Newtonian viscosity model could overestimate wall shear stress in intracranial aneurysm domes and underestimate rupture risk

Abstract

Computational fluid dynamics (CFD) simulations of intracranial aneurysm hemodynamics usually adopt the simplification of the Newtonian blood rheology model. A study was undertaken to examine whether such a model affects the predicted hemodynamics in realistic intracranial aneurysm geometries.
Pulsatile CFD simulations were carried out using the Newtonian viscosity model and two non-Newtonian models (Casson and Herschel-Bulkley) in three typical internal carotid artery saccular aneurysms (A, sidewall, oblong-shaped with a daughter sac; B, sidewall, quasi-spherical; C, near-spherical bifurcation). For each aneurysm model the surface distributions of shear rate, blood viscosity and wall shear stress (WSS) predicted by the three rheology models were compared.
All three rheology models produced similar intra-aneurysmal flow patterns: aneurysm A had a slowly recirculating secondary vortex near the dome whereas aneurysms B and C contained only a large single vortex. All models predicted similar shear rate, blood viscosity and WSS in parent vessels of all aneurysms and in the sacs of B and C. However, large discrepancies in shear rate, viscosity and WSS among predictions by the various rheology models were found in the dome area of A where the flow was relatively stagnant. Here the Newtonian model predicted higher shear rate and WSS values and lower blood viscosity than the two non-Newtonian models.
The Newtonian fluid assumption can underestimate viscosity and overestimate shear rate and WSS in regions of stasis or slowly recirculating secondary vortices, typically found at the dome in elongated or complex-shaped saccular aneurysms as well as in aneurysms following endovascular treatment. Because low shear rates and low WSS in such flow conditions indicate a high propensity for thrombus formation and rupture, CFD based on the Newtonian assumption may underestimate the propensity of these events.

Full text

ORIGINAL RESEARCH
Newtonian viscosity model could overestimate wall
shear stress in intracranial aneurysm domes and
underestimate rupture risk
Jianping Xiang,
1,2
Markus Tremmel,
1,3
John Kolega,
1,5
Elad I Levy,
1,3,4
Sabareesh K Natarajan,
1,3
Hui Meng
1,2,3
ABSTRACT
Objective Computational fluid dynamics (CFD) simulations
of intracranial aneurysm hemodynamics usually adopt the
simplification of the Newtonian blood rheology model.
A study was undertaken to examine whether such
a model affects the predicted hemodynamics in realistic
intracranial aneurysm geometries.
Methods Pulsatile CFD simulations were carried out
using the Newtonian viscosity model and two
non-Newtonian models (Casson and Herschel-Bulkley) in
three typical internal carotid artery saccular aneurysms
(A, sidewall, oblong-shaped with a daughter sac; B,
sidewall, quasi-spherical; C, near-spherical bifurcation).
For each aneurysm model the surface distributions of
shear rate, blood viscosity and wall shear stress (WSS)
predicted by the three rheology models were compared.
Results All three rheology models produced similar
intra-aneurysmal flow patterns: aneurysm A had a slowly
recirculating secondary vortex near the dome whereas
aneurysms B and C contained only a large single vortex.
All models predicted similar shear rate, blood viscosity
and WSS in parent vessels of all aneurysms and in the
sacs of B and C. However, large discrepancies in shear
rate, viscosity and WSS among predictions by the
various rheology models were found in the dome area of
A where the flow was relatively stagnant. Here the
Newtonian model predicted higher shear rate and WSS
values and lower blood viscosity than the two
non-Newtonian models.
Conclusions The Newtonian fluid assumption can
underestimate viscosity and overestimate shear rate and
WSS in regions of stasis or slowly recirculating secondary
vortices, typically found at the dome in elongated or
complex-shaped saccular aneurysms as well as in
aneurysms following endovascular treatment. Because
low shear rates and low WSS in such flow conditions
indicate a high propensity for thrombus formation and
rupture, CFD based on the Newtonian assumption may
underestimate the propensity of these events.
INTRODUCTION
Intracranial aneurysms (IAs) are pathological
dilations of arterial walls that affect approximately
2e5% of the entire population.
1 2
Ruptured IAs cause
subarachnoid hemorrhage and its sequelae, resulting
in significant morbidity and mortality.
3e5
Hemody-
namic stresses such as wall shear stress (WSS,
the tangential frictional stress caused by the action
of flowing blood on the vessel wall endothelium)
have been shown to play an important role in
IA pathophysiology of initiation and rupture.
