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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity for Prediction of Ventricular Arrhythmias and Mortality in Post-Infarct Patients
JACC: CLINICAL ELECTROPHYSIOLOGY
VOL.
-, NO. -, 2019
ª 2019 BY THE AMERICAN COLLEGE OF CARDIOLOGY FOUNDATION PUBLISHED BY ELSEVIER
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity for Prediction of Ventricular Arrhythmias and Mortality in Post-Infarct Patients Alexander F.A. Androulakis, MD,a Katja Zeppenfeld, MD, PHD,a Elisabeth H.M. Paiman, MD,b Sebastiaan R.D. Piers, MD, PHD,a Adrianus P. Wijnmaalen, MD, PHD,a Hans-Marc J. Siebelink, MD, PHD,a Marek Sramko, MD, PHD,a Hildo J. Lamb, MD, PHD,b Rob J. van der Geest, PHD,c Marta de Riva, MD,a Qian Tao, PHDc
ABSTRACT OBJECTIVES This study proposed entropy as a new late gadolinium enhanced cardiac magnetic resonance–derived parameter to evaluate tissue inhomogeneity, independent of signal intensity thresholds. This study hypothesized that entropy within the scar is associated with ventricular arrhythmias (VAs), whereas entropy of the entire left ventricular (LV) myocardium is associated with mortality. BACKGROUND In patients after myocardial infarction, the heterogeneity of fibrosis determines the substrate for VA. Fibrosis in remote areas has been associated with heart failure and mortality. Late gadolinium-enhanced cardiac magnetic resonance has been used to delineate fibrosis, but available methods depend on signal intensity thresholds and results have been inconsistent. METHODS Consecutive post–myocardial infarction patients undergoing late gadolinium enhanced cardiac magnetic resonance prior to implantable cardioverter-defibrillator implantation were included. From cardiac magnetic resonance imaging, total scar size, scar gray zone, scar transmurality, and tissue entropy were derived. Patients were followed for appropriate implantable cardioverter-defibrillator therapy and mortality. RESULTS A total of 154 patients (64 10 years, 84% male, LV ejection fraction 29 10%, 47% acute revascularization) were included. During a median follow-up of 56 (interquartile range: 40, 73) months, appropriate implantable cardioverter-defibrillator therapy occurred in 46 patients (30%), and 41 patients (27%) died. From multivariable analysis, higher entropy of the scar (hazard ratio [HR]: 1.9; 95% confidence interval [CI]: 1.0 to 3.5; p ¼ 0.042) was independently associated with VA, after adjusting for multivessel disease, acute revascularization, LV ejection fraction, scar gray zone, and transmurality. Entropy of the entire LV was independently associated with mortality (HR: 3.2; 95% CI: 1.1 to 9.9; p ¼ 0.038). CONCLUSIONS High entropy within the scar was associated with VA and may indicate an arrhythmogenic scar. High entropy of the entire LV was associated with mortality and may reflect a fibrosis pattern associated with adverse remodeling. (J Am Coll Cardiol EP 2019;-:-–-) © 2019 by the American College of Cardiology Foundation.
From the aDepartment of Cardiology, Leiden University Medical Center, Leiden, the Netherlands; bDepartment of Radiology, Leiden University Medical Center, Leiden, the Netherlands; and the cDivision of Image Processing, Department of Radiology, Leiden University Medical Center, Leiden, the Netherlands. This study was funded by NOW (Nederlandse Organisatie voor Wetenschappelijk Onderzoek - Dutch organisation for Scientific Research) Domain Applied and Engineering Sciences grant no. 12899. The Department of Cardiology (Leiden University Medical Center) has received unrestricted research grants from Edwards Lifesciences, Medtronic, Biotronik, and Boston Scientific. Dr. Zeppenfeld has received funding from a research grant awarded to the Department of Cardiology (Leiden University Medical Center) from Biosense Webster. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose. All authors attest they are in compliance with human studies committees and animal welfare regulations of the authors’ institutions and Food and Drug Administration guidelines, including patient consent where appropriate. For more information, visit the JACC: Clinical Electrophysiology author instructions page. Manuscript received June 12, 2018; revised manuscript received December 12, 2018, accepted December 12, 2018.
ISSN 2405-500X/$36.00
https://doi.org/10.1016/j.jacep.2018.12.005
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ABBREVIATIONS AND ACRONYMS ATP = antitachycardia pacing CI = confidence interval CMR = cardiac magnetic resonance imaging
GZ = gray zone HR = hazard ratio ICD = implantable cardioverter-defibrillator
IQR = interquartile range LGE = late gadolinium
P
atients after myocardial infarction
mortality. Histological studies demonstrated a higher
(MI) are at risk for ventricular arrhyth-
amount of fibrous tissue in noninfarcted myocardium
mias (VAs) and adverse left ventricu-
of hearts from patients with end-stage heart failure
lar (LV) remodeling, both related to cardiac
with an ischemic cause compared with control hearts
mortality (1,2). The implantable cardioverter-
(obtained from autopsies in patients who died of a
defibrillator (ICD) reduces mortality in pa-
noncardiovascular cause) (20–23). Remote fibrosis
tients considered at high risk for VA (1,3).
may be quantified as increased extracellular volume
However, during long-term follow-up, only
fraction using T 1 mapping, which has been associated
35% of post-MI patients who have received
with mortality independent from LVEF and MI size
an ICD for primary prevention of sudden
(2,24). However, T 1 mapping is usually restricted to a
cardiac death experience appropriate therapy
limited number of pre-selected slices (2,24,25), and it
(4).
is not a direct measure of tissue inhomogeneity.
Although several noninvasive parameters
In this work, we propose a new LGE-CMR–derived
have been suggested to identify patients at
method to quantify tissue inhomogeneity by the
risk for VA, the ICD indication for primary
entropy of the SI values and hypothesize the
prevention still relies on a reduced left
following: 1) entropy within the scar is a marker for
fraction
ventricular ejection fraction (LVEF) (5). Of
inhomogeneous
MI = myocardial infarction
interest, the vast majority of VAs that prompt
might be associated with MVT; and 2) entropy of the
enhancement
LV = left ventricle/left ventricular
LVEF = left ventricular ejection
scar
composition
and
therefore
MVT = monomorphic
ICD therapy in post-MI patients implanted
entire LV is a marker for overall inhomogeneous
ventricular tachycardia
for primary prevention are monomorphic
fibrosis in the LV and therefore might be associated
NYHA = New York Heart
ventricular tachycardias (MVT), suggesting
with adverse remodeling and mortality.
Association
that MVT contributes significantly to ar-
SI = signal intensity
rhythmogenic death in patients without an
ST = scar transmurality
ICD (6). MVT in post-MI patients are typically
METHODS
STmedian = median value of scar
due to scar-related re-entry facilitated by
PATIENTS. Data of consecutive patients with prior MI
transmurality
areas of slow conduction. Histological hall-
who underwent LGE-CMR before ICD implantation
VA = ventricular arrhythmia
marks of the arrhythmogenic substrate are
for primary or secondary prevention between 2003
VF = ventricular fibrillation
inhomogeneous areas within the scar, con-
and 2012 were collected. Patients who underwent
VT = ventricular tachycardia
sisting of surviving myocyte bundles imbed-
surgical LV reconstruction within 1 year after LGE-
ded and interspersed by fibrous tissue (7).
CMR and patients in whom the LGE-CMR quality
Late gadolinium enhanced (LGE) cardiac magnetic
was poor were excluded (Online Figure 1). The
resonance imaging (CMR) is the current gold standard
remaining patients constituted the final study popu-
to visualize scarred myocardium (8). Intermediate
lation. The diagnosis of MI was based on the presence
signal intensity (SI) values are assumed to indicate a
of subendocardial or transmural LGE areas in the
mixture of fibrotic and viable tissue, often referred to
perfusion territory of a significantly stenotic coronary
as gray zone (GZ). GZ delineation depends on partic-
artery (>70% stenosis on coronary angiogram).
ular SI thresholds from image analysis methods (9).
Patient medical records were reviewed for baseline
These methods rely on operator-defined areas with
clinical characteristics. At the day of ICD implanta-
maximum SI, areas with remote myocardium, or a
tion, serum creatinine was retrieved, and renal failure
combination of both as a reference. Prior studies have
was defined as creatinine blood level $1.4 mg/dl.
evaluated the association between the extent of the
In addition, details on prior ischemic events, acute
GZ and spontaneous and inducible VA, but with
reperfusion therapy during the first MI (within 24 h
conflicting results (10–18). To quantify the tissue in-
from onset of symptoms), and elective revasculari-
homogeneity while avoiding the inconsistency of
zation strategies were collected. Patients with a single
zone definition, we propose a new LGE-CMR–derived
MI
metric: entropy. Entropy is a classical measure of
were categorized as “acute revascularized” patients.
who
underwent
acute
reperfusion
therapy
uncertainty in information theory (19), and it mea-
Multivessel disease was defined as a significant
sures the uncertainty of tissue composition as
stenosis in $2 coronary arteries. Data on prior VA
reflected by the uncertainty of SI. Instead of parti-
episodes were collected. For patients who had un-
tioning zones by threshold, the entropy is computed
dergone ventricular tachycardia (VT)-ablation, all
from all SI values in LGE-CMR.
procedural reports were reviewed to determine
Progressive heart failure, due to adverse LV
procedural success.
remodeling and myocardial fibrosis in the (non-
The Dutch Central Committee on Human-Related
infarcted) myocardium, further contributes to cardiac
Research permits use of anonymous data without
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F I G U R E 1 Scar Transmurality LGE-CMR
(A) Endocardial (red) and epicardial (green) borders are manually traced. (B) Scar core zone (pink) and gray zone (yellow) are semiautomatically identified based on signal intensity threshold. (C) The transmurality of the total scar is computed along the radial transmural direction. CMR ¼ cardiac magnetic resonance; LGE ¼ late gadolinium enhancement.
prior approval of an institutional review board, if the
for irregularity as proposed by Shannon, allowing for
data are obtained for patient care and if the data do
an entropy range between 0 and 10 (19) (see Online
not contain identifiers that could be traced back to the
Methods), with 0 being a complete homogeneous
individual patient. All data used for this study were
distribution of SI values (consisting of only a single SI
acquired based on clinical care; any identifying
value) and 10 being the most inhomogeneous distri-
information was removed from the data.
bution of SI equally scattering in the SI range. The
CMR ANALYSIS. All images were acquired by a 1.5-T
Gyroscan
magnetic
resonance
imaging
scanner
(see the Online Methods in the Online Appendix). Data analysis was performed as described earlier
investigator who calculated entropy was blinded for patient outcome. Subsequently, the tissue entropy was quantified for both the scar region and the entire LV myocardium (Figure 2, Online Appendix).
to evaluate the LVEF, LV mass, and myocardial scar
ICD IMPLANTATION AND PROGRAMMING. Patients
(see Online Methods) (10). The scar was automatically
received an ICD or a cardiac resynchronization ther-
identified as myocardium with SI >35% of the maximum SI, the scar GZ as myocardium with SI >35% but <50% of the maximum SI, and scar core as myocardium with a SI $50% of the maximum SI
apy defibrillator for primary or secondary prevention according to the guidelines of the European Society of Cardiology that were valid at the time of implantation (26,27). ICD were typically programmed to include 3
(Figure 1B). Scar transmurality (ST) was calculated as
zones: monitor zone/VT1 zone (150 to 188 beats/min;
the percentage of scar from the total LV myocardial
no therapy/antitachycardia pacing (ATP) if indicated),
wall in the radial direction (Figure 1C). The median
VT2 zone (188 to 210 beats/min; ATP and shock), and
value of ST (ST median) was used as a measure of
ventricular fibrillation (VF) zone (>210 beats/min; if
the overall ST for each patient. The ST median was
available ATP during charging, and shock). In case of
divided into 4 categories: 1) 0% < ST median #25%; 2) 26% < ST median #50%; 3) 51 < ST median #75%; and 4) 76% < ST median #100%. Tissue inhomogeneity was quantified by the entropy of SI values within the tissue.
secondary prevention, programming was adapted according to the clinical VT. FOLLOW-UP. Patients were followed in the outpa-
tient clinic 2 months after ICD implantation and every
Introducing entropy to quantify tissue inhomo-
3 to 6 months thereafter. Follow-up visits included
geneity is based on the assumption that areas
clinical evaluation, device
with varying SI values in LGE represent tissue with
12-lead electrocardiogram. All episodes prompting
different
composition.
