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Comparison of peak wall stress and peak wall rupture
index in ruptured and asymptomatic intact abdominal
aortic aneurysms
T. P. Singh
1,3
, J. V. Moxon
1,2
, V. Iyer
1,3,4
, T. C. Gasser
5
, J. Jenkins
4
and J. Golledge
1,2,3,
*
1
Queensland Research Centre for Peripheral Vascular Disease, College of Medicine and Dentistry, Townsville, Australia
2
Australian Institute of Tropical Health and Medicine, James Cook University, Townsville, Australia
3
Department of Vascular and Endovascular Surgery, Townsville University Hospital, Townsville, Australia
4
Department of Vascular and Endovascular Surgery, Royal Brisbane and Women’s Hospital Brisbane Queensland Australia
5
KTH Solid Mechanics, Department of Engineering Mechanics, KTH Royal Institute of Technology, Stockholm, Sweden
*Correspondence to: Professor J. Golledge, Queensland Research Centre for Peripheral Vascular Disease, College of Medicine and Dentistry, James Cook University,
Townsville, Queensland 4811, Australia (e-mail: jonathan.golledge@jcu.edu.au)
Abstract
Background: Previous studies have suggested that finite element analysis (FEA) can estimate the rupture risk of an abdominal aortic
aneurysm (AAA); however, the value of biomechanical estimates over measurement of AAA diameter alone remains unclear. This
study aimed to compare peak wall stress (PWS) and peak wall rupture index (PWRI) in participants with ruptured and asymptomatic
intact AAAs.
Methods: The reproducibility of semiautomated methods for estimating aortic PWS and PWRI from CT images was assessed. PWS
and PWRI were estimated in people with ruptured AAAs and those with asymptomatic intact AAAs matched by orthogonal diameter
on a 1 : 2 basis. Spearman’s correlation coefficient was used to assess the association between PWS or PWRI and AAA diameter.
Independent associations between PWS or PWRI and AAA rupture were identified by means of logistic regression analyses.
Results: Twenty individuals were included in the analysis of reproducibility. The main analysis included 50 patients with an intact
AAA and 25 with a ruptured AAA. Median orthogonal diameter was similar in ruptured and intact AAAs (823 (i.q.r. 735–920) versus
810 (732–924) mm respectively; P¼0906). Median PWS values were 2868(2202–3296) and 2458 (2152–3023) kPa respectively
(P¼0192). There was no significant difference in PWRI between the two groups (P¼0982). PWS and PWRI correlated positively with
orthogonal diameter (both P<0001). Participants with high PWS, but not PWRI, were more likely to have a ruptured AAA after adjust-
ing for potential confounders (odds ratio 584, 95 per cent c.i. 122 to 2795; P¼0027). This association was not maintained in all sensi-
tivity analyses.
Conclusion: High aortic PWS had an inconsistent association with greater odds of aneurysm rupture in patients with a large AAA.
Introduction
Abdominal aortic aneurysm (AAA) is estimated to be responsible
for about 200 000 deaths per year worldwide
1–3
. AAA rupture is
thought to occur when the haemodynamic forces on the aortic
wall exceed the aortic wall strength
2,4
. Maximum AAA diameter
is the main measure used to predict the risk of AAA rupture and
inform patient management. Small asymptomatic AAAs (less
than 55 mm diameter in men and less than 50 mm in women) are
generally managed conservatively based on evidence from previ-
ous RCTs
5–8
. Some small AAAs rupture
9
and some large AAAs re-
main stable during a patient’s lifetime
7
, suggesting that aortic
diameter is not a perfect measure to estimate AAA rupture risk
and requirement for surgery. Given the risks and expense associ-
ated with AAA repair, more effective approaches are needed to
select patients for surgery to avoid unnecessary interventions
2,10
.