6e9
To this end, computational fluid dynamics (CFD) has
been widely used to obtain patient-specificflow
fields in IAs to assess potential risk of rupture.
8e12
CFD simulations often involve simplifying
assumptions of blood properties and boundary
conditions. One of the commonly adopted simpli-
fications in large vessels is the Newtonian fluid
model which prescribes a linear shear stress-strain
rate relationship (constant viscosity) for blood.
Although such a linear relationship represents
blood behavior at high shear rates, the non-
Newtonian effect becomes appreciated at low shear
rates because viscosity increases with decreasing
shear rate.
13
The inherent non-Newtonian charac-
teristics of blood result from the formation of
rouleaux or aggregates of red blood cells under low
shear conditions.
13
Although traditionally the Newtonian fluid
assumption for blood has been adopted in CFD
simulations of large vessels (such as arteries hosting
aneurysms),
14 15
the validity of such simplification
has not been tested for calculations of aneurysmal
hemodynamics in which the results are interpreted
to relate to IA pathophysiology. For example,
previous studies have shown that regions of low
WSS in the aneurysm sac are associated with IA
rupture
8911
as well as thrombus formation.
16
In
such regions the blood is relatively stagnant and is
therefore subjected to lower shear rates than in the
parent vessel. We suspected that, in these low WSS
regions, the non-Newtonian effects might not be
negligible.
The objective of this study was to test the
sensitivity of blood flow field, shear rate and WSS
predictions using different blood rheology models
in different types of patient-specific aneurysm
geometries. We aimed to determine whether
modeling based on the Newtonian assumption can
closely represent non-Newtonian models in typical
IA geometries, particularly in complex geometries
that may be associated with an increased risk of
thrombosis or rupture.
METHODS
Three cases of internal carotid artery (ICA) aneu-
rysms (identified as aneurysms A, B, and C (figure 1)
were selected from the study by Dhar et al
17
for the
present study. Aneurysm A (ruptured, in a 45-year-
old woman) was a sidewall aneurysm with an
<Additional data are published
online only. To view the file
please visit the journal online
(http://jnis.bmj.com).
1
Toshiba Stroke Research
Center, University at Buffalo,
State University of New York,
Buffalo, New York, USA
2
Department of Mechanical and
Aerospace Engineering,
University at Buffalo, State
University of New York, Buffalo,
New York, USA
3
Department of Neurosurgery
University at Buffalo, State
University of New York and
Millard Fillmore Gates Hospital,
Kaleida Health, Buffalo, New
York, USA
4
Department of Radiology
University at Buffalo, State
University of New York, Buffalo,
New York, USA
5
Department of Pathology &
Anatomical Sciences University
at Buffalo, State University of
New York, Buffalo, New York,
USA
Correspondence to
Dr Hui Meng, Toshiba Stroke
Research Center, University at
Buffalo, State University of
New York, 447 Biomedical
Research Building, 3435 Main
Street, Buffalo, NY 14214, USA;
huimeng@buffalo.edu
Received 7 June 2011
Revised 5 August 2011
Accepted 22 August 2011
Xiang J, Tremmel M, Kolega J, et al.J NeuroIntervent Surg (2011). doi:10.1136/neurintsurg-2011-010089 1 of 7
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irregular oblong shape and a daughter sac; aneurysm B (unrup-
tured, in a 68-year-old woman) was a sidewall aneurysm with
a quasi-spherical shape; and aneurysm C (unruptured, in a 66-
year-old man) was a near-spherical bifurcation aneurysm. In the
present study, sidewall aneurysms were defined as lesions
emanating off the side of the parent vessel with or without
a very small vascular branch, and bifurcation aneurysms were
defined as those located at major bifurcations in the cerebral
vessel.
11 18
Three-dimensional angiography images of the
patients’aneurysms were obtained with a Toshiba Infinix VFi/
BP frontal C-arm system (Toshiba America Medical Systems,
Tustin, California, USA). Three-dimensional images of the ICA
were then reconstructed in surface-triangulation format using
in-house software based on the open-source Visualization Tool
Kit libraries, as previously described.
17
Two widely applied non-Newtonian fluid models for blood,
the Casson and Herschel-Bulkley (H-B) models, were used for
the CFD simulations of the geometric ICA aneurysm models in
this study, along with the usual Newtonian fluid model.
16
The
mathematical details of these models are given in the online
appendix. Figure 2 shows viscosity versus shear rate for the three
rheology models. All three models provide similar viscosity
values at the high shear rates (>100/s) that are typical for large
arteries, but exhibit very different behaviors at low shear rates.