The
normalized
ICD therapy were reviewed by an experienced
according to a predefined range between 0 and 1,024
physician for exclusion of inappropriate therapies
for each patient. The scar and LV-entropy were
and categorization of the VA episodes in MVT or VF.
automatically
environment;
Appropriate device therapy was defined as any ATP or
MathWorks, Natick, Massachusetts) using the formula
ICD shock delivered for an MVT or VF. MVT on ICD
calculated
SI
was
interrogation, and a
(Matlab
3
4
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F I G U R E 2 Entropy Model and SI Histograms in 4 Subjects With Comparable LVEF
Continued on the next page
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
was defined as a VT with a morphologically stable farfield electrogram and a beat-to-beat cycle length
T A B L E 1 Baseline Characteristics
variation #30 ms. VF/polymorphic VT was defined as any VA with beat-to-beat variations in both far-field
Total Population (N ¼ 154)
Appropriate Therapy (n ¼ 46)
No Appropriate Therapy (n ¼ 108)
p Value
electrogram morphology and cycle length. VA was
Age, yrs
64 10
63 12
64 9
0.814
defined as sustained when lasting >30 s or when
Sex
130 (84)
43 (94)
87 (81)
0.043
treated with ATP or shock. All ICD recordings were
Smoking
76 (49)
22 (48)
54 (50)
0.825
analyzed by an experienced observer. In case of
Hypertension
71 (46)
21 (46)
50 (46)
0.983
death, the medical records concerning cause of
Hypercholesterolemia
74 (48)
21 (46)
53 (49)
0.910
Diabetes
32 (21)
5 (11)
27 (25)
0.048
Renal failure
28 (18)
11 (24)
17 (16)
0.229
Atrial fibrillation
31 (20)
9 (20)
22 (20)
0.909
follow-up was censored at the operation date. Medi-
NYHA functional class >II
51 (33)
17 (37)
34 (32)
0.509
cal records were reviewed to assess cardiac/noncar-
VT ablation prior to ICD
17 (11)
9 (20)
8 (7)
0.046
diac mortality.
Noninducible after ablation
death were obtained. In the event of late LV reconstruction (>1 year post-ICD implantation), patient
STATISTICAL ANALYSIS. Continuous variables are
Multivessel disease
6 (4)
4 (9)
2 (2)
0.066
102 (66)
35 (76)
67 (62)
0.080 0.962
Prior CABG
54 (35)
16 (35)
38 (35)
presented as mean SD, and categorical data are
Acute revascularization during index MI
72 (47)
15 (33)
57 (53)
0.022
summarized as frequencies and percentages. Differ-
Secondary prevention ICD
33 (21)
16 (35)
17 (16)
0.008
ences in baseline characteristics between patients
CRT
99 (64)
26 (57)
73 (68)
0.189
were analyzed using Student’s t-test or Fisher exact
LBBB
46 (29)
13 (28)
33 (31)
0.776
test, as appropriate.
RBBB
20 (13)
5 (11)
15 (14)
0.610
115 34
115 35
116 34
0.857
Univariable and multivariable Cox proportional hazards regression models were constructed to study
QRS interval, ms Medication Amiodarone
16 (10)
5 (11)
11 (10)
0.913
the relation between scar features and the 2 types of
Beta-blocker
127 (82)
40 (87)
87 (81)
0.394
endpoints, namely, mortality and appropriate ICD
Calcium channel blocker
therapy. Hazard ratios (HR) were obtained after
ACE inhibitor
adjustment
for
pre-determined
potential
con-
founders based on clinical relevance (for appropriate therapy: multivessel disease, acute revascularization, LVEF, GZ, and ST median ; and for mortality: age, renal
14 (9)
7 (15)
7 (7)
0.088
105 (68)
31 (67)
74 (69)
0.829
ARB
28 (18)
6 (13)
22 (20)
0.270
Statins
132 (86)
40 (87)
92 (85)
0.872
Any diuretic
96 (62)
30 (65)
66 (61)
0.678
Aldosterone antagonist
48 (31)
12 (26)
34 (32)
0.356
failure, New York Heart Association [NYHA] func-
Values are mean SD or n (%).
tional class >II, multivessel disease, prior coronary
ACE ¼ angiotensin converting enzyme; ARB ¼ angiotensin II receptor inhibitor; CABG ¼ coronary artery bypass graft; CRT ¼ cardiac resynchronization therapy; ICD ¼ implantable cardioverter-defibrillator; LBBB ¼ left bundle branch block; MI ¼ myocardial infarction; NYHA ¼ New York Heart Association functional class; RBBB ¼ right bundle branch block; VT ¼ ventricular tachycardia.
artery bypass graft, LVEF, scar size, and scar entropy). HR with 95% confidence intervals (CIs) are reported. All tests were 2-sided, and p < 0.05 was considered statistically significant. Spline curves were fitted for
below the median value. The cumulative mortality
the univariable and multivariable associations be-
during follow-up was compared between patients
tween scar entropy and the HR (log scale) of ICD
with entropy in the entire LV above versus below the
therapy and the univariable and multivariable asso-
median value.
ciations between entropy of the entire LV and the HR (log scale) of mortality. Using Kaplan-Meier survival
RESULTS
analyses, the cumulative incidence of appropriate ICD therapy during follow-up was compared between
BASELINE
patients with entropy within the scar above versus
period, a total of 188 post-MI patients underwent
CHARACTERISTICS. During
the
study
F I G U R E 2 Continued
(A[1,2]) Model histograms of a virtual homogeneous signal intensity (SI) distribution and a virtual inhomogeneous SI distribution resulting in an entropy of 0 and 10, respectively, using the formula proposed by Shannon. (B[1,2], C[1,2]) SI histograms from 4 patients, which are used for entropy computation along with short-axis views of late gadolinium enhancement cardiac magnetic resonance. (B[1,2])Patients with a similar scar core, gray zone, and left ventricular (LV) ejection fraction. However, the patient in B(1) had a high scar entropy and experienced ventricular arrhythmia, whereas the patient in B(2) had a low scar entropy and did not experience ventricular arrhythmia. (C[1,2]) Patients with a similar scar size, gray zone, and LV ejection fraction. The patient in C(1) had a high LV entropy and died (due to heart failure) during follow-up, whereas the patient in C(2) had a low LV entropy and survived. B(3) Ventricular tachycardia (VT)-free survival in patients with scar entropy above versus below the median value. (C[3]) Survival in patients with LV entropy above versus below the median value.
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(age 64 10 years, 84% male) constituted the
T A B L E 2 MRI Characteristics and Appropriate Therapy
All Patients (N ¼ 154)
Appropriate Therapy (n ¼ 46)
study population. In 121 patients (79%), an ICD No Appropriate Therapy (n ¼ 108)
p Value
0.440
was
implanted
for
primary
prevention
and
in
33 patients (21%) for secondary prevention. In 77 of
LVEF, %
29 10
28 13
30 9
LV mass, g
151 36
155 39
149 35
0.325
Total scar, g
47 26
48 26
47 26
0.784
the indication was established based on the 2003
Gray zone, g
19 9
20 11
18 9
0.412
European Society of Cardiology guidelines update
121 patients receiving the ICD for primary prevention,
(Class IIa recommendation if LVEF <30%) (26). The
Median scar, % transmurality
remaining 44 patients received the ICD according
0–25
3 (2)
0 (0)
3 (3)
0.342
25–50
36 (23)
11 (24)
25 (23)
0.918
50–75
66 (43)
25 (54)
41 (38)
0.060
75–100
49 (32)
10 (22)
39 (36)
0.064
NYHA functional class $II despite optimal medical
In scar
7.82 0.5
7.94 0.5
7.77 0.6
0.074
ICD implanted for secondary prevention, 17 had un-
In entire LV
8.09 0.7
8.14 0.7
8.08 0.7
0.630
dergone VT ablation prior to ICD implantation. Of
to the 2008 European Society of Cardiology guidelines (Class Ia recommendation if LVEF #35% and therapy) (27). Of the 33 patients who had an
Entropy
those, 6 were rendered noninducible for any VT after
Values are mean SD or n (%).
ablation. Three patients underwent VT-ablation prior
LV ¼ left ventricular; LVEF ¼ left ventricular ejection fraction; MRI ¼ magnetic resonance imaging.
to LGE-CMR. Baseline characteristics are shown LGE-CMR prior to ICD implantation. Twenty patients
in Table 1.
who underwent early LV reconstruction and 14 in
CMR PARAMETERS. The LVEF of the study popula-
whom only a poor quality CMR was available for
tion was 29 10%; the total infarct size was 47 26 g;
analysis were excluded. The remaining 154 patients
and the infarct GZ size was 19 9 g. The most prevalent ST median was 50% to 75%, which was observed in 66 patients (43%). The entropy was 7.8 0.5 for the
T A B L E 3 Univariate and Multivariable Analysis for Appropriate Therapy
Univariate HR
total infarct scar and 8.0 0.7 for the entire LV.
Multivariable
95% CI
p Value
Age, per year
1.0
1.0–1.0
0.906
Sex
3.5
1.1–11.4
0.035
HR
95% CI
p Value
Detailed CMR data are shown in Table 2. FOLLOW-UP. During
a
median
follow-up
of
56
(interquartile range [IQR]: 40 to 73) months, 46 pa-
Hypertension
1.0
0.5–1.8
0.973
Atrial fibrillation
1.0
0.5–2.0
0.942
NYHA functional class >II
1.3
0.7–2.4
0.347
therapy (44 of 46 for MVT) and 41 patients (27%) died,
tients (30%) received at least 1 appropriate ICD
QRS interval >120 ms
0.8
0.4–1.7
0.620
among which 22 deaths (50%) were due to a cardiac
Secondary prevention ICD
2.6
1.4–4.8
0.002
cause. Seven patients (5%) were lost to follow-up
CRT-D
0.6
0.3–1.1
0.087
after a median follow-up period of 42 months
ACE inhibitor or ARB
0.7
0.3–1.5
0.352
(IQR: 39, 46).
Aldosterone antagonist
0.7
0.4–1.3
0.263
Beta-blocker
1.2
0.5–2.9
0.639
Multivessel disease
2.1
1.0–4.3
0.036
CABG
1.1
0.6–2.0
0.830
Acute revascularization
0.5
0.3–0.9
0.8
0.6–1.3
APPROPRIATE ICD THERAPY. Patients who received
Extent of CAD
any appropriate ICD therapy during follow-up had 1.6
0.7–3.5
0.199
0.016
0.6
0.3–1.1
0.076
0.224
1.1
0.7–1.6
0.554
MRI characteristics LVEF, per 10% LV mass, per 10 g
1.1
1.0–1.2
0.114
Total scar, per 10 g
1.0
0.9–1.2
0.413
Scar gray zone, per 10 g
1.2
0.9–1.6
0.173
0–25
0
0.0–161
0.463
25–50
1.0
0.5–1.9
0.914
50–75
1.8
1.0–3.1
0.055
during the first MI (33% vs. 53%; p ¼ 0.022) and had more often a secondary prevention indication (35% vs. 16%; p ¼ 0.008). No other differences in baseline clinical characteristics were observed between patients with or without appropriate ICD therapies
1.2
0.9–1.7
0.287
Scar transmurality, %
75–100
less frequently undergone acute revascularization
(Table 1). LVEF, LV size, total infarct size, and GZ size were
0.6
0.3–1.2
0.123
Entropy in scar, per 1
1.9
1.1–3.3
0.029
LV entropy, per 1
1.2
0.8–1.8
0.368
comparable between patients with or without appro1.6
0.9–3.0
0.105
priate therapies. The STmedian of 50% to 75% tended to be more prevalent in those who received appro-
1.9
1.0–3.5
0.042
priate therapy (54% vs. 38%; p ¼ 0.06). In addition, patients receiving appropriate ICD therapy tended to have a higher entropy within the scar than did
CAD ¼ coronary artery disease; CI ¼ confidence interval; CRT-D ¼ cardiac resynchronization therapy defibrillator; HR ¼ hazard ratio; other abbreviations as in Tables 1 and 2.
patients without appropriate therapy (7.94 0.5 vs. 7.77 0.6; p ¼ 0.07) (Table 2).
