognized, that Non-uniform hemodynamics following a
bypass operation contributes to restenosis. Literature ﬁndings suggest that factors that inﬂuence the progression of
the restenosis include, individual blood rheology, local arterial geometry, placement of the junctions, graft diameters
699
and graft surface characteristics [1,2]. Moreover, bypass failure
can occur due to the focal development of anastomotic intimal hyperplasia. Additionally, surgical injury aggravated by
compliance mismatch between the graft and artery has been
suggested as an initiating factor for progress of wall thickening
along the suture line [4,5].
It is stated that the hemodynamics of CABG have major
factors to clinical implications. In addition, the anastomotic
angle was mentioned as an important factor inﬂuences the
hemodynamic properties such as: wall shear stress and ﬂow
conditions of the graft. The correct anastomotic angles can
be analyzed by CFD, will optimize hemodynamic conditions
and extend the patency rate of myocardial revascularization.
Moreover, it has been argued that optimized hemodynamics,
adopted from CFD analysis, could extend the patency rate of
myocardial revascularization of the CABG. In addition, it was
very clear from various numerical results that the anastomotic angles and conﬁguration of the junction area greatly
dominate the ﬂow conditions around the heel, around the
toe and across the anastomotic bed. Recently, Dur et al. [82]
applied Computer-Aided Design coupling with CFD method
to optimize hemodynamic of CABG. The proposed CABG conﬁguration was based on surgical planning paradigm and was
used to evaluate the local hemodynamics and acute hemodynamic readjustments of coronary bypass surgery. The authors
reported that the proposed procedure could be successfully
used to aid surgical decision-making process in time-critical,
patient-speciﬁc coronary artery bypass operations before the
in vivo execution. However, it was also pointed out that there
is still a need to minimize local ﬂow disturbances, circulation zone, and to maximize the conduit energy efﬁciency of
the proposed conﬁguration. Such improvement of the hemodynamics could be obtained by optimizing the anastomosis
geometry, graft length and transitional curvature of the vessel.
Determination of accurate local hemodynamics in bypass
grafts and the host artery is crucial for the general understanding of the cause of CABG failure. Such an understanding
is difﬁcult to obtain as a small diameter of coronary arteries
and the complex interaction of ﬂuid forces and deformation
of artery is difﬁcult to determine accurately in vivo. Therefore, in vitro experimental and numerical investigations using
ideal and realistic models of CABG have been used extensively to gain insight into the hemodynamics and mechanical
forces and their implications on the design and optimization of the graft. It is clear from the above literature that
geometric features such as graft-to-artery diameter, anastomotic angle and junction shape and vessel curvature exert
signiﬁcant inﬂuence on hemodynamics. Geometric features
vary widely depending upon the coronary system receiving
the graft and the source of graft ﬂow. However, quantitative
comparison of the results of the coronary studies is difﬁcult
because of the non-uniform treatment of graft and artery
ﬂows. Non-uniform distributions of wall shear stress and
strong secondary ﬂows have been reported in almost all the
CABG conﬁgurations. One therefore concludes that physiological pulsatile ﬂow waveforms and correct static anastomotic
geometry are prerequisites for conducting consistent clinically relevant simulation of ﬂow hemodynamics in CABGs.
Dynamic changes in wall structure and position arising from
cardiac movement [83,84] and distensible wall-mechanics
700
Table 4 – Coronary artery bypass grafts researches and its conﬁgurations.
