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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3592_Библиотеки_им_академика_М_И_Перельмана
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Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
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T
ττ=
ττ=
1
T
T
dt
∫
wmean
0
T
dt1. (4.40)
∫
wmag
0
(4.39)
A low value of TAWSS (lower than 0.4 Pa) stimulates the pro-atherogenic
endothelial phenotype [13], and perturbed endothelial alignments on the walls of
vessels are induced at regions where the instantaneous WSS deviates from the main
flow direction in a large fraction of the cardiac cycle, and it can be identified as
regions of high OSI [11]. The OSI has a range between 0 and 0.5, where 0.5 defines
purely oscillatory flow. Areas of high OSI would lead to endothelial dysfunction and
atherogenesis and hence the detection of such zones is very important.
Figure 4.8 summarizes the endothelial OSI distribution in vessels containing
abnormalities, either in the form of aneurysm or stenosis. Varying flow rates as well
Figure 4.8. OSI distribution plot at different viscosities (PL = power-law, Que = Quemada) and at different
flow rates (Re I and Re II).
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as different viscosity models (namely the power-law model and Quemada model) are
considered for the assessment simultaneously. Insignificant variations of OSI
distributions are observed between the power-law and Quemada viscosity models.
Modulation of the flow rate induces changes in OSI distribution —dual peaks are
observed at higher flow rates in comparison to single peaks at lower flow rates in
aneurismal vessels. The peaks of the OSI are found to be higher in magnitude as the
flow rate increases in aneurismal vessels, whereas insignificant modulation of the
magnitude of the same are observed in stenosed vessels, irrespective of increased
flow rates.
4.5.2 Relative residual time
The combination of the OSI and TAWSS is also known as relative residual time
(RRT), which is proportional to the residence time of blood particles near the wall:
=
RRT
Several studies [10, 15, 17, 18] recommended RRT as a single metric of low and
oscillating shear.
RRT distributions along the entire length of endothelial linings are shown in
figure 4.9. The spatial magnitude of RRT remains several folds higher in vessels with
aneurysm than stenosis. The aneurismal vessel exhibits an increase in RRT values
with flow rate, whereas RRT decreases with an increase in flow rate in stenosed
vessels. Interestingly, an effect of the viscosity model is found in the case of RRT
distributions. The peak magnitude of RRT in an aneurismal vessel is found to be
higher when considering the Quemada viscosity model (about 300 ms) for a higher
flow rate (Re II), whereas the power-law model exhibits a higher value of RRT
(about 350 ms) for a lower flow rate (Re I). The stenosed blood vessel has the highest
RRT values (about 20 ms and 10 ms for Re I and Re II, respectively) when
considering the power-law viscosity model, whereas it attenuates in the Quemada
model (about 12 ms and 9 ms for Re I and Re II, respectively). The maximum values
of RRT distributions are found at the periphery of the aneurismal vessel, whereas
they are found more in the immediate downstream in the stenosed vessel.
(1 2 OSI) TAWSS
−× ×
1
.
(4.41)
4.6 Conclusion
A two-dimensional axi-symmetric geometry of a blood vessel is created containing a
stenosis profile, which was pre-defined according to [9]. The severity of the stenoses
was varied from 25%–80% and realistic pulsating flow profiles were used to realize
influx of blood through the geometry. Non-Newtonian rheological models, namely
the Casson model, Carreau model, cross model, power-law model and Quemada
model, are generally used along with the Newtonian model to represent the
rheological properties of blood in a diseased state. Various shear-stress parameters
such as WSS, OSI and RRT are used for qualitative analysis of higher stress
distributions and their behavior near the wall of the vessel downstream of the
stenosis. The transport phenomena of flow structures in vessels containing severe
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Figure 4.9. RRT distribution plot at different viscosities (PL = power-law, Que = Quemada) and at different
flow rates (Re I and Re II).
aneurysms of the saccular type are also presented here. The aneurismal profile was
adapted from a pre-defined aneurismal function proposed by [16]. The pulsating
flow profiles discussed in this chapter are varied with different Reynolds numbers
and the influences of flow rate on the depth of aneurysm are measured in the form of
distributions of defined shear-stress markers at the wall i.e. WSS, OSI and RRT.
