Substrate Spatial Complexity Analysis for the Prediction of Ventricular Arrhythmias in Patients with Ischemic Cardiomyopathy

Abstract

Background -

Transition zones between healthy myocardium and scar form a spatially complex substrate that may give rise to reentrant ventricular arrhythmias (VA). We sought to assess the utility of a novel machine learning (ML) approach for quantifying 3D spatial complexity of grayscale patterns on late gadolinium enhanced cardiac magnetic resonance images (LGE-CMR) to predict VA in patients with ischemic cardiomyopathy (ICM).

Methods -

122 consecutive ICM patients with left ventricular ejection fraction ≤35% without prior history of VA underwent LGE-CMR. From raw grayscale data, we generated graphs encoding the 3D geometry of the left ventricle (LV). A novel technique, adapted to these graphs, assessed global regularity of signal intensity patterns using Fourier-like analysis and generated a substrate spatial complexity (SSC) profile for each patient. An ML statistical algorithm was employed to discern which SSC profiles correlated with VA events (appropriate ICD firings and arrhythmic sudden cardiac death) at 5 years of follow-up. From the statistical ML results, a complexity score (CS) ranging from 0–1 was calculated for each patient and tested using multivariable Cox regression models.

Results -

At 5 years of follow-up, 40 patients had VA events. The ML algorithm classified with 81% overall accuracy and correctly classified 86% of those without VA. Overall negative predictive value was 91%. Average CS was significantly higher in patients with VA events versus those without (0.5 ± 0.5 vs 0.1 ± 0.2; p<0.0001) and was independently associated with VA events in a multivariable model (hazard ratio = 1.5 [1.2– 2.0]; p=0.002).

Conclusions -

SSC analysis of LGE-CMR images may be helpful in refining VA risk in patients with ICM, particularly to identify low risk patients who may not benefit from prophylactic ICD therapy.

Graphical Abstract

Introduction

Ventricular arrhythmias (VA) are a common cause of death in the United States.¹ The most widely accepted approach to risk stratification for VA is based on the assessment of left ventricular (LV) systolic function.² However, most patients with LV systolic dysfunction do not suffer from VA and conversely, most VA events occur in patients without LV systolic dysfunction.^3,4 Therefore, more accurate risk stratification techniques are needed to better identify which patients are most likely to benefit from prophylactic therapy such as primary-prevention implantable cardioverter defibrillators (ICD), and mitigate the risks associated with ICD placement in patients unlikely to benefit.

The cardiac magnetic resonance imaging technique of late gadolinium enhancement (LGE-CMR) enables the non-invasive detection of potentially arrhythmogenic substrate and is a strong predictor of VA events in patients with ischemic cardiomyopathy (ICM).^5,6 However, most ICM patients with LGE do not suffer from VA. Beyond detection of the presence of LGE, analysis of LGE characteristics enables estimation of electrophysiologic properties and more precise prediction of arrhythmic outcomes. Regions of LGE with intermediate signal intensity (SI) (gray zones) represent areas of transition from normal myocardium to scar, may harbor critical components of re-entrant circuits, and predict inducible VA in patients with ICM.^7–12 However, not all patients with larger regions of gray zone infarction will have VA events. There is therefore a potentially useful role for further imaging analysis techniques to improve characterization of the arrhythmogenic substrate.

Our hypothesis in this study was that the propensity of a specific region of admixed normal myocardium and scar to give rise to a VA may relate to the degree of spatial complexity within or around that region. Our aims were to: 1. Develop a novel method for assessing myocardial substrate spatial complexity (SSC); and 2. Assess the utility of the SSC method to predict VA events in patients with ICM. While prior studies have approached substrate complexity by focusing on entropy without consideration for spatial relationships, our approach was specifically designed to characterize the heterogeneity of spatial relationships among different regions of myocardium in 3 dimensions. More specifically, our method focused on global scar irregularity as characterized by Fourier coefficients. We tailored classical Fourier modes to apply to the personal size and geometry of each individual heart. We then sought to combine information about global SI irregularity into an SCC profile unique to each patient that could be used to predict VA events.