Finite-volume meshes consisting of approximately 300 000 to 1
million elements were created for the flow domain of each ICA
aneurysm model using ANSYS ICEM CFD (ANSYS, Canons-
burg, Pennsylvania, USA). The NaviereStokes equations were
solved numerically under pulsatile flow conditions using the
CFD solver Star-CD (CD Adapco, Melville, New York, USA). In
all simulations a mean flow rate of 4.6 ml/s at the ICA
19
was
used as the inlet boundary condition, and a pulsatile velocity
waveform measured from transcranial Doppler ultrasound
images obtained from a normal subject was scaled to the mean
flow rate. Traction-free boundary conditions were implemented
at the outlets. The mass flow rate through each outlet artery
was proportional to the cube of its diameter based on the
principle of optimal work.
20
Detailed flow-governing equations
and numerical methods of CFD simulations are shown in the
online appendix. For each aneurysm geometry we performed
three pulsatile flow simulations using the Newtonian model, the
Casson model and the H-B model, respectively. In this study we
were only concerned with the shear rate, viscosity and WSS
averaged over one cardiac cycle. In this paper, mention of these
parameters implies time-averaged values over one cardiac cycle.
In our analysis of the CFD hemodynamic data we plotted the
luminal distributions of shear rate, viscosity and WSS derived
from each simulation. For quantitative comparison of different
rheology models, we calculated the average shear rate and the
average blood viscosity over the aneurysm dome volume and the
average WSS over the aneurysm dome surface. Here the aneu-
rysm sac was divided into dome, body and neck regions, each
occupying one-third of the aneurysm height.
21
Average values
for the parent vessel parameters were calculated similarly from
the reconstructed parent vessel segments, including the
branches.
RESULTS
Flow characterization
CFD simulations using all three rheology models produced very
similar flow patterns in each ICA aneurysm. Figure 3 shows the
time-averaged flow patterns on representative cross-sectional
planes predicted by CFD using the Newtonian model. Although
aneurysms B and C contained a typical large single vortex with
inflow and outflow pathways, aneurysm A harbored an addi-
tional secondary vortex near the dome that was slowly recir-
culating or nearly stagnant. Time-resolved visualization of the
pulsatile flow field (not shown) revealed that the primary
vortices within all three aneurysms were stable, whereas the
secondary vortex in aneurysm A was slowly oscillating. These
results were similar to those obtained with the non-Newtonian
models (not shown).
Figure 1 Three patient-specific
internal carotid artery aneurysm models
used in this study: aneurysm A,
a sidewall aneurysm with an irregular
oblong shape and a daughter sac;
aneurysm B, a sidewall aneurysm with
a quasi-spherical shape; aneurysm C,
a near-spherical bifurcation aneurysm.
Figure 2 Viscosity versus shear rate for the three blood rheology
models. These models give different stress-strain rate relations at low
shear rates but exhibit similar constant viscosity at the high shear rates
(>100/s) that are typically encountered with blood flow in large arteries.
s
is the shear stress, mis the dynamic viscosity, _
g
is the shear rate,
s
0
is
the yield stress and m
N
is the Newtonian viscosity. Details of these
rheology models are given in the online appendix. Pa, Pascal; s, second.
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Shear rate
Figure 4 shows the luminal distributions of shear rate calculated
using the three rheological models for each aneurysm geometry.
Because the non-Newtonian effect becomes most appreciated at
very low shear rates (figure 2), a logarithmic scale was used to
accentuate this effect for comparison between the different
blood rheology models (figure 4). In each case the Casson model
and H-B model predicted distributions that were similar to those
associated with the Newtonian model, except for the dome of
aneurysm A which featured a low shear rate zone. Figure 5
provides a quantitative comparison of shear rate values that
were volume-averaged in the aneurysm dome (top one-third of
the sac) and in the parent vessel, calculated by all three rheology
models.
In the dome of aneurysm A the Casson model and H-B model
predicted average shear rates that were only 53% and 43%,
respectively, of the values obtained with the Newtonian model.
Elsewhere (ie, in the rest of aneurysm A and in aneurysms B and
C) the discrepancies were less than 3%. In other words, the
Newtonian model overestimated the shear rate in the dome of
aneurysm A, a predominantly low shear region.