Authors
1997
2005
1993
Type
Numerical simulation
Qiu and Tarbell [49]
1996
Numerical simulation, In vitro
experiment
Numerical simulation
Weston [50]
1996
In vitro experiment
Sottiurai [72]
1999
Surgical Review
Rickard [13]
2009
Numerical simulation
Methods/conﬁgurations
Fluid
Reynold
number
Womersley
number
Review
Review
Newtonian
16% undersized (mean)
diameter graft model
6% undersized, 16%
undersized, and 13%
oversized graft models
Reversed saphenous
vein
In situ saphenous vein
Nonreversed
translocated saphenous
vein
Invaginating, ﬁsh
mouth, oblique section,
wedge excision
UCON 50-HB-55,
Union Carbide
= 1059 kg/m3
Steady, Re = 250
and 400
Oscillatory ﬂow,
Re = 150, peak
Re = 300
Sinusoidal ﬂow
Co = ( d/d)/ P
˛ = 3.9
Pulsatile
= 0.005 kg/ms
End-to-side anastomosis
Fei et al. [85]
1994
Numerical simulation
Staalsen et al. [86]
1995
In vivo experiment
Hughes and How [87]
1996
In vitro experiment
Lei et al. [61]
1997
Numerical simulation
30◦ , Rh–g = 2:1
Numerical simulation, In vitro
experiment, MRI ﬂow
Synthetic graft/vein
patch 10◦ , Rh–g = 2:1;
optimal anastomosis
geometry Rh–g = 1.6:1
45◦ planar and
non-planar
Sherwin et al. [64]
2000
Defomation
and
compliance
Anastomosis angle: 20◦ ,
30◦ , 40◦ , 45◦ , 50◦ , 60◦ and
70◦
Anastomosis angle: 15◦ ,
45◦ , 90◦
Anastomosis angle: 15◦ ,
30◦ , 45◦
Re = 100, Re = 205
= 0.034815 dyness/cm2
Re = 400 to 500
˛=6
Steady Re range
300–1000
Sinusoidal ﬂow,
mean
Re = 300 or 500
Re = 365 and
f = 100, Re = 113.5
and f = 60
˛ = 9.7
= 1.055 g/ml
= 3.416 × 10−6 m2 s−1 Steady Re range
250–600
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
Review papers
Ku [6]
Migliavacca and Dubini [59]
End-to-end anastomosis
Kim et al. [48]
Year
– Table 4 (Continued)
Authors
Year
Type
Methods/conﬁgurations
75% stenosis, 45◦
anastomosis
30◦
Deplano et al. [58]
2001
Numerical simulation
45◦ , Ratiohost–graft 1.0
Perktold et al. [53]
2002
Numerical simulation, in vivo
results
Taylor-patch and
Miller-cuff anastomoses
grafts
Papaharilaou et al. [55]
2002
Leuprecht et al. [63]
2002
Numerical simulation, In vitro
experiment, MRI ﬂow
Numerical simulation
45◦ planar and
non-planar
Conventional type and
Miller cuff type of
anastomosis
Deplano et al. [88]
2004
Numerical simulation
90◦ bifurcation, Palmaz
stent
2001
Kute and Vorp [60]
Heise et al. [62]
2004
PIV measurement
Taylor-patch, Miller-cuff
and femoro-crural patch
prosthesis anastomoses
grafts
Ku et al. [21]
2005
Numerical simulation, In vitro
experiment, MRI ﬂow
45◦ anastomosis
Qiao and Liu [56]
2006
Numerical simulation
30◦
Freshwater et al. [2]
2006
Numerical simulation
Frauenfelder et al. [77]
2007
Numerical simulation
Ratiohost–graft 1.46; 1.0;
0.81
20◦ , 40◦ , 60◦ ,
anastomosis angle
In vivo CT coronary
angiography data
construct end-to-side
and side-to-side
anastomosis grafts
In vitro
= 7.2 cP
= 3.5 cP
= 1000 kg m−3
= 3.6 × 10−6 m2 s−1
= 1000 kg m−3
= 3.9 × 10−3 Pa s
Reynold
number
Steady Re range
72–295
Re = 150
Womersley
number
˛ = 2.2
Pulsatile
Pulsatile,
ReConv = 399,
ReT = 379,
ReM = 384
˛Conv = 2.94
˛T = 3.09,
˛M = 3.06
˛=4
= 3.9 × 10−3 Pa s
Sinusoidal ﬂow,
Re range 62–437
Re = 380
= 1044 kg m−3
= 3.6 × 10−6 m2 s−1
Remax = 197
˛ = 4.77
= 1044 kg m−3
= 3.4 × 10−6 m2 s−1
= 1050 kg m−3
42% glycerine
and 58% water
= 4 mPa s
= 0.036 dyness/cm2
= 1.1 g/ml
= 0.0424 g/(cm s)
˛ = 3.13
Re = 240
Re = 770
˛ = 17
Pulsatile,
Repeak = 111.7
˛ = 1.82
= 1.06 g/cm3
Newtonian
= 3.7 × 10−3 Pa s
Defomation
and
compliance
Weak
coupling
FSI
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
2001
Numerical simulation, In vitro
experiment
Numerical simulation
Bertolotti et al. [24]
Fluid
Pulsatile
Re range
250–1650
˛ = 2.1 to 3.5
= 1060 kg m−3
701
702
– Table 4 (Continued)
Authors
Year
Type
Methods/conﬁgurations
Fluid
2007
2008
Numerical simulation
Numerical simulation
T, Y, and sequential
Typical T and grafts
= 3.5 × 10−6 m2 s−1
= 3.5 × 10−6 m2 s−1
Do et al. [7]
2010
Numerical simulation
Various angles and ratio
of host grafts
anastomosis
= 4 × 10−3 Pa s
Re range 55–222
Pulsatile: Re
89–389
Peak Re = 1350
and 900
Womersley
number
Defomation
and
compliance
˛ = 2.75
˛ < 3.67
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
Politis et al. [31]
Politis et al. [32]
Reynold
number
= 1100 kg m−3
Side-to-side anastomosis
Bonert et al. [70]
2002
Numerical simulation
Parallel equal and small
host, diamond equal
and small host (90◦ ),
End to side equal host
= 3.5 × 10−6 m2 s−1
Re = 194
˛ = 1.81
= 1.06 g/ml
Bypass modiﬁcation
Chua et al. [65]
Sankaranarayanan et al.