Methods

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Patient population, device programming and follow-up

This was a retrospective analysis of the prospective observational registry, Left Ventricular Structural Predictors of SCD (NCT01076660). Patients with clinical criteria for primary prevention ICD insertion based on left ventricular ejection fraction (LVEF) ≤35% were approached for enrollment prior to device placement at 3 sites: Johns Hopkins Medical Institutions (Baltimore, MD), Christiana Care Health System (Newark, DE), and the University of Maryland (Baltimore, MD). A total of 382 patients were enrolled between November 2003 and April 2015, 328 of whom were concurrently enrolled in the PROSE-ICD registry (Prospective Observational Study of Implantable Cardioverter Defibrillators, NCT00733590). Patients were excluded if they had contraindications to CMR, New York Heart Association (NYHA) functional class IV, acute myocarditis, acute sarcoidosis, infiltrative disorders (e.g. amyloidosis), congenital heart disease, hypertrophic cardiomyopathy, or renal insufficiency (creatinine clearance <30 ml/min after July 2006 or <60 ml/min after February 2007). The protocol was approved by the institutional review boards at each site, and all participants provided informed consent.

The CMR imaging was performed as close in time to ICD implantation as was logistically possible (median time, 3 days). For the current analysis, only the 167 patients with ICM and LGE-CMR were considered. Among these, 17 were deemed to have sub-optimal CMR image quality and were excluded. Among the remaining 150 patients, 122 had completed either 5 years of follow-up without a VA event or experienced a VA event within 5 years of follow-up. These 122 patients were the focus of the current study.

The study participants underwent single-chamber or dual-chamber ICD, or cardiac resynchronization with an ICD (CRT-D) implantation based on current guidelines. The systems used were manufactured by Boston Scientific (Natick, MA), Medtronic (Minneapolis, MN) and St. Jude Medical (St. Paul, MN). The programming of anti-tachycardia therapies was left to the discretion of the operators. Study participants were evaluated every 6 months and after any ICD shock event. ICDs were interrogated in person or via remote transmission, and all arrhythmic events were adjudicated by 2 clinical cardiac electrophysiologists blinded to all other patient data. Each electrophysiologist independently determined the rhythm at the time of initial detection and after therapy delivery. Disagreements on the diagnosed rhythm were reviewed by a third electrophysiologist for final adjudication. Patients who were not seen in clinic underwent a telephone interview to update history. The primary endpoint was predefined as the first occurrence of an appropriate ICD shock for sustained VT, ventricular fibrillation, or sudden cardiac death presumed due to VA. Deaths were classified according to the most proximate cause after review of available ICD interrogations, medical records, death certificates, autopsy reports, and eyewitness accounts.

CMR Acquisition

All CMR images were acquired on 1.5-T magnetic resonance imaging units (GE Medical Systems, Waukesha, Wisconsin; or Avanto, Siemens, Erlangen, Germany) using electrocardiographic gating and breath holding as previously described.¹³ A cardiac phased-array receiver coil was placed anteriorly and posteriorly on the chest. Eight to 14 short-axis slices were prescribed to cover the entire LV. Late gadolinium-enhanced images were acquired 15 to 30 minutes after a total injection of 0.2 mmol/kg gadodiamide (Omniscan, GE Healthcare Technologies) with an inversion recovery fast gradient echo pulse sequence in the same short-axis locations as the cine images.^10,11 Typical imaging parameters¹² were as follows: TR 5.4 ms, echo time 1.3 ms, average in-plane spatial resolution 1.5–2.4 mm, 8-mm slice thickness, 2-mm gap, inversion time (TI) 175 to 250 ms (adjusted to null the signal of normal myocardium), 2 excitations, 1 R-R interval imaging, flip angle 20°, 350-ms time delay after the R wave, and 24 views per segment.