Viscosity
Blood viscosity distributions at the luminal wall from the two
non-Newtonian models generally showed no large variations
and were similar to the Newtonian viscosity (figure 6). The only
exception was the dome of aneurysm A where substantially
higher viscosity values were observed when using the Casson or
H-B model. Here the average viscosities predicted by the Casson
and H-B models were 174% and 274% of the Newtonian model,
respectively (figure 5)dthat is, the Newtonian model did not
reflect the drastically increased viscosity in the stagnant region
in the dome of aneurysm A.
Wall shear stress
Figure 7 shows the luminal distributions of WSS predicted by all
three rheology models. For ease of comparison, the WSS is
normalized by the local WSS value from the Newtonian model
Figure 3 Flow patterns (velocity
vector field averaged over a cardiac
cycle) on a representative cross-
sectional plane in aneurysms A, B and C
(based on the Newtonian model; similar
to results from the two non-Newtonian
models). Note that all aneurysms had
a large vortex, but aneurysm A has an
additional secondary vortex near the
dome.
Figure 4 Local logarithmic shear rate
distribution at the lumen in aneurysms
A, B and C. In each case the Casson
and Herschel-Bulkley (H-B) models
predicted similar distribution to the
Newtonian model, except for the dome
of aneurysm A where considerably
lower shear rate values were predicted
by both non-Newtonian models than the
Newtonian model.
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prediction. Because of this normalization, the Newtonian results
(left column) appear to have unity WSS distributions (ie, all
values are 1). In each aneurysm case the Newtonian and Casson
models predicted similar WSS, except in the dome of aneurysm
A where the Casson model prediction was considerably
lowerdas low as 55% of the Newtonian prediction (observation
from figure 7) at the tip of the dome. The H-B model (right
column) predicted slightly lower WSS (approximately 5% less)
than the Newtonian model, except in the dome of aneurysm A
where the H-B model predicted as low as 60% of the Newtonian
model (observation from figure 7) at the tip of the dome.
Figure 5 provides quantitative comparisons of the surface-
averaged WSS in the aneurysm dome region and in the parent
vessels predicted by the three models. The average WSS predicted
by the Casson and H-B models was 71% and 76%, respectively,
of the Newtonian WSS, showing that the Newtonian model
overestimated WSS in the dome of aneurysm A.
DISCUSSION
Previous studies have investigated the influence of non-Newto-
nian blood rheology on CFD modeling in idealized geometric
models of aneurysms. Those models usually consist of a sphere
on a cylindrical tube (straight or curved) which possesses perfect
symmetry that does not exist in real aneurysms. Fisher et al
22
virtually created different types of idealized aneurysms,
including bifurcation and sidewall aneurysms on straight and
curved vessels. Valencia et al
23
studied the non-Newtonian effect
on two virtual saccular aneurysm models with different incli-
nation angles and one model of a non-diseased basilar artery.
Such perfect symmetry is unrealistic and may cause misleading
flow patterns because realistic anatomical aneurysm geometry
can have complex flow dynamics that idealized geometries
cannot capture. Such complex flow dynamics could be caused by
vessel curvature or tortuosity, which influence the flow entering
and circulating within the aneurysm sac and thus shear stress on
the aneurysm wall.
15
Furthermore, patients’aneurysms are
often non-spherical or have multiple lobes and, because of these
irregular shapes, can harbor various disturbed flow patterns
including secondary and/or unsteady vortices.
17 24e26
Blood
rheology results based on idealized aneurysm models do
not therefore reflect many important features of real anatomy.
23
In the current study, geometric models of typical realistic
ICA aneurysms representing an oblong sidewall aneurysm,
a near-spherical sidewall aneurysm and a near-spherical
bifurcation aneurysm were used to investigate the influence of
non-Newtonian blood rheology on CFD simulations.
Our results indicate that the Newtonian fluid assumption in
general is acceptable in CFD modeling of healthy vessels and
Figure 5 Shear rate, viscosity and wall shear stress (WSS) averaged in the dome and in the parent vessel from computational fluid dynamics using
the three rheology models (aneurysms A, B, and C). Shear rate and viscosity were volume-averaged whereas wall shear stress was averaged on the
luminal surface. All values presented were normalized by the Newtonian results.
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aneurysms that do not harbor regions of pronounced low shear.
However, the current data suggest that the non-Newtonian
properties of blood should be considered when modeling
hemodynamics in aneurysms with slow and recirculating flow
regions (low shear flow), which are typically found in aneu-
rysms with complex geometry like aneurysm A with an irregular
oblong shape and a daughter aneurysm.
These types of aneurysms are generally suspected to be
dangerous and command attention for treatment, as low WSS
has been shown to be associated with aneurysm rupture
8911
and low shear rates may cause clot formation.