[66]
2005
Numerical simulation
A completed
anastomosis model
2005
Numerical simulation
Anastomosis in the
right and left
aorto-saphenous bypass
grafts
Qiao et al. [27]
2006
Numerical simulation
Two-way coronary
artery bypass graft
Sankaranarayanan et al.
[25]
2006
Numerical simulation
An out-of-plane CABG
model
Fan et al. [28]
2008
Numerical simulation
An S-type bypass
Kabinejadian et al. [12]
2010
Numerical simulation
Side-to-side and
end-to-side
combination
= 4.08 × 10−3 Pa s
= 1055 kg m−3
= 4.08 × 10−3 Pa s
Pulsatile
= 1050 kg m−3
= 3.5 × 10−3 Pa s
Re = 204.7
= 1050 kg m−3
= 4.08 × 10−3 Pa s
Pulsatile
= 1050 kg m−3
= 3.48 × 10−3 Pa s
= 1050 kg m−3
= 4.08 × 10−3 Pa s
˛ = 6.14
Re = 250
Re = 40 to 421
= 1050 kg m−3
CT scan and simulation
Jin et al. [74]
2004
Numerical simulation
Boutsianis et al. [75]
2004
CT scan and numerical simulation
CT scan model to
computational ﬂuid
dynamics
Real coronary artery
geometry
= 3.5 × 10−3 Pa s
= 1060 kg m−3
Pulsatile
Rigid wall
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
[4] may then be added to reﬁne the model when studying
distortion and stressing of the vessel walls. The effect of
different ﬂow waveforms, artery ﬂow conditions as well as
coronary artery bypass conﬁgurations on hemodynamics has
been studied by many authors (see for example the reference
Tables 2 and 4).
In a nutshell, although there are a numerous publications
on the hemodynamics of various coronary arteries bypass
graft designs, literature still does not provide deﬁnitive clariﬁcation on the optimum anastomosis geometry, graft length
and transitional curvature to achieve hemodynamic characteristics that promote failure-free bypass conduits. Therefore,
there is still a need for further hemodynamics analysis
of possible anastomosis conﬁgurations using real realistic
patient-speciﬁc boundary conditions with different degree of
intimal thickening. Moreover, the knowledge of FSI in CABG
is not fully investigated, especially in case of coupling the
deformation of the heart, the artery wall with the blood ﬂow.
Finally, it appears that there are only few in vivo animal experiments found in literature which are essential for validation
and clinical adoption of any proposed conﬁgurations [12].
references
[1] M. Lei, C. Kleinstreuer, G.A. Truskey, A focal stress
gradient-dependent mass transfer mechanism for
atherogenesis in branching arteries, Medical Engineering
and Physics 18 (4) (1996) 326–332.
[2] I.J. Freshwater, Y.S. Morsi, T. Lai, The effect of angle on wall
shear stresses in a LIMA to LAD anastomosis: numerical
modelling of pulsatile ﬂow, Proceedings of the Institution of
Mechanical Engineers, Part H: Journal of Engineering in
Medicine 220 (7) (2006) 743–757.
[3] V.S. Sottiurai, J.S.T. Yao, W.R. Flinn, R.C. Batson, Intimal
hyperplasia and neointima: an ultrastructural analysis of
thrombosed grafts in humans, Surgery 93 (6) (1983) 809–817.
[4] M. Hofer, G. Rappitsch, K. Perktold, W. Trubel, H. Schima,
Numerical study of wall mechanics and ﬂuid dynamics in
end-to-side anastomoses and correlation to intimal
hyperplasia, Journal of Biomechanics 29 (10) (1996)
1297–1308.