Biomechanical imaging analyses can be performed non-inva-
sively by applying methods such as finite element analysis (FEA)
to CT images to estimate AAA rupture risk
4,11
. Recently devel-
oped interfaces are user-friendly, time-efficient and semiauto-
matic, enabling clinicians with non-engineering backgrounds to
use this technology
12,13
. Peak wall stress (PWS) is an estimation
of the maximum mechanical tensile stress that arises in the AAA
wall. A previous meta-analysis
4
reported that PWS is greater in
symptomatic or ruptured AAAs compared with intact AAAs, al-
though the results were confounded by differences in maximum
diameter between groups. Subsequent studies have also had a
mismatch in aortic diameter between ruptured and intact
AAAs
4,11
, and other design weaknesses, such as a small sample
size
11
and limited validation of the methods used to estimate
PWS
14,15
. It therefore remains unclear whether high PWS is
Received: May 2, 2020. Revised: July 1, 2020. Accepted: July 22, 2020
V
CThe Author(s) 2020. Published by Oxford University Press on behalf of BJS Society Ltd. All rights reserved.
For permissions, please email: journals.permissions@oup.com
2BJS, 2021, 108, 652–658
DOI: 10.1002/bjs.11995
Advance Access Publication Date: 30 September 2020
Original Article
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associated with AAA rupture independent of aortic diameter.
Furthermore, recent studies have reported that peak wall rupture
index (PWRI)
11
, which represents the ratio between maximum
wall stress and wall strength, may be superior to PWS in estimat-
ing AAA rupture risk
16
. To address some of the limitations of
these previous investigations, the present study aimed to com-
pare PWS and PWRI in ruptured and asymptomatic intact AAAs
from participants with matched aortic diameter.
Methods
This was a retrospective case–control study in which cases with
ruptured AAAs were matched 1 : 2 with controls with asymptom-
atic intact AAAs. Maximum anterior–posterior AAA diameter was
matched between cases and controls to within 2 mm. Ethics and
governance approvals were obtained from the Human Research
Ethics Committees of the Royal Brisbane and Women’s Hospital
(RBWH) and the Townsville Hospital and Health Services (HREC/
11/QRBW/198; SSA/11/QTHS/159).
Participants
Participants were selected retrospectively from databases main-
tained at RBWH and Townsville University Hospital
17
. AAA was
defined by a maximum orthogonal diameter of at least 30 mm.
AAA rupture was defined by the presence of blood within the ret-
roperitoneum or peritoneum identified by CT by a consultant
vascular specialist
17
. Participants with an asymptomatic intact
AAA were individuals who had an incidental finding of an AAA
and were referred to a vascular specialist for management. For
inclusion in the study, a CT angiogram suitable for FEA was re-
quired. Patients with a juxtarenal or thoracoabdominal aneu-
rysm or massive contrast extravasation (in the event of rupture)
were excluded
18
. Participants either had to have a ruptured AAA
or an asymptomatic intact AAA at the time CT was performed.
Patients with a symptomatic intact AAA or who had undergone
previous AAA repair were excluded.
Cardiovascular risk factors
Data on cardiovascular risk factors were obtained from existing
databases and patient records
17,19,20
. Clinical characteristics col-
lected included: age, sex, hypertension, diabetes, ischaemic heart
disease (IHD), stroke, chronic obstructive pulmonary disease
(COPD), smoking and current medications. Smoking classification
was based on smoking history, defined as ever or never smoked.
Medications registered included aspirin, other antiplatelet
agents, angiotensin-converting enzyme inhibitor, angiotensin II
receptor blocker (ARB), statin and metformin. Hypertension, dia-
betes, IHD, stroke and COPD were defined by a history of diagno-
sis or treatment for these conditions
17
.
CT acquisition
A 64-slice multiscanner (Philips, North Ryde, New South Wales,
Australia) was used to obtain contrast-enhanced CT images at 3-
mm intervals under a set acquisition protocol, as described previ-
ously
17,21
. UltravistV
R300 contrast (100 ml; Bayer, Wayne, New
Jersey, USA) was administered intravenously using a previously
validated automatic injection driver system (MEDRAD,
Warrendale, Pennsylvania, USA)
17,21–23
. The CT imaging was trig-
gered when the Hounsfield unit at the centre of the aorta reached
130 after the injection of contrast
17
.
Assessment of aneurysm morphology
A Philips MxView Visualisation Workstation was used to estimate
maximum aortic diameter by following a previously validated
protocol
22,23
. A region of interest (ROI) was selected, which was
restricted to the slice inferior to the origin of the lowest renal ar-
tery (excluding accessory arteries) to the slice superior the aortic
bifurcation. This ROI was viewed to identify areas of maximal di-
ameter, and multiple measurements were taken using electronic
callipers. Anterior–posterior outer-to-outer orthogonal diameters
were estimated by tracing the lumen of the infrarenal aorta and
measuring perpendicular to this axis. The measurement was
recorded to the nearest 01mm
17,23,24
. The reproducibility of this
method has been reported to be high (coefficient of variation less
than 4 per cent)
24
.