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PREDICTORS
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
OF
APPROPRIATE
ICD
THERAPY.
Clinical variables associated with appropriate ICD therapy
were
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presence
of
multivessel
T A B L E 4 MRI Characteristics and Mortality
All Patients (N ¼ 154)
Deceased (n ¼ 41)
Survived (n ¼ 113)
p Value
LVEF, %
29 10
24 10
31 10
<0.001
LV mass, g
151 36
160 33
148 37
0.053
Total scar, g
47 26
62 32
42 21
<0.001
Gray zone, g
19 9
23 10
17 9
0.001
disease
(HR: 2.1; 95% CI: 1.0 to 4.3; p ¼ 0.036), acute revascularization during the first infarction (HR: 0.5; 95% CI: 0.3 to 0.9; p ¼ 0.016), and VA prior to ICD implantation (HR: 2.6; 95% CI: 1.4 to 4.8; p ¼ 0.002). A higher entropy within the scar was the only CMR-
Median transmurality, %
derived parameter associated with appropriate ICD
0–25
3 (2)
2 (5)
1 (1)
0.173
therapy (HR: 1.9 per unit entropy; 95% CI: 1.1 to 3.3;
25–50
36 (23)
6 (14)
30 (27)
0.123
p ¼ 0.029). The ST median of 50% to 75% showed a
50–75
66 (43)
21 (50)
45 (40)
0.207
75–100
49 (32)
12 (29)
37 (33)
0.682
In scar
7.82 0.5
8.05 0.4
7.74 0.6
0.001
In entire LV
8.09 0.7
8.47 0.6
7.96 0.7
<0.001
trend (HR: 1.8; 95% CI: 1.0 to 3.1; p ¼ 0.055). On multivariable analysis, the entropy within the scar remained the only CMR-derived parameter associated
Entropy
with appropriate ICD therapy (HR: 1.9 per unit entropy; 95% CI: 1.0 to 3.5; p ¼ 0.042), independent of LVEF, acute revascularization, multivessel disease,
Values are mean SD or n (%). Abbreviations as in Table 1 and 2.
GZ size, and the STmedian of 50% to 75% (Table 3, Figure 2B(3)). Of note, univariable and multivariable association between entropy and ICD therapy is
LV (HR: 3.2 per unit entropy; 95% CI: 1. 1 to 9.9;
approximately linear (Online Figure 2).
p ¼ 0.038) and renal failure (HR: 2.4: 95% CI: 1.1 to 5.1;
MORTALITY. Patients who died during follow-up
mortality
p ¼ 0.032) remained independently associated with (Table
5).
Furthermore,
the
observed
were of similar age at ICD implantation; more frequently had diabetes (34% vs. 16%; p ¼ 0.014), renal failure (37% vs. 12%; p < 0.001), multivessel
T A B L E 5 Univariate and Multivariable Analysis for Mortality
disease (85% vs. 59%; p ¼ 0.001); and had a higher
Univariate
NYHA functional class (Online Table 1). In addition,
Multivariable
HR
95% CI
p Value
HR
95% CI
p Value
these patients had a lower CMR-derived LVEF (24%
Age, per year
1.0
1.0–1.1
0.156
1.0
1.0–1.0
0.384
vs. 31%; p < 0.001), a larger total scar (62 g vs. 42 g;
Sex
2.6
0.8–8.4
0.115
p < 0.001), and a larger GZ (23 g vs. 17 g; p ¼ 0.001). Of
Diabetes
2.5
1.3–4.7
0.007
importance, the entropy within the scar and within
Renal failure
2.9
1.6–5.6
0.001
2.4
1.1–5.1
0.032
the entire LV was significantly higher in deceased
CRT-D
1.3
0.6–2.5
0.512 1.0
0.5–2.3
0.962
patients (8.05 0.4 vs. 7.74 0.6; p ¼ 0.001 and 8.47 0.6 vs. 7.96 0.7; p < 0.001, respectively) (Table 4).
Atrial fibrillation
1.4
0.7–2.8
0.332
NYHA functional class >II
2.9
1.5–5.4
0.001
QRS interval >120 ms
2.4
1.3–4.5
0.006
ACE inhibitor or ARB
0.9
0.4–2.1
0.866
regression analysis, diabetes (HR: 2.5; 95% CI: 1.3 to
Aldosterone antagonist
1.4
0.7–2.7
0.282
4.7; p ¼ 0.007), renal failure (HR: 2.9; 95% CI: 1.6 to
Beta-blocker
0.8
0.4–1.7
0.758
PREDICTORS
OF
MORTALITY. In
univariate Cox
5.6; p ¼ 0.001), a higher NYHA functional class (>II: HR: 2.9; 95% CI: 1.5 to 5.4; p ¼ 0.001), QRS >120 ms (HR: 2.4; 95% CI: 1.3 to 4.5; p ¼ 0.006), presence of multivessel disease (HR: 4.6; 95% CI: 1.6
Extend of CAD Multivessel disease
4.6
1.6–12.9
0.004
3.0
1.0–8.9
0.054
CABG
1.9
1.0–3.6
0.041
1.8
0.9–3.7
0.090
Acute revascularization
0.3
0.2–0.7
0.004 0.9
0.6–1.4
0.778
1.1
1.0–1.2
0.149
MRI characteristics
to 12.9; p ¼ 0.004), prior coronary artery bypass graft
LVEF, per 10% increase
0.5
0.4–0.7
<0.001
(HR: 1.9; 95% CI: 1.0 to 3.6; p ¼ 0.041), LVEF (HR: 0.5;
LV mass, per 10 g
1.1
1.0–1.2
0.042
95% CI: 0.4 to 0.7; p < 0.001), LV mass (HR: 1.1; 95% CI: 1.0 to 1.2; p ¼ 0.042), scar size (HR: 1.2; 95% CI: 1.1 to 1.3; p < 0.001), GZ size (HR: 1.5; 95% CI: 1.2 to 2.0;
Total scar, per 10 g
1.2
1.1–1.3
<0.001
Scar gray zone, per 10 g
1.5
1.2–2.0
0.002 0.194
Median transmurality, % 0–25
2.6
0.6–10.7
p ¼ 0.002), entropy within scar (HR: 2.6; 95% CI: 1.4 to
25–50
0.6
0.2–1.3
0.197
4.9; p ¼ 0.003), and LV entropy (HR: 2.4; 95% CI: 1.5
50–75
1.3
0.7–2.4
0.401
to 3.9; p < 0.001) were associated with mortality
1.0
0.5–1.9
0.914
(Figure 2B(3)). A history of acute revascularization
Entropy in scar, per 1
2.6
1.4–4.9
0.003
0.4
0.1–1.8
0.281
during the first MI was associated with lower
LV entropy, per 1
2.4
1.5–3.9
<0.001
3.2
1.1–9.9
0.038
mortality (HR: 0.3; 95% CI: 0.2 to 0.7; p ¼ 0.004). In multivariable analysis, the entropy in the entire
75–100
Abbreviations as in Tables 1 to 3.
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
univariable and multivariable association between
for defining the GZ was applied (15–18) (Online
entropy in the entire LV and mortality is approxi-
Table 2).
mately linear (Online Figure 2).
Of importance, catheter mapping studies, using real-time integration of LGE-CMR–derived scar char-
DISCUSSION
acteristics, demonstrated that only 29% to 55% of all VT-related sites in post-MI patients were located
In the present study, we have introduced entropy as a
within the GZ area, suggesting that this parameter
new parameter to assess tissue inhomogeneity from
may not be sufficient to identify the arrhythmogenic
LGE-CMR, for both the scar and the entire LV
substrate (30,31). Of interest, the mean scar trans-
myocardium. We found that in post-MI patients, the
murality at the VT-related sites was reported to be 75
entropy within the scar was the only CMR-derived
22% and 73 21%, respectively (30,32), which is in
parameter associated with VA and that the entropy
line with our observation that a ST median of 50% to
in the entire LV was independently associated with
75% tended to be associated with VA.
mortality. RISK
ASSESSMENT
ENTROPY OF THE INFARCT SCAR. The present study FOR
VA
AFTER
MI. Current
proposes
a
novel
CMR-derived
parameter
that
guidelines on ICD implantation for primary preven-
directly assesses the tissue inhomogeneity by en-
tion in post-MI patients are based on a reduced LVEF
tropy, which describes uncertainty in LGE signal (19).
(5). However, the majority of patients implanted for
We assume that with the current LGE resolution and
primary prevention do not benefit from the ICD (4).
quality, the signal intensity distribution in the scar
Multiple factors play a role in risk stratification, and
and myocardium, as quantified by the entropy, can
prevention of death in this population has been
differentiate the tissue composition to a certain
shown to be a complex issue. The risk of sudden
extent that is clinically relevant. In contrast to GZ
death in patients after MI has a biphasic temporal
quantification, computation of entropy does not
course. In the early phase after MI, VAs are common
require subdividing the scar region into 2 zones,
but ICD implantation does not improve patient sur-
therefore avoiding thresholds. In addition, the en-
vival because of the competing risks (28). Patients
tropy is richer in information than the GZ size is
who have survived this early phase remain at risk,
because entropy utilizes the entire SI distribution,
however, for scar-related re-entry MVT (29). Identi-
potentially capturing subtle variations in tissue
fication of patients at risk for late re-entrant VT is of
composition beyond the size of a particular zone.
upmost importance because these patients benefit
In our study, we found a statistically significant
from prophylactic ICD implantation. Accordingly,
association between entropy within the scar and
noninvasive parameters to predict the occurrence of
occurrence of VA. In multivariable analysis, the en-
VA are important. Of interest, the vast majority of
tropy within the scar remained the only CMR-derived
reported arrhythmia episodes that prompt appro-
parameter associated with VA. As such, entropy
priate ICD therapy are MVT (6). In post-MI patients,
calculated from 2-dimensional LGE MR imaging
MVT are typically due to scar-related re-entry
seems to be a promising parameter to indicate the
dependent on areas of inhomogeneous tissue con-
presence of an arrhythmogenic scar.
sisting of surviving myocytes imbedded and interspersed by fibrous tissue (7). Therefore, noninvasive identification of inhomogeneous scars is a logical and promising parameter for risk stratification.
ENTROPY OF THE ENTIRE LV. Patients with prior MI
are also at risk for heart failure due to progressive adverse remodeling not only within the scar area but also within remote noninfarcted myocardium. In pa-
CMR PARAMETERS AND VA. The most extensively
tients with end-stage heart failure due to coronary
evaluated surrogate for scar inhomogeneity is the
artery
scar GZ (Online Table 2) (10–18). Delineation of the GZ
showed an increased amount of fibrous tissue in the
disease,
explanted/post-mortem
hearts
requires predefined SI thresholds. Different methods
noninfarcted myocardium (20–23). T 1 mapping has
have been applied to determine these SI thresholds,
been suggested to noninvasively determine the
which either use the areas with maximum SI, areas
extracellular volume fraction as a surrogate for
with normal remote myocardium, or a combination of
diffuse fibrosis in noninfarcted myocardium (25,33).
both (10–18). While some studies reported an associ-
Increased ECV quantified by T 1 mapping has been
ation between the GZ size and occurrence of VA
associated with progressive heart failure, mortality,
(10,11,13–15), others, including the current study,
or combined endpoint (2,24,33) However, in current
could not confirm such an association (15,17,18). This
clinical practice, T1 mapping is usually restricted to
inconsistency remained, even when the same method
a limited number of pre-selected slices, and its
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
precision is affected by motion artifacts (2,24,25). In
studies. Studies to validate the histological basis of
contrast, whole-heart LGE scan is more accessible. It
entropy are warranted.
requires less acquisition time than T 1 /extracellular volume fraction mapping, with higher spatial reso-
CONCLUSIONS
lution and precision (i.e., free of T1-fitting error). The current clinical resolution of LGE scans is not yet
The entropy, a newly proposed LGE-CMR–derived
sufficient to detect homogeneous distributed (and
parameter, can be used to quantify tissue in-
fibrosis
a
homogeneity. In post-MI patients, the entropy within
microscopic level (34); nevertheless, patchy fibrosis
the scar was the only LGE-CMR–derived parameter
and thicker strands of fibrosis, typical for (irrevers-
independently associated with VA and therefore
ible) replacement fibrosis, may well be detectable as
seems to be a promising marker for an inhomoge-
inhomogeneous tissue by LV entropy. Hence, in the
neous and arrhythmogenic scar. Entropy in the entire
current study, entropy of the entire LV has been
LV was independently associated with mortality,
chosen as measure of global tissue inhomogeneity,
indicating the presence of adverse and perhaps irre-
and was associated with mortality independent of
versible remodeling.
potentially
reversible)
interstitial
on
age, renal failure, multivessel disease, prior coronary artery bypass graft, LVEF, and entropy in the scar.