[5] P.D. Ballyk, C. Walsh, J. Butany, M. Ojha, Compliance
mismatch may promote graft–artery intimal hyperplasia by
altering suture-line stresses, Journal of Biomechanics 31 (3)
(1997) 229–237.
[6] D.N. Ku, Blood ﬂow in arteries, Annual Review of Fluid
Mechanics 29 (1997) 399–434.
[7] H. Do, A.A. Owida, W. Yang, Y.S. Morsi, Numerical simulation
of the haemodynamics in end-to-side anastomoses,
International Journal for Numerical Methods in Fluids (2010).
[8] A. Owida, H. Do, W. Yang, Y.S. Morsi, PIV measurements and
numerical validation of end-to-side anastomosis, Journal of
Mechanics in Medicine and Biology 10 (1) (2010) 123–138.
[9] J.M. Zhang, L.P. Chua, D.N. Ghista, T.M. Zhou, Y.S. Tan,
Validation of numerical simulation with PIV measurements
for two anastomosis models, Medical Engineering and
Physics 30 (2) (2008) 226–247.
[10] E. Kouhi, Y.S. Morsi, S.H. Masood, Haemodynamic analysis of
coronary artery bypass grafting in a non-linear deformable
artery and Newtonian pulsatile blood ﬂow, Proceedings of
the Institution of Mechanical Engineers, Part H: Journal of
Engineering in Medicine 222 (8) (2008) 1273–1287.
703
[11] A.M. Ahmed Owida, In vitro study of haemodynamic
stresses and endothelialisation of artiﬁcial coronary
arteries, PhD, Swinburne University of Technology, 2009.
[12] F. Kabinejadian, L.P. Chua, D.N. Ghista, M.
Sankaranarayanan, Y.S. Tan, A novel coronary artery bypass
graft design of sequential anastomoses, Annals of
Biomedical Engineering 38 (10) (2010) 3135–3150.
[13] R.F. Rickard, C. Meyer, D.A. Hudson, Computational
modeling of microarterial anastomoses with size
discrepancy (small-to-large), Journal of Surgical Research
153 (1) (2009) 1–11.
[14] V. Kanyanta, A. Ivankovic, A. Karac, Validation of a
ﬂuid–structure interaction numerical model for predicting
ﬂow transients in arteries, Journal of Biomechanics 42 (11)
(2009) 1705–1712.
[15] J. Anderson, Computational Fluid Dynamics: The Basics
with Applications, McGraw-Hill, 1995.
[16] R. Temam, Navier–Stokes Equations: Theory and Numerical
Analysis, AMS Chelsea Pub., 2001.
[17] C. Bertolotti, V. Deplano, Three-dimensional numerical
simulations of ﬂow through a stenosed coronary bypass,
Journal of Biomechanics 33 (8) (2000) 1011–1022.
[18] J. Vimmr, A. Jonásová, Non-Newtonian effects of blood ﬂow
in complete coronary and femoral bypasses, Mathematics
and Computers in Simulation 80 (6) (2010) 1324–1336.
[19] D. Lee, J.M. Su, H.Y. Liang, A numerical simulation of steady
ﬂow ﬁelds in a bypass tube, Journal of Biomechanics 34 (11)
(2001) 1407–1416.
[20] S.E. Langerak, H.W. Vliegen, J.W. Jukema, P. Kunz, A.H.
Zwinderman, H.J. Lamb, E.E. Van der Wall, A. De Roos, Value
of magnetic resonance imaging for the noninvasive
detection of stenosis in coronary artery bypass grafts and
recipient coronary arteries, Circulation 107 (11) (2003)
1502–1508.
[21] J.P. Ku, C.J. Elkins, C.A. Taylor, Comparison of CFD and MRI
ﬂow and velocities in an in vitro large artery bypass graft
model, Annals of Biomedical Engineering 33 (3) (2005)
257–269.
[22] N.I. Stauder, B. Klumpp, H. Stauder, G. Blumenstock, M.
Fenchel, A. Küttner, C.D. Claussen, S. Miller, Assessment of
coronary artery bypass grafts by magnetic resonance
imaging, British Journal of Radiology 80 (960) (2007)
975–983.
[23] F. Kajiya, K. Tsujioka, Y. Ogasawara, Y. Wada, S. Matsuoka, S.
Kanazawa, O. Hiramatsu, S.I. Tadaoka, M. Goto, T. Fujiwara,
Analysis of ﬂow characteristics in poststenotic regions of
the human coronary artery during bypass graft surgery,
Circulation 76 (5) (1987) 1092–1100.