Scar analysis

For this study, the SI threshold values to define scar regions were determined from a semi-automatic full width half maximum approach developed previously by our group.¹² Infarct core was defined as myocardium with SI >50% of the maximal SI. Gray zone was defined as myocardium with SI > SI of remote healthy myocardium but < 50% maximal SI. Shannon Entropy (SE) was calculated for each heart allowing for an entropy range from 0–10 using the formula below, where x is SI and p(x_i) is the probability distribution for SI values

$$\mathit{\text{Entropy}}=- \sum _{i=1}^{n}p(x_i)lo{g}_{2}p(x_i)$$

Spatial Complexity Analysis

The image analyses for scar complexity were performed with DICOM (Digital Imaging and Communications in Medicine) images using a dedicated software package, CardioViz (Asclepios Research Project, Inria Sophia Antipolis, France) and were performed by investigators blinded to clinical outcomes. Late gadolinium-enhanced images obtained in the short axis without phase sensitive inversion recovery were used for substrate characterization. Endocardial and epicardial borders were traced by a trained observer. Figure 1 provides a flow diagram of the SSC analysis methodology.

Figure 1.

Substrate Spatial Complexity Analysis Workflow. Signal intensity patterns from LGE-CMR imaging were analyzed using a Fourier-like technique for assessment of global irregularity. This analysis generated features that were used in a statistical machine learning algorithm, which yielded a complexity score ranging from 0 to 1, where 0 represents low arrhythmic risk and 1 represents high arrhythmic risk.

Patient-Specific Graphs of LV Size and Geometry

We generated graphs encoding patient-specific left ventricular (LV) size and geometry as follows:

1. DICOM images were translated into 3-dimensional arrays of SI values incorporating the z-axis position of each slice. Each LV voxel was associated with a 3-dimensional vector (or point), together with the corresponding SI value. Let N be the number of LV voxels (or points); typically N is of order of 5,000–6,000.

2. For each patient, a similarity graph was generated as follows: the vertices of the graph consist of the N points x_i (where i indexes each point or voxel); each point x_i was connected to its 100 nearest neighbors (in 3-dimensions), denoted x_j (where j indexes each neighbor), with an edge weight calculated based on the formula^14,15:

   $$W_{i,j}=e^{-{\left|\left|x_i-x_j\right|\right|}^2/{\sigma }_{i,j}}+e^{-{\left|\left|x_i-x_j\right|\right|}^2/{\sigma }_{j,i}}$$

   where ||.|| denotes the distance in 3-dimensional Euclidean space. The local scale parameter σ_i,j is the distance between x_i and its 5th nearest neighbor.

   This defines, for each patient, the N × N weight matrix W, which contains the complete information about the weighted graph and encodes similarity information as a function of distance between points x_i.

3. From the weight matrix W described above, we calculated the diagonal degree matrix D defined on the diagonals by:

   $$D_{i,i}= \sum _{j=1}^N{W}_{i,j}$$

Fourier-Like Analysis

In order to extract information about the global irregularity of the SI pattern, we developed a novel Fourier-like technique for assessing SCC. Using the graph G of each patient’s LV, we derived sine-like functions φ_i at varying frequencies i to fit the specific size and shape of the individual LV. These sine-like functions were generated as follows^14–17:

1. We defined the normalized Laplacian matrix L on the graph G as:

   $$L=I-D^{1/2}W{D}^{1/2}$$

   where I represents the NxN identity matrix.

2. We then calculated the bottom eigenvectors of L, i.e. the ones with eigenvalues closest to 0, the smallest eigenvalue of L. These eigenvectors are the lowest frequency sine-like functions that oscillate over the surface of the graph. We opted to use a mix of the lowest-frequency sine-like functions φ_k, k=1…5, and medium frequency sine-like functions φ_t, t=18…24, based on our pilot experience with the performance of more and fewer frequencies in the overall algorithm. These 12 sine-like functions comprised a template against which the SI pattern of the LV was compared (see steps 5 and 6 below and Figure 2).