Various parameters, such as mean velocity, r.m.s. velocity, turbulent intensity,
velocity flatness, velocity skewness, and maximum velocity and minimum velocity
over every cardiac cycle, can also be evaluated as primary parameters for evaluating
the probability of secondary stenoses in post-stenotic regions. Some derivative
parameters, such as WSS, stenosis length, the pressure drop coef fi cient and pressure
recovery factors, can also be used to validate the results obtained from different
numerical investigation of stenosed blood vessels in two-dimensional form.
Biological flow is a complex domain of research involving mechanics, physiology,
chemistry, etc. The current chapter addresses certain issues for pathological vessels
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involving modeling and experiments. The following areas might motivate reader to
further study:
• The transition and turbulent regimes of hemodynamics need further
attention.
• The investigation of the hemodynamics of blood through smaller capillaries is
an unexplored area.
• The interactions of endothelial cells on the intimal lining with the hemodynamics of blood can be investigated by conducting experiments at the cellular
level.
• The investigation of changes in cellular properties in extracellular fluids on
exposure to high shear rate fluid dynamics can be performed using mathematical modeling and is a potential area of research.
• The cellular diffusion of mass transport across various layers of blood vessel
under the influence of high shear rate in a diseased condition of the vessel is
another unexplored area.
References
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York: Wiley)
[2] Bit A and Chattopadhyay H 2018 Acute aneurysm is more critical than acute stenoses in
blood vessels: a numerical investigation using stress markers BioNanoScience
[3] Bit A and Chattopadhyay H 2014a Assessment of rheological models for prediction of
transport phenomena in stenosed artery Prog. Comput. Fluid Dyn. Int. J.
[4] Bit A and Chattopadhyay H 2014b Numerical investigations of pulsatile flow in stenosed
artery Acta Bioeng. Biomech. 16 33–44
[5] Bit A, Ghagare D, Rizvanov A A and Chattopadhyay H 2017 Assessment of influences of
stenoses in right carotid artery on left carotid artery using wall stress marker BioMed. Res.
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[6] Chien S, Usami S, Dellenback R and Gregersen M 1967 Blood viscosity: Influence of
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[7] Cross M M 1965 Rheology of non-Newtonian fluids: a new flow equation for pseudoplastic
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[9] Drikakis D, Milionis C, Pal S K and Shapiro E 2011 Assessment of the applicability of
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[10] He X and Ku D N 1996 Pulsatile flow in the human left coronary artery bifurcation: average
conditions ASME J. Biomech. Eng.
[11] Himburg H A, Grzybowski D M, Hazel A, LaMack J A, Li X M and Friedman M H 2004
Spatial comparison between wall shear stress measures and porcine arterial endothelial
permeability Am. J. Physiol. Heart Circ.
[12] Himburg H A and Friedman M H 2006 Correspondence of low mean shear and high
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[13] Huang C, Chai Z and Shi B 2013 Non-Newtonian effects on hemodynamic characteristics of
blood flow in stented cerebral aneurysm Commun. Comput. Phys.
[14] Jespersen S N and Østergaard L 2012 The roles of cerebral blood flow, capillary transit time
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[15] Lee S W, Antiga L and Steinman D A 2009 Correlations among indicators of disturbed flow
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[16] Molla M M and Paul M C 2012 LES of non-Newtonian physiological blood flow in a model
of arterial stenosis J. Med. Eng. Phys.
[17] Morbiducci U, Gallo D, Ponzini R, Massai D, Antiga L, Redaelli A, Deriu M A and
Montevecchi F M 2011 On the importance of blood rheology for bulk flow in hemodynamic
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[18] Morbiducci U, Gallo D, Ponzini R, Massai D, Consolo F, Bignardi C, Deriu M A, Antiga L
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[19] Neofytou P and Drikakis D 2003 Effects of blood models on flow through a stenosis Int. J.