[24] C. Bertolotti, V. Deplano, J. Fuseri, P. Dupouy, Numerical and
experimental models of post-operative realistic ﬂows in
stenosed coronary bypasses, Journal of Biomechanics 34 (8)
(2001) 1049–1064.
[25] M. Sankaranarayanan, D.N. Ghista, L.P. Chua, Y.S. Tan, G.S.
Kassab, Analysis of blood ﬂow in an out-of-plane CABG
model, American Journal of Physiology-Heart and
Circulatory Physiology 291 (1) (2006) H283–H295.
[26] D.F. Young, F.Y. Tsai, Flow characteristics in models of
arterial stenoses. II. Unsteady ﬂow, Journal of Biomechanics
6 (5) (1973) 547–559.
[27] A. Qiao, Y. Liu, Z. Guo, Wall shear stresses in small and large
two-way bypass grafts, Medical Engineering and Physics 28
(3) (2006) 251–258.
[28] Y. Fan, Z. Xu, W. Jiang, X. Deng, K. Wang, A. Sun, An S-type
bypass can improve the hemodynamics in the bypassed
arteries and suppress intimal hyperplasia along the host
artery ﬂoor, Journal of Biomechanics 41 (11) (2008) 2498–2505.
[29] J. Chen, X.-Y. Lu, W. Wang, Non-Newtonian effects of blood
ﬂow on hemodynamics in distal vascular graft anastomoses,
Journal of Biomechanics 39 (11) (2006) 1983–1995.
704
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
[30] Y.H. Kim, J.E. Kim, Y. Ito, A.M. Shih, B. Brott, A. Anayiotos,
Hemodynamic analysis of a compliant femoral artery
bifurcation model using a ﬂuid structure interaction
framework, Annals of Biomedical Engineering 36 (11) (2008)
1753–1763.
[31] A.K. Politis, G.P. Stavropoulos, M.N. Christolis, F.G.
Panagopoulos, N.S. Vlachos, N.C. Markatos, Numerical
modeling of simulated blood ﬂow in idealized composite
arterial coronary grafts: steady state simulations, Journal of
Biomechanics 40 (5) (2007) 1125–1136.
[32] A.K. Politis, G.P. Stavropoulos, M.N. Christolis, P.G.
Panagopoulos, N.S. Vlachos, N.C. Markatos, Numerical
modelling of simulated blood ﬂow in idealized composite
arterial coronary grafts: transient ﬂow, Journal of
Biomechanics 41 (1) (2008) 25–39.
[33] S. Owen, A Survey
of Unstructured Mesh Generation Technology. Available from:
http://www.andrew.cmu.edu/user/sowen/survey/index.html.
[34] C. Guivier-Curien, V. Deplano, E. Bertrand, Validation of a
numerical 3-D ﬂuid–structure interaction model for a
prosthetic valve based on experimental PIV measurements,
Medical Engineering and Physics 31 (8) (2009) 986–993.
[35] Y.S. Morsi, W.W. Yang, C.S. Wong, S. Das, Transient
ﬂuid–structure coupling for simulation of a trileaﬂet heart
valve using weak coupling, Journal of Artiﬁcial Organs 10 (2)
(2007) 96–103.
[36] C.A. Figueroa, I.E. Vignon-Clementel, K.E. Jansen, T.J.R.
Hughes, C.A. Taylor, A coupled momentum method for
modeling blood ﬂow in three-dimensional deformable
arteries, Computer Methods in Applied Mechanics and
Engineering 195 (41–43) (2006) 5685–5706.
[37] J. Donea, S. Giuliani, J.P. Halleux, An arbitrary
lagrangian-eulerian ﬁnite element method for transient
dynamic ﬂuid–structure interactions, Computer Methods in
Applied Mechanics and Engineering 33 (1–3) (1982) 689–723.
[38] A. Valencia, M. Villanueva, Unsteady ﬂow and mass transfer
in models of stenotic arteries considering ﬂuid–structure
interaction, International Communications in Heat and
Mass Transfer 33 (8) (2006) 966–975.
[39] R. Glowinski, T.-W. Pan, J. Periaux, Fictitious domain method
for Dirichlet problem and applications, Computer Methods
in Applied Mechanics and Engineering 111 (3–4) (1994)
283–303.