ADDRESS
The association between LV entropy and mortality
Zeppenfeld, and Dr. Q. Tao, Leiden University Medi-
may reflect adverse and irreversible, inhomogeneous
cal Center, Department of Cardiology, Department of
remodeling of the post-infarct LV.
Radiology (C-03-Q), P.O. Box 9600, 2300 RC Leiden,
STUDY LIMITATIONS. This study has a relatively
limited sample size and a retrospective single-center study design. All LGE images were acquired with the same MR equipment and protocol. The generalizability of the metric to multicenter, multivendor data requires further investigation. Our study includes 17 patients who underwent VT ablation prior to ICD implantation, which can influence consecutive VT events. Three patients underwent VT ablation prior to LGE-CMR. However, the number of patients with complete
procedural
success
defined
as
non-
inducibility after VT-ablation was low. In the present study, the LGE-CMR
images were
acquired as
2-dimensional short-axis images by a 1.5-T MR imaging scanner, and our results are only applicable to 2-dimensional LGE techniques with the same MR protocol. Furthermore, our results need to be validated
in
a
prospective
group.
Recently,
more
advanced MR imaging protocols with a higher resolution have been developed, which potentially yield
FOR
CORRESPONDENCE:
Dr.
Katja
the Netherlands. E-mail: [email protected] OR [email protected]. PERSPECTIVES COMPETENCY IN MEDICAL KNOWLEDGE: Entropy as a newly proposed LGE-CMR–based measure for tissue composition has potentially important clinical implications. The association between high entropy within the scar and VA in post-MI patients suggests that scar entropy may serve as an additional parameter for risk stratification. The association of a higher entropy of the entire LV with mortality suggests that this LGE-CMR–derived parameter for tissue composition may be used to monitor disease progression, and perhaps for early identification of patients with adverse LV remodeling and unfavorable outcome. TRANSLATIONAL OUTLOOK: Further studies are needed to validate the association between entropy and VA/mortality, including the application of advanced high-resolution 3-dimensional LGE-CMR image acquisition.
entropy measures of higher sensitivity in future
REFERENCES 1. Moss AJ, Zareba W, Hall WJ, et al., for the Multicenter Automatic Defibrillator Implantation
across the spectrum of ejection fraction and heart failure stage. J Am Heart Assoc 2015;4:
Trial II Investigators. Prophylactic implantation of a defibrillator in patients with myocardial infarction and reduced ejection fraction. N Engl J Med 2002;346:877–83.
e002613.
tachyarrhythmia by an implanted defibrillator. Circulation 2004;110:3760–5.
2. Schelbert EB, Piehler KM, Zareba KM, et al.
3. Bardy GH, Lee KL, Mark DB, et al., for the SCDHeFT Investigators. Amiodarone or an implantable cardioverter-defibrillator for congestive heart failure. N Engl J Med 2005;352:225–37.
5. Priori SG, Blomstrom-Lundqvist C, Mazzanti A, et al. 2015 ESC guidelines for the management of patients with ventricular arrhythmias and the prevention of sudden cardiac death: the Task Force for the Management of Patients with Ven-
Myocardial fibrosis quantified by extracellular volume is associated with subsequent hospitalization for heart failure, death, or both
4. Moss AJ, Greenberg H, Case RB, et al., for the MADIT-II Research Group. Long-term clinical course of patients after termination of ventricular
tricular Arrhythmias and the Prevention of Sudden Cardiac Death of the European Society of Cardiology (ESC). Endorsed by Association for European
9
10
Androulakis et al.
JACC: CLINICAL ELECTROPHYSIOLOGY VOL.
Paediatric and Congenital Cardiology (AEPC). Eur Heart J 2015;36:2793–867. 6. Daubert JP, Zareba W, Hall WJ, et al., for the MADIT II Study Investigators. Predictive value of ventricular arrhythmia inducibility for subsequent ventricular tachycardia or ventricular fibrillation in Multicenter Automatic Defibrillator Implantation Trial (MADIT) II patients. J Am Coll Cardiol 2006; 47:98–107. 7. de Bakker JM, van Capelle FJ, Janse MJ, et al. Slow conduction in the infarcted human heart: “zigzag” course of activation. Circulation 1993;88: 915–26. 8. Wu E, Judd RM, Vargas JD, Klocke FJ, Bonow RO, Kim RJ. Visualisation of presence, location, and transmural extent of healed Q-wave and non-Q-wave myocardial infarction. Lancet 2001;357:21–8. 9. Kim RJ, Fieno DS, Parrish TB, et al. Relationship of MRI delayed contrast enhancement to irreversible injury, infarct age, and contractile function. Circulation 1999;100:1992–2002. 10. Roes SD, Borleffs CJ, van der Geest RJ, et al. Infarct tissue heterogeneity assessed with contrast-enhanced MRI predicts spontaneous ventricular arrhythmia in patients with ischemic cardiomyopathy and implantable cardioverterdefibrillator. Circ Cardiovasc Imaging 2009;2: 183–90. 11. Schmidt A, Azevedo CF, Cheng A, et al. Infarct tissue heterogeneity by magnetic resonance imaging identifies enhanced cardiac arrhythmia susceptibility in patients with left ventricular dysfunction. Circulation 2007;115:2006–14. 12. Wu KC, Gerstenblith G, Guallar E, et al. Combined cardiac magnetic resonance imaging and Creactive protein levels identify a cohort at low risk for defibrillator firings and death. Circ Cardiovasc Imaging 2012;5:178–86. 13. Robbers LF, Delewi R, Nijveldt R, et al. Myocardial infarct heterogeneity assessment by late gadolinium enhancement cardiovascular magnetic resonance imaging shows predictive value for ventricular arrhythmia development after acute myocardial infarction. Eur Heart J Cardiovasc Imaging 2013;14:1150–8. 14. Rayatzadeh H, Tan A, Chan RH, et al. Scar heterogeneity on cardiovascular magnetic resonance as a predictor of appropriate implantable cardioverter defibrillator therapy. J Cardiovasc Magn Reson 2013;15:31.
-, NO. -, 2019 - 2019:-–-
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
quantification measures for late gadolinium enhancement magnetic resonance imaging. Circ Cardiovasc Imaging 2012;5:448–56. 16. de Haan S, Meijers TA, Knaapen P, Beek AM, van Rossum AC, Allaart CP. Scar size and characteristics assessed by CMR predict ventricular arrhythmias in ischaemic cardiomyopathy: comparison of previously validated models. Heart 2011;97:1951–6. 17. Klem I, Weinsaft JW, Bahnson TD, et al. Assessment of myocardial scarring improves risk stratification in patients evaluated for cardiac defibrillator implantation. J Am Coll Cardiol 2012; 60:408–20. 18. Boye P, Abdel-Aty H, Zacharzowsky U, et al. Prediction of life-threatening arrhythmic events in patients with chronic myocardial infarction by contrast-enhanced CMR. J Am Coll Cardiol Img 2011;4:871–9. 19. Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27:379–423. 20. Bishop JE, Greenbaum R, Gibson DG, Yacoub M, Laurent GJ. Enhanced deposition of predominantly type I collagen in myocardial disease. J Mol Cell Cardiol 1990;22:1157–65. 21. Beltrami CA, Finato N, Rocco M, et al. Structural basis of end-stage failure in ischemic cardiomyopathy in humans. Circulation 1994;89: 151–63.
and Chronic Heart Failure 2008 of the European Society of Cardiology. Developed in collaboration with the Heart Failure Association of the ESC (HFA) and endorsed by the European Society of Intensive Care Medicine (ESICM). Eur Heart J 2008;29:2388–442. 28. Hohnloser SH, Kuck KH, Dorian P, et al., for the DINAMIT Investigators. Prophylactic use of an implantable cardioverter-defibrillator after acute myocardial infarction. N Engl J Med 2004;351: 2481–8. 29. Kuck KH, Schaumann A, Eckardt L, et al., for the VTACH Study Group. Catheter ablation of stable ventricular tachycardia before defibrillator implantation in patients with coronary heart disease (VTACH): a multicentre randomised controlled trial. Lancet 2010;375:31–40. 30. Piers SR, Tao Q, de Riva Silva M, et al. CMRbased identification of critical isthmus sites of ischemic and nonischemic ventricular tachycardia. J Am Coll Cardiol Img 2014;7:774–84. 31. Desjardins B, Crawford T, Good E, et al. Infarct architecture and characteristics on delayed enhanced magnetic resonance imaging and electroanatomic mapping in patients with postinfarction ventricular arrhythmia. Heart Rhythm 2009;6:644–51.
22. Mukherjee D, Sen S. Alteration of collagen phenotypes in ischemic cardiomyopathy. J Clin
32. Sasaki T, Miller CF, Hansford R, et al. Myocardial structural associations with local electrograms: a study of postinfarct ventricular tachycardia pathophysiology and magnetic resonance-based noninvasive mapping. Circ
Invest 1991;88:1141–6.
Arrhythm Electrophysiol 2012;5:1081–90.
23. Volders PG, Willems IE, Cleutjens JP, Arends JW, Havenith MG, Daemen MJ. Interstitial collagen is increased in the non-infarcted human myocardium after myocardial infarction. J Molec Cell Cardiol 1993;25:1317–23.
33. Iles L, Pfluger H, Phrommintikul A, et al. Evaluation of diffuse myocardial fibrosis in heart failure with cardiac magnetic resonance contrastenhanced T1 mapping. J Am Coll Cardiol 2008; 52:1574–80.
24. Wong TC, Piehler K, Meier CG, et al. Associa-
34. Schelbert EB, Hsu LY, Anderson SA, et al. Late gadolinium-enhancement cardiac magnetic resonance identifies postinfarction myocardial fibrosis
tion between extracellular matrix expansion quantified by cardiovascular magnetic resonance and short-term mortality. Circulation 2012;126: 1206–16. 25. Kammerlander AA, Marzluf BA, ZotterTufaro C, et al. T1 mapping by CMR imaging: from histological validation to clinical implication. J Am Coll Cardiol Img 2016;9:14–23. 26. Priori SG, Aliot E, Blomstrom-Lundqvist C, et al. Update of the guidelines on sudden cardiac death of the European Society of Cardiology. Eur Heart J 2003;24:13–5.
15. Gao P, Yee R, Gula L, et al. Prediction of arrhythmic events in ischemic and dilated cardio-
27. Dickstein K, Cohen-Solal A, Filippatos G, et al. ESC guidelines for the diagnosis and treatment of
myopathy patients referred for implantable cardiac defibrillator: evaluation of multiple scar
acute and chronic heart failure 2008: the Task Force for the Diagnosis and Treatment of Acute
and the border zone at the near cellular level in ex vivo rat heart. Circ Cardiovasc Imaging 2010;3: 743–52.
KEY WORDS cardiac magnetic resonance, diffuse fibrosis, entropy, late gadolinium enhancement, magnetic resonance imaging, sudden death, ventricular arrhythmia
A PPE NDI X For supplemental Methods including figures and tables, please see the online version of this paper.
VOL.