3. We next defined the function F which takes on the SI value of each point/vertex of the graph G.

4. The eigenvenctors were then aligned in order to increase the likelihood that the Fourier modes were positive or negative in similar areas across all hearts, allowing the Fourier coefficients below to be compared across hearts.

5. We then calculated inner products between the function on the graph F and the aligned sine-like functions φ_k which generated Fourier coefficients as follows:

   $$SSC\left(k\right):=(F,{\phi }_k)=\sum _{x_i}F\left(x_i\right){\phi }_k\left(x_i\right)$$

6. These Fourier coefficients were then used as features in the ML algorithm described below, by selecting a set of coefficients corresponding to the pre-specified eigenvectors.

Figure 2.

Fourier-Like Analysis. Signal intensity patterns from LGE-CMR imaging were analyzed using a novel Fourier-like technique. Eigenvectors (sine-like functions) of varying frequencies oscillating over graphs encoding patient-specific LV size and geometry were compared with signal intensity patterns to generate Fourier coefficients. These coefficients were then used in the ML algorithm. Each panel (A, B and C) shows a different eigenvector frequency. Colors represent amplitude of the sine-like function.

Statistical Machine Learning and Complexity Score

The Fourier coefficients comprised an SSC profile for each patient. These profiles served as inputs to a supervised statistical ML algorithm: each profile labeled according to whether or not the patient had a VA event during follow-up. We used a support vector machine with a polynomial kernel of order 3 to perform classification. We utilized the Monte Carlo cross-validation method where on each run 10% of patients, chosen randomly with a fixed ratio of VA and non-VA patients in each set (equal to the corresponding ratio for the whole data set), was held for testing and the algorithm was trained on the remaining patients. A total of 5000 runs were performed. We then generated a complexity score (CS) for each patient as follows:

$$\mathrm{\text{CS}}=\left[\mathrm{\text{Number}}\mathrm{\text{of}}\mathrm{\text{runs}}\mathrm{\text{where}}a\mathrm{\text{patient}}\mathrm{\text{was}}\mathrm{\text{included}}\mathrm{\text{in}}\mathrm{\text{a}}\mathrm{\text{testing}}\mathrm{\text{set}}\mathrm{\text{and}}\mathrm{\text{was}}\mathrm{\text{predicted}}\mathrm{\text{to}}\mathrm{\text{have}}\mathrm{\text{a}}\mathrm{\text{VA}}\mathrm{\text{event}}\right]/\left[\mathrm{\text{Total}}\mathrm{\text{number}}\mathrm{\text{of}}\mathrm{\text{runs}}\mathrm{\text{in}}\mathrm{\text{which}}\mathrm{\text{that}}\mathrm{\text{patient}}\mathrm{\text{was}}\mathrm{\text{included}}\mathrm{\text{in}}\mathrm{\text{the}}\mathrm{\text{testing}}\mathrm{\text{set}}\right]$$

Statistical Analysis

All analyses were performed using Stata software, version 15 (StataCorp, College Station, TX, USA). Continuous data is presented as mean ± SD while categorical variables are presented as percentages. Comparisons between patients with versus without VA events were performed using the Student t-test (continuous variables) and the Fischer exact test (categorical variables). A P-value of <0.05 was considered statistically significant. To assess for independent associations between clinical or imaging parameters and VA events by 5 years of follow up, we performed multivariable logistic regression analysis. To assess for independent associations between clinical or imaging parameters and VA events on a time-to-event basis we performed multivariable Cox regression analysis. We adjusted for the following in the multivariable model: age, sex, race, and variables that were significant on univariable analysis. To assess the effects of competing risk from non-arrhythmic death on the multivariable model, competing risk regression analysis was performed using non-arrhythmic death as the competing event.