Biomechanical analyses
FEA was performed using a semiautomated technique with a
commercially available program (A4 Research 5.0; VASCOPS,
Graz, Austria)
12,13
. First, the CT image was acquired using the
hospital Picture Archiving and Communicating System, and the
AAA region was selected for analysis. Next, a ROI from the
infrarenal aorta to the iliac bifurcation was selected and a three-
dimensional (3D) reconstruction of the AAA created (Fig.1).
Manual modifications of the vessel wall and lumen were per-
formed where necessary using the closed polygon tool. This was
commonly required in ruptured AAA cases. The 3D model was
then processed into a hexahedral mesh to prevent volume lock-
ing of incompressible solids. FEA meshes were required to com-
prise more than 7000 finite elements to ensure accuracy of the
FEA calculations. Low-quality meshes were optimized by mesh
refinement. The model was adjusted for patient-specific and geo-
metric factors
25,26
. Specifically, the mechanical properties of
intraluminal thrombus (ILT) and the AAA wall were described by
isotropic material models
26,27
. AAA wall elasticity was modelled
with an Yeoh-type strain energy function
28
, whereas the ILT was
modelled with an Ogden-type strain energy function which
accounts for the proportional decrease in ILT stiffness from the
luminal to abluminal layer
25
, as reported in previous in vitro test-
ing
26
. AAA wall strength distribution was estimated using a sta-
tistical model incorporating ILT thickness, AAA diameter, sex
and family history of AAA
26
. Wall strength values related to these
variables were estimated from tensile testing of human AAA wall
specimens, as described previously
26,29
. The AAA FEA model was
pressurized by inputting BP, which in turn estimated the me-
chanical stress on the aortic wall
12,26,29
. The present study used a
standardized BP of 140/80 mmHg for the main analysis, and sen-
sitivity analyses were performed using a lower (120/70 mmHg)
and higher (160/90 mmHg) BP. The geometric properties calcu-
lated included total vessel volume and total ILT volume. The bio-
mechanical measures estimated were PWS and PWRI
11,11,12
. PWS
estimated maximum tensile stress applied to the aortic wall
based on AAA morphology and BP. PWRI represented the maxi-
mum ratio between wall stress and the estimated local wall
strength
18
.
Assessment of intraobserver reproducibility
The intraobserver reproducibility of estimates of PWS was evalu-
ated by assessment of a group of randomly selected CT images
from an equal number of asymptomatic intact and ruptured
AAAs. The images were examined on two separate occasions by
the same observer 48 h apart. The concordance correlation coeffi-
cient and coefficient of variation were calculated. Bland and
Singh et al.| 653
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Altman’s method
30
was used to estimate mean difference and 95
per cent confidence intervals.
Statistical analysis
The sample size calculation was based on the findings of a previ-
ous study
15
that compared PWS in participants with symptom-
atic or ruptured and asymptomatic intact AAAs at standardized
BP. In that study, patients were not matched for diameter but dif-
ferences in aortic diameter were not significant. The estimated
mean(s.d.) PWS was 111(051) and 067(030) MPa in symptomatic
or ruptured and asymptomatic AAAs respectively. To demon-
strate a similar difference in PWS at a power of 90 per cent (a
005), it was estimated that at least 15 ruptured AAA cases and 31
intact AAA controls were required. Sample size calculations were
performed using G*Power (version 3.1.9.6)
31
. To allow for images
in which there were technical difficulties in estimating PWS, 25
participants with a ruptured and 50 with an intact AAA were in-
cluded.