-, NO. -, 2019
ª 2019 BY THE AMERICAN COLLEGE OF CARDIOLOGY FOUNDATION PUBLISHED BY ELSEVIER
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity for Prediction of Ventricular Arrhythmias and Mortality in Post-Infarct Patients Alexander F.A. Androulakis, MD,a Katja Zeppenfeld, MD, PHD,a Elisabeth H.M. Paiman, MD,b Sebastiaan R.D. Piers, MD, PHD,a Adrianus P. Wijnmaalen, MD, PHD,a Hans-Marc J. Siebelink, MD, PHD,a Marek Sramko, MD, PHD,a Hildo J. Lamb, MD, PHD,b Rob J. van der Geest, PHD,c Marta de Riva, MD,a Qian Tao, PHDc
ABSTRACT OBJECTIVES This study proposed entropy as a new late gadolinium enhanced cardiac magnetic resonance–derived parameter to evaluate tissue inhomogeneity, independent of signal intensity thresholds. This study hypothesized that entropy within the scar is associated with ventricular arrhythmias (VAs), whereas entropy of the entire left ventricular (LV) myocardium is associated with mortality. BACKGROUND In patients after myocardial infarction, the heterogeneity of fibrosis determines the substrate for VA. Fibrosis in remote areas has been associated with heart failure and mortality. Late gadolinium-enhanced cardiac magnetic resonance has been used to delineate fibrosis, but available methods depend on signal intensity thresholds and results have been inconsistent. METHODS Consecutive post–myocardial infarction patients undergoing late gadolinium enhanced cardiac magnetic resonance prior to implantable cardioverter-defibrillator implantation were included. From cardiac magnetic resonance imaging, total scar size, scar gray zone, scar transmurality, and tissue entropy were derived. Patients were followed for appropriate implantable cardioverter-defibrillator therapy and mortality. RESULTS A total of 154 patients (64 10 years, 84% male, LV ejection fraction 29 10%, 47% acute revascularization) were included. During a median follow-up of 56 (interquartile range: 40, 73) months, appropriate implantable cardioverter-defibrillator therapy occurred in 46 patients (30%), and 41 patients (27%) died. From multivariable analysis, higher entropy of the scar (hazard ratio [HR]: 1.9; 95% confidence interval [CI]: 1.0 to 3.5; p ¼ 0.042) was independently associated with VA, after adjusting for multivessel disease, acute revascularization, LV ejection fraction, scar gray zone, and transmurality. Entropy of the entire LV was independently associated with mortality (HR: 3.2; 95% CI: 1.1 to 9.9; p ¼ 0.038). CONCLUSIONS High entropy within the scar was associated with VA and may indicate an arrhythmogenic scar. High entropy of the entire LV was associated with mortality and may reflect a fibrosis pattern associated with adverse remodeling. (J Am Coll Cardiol EP 2019;-:-–-) © 2019 by the American College of Cardiology Foundation.
From the aDepartment of Cardiology, Leiden University Medical Center, Leiden, the Netherlands; bDepartment of Radiology, Leiden University Medical Center, Leiden, the Netherlands; and the cDivision of Image Processing, Department of Radiology, Leiden University Medical Center, Leiden, the Netherlands. This study was funded by NOW (Nederlandse Organisatie voor Wetenschappelijk Onderzoek - Dutch organisation for Scientific Research) Domain Applied and Engineering Sciences grant no. 12899. The Department of Cardiology (Leiden University Medical Center) has received unrestricted research grants from Edwards Lifesciences, Medtronic, Biotronik, and Boston Scientific. Dr. Zeppenfeld has received funding from a research grant awarded to the Department of Cardiology (Leiden University Medical Center) from Biosense Webster. All other authors have reported that they have no relationships relevant to the contents of this paper to disclose. All authors attest they are in compliance with human studies committees and animal welfare regulations of the authors’ institutions and Food and Drug Administration guidelines, including patient consent where appropriate. For more information, visit the JACC: Clinical Electrophysiology author instructions page. Manuscript received June 12, 2018; revised manuscript received December 12, 2018, accepted December 12, 2018.
ISSN 2405-500X/$36.00
https://doi.org/10.1016/j.jacep.2018.12.005
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ABBREVIATIONS AND ACRONYMS ATP = antitachycardia pacing CI = confidence interval CMR = cardiac magnetic resonance imaging
GZ = gray zone HR = hazard ratio ICD = implantable cardioverter-defibrillator
IQR = interquartile range LGE = late gadolinium
P
atients after myocardial infarction
mortality. Histological studies demonstrated a higher
(MI) are at risk for ventricular arrhyth-
amount of fibrous tissue in noninfarcted myocardium
mias (VAs) and adverse left ventricu-
of hearts from patients with end-stage heart failure
lar (LV) remodeling, both related to cardiac
with an ischemic cause compared with control hearts
mortality (1,2). The implantable cardioverter-
(obtained from autopsies in patients who died of a
defibrillator (ICD) reduces mortality in pa-
noncardiovascular cause) (20–23). Remote fibrosis
tients considered at high risk for VA (1,3).
may be quantified as increased extracellular volume
However, during long-term follow-up, only
fraction using T 1 mapping, which has been associated
35% of post-MI patients who have received
with mortality independent from LVEF and MI size
an ICD for primary prevention of sudden
(2,24). However, T 1 mapping is usually restricted to a
cardiac death experience appropriate therapy
limited number of pre-selected slices (2,24,25), and it
(4).
is not a direct measure of tissue inhomogeneity.
Although several noninvasive parameters
In this work, we propose a new LGE-CMR–derived
have been suggested to identify patients at
method to quantify tissue inhomogeneity by the
risk for VA, the ICD indication for primary
entropy of the SI values and hypothesize the
prevention still relies on a reduced left
following: 1) entropy within the scar is a marker for
fraction
ventricular ejection fraction (LVEF) (5). Of
inhomogeneous
MI = myocardial infarction
interest, the vast majority of VAs that prompt
might be associated with MVT; and 2) entropy of the
enhancement
LV = left ventricle/left ventricular
LVEF = left ventricular ejection
scar
composition
and
therefore
MVT = monomorphic
ICD therapy in post-MI patients implanted
entire LV is a marker for overall inhomogeneous
ventricular tachycardia
for primary prevention are monomorphic
fibrosis in the LV and therefore might be associated
NYHA = New York Heart
ventricular tachycardias (MVT), suggesting
with adverse remodeling and mortality.
Association
that MVT contributes significantly to ar-
SI = signal intensity
rhythmogenic death in patients without an
ST = scar transmurality
ICD (6). MVT in post-MI patients are typically
METHODS
STmedian = median value of scar
due to scar-related re-entry facilitated by
PATIENTS. Data of consecutive patients with prior MI
transmurality
areas of slow conduction. Histological hall-
who underwent LGE-CMR before ICD implantation
VA = ventricular arrhythmia
marks of the arrhythmogenic substrate are
for primary or secondary prevention between 2003
VF = ventricular fibrillation
inhomogeneous areas within the scar, con-
and 2012 were collected. Patients who underwent
VT = ventricular tachycardia
sisting of surviving myocyte bundles imbed-
surgical LV reconstruction within 1 year after LGE-
ded and interspersed by fibrous tissue (7).
CMR and patients in whom the LGE-CMR quality
Late gadolinium enhanced (LGE) cardiac magnetic
was poor were excluded (Online Figure 1). The
resonance imaging (CMR) is the current gold standard
remaining patients constituted the final study popu-
to visualize scarred myocardium (8). Intermediate
lation. The diagnosis of MI was based on the presence
signal intensity (SI) values are assumed to indicate a
of subendocardial or transmural LGE areas in the
mixture of fibrotic and viable tissue, often referred to
perfusion territory of a significantly stenotic coronary
as gray zone (GZ). GZ delineation depends on partic-
artery (>70% stenosis on coronary angiogram).
ular SI thresholds from image analysis methods (9).
Patient medical records were reviewed for baseline
These methods rely on operator-defined areas with
clinical characteristics. At the day of ICD implanta-
maximum SI, areas with remote myocardium, or a
tion, serum creatinine was retrieved, and renal failure
combination of both as a reference. Prior studies have
was defined as creatinine blood level $1.4 mg/dl.
evaluated the association between the extent of the
In addition, details on prior ischemic events, acute
GZ and spontaneous and inducible VA, but with
reperfusion therapy during the first MI (within 24 h
conflicting results (10–18). To quantify the tissue in-
from onset of symptoms), and elective revasculari-
homogeneity while avoiding the inconsistency of
zation strategies were collected. Patients with a single
zone definition, we propose a new LGE-CMR–derived
MI
metric: entropy. Entropy is a classical measure of
were categorized as “acute revascularized” patients.
who
underwent
acute
reperfusion
therapy
uncertainty in information theory (19), and it mea-
Multivessel disease was defined as a significant
sures the uncertainty of tissue composition as
stenosis in $2 coronary arteries. Data on prior VA
reflected by the uncertainty of SI. Instead of parti-
episodes were collected. For patients who had un-
tioning zones by threshold, the entropy is computed
dergone ventricular tachycardia (VT)-ablation, all
from all SI values in LGE-CMR.
procedural reports were reviewed to determine
Progressive heart failure, due to adverse LV
procedural success.
remodeling and myocardial fibrosis in the (non-
The Dutch Central Committee on Human-Related
infarcted) myocardium, further contributes to cardiac
Research permits use of anonymous data without
JACC: CLINICAL ELECTROPHYSIOLOGY VOL.
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Androulakis et al.
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F I G U R E 1 Scar Transmurality LGE-CMR
(A) Endocardial (red) and epicardial (green) borders are manually traced. (B) Scar core zone (pink) and gray zone (yellow) are semiautomatically identified based on signal intensity threshold. (C) The transmurality of the total scar is computed along the radial transmural direction. CMR ¼ cardiac magnetic resonance; LGE ¼ late gadolinium enhancement.
prior approval of an institutional review board, if the
for irregularity as proposed by Shannon, allowing for
data are obtained for patient care and if the data do
an entropy range between 0 and 10 (19) (see Online
not contain identifiers that could be traced back to the
Methods), with 0 being a complete homogeneous
individual patient. All data used for this study were
distribution of SI values (consisting of only a single SI
acquired based on clinical care; any identifying
value) and 10 being the most inhomogeneous distri-
information was removed from the data.
bution of SI equally scattering in the SI range. The
CMR ANALYSIS. All images were acquired by a 1.5-T
Gyroscan
magnetic
resonance
imaging
scanner
(see the Online Methods in the Online Appendix). Data analysis was performed as described earlier
investigator who calculated entropy was blinded for patient outcome. Subsequently, the tissue entropy was quantified for both the scar region and the entire LV myocardium (Figure 2, Online Appendix).
to evaluate the LVEF, LV mass, and myocardial scar
ICD IMPLANTATION AND PROGRAMMING. Patients
(see Online Methods) (10). The scar was automatically
received an ICD or a cardiac resynchronization ther-
identified as myocardium with SI >35% of the maximum SI, the scar GZ as myocardium with SI >35% but <50% of the maximum SI, and scar core as myocardium with a SI $50% of the maximum SI
apy defibrillator for primary or secondary prevention according to the guidelines of the European Society of Cardiology that were valid at the time of implantation (26,27). ICD were typically programmed to include 3
(Figure 1B). Scar transmurality (ST) was calculated as
zones: monitor zone/VT1 zone (150 to 188 beats/min;
the percentage of scar from the total LV myocardial
no therapy/antitachycardia pacing (ATP) if indicated),
wall in the radial direction (Figure 1C). The median
VT2 zone (188 to 210 beats/min; ATP and shock), and
value of ST (ST median) was used as a measure of
ventricular fibrillation (VF) zone (>210 beats/min; if
the overall ST for each patient. The ST median was
available ATP during charging, and shock). In case of
divided into 4 categories: 1) 0% < ST median #25%; 2) 26% < ST median #50%; 3) 51 < ST median #75%; and 4) 76% < ST median #100%. Tissue inhomogeneity was quantified by the entropy of SI values within the tissue.
secondary prevention, programming was adapted according to the clinical VT. FOLLOW-UP. Patients were followed in the outpa-
tient clinic 2 months after ICD implantation and every
Introducing entropy to quantify tissue inhomo-
3 to 6 months thereafter. Follow-up visits included
geneity is based on the assumption that areas
clinical evaluation, device
with varying SI values in LGE represent tissue with
12-lead electrocardiogram. All episodes prompting
different
composition.