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[20] Quemada D 1977 Rheology of concentrated disperse systems III. General features of the
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[23] Walburn F J and Schneck D J 1976 A constitutive equation for whole human blood
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Vascular and Intravascular Imaging Trends, Analysis, and
Challenges, Volume 1
Stent applications
Petia Radeva and Jasjit S Suri
Chapter 5
Fast virtual endovascular stenting: technique,
validation and applications in computational
haemodynamics
Ignacio Larrabide
5.1 Motivation
Although most intracranial aneurysms (IAs) remain asymptomatic, some of them
tend to grow and eventually rupture. The rupture of these aneurysms has an
incidence of 1%–2% in the adult population [1]. The rupture of an aneurysm leaks
blood into the space occupied by cerebro-spinal fluid (CSF). This event is called a
sub-arachnoid haemorrhage (SAH), which is associated with significant indices of
morbidity and mortality. Between 10% and 20% of SAH patients die before
receiving medical attention [2] and approximately one third die in the first 30 days
after their intake, resulting in an overall mortality rate of 50% [3]. Of the patients
who survive, between a third and half have neurological sequelae.
In addition to symptomatic aneurysms, it is expected that between 0.1%–0.5% of
all magnetic resonance imaging (MRI) and computed tomography (CT) studies
performed per year will lead to the incidental discovery of asymptomatic IAs in
patients arriving at the hospital for other reasons. Therefore, the decision of whether
to treat a patient with an IA must take many aspects into consideration. Different
risk factors have been associated with an increased likelihood of rupture and often
some kind of treatment is required [4, 5]. Neurovascular specialists currently
consider many features as important when evaluating unruptured intracranial
aneurysms (UIAs). The size of the IA, any history of sub-arachnoid haemorrhage
and an AI located in the posterior circulation are the most significant risk factors
indicating rupture of UIAs. However, a full understanding of the nature of UIAs is
lacking [6].
doi:10.1088/2053-2563/ab01fach5 5-1 ª IOP Publishing Ltd 2019
Vascular and Intravascular Imaging Trends, Analysis, and Challenges, Volume 1
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Taking all the risk factors into consideration, the selection of an appropriate
treatment for an IA patient should consider a balance between the risk of aneurysm
rupture and the risk of treatment. In the last decade, there have been major advances
in the diagnosis and treatment of IAs as a result of major technological developments in diagnostic imaging and intervention as well as a new generation of
therapeutic devices [7].
When treating IAs, stents can be used as a scaffold to maintain coils inside the
aneurysm cavity when treating broad-neck aneurysms [8]. However, the implantation of neurovascular stents has shown to have an impact on the local curvature of
the vessel [9, 10]. Previous studies have proven that, apart from their role as a
mechanical support, stents used as scaffolds can also play a role in the diversion of
flow away from the aneurysm [11].
In the past few years, computational modelling of intracranial stenting allowed
the development of different studies that help in understanding the effects of
treatment under different circumstances. The study of local haemodynamics in
IAs has proven to be essential in understanding this disease and its various treatment
alternatives. Recent advances in computational capabilities have made this possible,
leading to a huge development of the field of bio-medical engineering in the study of
IAs. Early work by Cebral et al [12] was focused on assessing the risk of rupture of
IAs, and evaluating the effect of having cyclic topology in the cerebral vasculature
[13]. The work of Meng et al [14, 15] showed that complex haemodynamics at the
apex of an arterial bifurcation induces vascular remodelling resembling aneurysm
initiation. In their study, the authors used computational fluid dynamics (CFD) to
reproduce haemodynamic conditions at bifurcations which were then compared to
biological tissue samples subject to equivalent flow insult. Geers et al have focused
on studying the sensitivity of computational haemodynamics to different imaging
modalities [16], where patient-specific flow simulations were performed from
computed tomography angiography (CTA) and three-dimensional rotational
angiography (3DRA) for 11 individuals. The effect of steady-state versus transient
simulations was also assessed, showing a remarkable reduction in computational
time [17].