[40] F. Bertrand, P.A. Tanguy, F. Thibault, A three-dimensional
ﬁctitious domain method for incompressible ﬂuid ﬂow
problems, International Journal for Numerical Methods in
Fluids 25 (6) (1997) 719–736.
[41] F.P.T. Baaijens, A ﬁctitious domain/mortar element method
for ﬂuid–structure interaction, International Journal for
Numerical Methods in Fluids 35 (7) (2001) 743–761.
[42] F.L. Xiong, C.K. Chong, PIV-validated numerical modeling of
pulsatile ﬂows in distal coronary end-to-side anastomoses,
Journal of Biomechanics 40 (13) (2007) 2872–2881.
[43] J.B. Pietsch, K.B. Stokes, H.E. Beardmore, Esophageal atresia
with tracheoesophageal ﬁstula: end-to-end versus
end-to-side repair, Journal of Pediatric Surgery 13 (6, Suppl.
1) (1978) 677–681.
[44] A. Nabuchi, A. Kurata, K. Tsukuda, Y. Miyoshi, Bi-directional
single anastomotic technique for the proximal anastomosis
of free grafts (the saphenous vein or radial artery) to the
ascending aorta in coronary artery bypass grafting surgery,
Annals of Thoracic and Cardiovascular Surgery: Ofﬁcial
Journal of the Association of Thoracic and Cardiovascular
Surgeons of Asia 7 (2) (2001) 122–124.
[45] M.T.C. Hoedt, H. Van Urk, W.C.J. Hop, A. Van der Lugt, C.H.A.
Wittens, A comparison of distal end-to-side and end-to-end
anastomoses in femoropopliteal bypasses, European Journal
of Vascular and Endovascular Surgery 21 (3) (2001) 266–270.
[46] P.B. Dobrin, R. Mirande, S. Kang, Q.S. Dong, R. Mrkvicka,
Mechanics of end-to-end artery-to-PTFE graft anastomoses,
Annals of Vascular Surgery 12 (4) (1998) 317–323.
[47] N. Baumgartner, P.B. Dobrin, M. Morasch, Q.-S. Dong, R.
Mrkvicka, Inﬂuence of suture technique and suture material
selection on the mechanics of end-to-end and end-to-side
anastomoses, The Journal of Thoracic and Cardiovascular
Surgery 111 (5) (1996) 1063–1072.
[48] Y.H. Kim, K.B. Chandran, T.J. Bower, J.D. Corson, Flow
dynamics across end-to-end vascular bypass graft
anastomoses, Annals of Biomedical Engineering 21 (4) (1993)
311–320.
[49] Y. Qiu, J.M. Tarbell, Computational simulation of ﬂow in the
end-to-end anastomosis of a rigid graft and a compliant
artery, ASAIO Journal 42 (5) (1996) M702–M709.
[50] M.W. Weston, K. Rhee, J.M. Tarbell, Compliance and
diameter mismatch affect the wall shear rate distribution
near an end-to-end anastomosis, Journal of Biomechanics
29 (2) (1996) 187–198.
[51] Rickard, F. Rory, Chris Meyer, A. Don, Hudson,
Computational modeling of microarterial anastomoses with
size discrepancy (small-to-large), The Journal of surgical
research 153 (1) (2009) 1–11.
[52] O. Schouten, M.T.C. Hoedt, C.H.A. Wittens, W.C.J. Hop,
M.R.H.M. van Sambeek, H. van Urk, B.C.V.M. Disselhoff,
T.H.A. Bikkers, J.A. Kriele, R.J. Dinkelman, End-to-end versus
end-to-side distal anastomosis in femoropopliteal bypasses;
results of a randomized multicenter trial, European Journal
of Vascular and Endovascular Surgery 29 (5) (2005)
457–462.
[53] K. Perktold, A. Leuprecht, M. Prosi, T. Berk, M. Czerny, W.
Trubel, H. Schima, Fluid dynamics, wall mechanics, and
oxygen transfer in peripheral bypass anastomoses, Annals
of Biomedical Engineering 30 (4) (2002) 447–460.
[54] R.S. Taylor, A. Loh, R.J. McFarland, M. Cox, J.F. Chester,
Improved technique for polytetraﬂuoroethylene bypass
grafting: long-term results using anastomotic vein patches,
British Journal of Surgery 79 (4) (1992) 348–354.
[55] Y. Papaharilaou, D.J. Doorly, S.J. Sherwin, The inﬂuence of
out-of-plane geometry on pulsatile ﬂow within a distal
end-to-side anastomosis, Journal of Biomechanics 35 (9)
(2002) 1225–1239.