Data were not normally distributed when assessed using Q-Q
plots and the Kolmogorov–Smirnov test. Pearson’s v
2
and Mann–
Whitney Utests were used to compare variables between the two
groups. Spearman’s correlation coefficient was used to assess the
association between PWS or PWRI and AAA diameter. To evalu-
ate the relationship between low and high PWS or PWRI and rup-
ture, patients were stratified into groups with low (275 kPa or
less) and high (more than 275 kPa) PWS, and low (0910 and un-
der) and high (over 0910) PWRI. Patients were stratified into
these groups based on the approximate median PWS and PWRI of
the cohort using methods described previously
32
. A further analy-
sis was undertaken using PWS or PWRI as a continuous variable,
with results expressed per increase in PWS or PWRI of approxi-
mately the standard deviation in the population. Multivariable
logistic regression analysis was performed to examine the inde-
pendent associations between PWS or PWRI and ruptured AAA,
adjusting for potential confounders
33
or variables that were
found to differ significantly between asymptomatic intact and
ruptured AAAs. The variables adjusted for were: age, sex, smok-
ing, orthogonal diameter, IHD, hypertension, diabetes and ARB
prescription. Statistical significance was assumed at P<0050. All
analyses were done using StataV
Rversion 16.1 (StataCorp, College
Station, Texas, USA).
Sensitivity analyses were conducted to assess the robustness
of the results. To account for potential underestimation or over-
estimation of PWS and PWRI owing to the use of a single BP value
(140/80 mmHg), PWS and PWRI were also estim ated using low
and high BPs (120/70 and 160/90 mmHg respectively). Another
analysis examined the differences in PWS and PWRI between
ruptured and intact AAAs in men only to account for the over-
representation of women among the participants with a ruptured
AAA in the cohort.
Results
Twenty-five patients with a ruptured AAA and 50 with an asymp-
tomatic intact AAA were included. Patients with a ruptured AAA
were more likely to be women (28 versus 6 per cent; P¼0008) and
more likely to be prescribed an ARB (Table 1).
Intraobserver reproducibility
The analysis included ten patients with a ruptured AAA and ten
with an intact aneurysm. The coefficients of variation for repro-
ducibility of PWS for asymptomatic and ruptured AAAs were 27
and 43 per cent respectively. Bland–Altman plots suggested that
differences in PWS estimates between readings were similar
across the range of PWS (Table S1,Figs S1 and S2,supporting infor-
mation).
Peak wall stress and peak wall rupture index
Maximum orthogonal aortic diameter was similar in both groups
(Table 2). PWS was greater in ruptured AAAs than asymptomatic
intact AAAs, although the difference was not statistically signifi-
cant: median 2868 (i.q.r. 2202–3296) versus 2458(2152–
Fig. 1 Three-dimensional segmentation of an abdominal aortic aneurysm using finite element analysis
aAxial and bsagittal views of an abdominal aortic aneurysm (AAA). cThree-dimensional (3D) segmentation produced using finite element analysis on the CT image of
an AAA. The red arrow indicates an area of high peak wall stress. The blue and green areas represent intraluminal thrombus and the exterior wall of the AAA
respectively.
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3023) kPa respectively (P¼0192). There was no significant differ-
ence in PWRI between groups (Table 2). PWS (r¼058, P<0001)
and PWRI (r¼056, P<0001) correlated positively with aortic di-
ameter (Fig.2).
Adjusted analysis
Patients were grouped into those with low (275 or less kPa) and
high (over 275 kPa) PWS. Univariable logistic regression suggested
that high PWS was not significantly associated with ruptured
AAA (odds ratio (OR) 191, 95 per cent c.i. 072 to 504; P¼0192).
After adjusting for potential confounders, participants with a
high PWS were five times more likely to have a ruptured AAA
than those with a low PWS (OR 584, 122 to 2795; P¼0027)
(Table 3). High PWRI was not significantly associated with AAA
rupture in the logistic regression analyses. Secondary analyses
using PWS or PWRI as continuous variables suggested no
significant association with AAA rupture in either univariable or
multivariable analyses (Table 3).
Sensitivity analyses
PWS and PWRI was similar in the asymptomatic intact and rup-
tured AAA groups when computed at low and high BP (Table S2,
supporting information). After adjusting for potential confound-
ers, participants with a high PWS were more likely to have a rup-
tured AAA than those with a low PWS at both low (OR 467, 95 per
cent c.i. 105 to 2062; P¼0042) and high (OR 499, 111 to 2247;
P¼0036) BPs (Table S3,supporting information). The results of a
sensitivity analysis involving 65 men only were similar to those
of the main analysis (Table S4 and S5,supporting information).