Results

Baseline characteristics, CMR findings, and Arrhythmic Events

Table 1 summarizes baseline patient characteristics and CMR findings of all patients included in this analysis. There were no significant differences in patients not included except for follow-up duration (Supplemental Table 1). A total of 122 consecutive patients were analyzed. The mean age was 60±11 years; 106 patients (87%) were male; and 101 patients (83%) were Caucasian. The average CMR-derived LVEF was 28±8% and was significantly lower in patients with VA events as compared with those without (25±1 vs 30±1%; p = 0.0004). The left ventricular end-diastolic volume (262±12 vs 216±7 cc; p = 0.0006) and left ventricular end-systolic volume (197±10 vs 153±6 cc; p = 0.0001) were significantly higher in patients with VA events as compared to those without.

Table 1.

Baseline characteristics and imaging findings.

		All (n = 122)	VA+ (n = 40)	VA- (n = 82)	p-Value
Demographics
	Age (yrs)	60±11	59±12	61±11	0.39
	Male sex (n[%])	106 (87)	34 (85)	72 (88)	0.78
	Caucasian (n[%])	101 (83)	34 (84)	68 (83)	1.00
	Duration of CM (years)	5.4±5.9	7±6	5±5	0.02
Cardiac Risk Factors
	Hypertension (n[%])	80 (66)	28 (70)	52 (63)	0.55
	Hyperlipidemia (n[%])	96 (79)	30 (75)	66 (80)	0.49
	DM (n[%])	37 (30)	11 (28)	26 (32)	0.68
	Tobacco use (n[%])	80 (66)	27 (68)	53 (65)	0.84
Laboratory Values
	SCr (mg/ dL)	0.99±0.30	1.04±0.39	0.97±0.25	0.24
ECG Parameters
	QRSD (ms)	115±28	122±26	112±28	0.04
Medications
	AAD (n[%])	9 (7)	5 (14)	4 (5)	0.15
	Aspirin (n[%])	111 (91)	34 (85)	77 (94)	0.17
	Statin (n[%])	112 (92)	37 (93)	75 (91)	1.00
	Beta Blocker (n[%])	113 (93)	37 (93)	76 (93)	1.00
CMR Indices
	LVEF (%)	23±8	25±8	30±7	0.004
	LVEDV (cc)	231±96	262±74	216±61	0.006
	LVESV (cc)	168±60	197±61	153±141	0.001
	Total Scar (g)	38±20	47±22	24±17	0.0005
	Core Scar (g)	23±13	28±15	21±11	0.005
	Gray Zone (g)	16±9	20±10	14±8	0.004

AAD = antiarrhythmic drug; CM = cardiomyopathy; CMR = cardiac magnetic resonance imaging; DM = diabetes mellitus; ECG = electrocardiogram; LVEDV = left ventricular end diastolic volume; LVEF = left ventricular ejection fraction; LVESV = left ventricular end systolic volume; QRSD = QRS duration; SCr = serum creatinine

The total scar mass (47±4 vs 34±2 g; p = 0.0005), core scar mass (28±2 vs 21±1 g; p = 0.005), and gray zone mass (20±2 vs 14±1 g; p = 0.0004) were significantly higher in patients with VA events as compared with those without. The mean time from diagnosis of cardiomyopathy to CMR imaging was significantly longer in patients with VA events as compared with those without (7±1 vs 5±1 years; p = 0.02). The mean QRS duration was significantly longer in patients with VA events as compared with those without (122±4 vs 112±3 ms; p = 0.04). There were no other significant differences between the 2 groups. Comparing patients with and without VA events, there was no significant difference in SE: 5.2 ± 0.7 vs 5.3 ± 1.0.