16
Xiang et al
11
demonstrated that the rupture of IAs correlated with low WSS
in their study of 119 aneurysms. Ishida et al
27
identified the
rupture points of eight ruptured middle cerebral artery aneu-
rysms to be located in regions of the lowest WSS. The Newto-
nian model cannot capture the increased viscosity in such low
shear regions and consequently overestimates the shear rate and
WSS. When the non-Newtonian effects are neglected in such
aneurysms, the shear rate and WSS appear falsely higher in the
low shear regions and thus could under-represent the risk of clot
formation and aneurysm rupture.
In clinical practice, coil embolization or flow diverter treat-
ment for cerebral aneurysms reduces the intra-aneurysmal flow,
as indicated by contrast stagnancy at the dome, thereby
reducing shear rate (thus promoting clotting) and WSS (thus
increasing rupture risk).
24 28
If intra-aneurysm thrombosis does
not develop quickly and completely to fill the whole sac
but leaves a part of the aneurysmal wall exposed to low WSS for
an extended period of time, such treatments could result in
deterioration of the wall via inflammatory cell infiltration
(caused by low WSS and immature thrombus
29
) and thus an
increased propensity of rupture.
24
However, we believe that in
most situations clotting happens much faster than the wall
degradation. Thus, coil or flow diverter embolization, by
massively increasing stasis, usually induces a healing response
through thrombosis and subsequent cicatrization. It is impor-
tant to note, however, that there have been reports of aneurysm
rupture after coil or flow diverter treatments.
29
The typical
aneurysmal flow after coil or flow diverter implantation has
high stasis with a very low shear rate and WSS. Hence, the same
precaution regarding the choice of blood rheology model
should be taken in hemodynamic modeling of post-treatment
aneurysms.
Despite our concerns regarding the application of the
Newtonian assumption in CFD of IAs, we do not suggest that
all CFD analyses be conducted with non-Newtonian rheology.
The Newtonian model has its merits: it is simple and easy to
use, implicit in all commercial CFD software and accurate
enough in most situations unless low shear regions are present.
Furthermore, our data show that Newtonian models produce
flow patterns roughly consistent with non-Newtonian models.
Hence, if the researcher only wants to know the intra-aneu-
rysmal flow patterns but not WSS or shear rate, routine CFD
with Newtonian assumption might be sufficient.
Non-Newtonian models have their drawbacks. Implementa-
tion of non-Newtonian models in CFD requires writing
Figure 6 Local blood viscosity
distribution at the luminal wall for each
aneurysm predicted by computational
fluid dynamics using the three rheology
models. The Casson and Herschel-
Bulkley (H-B) models generally show
little deviation from the Newtonian
viscosity, except for the dome in
aneurysm A where they predicted much
higher viscosity.
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subroutines or using specialized CFD software, which might not
be available to all researchers. Moreover, non-Newtonian models
sometimes may underperform. For example, in the H-B model,
the viscosity has no lower limit when shear rate tends to
infinity. Hence, at very high shear rates where blood is expected
to behave like a Newtonian fluid with a constant viscosity, the
H-B model would produce unrealistically lower viscosity values.
This behavior causes viscosity values in the parent arteries in our
study to fall below the Newtonian value (figures 2 and 6) and
may unduly influence the flow field. In our study, at a shear rate
of 10 000/s, the corresponding viscosity in the H-B model is
2.5 cP compared with the Newtonian viscosity of 3.5 cP.
As a simplified heuristic to aid decision-making for future
aneurysm hemodynamics modeling projects, we suggest using
non-Newtonian rheology modeling in the following situations
where regions of high stasis or slow recirculation are expected,
especially when quantitative information of shear rate, WSS or
WSS-based quantities such as oscillatory shear index are desired:
(1)Aneurysms with size ratio >2. Size ratio is defined as the
maximal diameter of the aneurysm divided by the parent vessel
diameter.
17
Tremmel et al
25
demonstrated that, once the size
ratio becomes >2, the single aneurysmal flow vortex splits into
multiple vortices and the low WSS area increases drastically.
Dhar et al
17
found that size ratio can significantly separate
ruptured from unruptured aneurysms, and this finding has been
supported by other studies.
11 30 31
Furthermore, Dhar et al
17
found the optimal threshold for size ratio to be 2.05.
(2) Aneurysms with daughter aneurysms or blebs.
(3) Aneurysms after coil or flow diverter implantation.