In addition, flow diversion has gained considerable attention for its high rate of
success and simplicity [18–21]. To better understand these mechanisms anatomically
and bio-mechanically, different computational techniques have been developed
[22, 23], which should be properly evaluated before becoming part of everyday
clinical practice. In this text we describe some of the latest advances in IA modelling
and its applications in the study of intra-aneurysmal haemodynamics.
5.2 Virtual stenting
A considerable amount of work has been devoted over the past few years to
developing computational models of cerebrovascular stents, their physical behaviour and to assess their efficiency for treatment using computational simulation.
The first models for the computational simulation of stents were developed for
modelling coronary stents. These approaches were primarily based on the finite
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element method (FEM) and aimed at modelling the stent’s mechanical properties
and its interaction with the vessel wall from a strictly mechanical point of view
[24, 25]. The fact that coronary stenting is typically done with balloon-inflated
stents, posed additional problems for their modelling. In many cases, the treatment
of coronaries requires more than one device, which has also been considered more
recently [26, 27].
Modelling of cerebral stets has also been considered from a purely mechanical
point of view. Initial work by De Beule et al was aimed at the optimization of
braided cerebral stents, through detailed modelling using the FEM [28]. More recent
work by Ma and co-workers presents a methodology for the mechanical FEM
simulation of densely braided cerebral stents, which is used for modelling in detail
the device mechanics and its individual threads and their behaviour during treatment
[29, 30]. These methods are extremely accurate in modelling the mechanical
behaviour of the stent and its interaction with the vessel wall. However, their setup and computational time can be extensive, making their use in daily clinical
practice cumbersome.
The early work of Ohta et al [31, 32] showed the effects of stents in intraaneurysmal haemodynamics, proving the feasibility of computational models in
assessing the stenting treatment of aneurysms. In the work of Cebral and Lohner
[12], further developed by Appanaboyina et al [33], a deformable cylinder model is
used to adjust an intracranial stent to the patient anatomy. Later, the design of the
stent is mapped onto the deformed cylinder to obtain a 3D representation of the
deployed stent. Janiga and colleagues [34] proposed a free-form deformation
method, which allows the virtual implantation of intracranial stent models into
complex patient-specific geometries. This technique was also used in combination
with CFD simulations to characterize the inflow and the corresponding residence
time in the aneurysm. The work of Peack et al has explored the use of deformable
models in combination with lineal and torsional spring analogies to deploy different
kinds of stents in realistic geometries. Furthermore, they explored the use of
thrombosis models to study the occlusion of intracranial aneurysms [35]. These
methods make extensive use of simplification assumptions, making them computationally more efficient and simpler. However, they are not capable of representing
many of the details of these stents’ behaviour and their interaction with the vessel
wall.
In this chapter we present results obtained for techniques assuming simplification
assumptions, designed for a faster performance. This technique is considered to be
simple, keeping in mind its potential use in a clinical context. In the following section
the fast virtual stenting (FVS) method is described. This method is based on an
extension of simplex deformable models with stent-specific geometrical constraints.
5.3 The fast virtual stenting method
The fast virtual stenting (FVS) method was initially developed to serve as a tool for
treatment planning and to provide a fast and simple representation of different stent
models inside the patient’s own anatomy. FVS is based on simplex deformable
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meshes and geometrical constraints that account for the shape and design of the
stent being modelled, and was initially developed a few years ago [36, 37].