The
normalized
ICD therapy were reviewed by an experienced
according to a predefined range between 0 and 1,024
physician for exclusion of inappropriate therapies
for each patient. The scar and LV-entropy were
and categorization of the VA episodes in MVT or VF.
automatically
environment;
Appropriate device therapy was defined as any ATP or
MathWorks, Natick, Massachusetts) using the formula
ICD shock delivered for an MVT or VF. MVT on ICD
calculated
SI
was
interrogation, and a
(Matlab
3
4
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F I G U R E 2 Entropy Model and SI Histograms in 4 Subjects With Comparable LVEF
Continued on the next page
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5
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
was defined as a VT with a morphologically stable farfield electrogram and a beat-to-beat cycle length
T A B L E 1 Baseline Characteristics
variation #30 ms. VF/polymorphic VT was defined as any VA with beat-to-beat variations in both far-field
Total Population (N ¼ 154)
Appropriate Therapy (n ¼ 46)
No Appropriate Therapy (n ¼ 108)
p Value
electrogram morphology and cycle length. VA was
Age, yrs
64 10
63 12
64 9
0.814
defined as sustained when lasting >30 s or when
Sex
130 (84)
43 (94)
87 (81)
0.043
treated with ATP or shock. All ICD recordings were
Smoking
76 (49)
22 (48)
54 (50)
0.825
analyzed by an experienced observer. In case of
Hypertension
71 (46)
21 (46)
50 (46)
0.983
death, the medical records concerning cause of
Hypercholesterolemia
74 (48)
21 (46)
53 (49)
0.910
Diabetes
32 (21)
5 (11)
27 (25)
0.048
Renal failure
28 (18)
11 (24)
17 (16)
0.229
Atrial fibrillation
31 (20)
9 (20)
22 (20)
0.909
follow-up was censored at the operation date. Medi-
NYHA functional class >II
51 (33)
17 (37)
34 (32)
0.509
cal records were reviewed to assess cardiac/noncar-
VT ablation prior to ICD
17 (11)
9 (20)
8 (7)
0.046
diac mortality.
Noninducible after ablation
death were obtained. In the event of late LV reconstruction (>1 year post-ICD implantation), patient
STATISTICAL ANALYSIS. Continuous variables are
Multivessel disease
6 (4)
4 (9)
2 (2)
0.066
102 (66)
35 (76)
67 (62)
0.080 0.962
Prior CABG
54 (35)
16 (35)
38 (35)
presented as mean SD, and categorical data are
Acute revascularization during index MI
72 (47)
15 (33)
57 (53)
0.022
summarized as frequencies and percentages. Differ-
Secondary prevention ICD
33 (21)
16 (35)
17 (16)
0.008
ences in baseline characteristics between patients
CRT
99 (64)
26 (57)
73 (68)
0.189
were analyzed using Student’s t-test or Fisher exact
LBBB
46 (29)
13 (28)
33 (31)
0.776
test, as appropriate.
RBBB
20 (13)
5 (11)
15 (14)
0.610
115 34
115 35
116 34
0.857
Univariable and multivariable Cox proportional hazards regression models were constructed to study
QRS interval, ms Medication Amiodarone
16 (10)
5 (11)
11 (10)
0.913
the relation between scar features and the 2 types of
Beta-blocker
127 (82)
40 (87)
87 (81)
0.394
endpoints, namely, mortality and appropriate ICD
Calcium channel blocker
therapy. Hazard ratios (HR) were obtained after
ACE inhibitor
adjustment
for
pre-determined
potential
con-
founders based on clinical relevance (for appropriate therapy: multivessel disease, acute revascularization, LVEF, GZ, and ST median ; and for mortality: age, renal
14 (9)
7 (15)
7 (7)
0.088
105 (68)
31 (67)
74 (69)
0.829
ARB
28 (18)
6 (13)
22 (20)
0.270
Statins
132 (86)
40 (87)
92 (85)
0.872
Any diuretic
96 (62)
30 (65)
66 (61)
0.678
Aldosterone antagonist
48 (31)
12 (26)
34 (32)
0.356
failure, New York Heart Association [NYHA] func-
Values are mean SD or n (%).
tional class >II, multivessel disease, prior coronary
ACE ¼ angiotensin converting enzyme; ARB ¼ angiotensin II receptor inhibitor; CABG ¼ coronary artery bypass graft; CRT ¼ cardiac resynchronization therapy; ICD ¼ implantable cardioverter-defibrillator; LBBB ¼ left bundle branch block; MI ¼ myocardial infarction; NYHA ¼ New York Heart Association functional class; RBBB ¼ right bundle branch block; VT ¼ ventricular tachycardia.
artery bypass graft, LVEF, scar size, and scar entropy). HR with 95% confidence intervals (CIs) are reported. All tests were 2-sided, and p < 0.05 was considered statistically significant. Spline curves were fitted for
below the median value. The cumulative mortality
the univariable and multivariable associations be-
during follow-up was compared between patients
tween scar entropy and the HR (log scale) of ICD
with entropy in the entire LV above versus below the
therapy and the univariable and multivariable asso-
median value.
ciations between entropy of the entire LV and the HR (log scale) of mortality. Using Kaplan-Meier survival
RESULTS
analyses, the cumulative incidence of appropriate ICD therapy during follow-up was compared between
BASELINE
patients with entropy within the scar above versus
period, a total of 188 post-MI patients underwent
CHARACTERISTICS. During
the
study
F I G U R E 2 Continued
(A[1,2]) Model histograms of a virtual homogeneous signal intensity (SI) distribution and a virtual inhomogeneous SI distribution resulting in an entropy of 0 and 10, respectively, using the formula proposed by Shannon. (B[1,2], C[1,2]) SI histograms from 4 patients, which are used for entropy computation along with short-axis views of late gadolinium enhancement cardiac magnetic resonance. (B[1,2])Patients with a similar scar core, gray zone, and left ventricular (LV) ejection fraction. However, the patient in B(1) had a high scar entropy and experienced ventricular arrhythmia, whereas the patient in B(2) had a low scar entropy and did not experience ventricular arrhythmia. (C[1,2]) Patients with a similar scar size, gray zone, and LV ejection fraction. The patient in C(1) had a high LV entropy and died (due to heart failure) during follow-up, whereas the patient in C(2) had a low LV entropy and survived. B(3) Ventricular tachycardia (VT)-free survival in patients with scar entropy above versus below the median value. (C[3]) Survival in patients with LV entropy above versus below the median value.
Androulakis et al.
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
(age 64 10 years, 84% male) constituted the
T A B L E 2 MRI Characteristics and Appropriate Therapy
All Patients (N ¼ 154)
Appropriate Therapy (n ¼ 46)
study population. In 121 patients (79%), an ICD No Appropriate Therapy (n ¼ 108)
p Value
0.440
was
implanted
for
primary
prevention
and
in
33 patients (21%) for secondary prevention. In 77 of
LVEF, %
29 10
28 13
30 9
LV mass, g
151 36
155 39
149 35
0.325
Total scar, g
47 26
48 26
47 26
0.784
the indication was established based on the 2003
Gray zone, g
19 9
20 11
18 9
0.412
European Society of Cardiology guidelines update
121 patients receiving the ICD for primary prevention,
(Class IIa recommendation if LVEF <30%) (26). The
Median scar, % transmurality
remaining 44 patients received the ICD according
0–25
3 (2)
0 (0)
3 (3)
0.342
25–50
36 (23)
11 (24)
25 (23)
0.918
50–75
66 (43)
25 (54)
41 (38)
0.060
75–100
49 (32)
10 (22)
39 (36)
0.064
NYHA functional class $II despite optimal medical
In scar
7.82 0.5
7.94 0.5
7.77 0.6
0.074
ICD implanted for secondary prevention, 17 had un-
In entire LV
8.09 0.7
8.14 0.7
8.08 0.7
0.630
dergone VT ablation prior to ICD implantation. Of
to the 2008 European Society of Cardiology guidelines (Class Ia recommendation if LVEF #35% and therapy) (27). Of the 33 patients who had an
Entropy
those, 6 were rendered noninducible for any VT after
Values are mean SD or n (%).
ablation. Three patients underwent VT-ablation prior
LV ¼ left ventricular; LVEF ¼ left ventricular ejection fraction; MRI ¼ magnetic resonance imaging.
to LGE-CMR. Baseline characteristics are shown LGE-CMR prior to ICD implantation. Twenty patients
in Table 1.
who underwent early LV reconstruction and 14 in
CMR PARAMETERS. The LVEF of the study popula-
whom only a poor quality CMR was available for
tion was 29 10%; the total infarct size was 47 26 g;
analysis were excluded. The remaining 154 patients
and the infarct GZ size was 19 9 g. The most prevalent ST median was 50% to 75%, which was observed in 66 patients (43%). The entropy was 7.8 0.5 for the
T A B L E 3 Univariate and Multivariable Analysis for Appropriate Therapy
Univariate HR
total infarct scar and 8.0 0.7 for the entire LV.
Multivariable
95% CI
p Value
Age, per year
1.0
1.0–1.0
0.906
Sex
3.5
1.1–11.4
0.035
HR
95% CI
p Value
Detailed CMR data are shown in Table 2. FOLLOW-UP. During
a
median
follow-up
of
56
(interquartile range [IQR]: 40 to 73) months, 46 pa-
Hypertension
1.0
0.5–1.8
0.973
Atrial fibrillation
1.0
0.5–2.0
0.942
NYHA functional class >II
1.3
0.7–2.4
0.347
therapy (44 of 46 for MVT) and 41 patients (27%) died,
tients (30%) received at least 1 appropriate ICD
QRS interval >120 ms
0.8
0.4–1.7
0.620
among which 22 deaths (50%) were due to a cardiac
Secondary prevention ICD
2.6
1.4–4.8
0.002
cause. Seven patients (5%) were lost to follow-up
CRT-D
0.6
0.3–1.1
0.087
after a median follow-up period of 42 months
ACE inhibitor or ARB
0.7
0.3–1.5
0.352
(IQR: 39, 46).
Aldosterone antagonist
0.7
0.4–1.3
0.263
Beta-blocker
1.2
0.5–2.9
0.639
Multivessel disease
2.1
1.0–4.3
0.036
CABG
1.1
0.6–2.0
0.830
Acute revascularization
0.5
0.3–0.9
0.8
0.6–1.3
APPROPRIATE ICD THERAPY. Patients who received
Extent of CAD
any appropriate ICD therapy during follow-up had 1.6
0.7–3.5
0.199
0.016
0.6
0.3–1.1
0.076
0.224
1.1
0.7–1.6
0.554
MRI characteristics LVEF, per 10% LV mass, per 10 g
1.1
1.0–1.2
0.114
Total scar, per 10 g
1.0
0.9–1.2
0.413
Scar gray zone, per 10 g
1.2
0.9–1.6
0.173
0–25
0
0.0–161
0.463
25–50
1.0
0.5–1.9
0.914
50–75
1.8
1.0–3.1
0.055
during the first MI (33% vs. 53%; p ¼ 0.022) and had more often a secondary prevention indication (35% vs. 16%; p ¼ 0.008). No other differences in baseline clinical characteristics were observed between patients with or without appropriate ICD therapies
1.2
0.9–1.7
0.287
Scar transmurality, %
75–100
less frequently undergone acute revascularization
(Table 1). LVEF, LV size, total infarct size, and GZ size were
0.6
0.3–1.2
0.123
Entropy in scar, per 1
1.9
1.1–3.3
0.029
LV entropy, per 1
1.2
0.8–1.8
0.368
comparable between patients with or without appro1.6
0.9–3.0
0.105
priate therapies. The STmedian of 50% to 75% tended to be more prevalent in those who received appro-
1.9
1.0–3.5
0.042
priate therapy (54% vs. 38%; p ¼ 0.06). In addition, patients receiving appropriate ICD therapy tended to have a higher entropy within the scar than did
CAD ¼ coronary artery disease; CI ¼ confidence interval; CRT-D ¼ cardiac resynchronization therapy defibrillator; HR ¼ hazard ratio; other abbreviations as in Tables 1 and 2.
patients without appropriate therapy (7.94 0.5 vs. 7.77 0.6; p ¼ 0.07) (Table 2).