When researchers are unsure whether a particular aneurysm
case commands non-Newtonian modeling, we suggest that they
first run a simple and quick steady-state CFD simulation using
the Newtonian model to determine whether a low shear flow
region exists. If it does, a non-Newtonian model could be used
for proper CFD simulation to obtain WSS and related quantities
such as oscillatory shear index.
This study has several limitations. First, only three aneurysm
cases were investigated. Although this can provide an initial
illustration of the effect of non-Newtonian rheology on aneu-
rysmal hemodynamics, conclusions should be validated in
follow-up studies that include a large number of cases. Second,
because we focused on comparing hemodynamics from different
rheology models, we kept the inlet boundary condition for the
CFD simulations the same, which may not accurately reflect the
patient-specific reality. Third, although non-Newtonian
rheology can improve the accuracy of blood flow simulations,
the non-Newtonian models are themselves also simplifications
and cannot perfectly mimic in vivo behavior. Finally, there is no
consensus as to which non-Newtonian model (Casson, H-B or
others) is superior. Further investigations are therefore needed
Figure 7 Wall shear stress (WSS)
distribution (normalized by local WSS
values from the Newtonian model) in
the lumens of aneurysms A, B and C. In
each case the Casson model predicted
a distribution that was similar to that of
the Newtonian model, except for the
dome of aneurysm A. The Herschel-
Bulkley (H-B) model predicted overall
slightly lower values and, in the dome
of aneurysm A, the non-Newtonian
models predicted considerably lower
WSS values than the Newtonian model.
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that are dedicated to produce a more consistent non-Newtonian
model, and care should be taken to accurately determine its
model parameters experimentally.
CONCLUSION
The Newtonian blood rheology assumption is usually acceptable
for CFD simulation of cerebral aneurysm hemodynamics but
could underestimate viscosity and overestimate shear rate and
WSS in the slowly recirculating flow regions that are typically
found at the dome in elongated or complex-shaped saccular
aneurysms, as well as in aneurysms following endovascular
treatment. Because low shear rates and low WSS in such flow
conditions indicate a high propensity for thrombus formation
and aneurysm rupture, Newtonian hemodynamics may under-
estimate the propensity of these events.
Acknowledgments We thank Paul H. Dressel BFA for assistance with preparation
of the illustrations and Debra J Zimmer AAS CMA-A for editorial assistance.
Disclosures Dr. Kolega, Dr. Natarajan, Dr. Tremmel, and Mr. Xiang have no final
relationships to disclose. Dr. Meng is the principal investigator of the aforementioned
NIH grant. Dr. Levy receives research grant support (principal investigator:
Stent-Assisted Recanalization in acute Ischemic Stroke, SARIS), other research
support (devices), and honoraria from Boston Scientific* and research support from
Codman & Shurtleff, Inc. and ev3/Covidien Vascular Therapies; has ownership
interests in Intratech Medical Ltd. and Mynx/Access Closure; serves as a consultant
on the board of Scientific Advisors to Codman & Shurtleff, Inc.; serves as a consultant
per project and/or per hour for Codman & Shurtleff, Inc., ev3/Covidien Vascular
Therapies, and TheraSyn Sensors, Inc.; and receives fees for carotid stent training
from Abbott Vascular and ev3/Covidien Vascular Therapies. Dr. Levy receives no
consulting salary arrangements. All consulting is per project and/or per hour. (*Boston
Scientific’s neurovascular business has been acquired by Stryker.)
Funding This work was partially supported by NIH grant R01NS064592 and a grant
from Toshiba Medical Systems.
Competing interests None.
Contributors HM and JX conceived and designed the research. JX acquired the data.
JX, MT, HM and JK analyzed and interpreted the data. JX, MT and HM performed
statistical analysis. HM handled funding and supervision. JX, HM, MT, SKN and JK
drafted the manuscript. All authors made critical revision of the manuscript for
important intellectual content and reviewed the final version of the manuscript.
Provenance and peer review Not commissioned; externally peer reviewed.
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PAGE fraction trail=7
Xiang J, Tremmel M, Kolega J, et al.J NeuroIntervent Surg (2011). doi:10.1136/neurintsurg-2011-010089 7 of 7
Hemorrhagic stroke
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doi: 10.1136/neurintsurg-2011-010089
published online September 19, 2011J NeuroIntervent Surg
Jianping Xiang, Markus Tremmel, John Kolega, et al.
underestimate rupture risk
intracranial aneurysm domes and
overestimate wall shear stress in
Newtonian viscosity model could
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