Discussion
The main analysis in this study found that patients with high
PWS were approximately five times more likely to have a rup-
tured AAA than those with lower PWS after adjusting for impor-
tant confounding factors. The result was robust when PWS was
computed at high and low BPs; however, there was no significant
association between PWS and AAA rupture when continuous val-
ues were used in the logistic regression analysis. No consistent
relationship between PWRI and AAA rupture was found.
The present investigation has a number of design strengths
compared with previously published studies
4,11,15,34,35
.
Differences in diameter between ruptured and asymptomatic in-
tact AAAs were not accounted for in many previous stud-
ies
4,15,34,35
. In the present study, ruptured and asymptomatic
intact AAAs were matched for diameter. A number of other steps
were taken to reduce bias, such as the use of a standardized BP,
and reproducible methods to estimate orthogonal AAA diameter
and biomechanical measurements
11
. Furthermore, the number
of patients included in the study was based on an a priori sample
size estimate. These factors support the reliability of the findings.
AAA diameter is an imperfect measure to identify which
patients should undergo surgery
2,36
. AAA repair carries a sub-
stantial risk of perioperative complications and some patients
will require reinterventions
2,36
. The findings of this study demon-
strate a potential benefit of using PWS as a surrogate marker of
AAA rupture risk to help identify which patients should be con-
sidered for surgery. There are, however, many limitations of this
technology which need to be addressed before it could be inte-
grated into clinical practice. First, there is no standardized ap-
proach to conducting FEA and many methods have been reported
although few have been validated
4,11
. Wall strength may be more
important than wall stress in the pathogenesis of AAA rupture,
but there is currently no accurate method of measuring this non-
invasively
37
. MRI and [
18
F]fluorodeoxyglucose PET may provide
useful information regarding the biology of the AAA wall
37,38
;
however, it is unlikely that there will be a wide uptake of such im-
aging modalities in clinical practice. The FEA method employed
in the present study used patient-specific factors to estimate wall
strength
25,26
. The median values of PWS or PWRI were used to
categorize participants into those with low and high PWS or
PWRI. Further validation of the FEA method in larger populations
is required to help define clinically useful cut-off values for PWS.
Finally, the diameters of asymptomatic intact and ruptured
AAAs included in this study were large, and the results may not
Table 1 Characteristics of patients with asymptomatic intact
and ruptured abdominal aortic aneurysms in diameter-
matched group of patients
Intact
AAA
(n¼50)
Ruptured
AAA
(n¼25)
P
‡
Age (years)* 74 (66–77) 74 (67–78) 0380
§
Sex ratio (M : F) 47 : 3 18 : 7 0008
Smoker
†
47 (94) 21 of 24 (88) 0338
Diabetes 9 (18) 3 of 24 (13) 0548
Ischaemic heart disease 26 (52) 9 of 24 (38) 0242
Hypertension 33 (66) 18 of 24 (75) 0434
Stroke 5 (10) 0 (0) 0109
COPD 12 (24) 3 of 23 (13) 0265
Aspirin 27 (54) 13 (52) 0870
Other antiplatelet 12 (24) 3 (12) 0221
ACE inhibitor 21 (42) 5 (20) 0059
ARB 4 (8) 10 (40) 0001
Statin 31 (62) 13 (52) 0407
Metformin 1 (2) 1 (4) 0612
Values in parentheses are percentages unless indicated otherwise;*values are
median (i.q.r.).
†
Current or ex-smokers. AAA, abdominal aortic aneurysm;
COPD, chronic obstructive pulmonary disease; ACE, angiotensin-converting
enzyme; ARB, angiotensin II receptor blocker.
‡
Pearson’s v
2
test, except
§
Mann–Whitney Utest.
Table 2 Estimated peak wall stress and peak wall rupture index
in asymptomatic intact and ruptured abdominal aortic
aneurysms
Intact
AAA
(n¼50)
Ruptured
AAA
(n¼25)
P*
Maximum orthogonal
diameter (mm)
810
(732–924)
823
(735–920)
0906
Total vessel
volume (cm
3
)
3427
(2006–5268)
3029
(2246–4663)
0866
Intraluminal thrombus
volume (cm
3
)
1430
(912–2371)
1714
(445–2238)
0597
PWS (kPa) 2458
(2152–3023)
2868
(2202–3296)
0192
PWRI 097
(068–146)
091
(057–185)
0982
Values are median (i.q.r.). AAA, abdominal aortic aneurysm; PWS, peak wall
stress; PWRI, peak wall rupture index.*Mann–Whitney Utest.