JACC: CLINICAL ELECTROPHYSIOLOGY VOL.
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PREDICTORS
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
OF
APPROPRIATE
ICD
THERAPY.
Clinical variables associated with appropriate ICD therapy
were
7
Androulakis et al.
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presence
of
multivessel
T A B L E 4 MRI Characteristics and Mortality
All Patients (N ¼ 154)
Deceased (n ¼ 41)
Survived (n ¼ 113)
p Value
LVEF, %
29 10
24 10
31 10
<0.001
LV mass, g
151 36
160 33
148 37
0.053
Total scar, g
47 26
62 32
42 21
<0.001
Gray zone, g
19 9
23 10
17 9
0.001
disease
(HR: 2.1; 95% CI: 1.0 to 4.3; p ¼ 0.036), acute revascularization during the first infarction (HR: 0.5; 95% CI: 0.3 to 0.9; p ¼ 0.016), and VA prior to ICD implantation (HR: 2.6; 95% CI: 1.4 to 4.8; p ¼ 0.002). A higher entropy within the scar was the only CMR-
Median transmurality, %
derived parameter associated with appropriate ICD
0–25
3 (2)
2 (5)
1 (1)
0.173
therapy (HR: 1.9 per unit entropy; 95% CI: 1.1 to 3.3;
25–50
36 (23)
6 (14)
30 (27)
0.123
p ¼ 0.029). The ST median of 50% to 75% showed a
50–75
66 (43)
21 (50)
45 (40)
0.207
75–100
49 (32)
12 (29)
37 (33)
0.682
In scar
7.82 0.5
8.05 0.4
7.74 0.6
0.001
In entire LV
8.09 0.7
8.47 0.6
7.96 0.7
<0.001
trend (HR: 1.8; 95% CI: 1.0 to 3.1; p ¼ 0.055). On multivariable analysis, the entropy within the scar remained the only CMR-derived parameter associated
Entropy
with appropriate ICD therapy (HR: 1.9 per unit entropy; 95% CI: 1.0 to 3.5; p ¼ 0.042), independent of LVEF, acute revascularization, multivessel disease,
Values are mean SD or n (%). Abbreviations as in Table 1 and 2.
GZ size, and the STmedian of 50% to 75% (Table 3, Figure 2B(3)). Of note, univariable and multivariable association between entropy and ICD therapy is
LV (HR: 3.2 per unit entropy; 95% CI: 1. 1 to 9.9;
approximately linear (Online Figure 2).
p ¼ 0.038) and renal failure (HR: 2.4: 95% CI: 1.1 to 5.1;
MORTALITY. Patients who died during follow-up
mortality
p ¼ 0.032) remained independently associated with (Table
5).
Furthermore,
the
observed
were of similar age at ICD implantation; more frequently had diabetes (34% vs. 16%; p ¼ 0.014), renal failure (37% vs. 12%; p < 0.001), multivessel
T A B L E 5 Univariate and Multivariable Analysis for Mortality
disease (85% vs. 59%; p ¼ 0.001); and had a higher
Univariate
NYHA functional class (Online Table 1). In addition,
Multivariable
HR
95% CI
p Value
HR
95% CI
p Value
these patients had a lower CMR-derived LVEF (24%
Age, per year
1.0
1.0–1.1
0.156
1.0
1.0–1.0
0.384
vs. 31%; p < 0.001), a larger total scar (62 g vs. 42 g;
Sex
2.6
0.8–8.4
0.115
p < 0.001), and a larger GZ (23 g vs. 17 g; p ¼ 0.001). Of
Diabetes
2.5
1.3–4.7
0.007
importance, the entropy within the scar and within
Renal failure
2.9
1.6–5.6
0.001
2.4
1.1–5.1
0.032
the entire LV was significantly higher in deceased
CRT-D
1.3
0.6–2.5
0.512 1.0
0.5–2.3
0.962
patients (8.05 0.4 vs. 7.74 0.6; p ¼ 0.001 and 8.47 0.6 vs. 7.96 0.7; p < 0.001, respectively) (Table 4).
Atrial fibrillation
1.4
0.7–2.8
0.332
NYHA functional class >II
2.9
1.5–5.4
0.001
QRS interval >120 ms
2.4
1.3–4.5
0.006
ACE inhibitor or ARB
0.9
0.4–2.1
0.866
regression analysis, diabetes (HR: 2.5; 95% CI: 1.3 to
Aldosterone antagonist
1.4
0.7–2.7
0.282
4.7; p ¼ 0.007), renal failure (HR: 2.9; 95% CI: 1.6 to
Beta-blocker
0.8
0.4–1.7
0.758
PREDICTORS
OF
MORTALITY. In
univariate Cox
5.6; p ¼ 0.001), a higher NYHA functional class (>II: HR: 2.9; 95% CI: 1.5 to 5.4; p ¼ 0.001), QRS >120 ms (HR: 2.4; 95% CI: 1.3 to 4.5; p ¼ 0.006), presence of multivessel disease (HR: 4.6; 95% CI: 1.6
Extend of CAD Multivessel disease
4.6
1.6–12.9
0.004
3.0
1.0–8.9
0.054
CABG
1.9
1.0–3.6
0.041
1.8
0.9–3.7
0.090
Acute revascularization
0.3
0.2–0.7
0.004 0.9
0.6–1.4
0.778
1.1
1.0–1.2
0.149
MRI characteristics
to 12.9; p ¼ 0.004), prior coronary artery bypass graft
LVEF, per 10% increase
0.5
0.4–0.7
<0.001
(HR: 1.9; 95% CI: 1.0 to 3.6; p ¼ 0.041), LVEF (HR: 0.5;
LV mass, per 10 g
1.1
1.0–1.2
0.042
95% CI: 0.4 to 0.7; p < 0.001), LV mass (HR: 1.1; 95% CI: 1.0 to 1.2; p ¼ 0.042), scar size (HR: 1.2; 95% CI: 1.1 to 1.3; p < 0.001), GZ size (HR: 1.5; 95% CI: 1.2 to 2.0;
Total scar, per 10 g
1.2
1.1–1.3
<0.001
Scar gray zone, per 10 g
1.5
1.2–2.0
0.002 0.194
Median transmurality, % 0–25
2.6
0.6–10.7
p ¼ 0.002), entropy within scar (HR: 2.6; 95% CI: 1.4 to
25–50
0.6
0.2–1.3
0.197
4.9; p ¼ 0.003), and LV entropy (HR: 2.4; 95% CI: 1.5
50–75
1.3
0.7–2.4
0.401
to 3.9; p < 0.001) were associated with mortality
1.0
0.5–1.9
0.914
(Figure 2B(3)). A history of acute revascularization
Entropy in scar, per 1
2.6
1.4–4.9
0.003
0.4
0.1–1.8
0.281
during the first MI was associated with lower
LV entropy, per 1
2.4
1.5–3.9
<0.001
3.2
1.1–9.9
0.038
mortality (HR: 0.3; 95% CI: 0.2 to 0.7; p ¼ 0.004). In multivariable analysis, the entropy in the entire
75–100
Abbreviations as in Tables 1 to 3.
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Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
univariable and multivariable association between
for defining the GZ was applied (15–18) (Online
entropy in the entire LV and mortality is approxi-
Table 2).
mately linear (Online Figure 2).
Of importance, catheter mapping studies, using real-time integration of LGE-CMR–derived scar char-
DISCUSSION
acteristics, demonstrated that only 29% to 55% of all VT-related sites in post-MI patients were located
In the present study, we have introduced entropy as a
within the GZ area, suggesting that this parameter
new parameter to assess tissue inhomogeneity from
may not be sufficient to identify the arrhythmogenic
LGE-CMR, for both the scar and the entire LV
substrate (30,31). Of interest, the mean scar trans-
myocardium. We found that in post-MI patients, the
murality at the VT-related sites was reported to be 75
entropy within the scar was the only CMR-derived
22% and 73 21%, respectively (30,32), which is in
parameter associated with VA and that the entropy
line with our observation that a ST median of 50% to
in the entire LV was independently associated with
75% tended to be associated with VA.
mortality. RISK
ASSESSMENT
ENTROPY OF THE INFARCT SCAR. The present study FOR
VA
AFTER
MI. Current
proposes
a
novel
CMR-derived
parameter
that
guidelines on ICD implantation for primary preven-
directly assesses the tissue inhomogeneity by en-
tion in post-MI patients are based on a reduced LVEF
tropy, which describes uncertainty in LGE signal (19).
(5). However, the majority of patients implanted for
We assume that with the current LGE resolution and
primary prevention do not benefit from the ICD (4).
quality, the signal intensity distribution in the scar
Multiple factors play a role in risk stratification, and
and myocardium, as quantified by the entropy, can
prevention of death in this population has been
differentiate the tissue composition to a certain
shown to be a complex issue. The risk of sudden
extent that is clinically relevant. In contrast to GZ
death in patients after MI has a biphasic temporal
quantification, computation of entropy does not
course. In the early phase after MI, VAs are common
require subdividing the scar region into 2 zones,
but ICD implantation does not improve patient sur-
therefore avoiding thresholds. In addition, the en-
vival because of the competing risks (28). Patients
tropy is richer in information than the GZ size is
who have survived this early phase remain at risk,
because entropy utilizes the entire SI distribution,
however, for scar-related re-entry MVT (29). Identi-
potentially capturing subtle variations in tissue
fication of patients at risk for late re-entrant VT is of
composition beyond the size of a particular zone.
upmost importance because these patients benefit
In our study, we found a statistically significant
from prophylactic ICD implantation. Accordingly,
association between entropy within the scar and
noninvasive parameters to predict the occurrence of
occurrence of VA. In multivariable analysis, the en-
VA are important. Of interest, the vast majority of
tropy within the scar remained the only CMR-derived
reported arrhythmia episodes that prompt appro-
parameter associated with VA. As such, entropy
priate ICD therapy are MVT (6). In post-MI patients,
calculated from 2-dimensional LGE MR imaging
MVT are typically due to scar-related re-entry
seems to be a promising parameter to indicate the
dependent on areas of inhomogeneous tissue con-
presence of an arrhythmogenic scar.
sisting of surviving myocytes imbedded and interspersed by fibrous tissue (7). Therefore, noninvasive identification of inhomogeneous scars is a logical and promising parameter for risk stratification.
ENTROPY OF THE ENTIRE LV. Patients with prior MI
are also at risk for heart failure due to progressive adverse remodeling not only within the scar area but also within remote noninfarcted myocardium. In pa-
CMR PARAMETERS AND VA. The most extensively
tients with end-stage heart failure due to coronary
evaluated surrogate for scar inhomogeneity is the
artery
scar GZ (Online Table 2) (10–18). Delineation of the GZ
showed an increased amount of fibrous tissue in the
disease,
explanted/post-mortem
hearts
requires predefined SI thresholds. Different methods
noninfarcted myocardium (20–23). T 1 mapping has
have been applied to determine these SI thresholds,
been suggested to noninvasively determine the
which either use the areas with maximum SI, areas
extracellular volume fraction as a surrogate for
with normal remote myocardium, or a combination of
diffuse fibrosis in noninfarcted myocardium (25,33).
both (10–18). While some studies reported an associ-
Increased ECV quantified by T 1 mapping has been
ation between the GZ size and occurrence of VA
associated with progressive heart failure, mortality,
(10,11,13–15), others, including the current study,
or combined endpoint (2,24,33) However, in current
could not confirm such an association (15,17,18). This
clinical practice, T1 mapping is usually restricted to
inconsistency remained, even when the same method
a limited number of pre-selected slices, and its
JACC: CLINICAL ELECTROPHYSIOLOGY VOL.
-, NO. -, 2019
Androulakis et al.