Deformable simplex models have been previously used by Delingette et al [38]in
object reconstruction and by Montagnat and Delingette for free-form [39] and
constrained [40] deformation. The main idea behind this methodology is the use of a
second-order partial differential equation for moving a mesh under the effect of
internal and external forces. A numerical approximation is obtained by a finite
difference discretization, which can be written as
t
t
+−
pp pp fp fp(1 ) .
i
i
tit
γαβ=+− − + +
()
i
t
() ()
int ext
i
t11
i
(5.1)
These models are usually discretized using simplex meshes, where at the mesh
boundary a free boundary condition is used. In
, two-simplex meshes are surface
representations that are closely related to triangular meshes. In particular, the
underlying graph that defines them is dual (figure 5.1). Complementary definitions
and additional information on simplex meshes can be found in the work of
Delingette [38].
Additionally, simplex meshes are not appropriate for representing stents as these
usually do not comply with the definition of a two-simplex mesh. To overcome this
limitation, geometrical information of the stent is also taken into account. This can
be obtained from a μ-CT scan of the stent or directly from the stent manufacturer
when possible. Geometrical characteristics of the stent in the ‘free’ state
(i.e. expanded outside the vessel) are used to guide the deformation of the mesh.
The geometrical characteristics recorded from the free state are set as the reference
configuration for the geometrical constraints. Four geometrical constraints are
considered:
• Stent design (strut pattern): As most stents have a repeating cell design, the
stent is modelled as a set of cells (figure 5.1(a)). By the repetition of stent cells,
the design of the whole stent is built. This approach allows mapping any stent
design on the simplex mesh by a simple repetition process.
• Strut length: Total length of a strut between the two ends where it is attached
to the stent mesh. This length is measured at the nominal (‘free’)
configuration.
Figure 5.1. (a) Example of a simplex mesh. The stent cells contain the information and description of the stent
design. (b) Example of an Enterprise stent (Cordis Neurovascular, Miami Lakes, FL, USA) and its
representation. (c) Example of a Silk stent (Balt Extrusion, Paris, France) and its representation.
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• Angle between struts: Angle between pairs of struts. This angle is measured at
the nominal configuration.
• Deployed stent radius: Corresponds to the stent radius in the free state
configuration and is considered as the equilibrium position for the expanding
force.
There are two reasons for using these constraints. First, these parameters are
sufficient to describe the global stent geometry if we are not interested in the detailed
structural behaviour of the stent, where additional information such as strut crosssectional shape, as well as distal and proximal stent designs, would be required.
Second, this information is relatively easy to obtain for different stents. Such
information is stored in a subset of points of the simplex mesh that we call stent
points.
The proposed method does not ensure nor force that the final configuration of the
stent fully conforms to the nominal stent configuration, implying that these are
imposed as ‘soft’ constraints. In this way, the deformation is stopped when internal
and external forces are balanced. The reason for using this simplification is that the
stent constraints are measured for the free state when released outside the vessel.
When released inside a vessel, the stent does not recover the free state configuration.
Then, the use of soft constraints, where a balance between internal and external
forces is required, seems more appropriate.
5.4 Validation—how accurate is accurate enough?
The FVS method has been developed as a technique for modelling different types of
stents implanted in intracranial aneurysms keeping in mind its use by clinicians. For
this reason, its computational efficiency and associated simulation time were
specifically taken into account as important factors. This method was also designed
to evaluate local haemodynamic alterations after stent implantation, by the use of
CFD.
The shape of the stent after implantation is considered for its validation, and the
effects of each model on posterior CFD simulations are also evaluated. The FVS
method has been validated using FEM models, and later combined with CFD. The
validation of FVS is developed in two stages. The FVS method is compared to
FEM models with different degrees of complexity, starting with highly detailed
descriptions of the mechanics of the stent and vessel wall, which are progressively
simplified [41].
5.4.1 FVS versus FEM—mechanics
In this study, the possibility of introducing suitable approximations in the computational models to progressively reduce their complexity and computational time was
studied. Two main questions were investigated in this study: (i) how much the stent
and vessel wall models have to be simplified to reduce the computational time such
that these methodologies can be suitable for the clinical environment and (ii) what
information we lose by simplifying these models and what its significance is. It is
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