[56] A. Qiao, Y. Liu, Inﬂuence of graft–host diameter ratio on the
hemodynamics of CABG, Bio-Medical Materials and
Engineering 16 (3) (2006) 189–201.
[57] R.G. Demaria, M. PicicheÌD, H. Vernhet, P. Battistella, P.
RouvieÌDre, J.M. Frapier, B. Albat, Internal thoracic arterial
grafts evaluation by multislice CT scan: a preliminary study,
Journal of Cardiac Surgery 19 (6) (2004) 475–480.
[58] V. Deplano, C. Bertolotti, O. Boiron, Numerical simulations of
unsteady ﬂows in a stenosed coronary bypass graft, Medical
and Biological Engineering and Computing 39 (4) (2001)
488–499.
[59] F. Migliavacca, G. Dubini, Computational modeling of
vascular anastomoses, Biomechanics and Modeling in
Mechanobiology 3 (4) (2005) 235–250.
[60] S.M. Kute, D.A. Vorp, The effect of proximal artery ﬂow on
the hemodynamics at the distal anastomosis of a vascular
bypass graft: computational study, Journal of Biomechanical
Engineering 123 (3) (2001) 277–283.
[61] M. Lei, J.P. Archie, C. Kleinstreuer, Computational design of a
bypass graft that minimizes wall shear stress gradients in
the region of the distal anastomosis, Journal of Vascular
Surgery 25 (4) (1997) 637–646.
[62] M. Heise, S. Schmidt, U. Krüger, R. Rückert, S. Rösler, P.
Neuhaus, U. Settmacher, Flow pattern and shear stress
distribution of distal end-to-side anastomoses. A
comparison of the instantaneous velocity ﬁelds obtained by
c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 8 ( 2 0 1 2 ) 689–705
[63]
[64]
[65]
[66]
[67]
[68]
[69]
[70]
[71]
[72]
[73]
[74]
[75]
particle image velocimetry, Journal of Biomechanics 37 (7)
(2004) 1043–1051.
A. Leuprecht, K. Perktold, M. Prosi, T. Berk, W. Trubel, H.
Schima, Numerical study of hemodynamics and wall
mechanics in distal end-to-side anastomoses of bypass
grafts, Journal of Biomechanics 35 (2) (2002) 225–236.
S.J. Sherwin, O. Shah, D.J. Doorly, J. Peiro, Y. Papaharilaou, N.
Watkins, C.G. Caro, C.L. Dumoulin, The inﬂuence of
out-of-plane geometry on the ﬂow within a distal
end-to-side anastomosis, Journal of Biomechanical
Engineering 122 (1) (2000) 86–95.
L.P. Chua, J. Zhang, T. Zhou, Numerical study of a complete
anastomosis model for the coronary artery bypass,
International Communications in Heat and Mass Transfer 32
(3–4) (2005) 473–482.
M. Sankaranarayanan, L.P. Chua, D.N. Ghista, Y.S. Tan,
Computational model of blood ﬂow in the aorto-coronary
bypass graft, BioMedical Engineering Online 4 (2005).
F. Iudicello, M.W. Collins, F.S. Henry, J.C. Jarvis, A. Shortland,
R. Black, S. Salmons, Review of modelling for arterial vessels
– simpliﬁed ventricular geometries, Advances in Fluid
Mechanics (1996) 179–194.
F.S. Henry, M.W. Collins, P.E. Hughes, T.V. How, Numerical
investigation of steady ﬂow in proximal and distal
end-to-side anastomoses, Journal of Biomechanical
Engineering 118 (3) (1996) 302–310.
M. Bonert, J.G. Myers, S.E. Fremes, C.R. Ethier, Inﬂuence of
graft/host diameter ratio on the hemodynamics in
sequential ita anastomoses, American Society of
Mechanical Engineers, Bioengineering Division (Publication)
BED 48 (2000) 265–266.
M. Bonert, J.G. Myers, S. Fremes, J. Williams, C.R. Ethier, A
numerical study of blood ﬂow in coronary artery bypass
graft side-to-side anastomoses, Annals of Biomedical
Engineering 30 (5) (2002) 599–611.
H. Niinami, Y. Takeuchi, Coronary artery bypass grafting
using side-to-side anastomosis. Kyobu geka, The Japanese
Journal of Thoracic Surgery 53 (9) (2000) 747–749.