- 2019:-–-
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
precision is affected by motion artifacts (2,24,25). In
studies. Studies to validate the histological basis of
contrast, whole-heart LGE scan is more accessible. It
entropy are warranted.
requires less acquisition time than T 1 /extracellular volume fraction mapping, with higher spatial reso-
CONCLUSIONS
lution and precision (i.e., free of T1-fitting error). The current clinical resolution of LGE scans is not yet
The entropy, a newly proposed LGE-CMR–derived
sufficient to detect homogeneous distributed (and
parameter, can be used to quantify tissue in-
fibrosis
a
homogeneity. In post-MI patients, the entropy within
microscopic level (34); nevertheless, patchy fibrosis
the scar was the only LGE-CMR–derived parameter
and thicker strands of fibrosis, typical for (irrevers-
independently associated with VA and therefore
ible) replacement fibrosis, may well be detectable as
seems to be a promising marker for an inhomoge-
inhomogeneous tissue by LV entropy. Hence, in the
neous and arrhythmogenic scar. Entropy in the entire
current study, entropy of the entire LV has been
LV was independently associated with mortality,
chosen as measure of global tissue inhomogeneity,
indicating the presence of adverse and perhaps irre-
and was associated with mortality independent of
versible remodeling.
potentially
reversible)
interstitial
on
age, renal failure, multivessel disease, prior coronary artery bypass graft, LVEF, and entropy in the scar.
ADDRESS
The association between LV entropy and mortality
Zeppenfeld, and Dr. Q. Tao, Leiden University Medi-
may reflect adverse and irreversible, inhomogeneous
cal Center, Department of Cardiology, Department of
remodeling of the post-infarct LV.
Radiology (C-03-Q), P.O. Box 9600, 2300 RC Leiden,
STUDY LIMITATIONS. This study has a relatively
limited sample size and a retrospective single-center study design. All LGE images were acquired with the same MR equipment and protocol. The generalizability of the metric to multicenter, multivendor data requires further investigation. Our study includes 17 patients who underwent VT ablation prior to ICD implantation, which can influence consecutive VT events. Three patients underwent VT ablation prior to LGE-CMR. However, the number of patients with complete
procedural
success
defined
as
non-
inducibility after VT-ablation was low. In the present study, the LGE-CMR
images were
acquired as
2-dimensional short-axis images by a 1.5-T MR imaging scanner, and our results are only applicable to 2-dimensional LGE techniques with the same MR protocol. Furthermore, our results need to be validated
in
a
prospective
group.
Recently,
more
advanced MR imaging protocols with a higher resolution have been developed, which potentially yield
FOR
CORRESPONDENCE:
Dr.
Katja
the Netherlands. E-mail: [email protected] OR [email protected]. PERSPECTIVES COMPETENCY IN MEDICAL KNOWLEDGE: Entropy as a newly proposed LGE-CMR–based measure for tissue composition has potentially important clinical implications. The association between high entropy within the scar and VA in post-MI patients suggests that scar entropy may serve as an additional parameter for risk stratification. The association of a higher entropy of the entire LV with mortality suggests that this LGE-CMR–derived parameter for tissue composition may be used to monitor disease progression, and perhaps for early identification of patients with adverse LV remodeling and unfavorable outcome. TRANSLATIONAL OUTLOOK: Further studies are needed to validate the association between entropy and VA/mortality, including the application of advanced high-resolution 3-dimensional LGE-CMR image acquisition.
entropy measures of higher sensitivity in future
REFERENCES 1. Moss AJ, Zareba W, Hall WJ, et al., for the Multicenter Automatic Defibrillator Implantation
across the spectrum of ejection fraction and heart failure stage. J Am Heart Assoc 2015;4:
Trial II Investigators. Prophylactic implantation of a defibrillator in patients with myocardial infarction and reduced ejection fraction. N Engl J Med 2002;346:877–83.
e002613.
tachyarrhythmia by an implanted defibrillator. Circulation 2004;110:3760–5.
2. Schelbert EB, Piehler KM, Zareba KM, et al.
3. Bardy GH, Lee KL, Mark DB, et al., for the SCDHeFT Investigators. Amiodarone or an implantable cardioverter-defibrillator for congestive heart failure. N Engl J Med 2005;352:225–37.
5. Priori SG, Blomstrom-Lundqvist C, Mazzanti A, et al. 2015 ESC guidelines for the management of patients with ventricular arrhythmias and the prevention of sudden cardiac death: the Task Force for the Management of Patients with Ven-
Myocardial fibrosis quantified by extracellular volume is associated with subsequent hospitalization for heart failure, death, or both
4. Moss AJ, Greenberg H, Case RB, et al., for the MADIT-II Research Group. Long-term clinical course of patients after termination of ventricular
tricular Arrhythmias and the Prevention of Sudden Cardiac Death of the European Society of Cardiology (ESC). Endorsed by Association for European
9
10
Androulakis et al.
JACC: CLINICAL ELECTROPHYSIOLOGY VOL.
Paediatric and Congenital Cardiology (AEPC). Eur Heart J 2015;36:2793–867. 6. Daubert JP, Zareba W, Hall WJ, et al., for the MADIT II Study Investigators. Predictive value of ventricular arrhythmia inducibility for subsequent ventricular tachycardia or ventricular fibrillation in Multicenter Automatic Defibrillator Implantation Trial (MADIT) II patients. J Am Coll Cardiol 2006; 47:98–107. 7. de Bakker JM, van Capelle FJ, Janse MJ, et al. Slow conduction in the infarcted human heart: “zigzag” course of activation. Circulation 1993;88: 915–26. 8. Wu E, Judd RM, Vargas JD, Klocke FJ, Bonow RO, Kim RJ. Visualisation of presence, location, and transmural extent of healed Q-wave and non-Q-wave myocardial infarction. Lancet 2001;357:21–8. 9. Kim RJ, Fieno DS, Parrish TB, et al. Relationship of MRI delayed contrast enhancement to irreversible injury, infarct age, and contractile function. Circulation 1999;100:1992–2002. 10. Roes SD, Borleffs CJ, van der Geest RJ, et al. Infarct tissue heterogeneity assessed with contrast-enhanced MRI predicts spontaneous ventricular arrhythmia in patients with ischemic cardiomyopathy and implantable cardioverterdefibrillator. Circ Cardiovasc Imaging 2009;2: 183–90. 11. Schmidt A, Azevedo CF, Cheng A, et al. Infarct tissue heterogeneity by magnetic resonance imaging identifies enhanced cardiac arrhythmia susceptibility in patients with left ventricular dysfunction. Circulation 2007;115:2006–14. 12. Wu KC, Gerstenblith G, Guallar E, et al. Combined cardiac magnetic resonance imaging and Creactive protein levels identify a cohort at low risk for defibrillator firings and death. Circ Cardiovasc Imaging 2012;5:178–86. 13. Robbers LF, Delewi R, Nijveldt R, et al. Myocardial infarct heterogeneity assessment by late gadolinium enhancement cardiovascular magnetic resonance imaging shows predictive value for ventricular arrhythmia development after acute myocardial infarction. Eur Heart J Cardiovasc Imaging 2013;14:1150–8. 14. Rayatzadeh H, Tan A, Chan RH, et al. Scar heterogeneity on cardiovascular magnetic resonance as a predictor of appropriate implantable cardioverter defibrillator therapy. J Cardiovasc Magn Reson 2013;15:31.
-, NO. -, 2019 - 2019:-–-
Entropy as a Novel Measure of Myocardial Tissue Heterogeneity
quantification measures for late gadolinium enhancement magnetic resonance imaging. Circ Cardiovasc Imaging 2012;5:448–56. 16. de Haan S, Meijers TA, Knaapen P, Beek AM, van Rossum AC, Allaart CP. Scar size and characteristics assessed by CMR predict ventricular arrhythmias in ischaemic cardiomyopathy: comparison of previously validated models. Heart 2011;97:1951–6. 17. Klem I, Weinsaft JW, Bahnson TD, et al. Assessment of myocardial scarring improves risk stratification in patients evaluated for cardiac defibrillator implantation. J Am Coll Cardiol 2012; 60:408–20. 18. Boye P, Abdel-Aty H, Zacharzowsky U, et al. Prediction of life-threatening arrhythmic events in patients with chronic myocardial infarction by contrast-enhanced CMR. J Am Coll Cardiol Img 2011;4:871–9. 19. Shannon CE. A mathematical theory of communication. Bell Syst Tech J 1948;27:379–423. 20. Bishop JE, Greenbaum R, Gibson DG, Yacoub M, Laurent GJ. Enhanced deposition of predominantly type I collagen in myocardial disease. J Mol Cell Cardiol 1990;22:1157–65. 21. Beltrami CA, Finato N, Rocco M, et al. Structural basis of end-stage failure in ischemic cardiomyopathy in humans. Circulation 1994;89: 151–63.
and Chronic Heart Failure 2008 of the European Society of Cardiology. Developed in collaboration with the Heart Failure Association of the ESC (HFA) and endorsed by the European Society of Intensive Care Medicine (ESICM). Eur Heart J 2008;29:2388–442. 28. Hohnloser SH, Kuck KH, Dorian P, et al., for the DINAMIT Investigators. Prophylactic use of an implantable cardioverter-defibrillator after acute myocardial infarction. N Engl J Med 2004;351: 2481–8. 29. Kuck KH, Schaumann A, Eckardt L, et al., for the VTACH Study Group. Catheter ablation of stable ventricular tachycardia before defibrillator implantation in patients with coronary heart disease (VTACH): a multicentre randomised controlled trial. Lancet 2010;375:31–40. 30. Piers SR, Tao Q, de Riva Silva M, et al. CMRbased identification of critical isthmus sites of ischemic and nonischemic ventricular tachycardia. J Am Coll Cardiol Img 2014;7:774–84. 31. Desjardins B, Crawford T, Good E, et al. Infarct architecture and characteristics on delayed enhanced magnetic resonance imaging and electroanatomic mapping in patients with postinfarction ventricular arrhythmia. Heart Rhythm 2009;6:644–51.
22. Mukherjee D, Sen S. Alteration of collagen phenotypes in ischemic cardiomyopathy. J Clin
32. Sasaki T, Miller CF, Hansford R, et al. Myocardial structural associations with local electrograms: a study of postinfarct ventricular tachycardia pathophysiology and magnetic resonance-based noninvasive mapping. Circ
Invest 1991;88:1141–6.
Arrhythm Electrophysiol 2012;5:1081–90.
23. Volders PG, Willems IE, Cleutjens JP, Arends JW, Havenith MG, Daemen MJ. Interstitial collagen is increased in the non-infarcted human myocardium after myocardial infarction. J Molec Cell Cardiol 1993;25:1317–23.
33. Iles L, Pfluger H, Phrommintikul A, et al. Evaluation of diffuse myocardial fibrosis in heart failure with cardiac magnetic resonance contrastenhanced T1 mapping. J Am Coll Cardiol 2008; 52:1574–80.
24. Wong TC, Piehler K, Meier CG, et al. Associa-
34. Schelbert EB, Hsu LY, Anderson SA, et al. Late gadolinium-enhancement cardiac magnetic resonance identifies postinfarction myocardial fibrosis
tion between extracellular matrix expansion quantified by cardiovascular magnetic resonance and short-term mortality. Circulation 2012;126: 1206–16. 25. Kammerlander AA, Marzluf BA, ZotterTufaro C, et al. T1 mapping by CMR imaging: from histological validation to clinical implication. J Am Coll Cardiol Img 2016;9:14–23. 26. Priori SG, Aliot E, Blomstrom-Lundqvist C, et al. Update of the guidelines on sudden cardiac death of the European Society of Cardiology. Eur Heart J 2003;24:13–5.
15. Gao P, Yee R, Gula L, et al. Prediction of arrhythmic events in ischemic and dilated cardio-
27. Dickstein K, Cohen-Solal A, Filippatos G, et al. ESC guidelines for the diagnosis and treatment of
myopathy patients referred for implantable cardiac defibrillator: evaluation of multiple scar
acute and chronic heart failure 2008: the Task Force for the Diagnosis and Treatment of Acute
and the border zone at the near cellular level in ex vivo rat heart. Circ Cardiovasc Imaging 2010;3: 743–52.
KEY WORDS cardiac magnetic resonance, diffuse fibrosis, entropy, late gadolinium enhancement, magnetic resonance imaging, sudden death, ventricular arrhythmia
A PPE NDI X For supplemental Methods including figures and tables, please see the online version of this paper.