Singh et al.| 655
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be generalizable to smaller AAAs
11
. Estimating PWS and PWRI in
small AAAs could potentially help identify AAAs that are more
likely to rupture and may benefit from closer surveillance, al-
though this is yet to be investigated in a large observational
study.
There are some limitations of this study. Although a signifi-
cant association between high PWS and AAA rupture was identi-
fied, confidence intervals were wide, which is reflective of the
small sample size. A larger number of patients was included,
however, than in previous investigations
13,15,39–41
. The design of
the present study required intact and ruptured AAAs to be
matched for diameter, which resulted in the exclusion of some
large AAAs for which diameter-matched asymptomatic intact
AAAs could not be found. Second, this study included patients
with CT performed after rupture and it is possible that the biome-
chanical forces before rupture were different
17
. Furthermore, the
participants with ruptured AAA needed to be suitable for the FEA
software used, which excluded patients with massive contrast
extravasation
18
. A standardized BP was used in this study, and it
is possible that PWS and PWRI were underestimated or overesti-
mated in some patients. A sensitivity analysis in which PWS and
PWRI were computed at low and high BPs was undertaken to ad-
dress this limitation. Although the two groups were balanced in
terms of medical co-morbidities, confounding owing to an
unmeasured risk factor cannot be excluded. It was not possible
to match for sex because of difficulties in identifying the required
number of women with asymptomatic intact AAAs that matched
in diameter with ruptured AAAs among women. This limitation
was addressed by adjusting for sex in the multivariable logistic
regression analysis as well as performing a sensitivity analysis re-
stricted to men only. Finally, this study included participants
recruited from centres in Queensland, Australia, and the general-
izability of the results needs to be confirmed in independent
cohorts from other states and countries.
Acknowledgements
The Townsville Hospital and Health Services Study, Education
and Research Trust Fund, and Queensland Government sup-
ported this work. J.G. holds a Practitioner Fellowship from the
National Health and Medical Research Council (1117061) and a
Senior Clinical Research Fellowship from the Queensland
Government, Australia. J.V.M. holds an Advance Queensland
Mid-Career fellowship from the Queensland Government. T.P.S.
holds a Junior Doctor Research Fellowship from the Queensland
Government. V.I. holds a Junior Doctor Research Fellowship from
the Queensland Government.
Disclosure: The authors declare no conflict of interest.
Fig. 2 Correlation between peak wall stress or peak wall rupture index and orthogonal diameter
Correlation between apeak wall stress and bpeak wall rupture index and orthogonal diameter. The shaded area represents the 95 per cent confidence interval. a
r¼058, P<0001; br¼056, P<0001.
Table 3 Logistic regression analyses examining the association
between high peak wall stress and peak wall rupture index and
abdominal aortic aneurysm rupture
Odds ratio P
PWS
Unadjusted analysis
PWS* 123 (076, 200) 0394
PWS 275 kPa 100 (reference)
PWS >275 kPa 191 (072, 504) 0192
Adjusted analysis
†
PWS* 176 (087, 358) 0117
PWS 275 kPa 100 (reference)
PWS >275 kPa 584 (122, 2795) 0027
PWRI
Unadjusted analysis
PWRI* 120 (075, 194) 0445
PWRI 0910 100 (reference)
PWRI >0910 092 (035, 241) 0870
Adjusted analysis
†
PWRI* 190 (083, 433) 0127
PWRI 0910 100 (reference)
PWRI >0910 089 (021, 370) 0869
Values in parentheses are 95 per cent confidence intervals.*Odds ratios
expressed per standard deviation increase in peak wall stress (PWS) and peak
wall rupture index (PWRI).
†
Adjusted for age, sex, smoking, orthogonal
diameter, ischaemic heart disease, hypertension, diabetes and angiotensin II
receptor blocker prescription.
656 | BJS, 2021, Vol. 108, No. 6
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Supporting information
Additional supporting information can be found online in the
Supporting Information section at the end of the article.
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