V.S. Sottiurai, Comparison of reversed, nonreversed
translocated, and in situ vein grafts in arterial
revascularization: techniques, cumulative patency,
versatility, and durability, International Journal of Angiology
8 (4) (1999) 197–202.
V.S. Sottiurai, Distal anastomotic intimal hyperplasia:
histocytomorphology, pathophysiology, etiology, and
prevention, International Journal of Angiology 8 (1) (1999)
1–10.
S. Jin, Y. Yang, J. Oshinski, A. Tannenbaum, J. Gruden, D.
Giddens, Flow Patterns and Wall Shear Stress Distributions
at Atherosclerotic-prone Sites in a Human Left Coronary
Artery – An Exploration Using Combined Methods of CT and
Computational Fluid Dynamics, 2004.
E. Boutsianis, H. Dave, T. Frauenfelder, D. Poulikakos, S.
Wildermuth, M. Turina, Y. Ventikos, G. Zund, Computational
simulation of intracoronary ﬂow based on real coronary
geometry, European Journal of Cardio-thoracic Surgery 26 (2)
(2004) 248–256.
705
[76] S.D. Ramaswamy, S.C. Vigmostad, A. Wahle, Y.G. Lai, M.E.
Olszeski, K.C. Braddy, T.M.H. Brennan, J.D. Rossen, M. Sonka,
K.B. Chandran, Fluid dynamic analysis in a human left
anterior descending coronary artery with arterial motion,
Annals of Biomedical Engineering 32 (12) (2004) 1628–1641.
[77] T. Frauenfelder, E. Boutsianis, T. Schertler, L. Husmann, S.
Leschka, D. Poulikakos, B. Marincek, H. Alkadhi, Flow and
wall shear stress in end-to-side and side-to-side
anastomosis of venous coronary artery bypass grafts,
BioMedical Engineering Online 6 (2007).
[78] G.S. Kassab, J.A. Navia, Biomechanical considerations in the
design of graft: the homeostasis hypothesis, Annual Review
of Biomedical Engineering (2006) 499–535.
[79] H.S. Bassiouny, S. White, S. Glagov, E. Choi, D.P. Giddens, C.K.
Zarins, Anastomotic intimal hyperplasia: mechanical injury
or ﬂow induced, Journal of Vascular Surgery 15 (4) (1992)
708–717.
[80] S. Cavalcanti, A. Tura, Hemodynamic and mechanical
performance of arterial grafts assessed by numerical
simulation: a design oriented study, Artiﬁcial Organs 23 (2)
(1999) 175–185.
[81] S.I. Bernad, T. Barbat, E.S. Bernad, R. Susan-Resiga,
Numerical blood ﬂow simulations in narrowed coronary
venous bypass graft, Journal of Chinese Clinical Medicine 4
(1) (2009) 1–10.
[82] O. Dur, S.T. Coskun, K.O. Coskun, D. Frakes, L.B. Kara, K.
Pekkan, Computer-aided patient-speciﬁc coronary artery
graft design improvements using CFD coupled shape
optimizer, Cardiovascular Engineering and Technology 2 (1)
(2011) 35–47.
[83] H.L. Wu, X.M. Ruan, M.Z. Zhang, Syndrome differentiation
patterns for peri-operative coronary heart disease patients
of coronary artery bypass graft, Zhongguo Zhong Xi Yi Jie He
Za Zhi 21 (6) (2001) 409–411.
[84] H. Zhu, M.H. Friedman, Vessel tracking by template string in
angiography, in: Proceedings of SPIE-The International
Society for Optical Engineering, 2001.
[85] D.Y. Fei, J.D. Thomas, S.E. Rittgers, The effect of angle and
ﬂow rate upon hemodynamics in distal vascular graft
anastomoses: a numerical model study, Journal of
Biomechanical Engineering 116 (3) (1994) 331–336.
[86] N.H. Staalsen, E.M. Pedersen, M. Ulrich, J. Winther, T.V. How,
J.M. Hasenkam, An in vivo model for studying the local
haemodynamics of end-to-side anastomoses, European
Journal of Vascular and Endovascular Surgery 9 (2) (1995)
152–161.
[87] P.E. Hughes, T.V. How, Effects of geometry and ﬂow division
on ﬂow structures in models of the distal end-to-side
anastomosis, Journal of Biomechanics 29 (7) (1996)
855–872.
[88] V. Deplano, C. Bertolotti, P. Barragan, Three-dimensional
numerical simulations of physiological ﬂows in a stented
coronary bifurcation, Medical and Biological Engineering
and Computing 42 (5) (2004) 650–659.