At 5 years of follow-up, 40 patients had at least 1 VA event and 82 patients did not have any VA events. Among patients with VA events, the first event was monomorphic VT in 25, ventricular fibrillation in 10, ventricular flutter in 2, polymorphic VT in 1, and in 2 patients the exact rhythm causing sudden cardiac death could not be confirmed. The mean time from CMR imaging to VA event was 4±3 years.

SSC Analysis

The SSC analysis had an overall accuracy of 81%. Patients who did not have VA events were correctly classified in 86% of ML runs. Patients who had VA events were correctly classified in 55% of runs. Correspondingly, the positive predictive value was 45%; negative predictive value was 91%; sensitivity was 55%; and specificity was 86%. The mean area under the curve (AUC) for all cross-validation runs was 0.72. The CS was significantly higher in patients with VA events compared to those without (0.5 ± 0.5 vs 0.1 ± 0.2; p<0.0001).

On univariate logistic regression analysis (Table 2), the following variables were significantly associated with the occurrence of VA events by 5 years of follow-up (i.e., binary yes/no outcome by 5 years of follow-up): LVEF (by quartiles, OR = 0.6 [0.4– 0.9]; p = 0.009), left ventricular end systolic volume (by quartiles, OR = 2.2 [1.5– 3.3]; p < 0.001), left ventricular end diastolic volume (by quartiles, OR = 1.9 [1.3– 2.7]; p = 0.001), core scar mass (by quartiles, OR = 1.6 [1.1– 2.3]; p = 0.01), gray scar mass (by quartiles, OR = 1.9 [1.3– 2.8]; p = 0.001), duration of cardiomyopathy (by quartiles, OR = 1.5 [1.1– 2.1]; p = 0.02), QRS duration (by quartiles, OR = 1.5 [1.0 – 2.1]; p = 0.03), and CS (by quartiles, OR = 1.7 [1.2– 2.3]; p = 0.001). Notably, Shannon entropy was not found to be associated with VA events (by quartiles, OR 0.7 [0.6– 1.2], p = 0.42). On multivariable logistic regression analysis, the CS was independently associated with VA events by 5 years of follow-up (by quartiles, OR = 1.9 [1.3– 2.9]; p = 0.002) and showed a stronger association than any other variable. The only other variable that remained significantly different in patients with VA events compared to those without on multivariable analysis was duration of cardiomyopathy (by quartiles, OR = 1.7 [1.1– 3.7]; p= 0.016).

Table 2.

Risk factors for occurrence of VA in univariable and adjusted multivariable logistic regression analyses

	Univariable Logistic Model			Multivariable Logistic Model
	OR	95% CI	p-Value	OR	95% CI	p-Value
Age (per quartile)	0.98	0.74– 1.29	0.86	0.86	0.54– 1.37	0.52
Male sex (vs. female)	0.78	0.26– 2.34	0.67	0.48	0.11– 2.20	0.35
Caucasian race (vs. non-Caucasian)	0.97	0.36– 2.63	0.95	0.48	0.12– 1.83	0.28
Hypertension (presence vs. absence)	1.35	0.60– 3.03	0.47
Diabetes (presence vs. absence)	0.82	0.35– 1.89	0.64
Hyperlipidemia (presence vs. absence)	0.73	0.30– 1.79	0.49
Duration of CM (per quartile)	1.50	1.06– 2.14	0.02	1.73	1.11– 2.71	0.016
QRS Duration (per quartile)	1.46	1.03– 2.06	0.03	1.57	0.96– 2.56	0.07
LVEF (per quartile)	0.62	0.43– 0.89	0.009	0.75	0.44– 1.27	0.29
LVESV* (per quartile)	2.25	1.51– 3.35	<0.001	1.57	0.91– 2.70	0.11
LVEDV (per quartile)	1.85	1.28– 2.69	0.001
Core Scar (per quartile)	1.61	1.12– 2.30	0.01	1.11	0.61– 2.02	0.73
Gray Zone (per quartile)	1.92	1.31– 2.80	0.001	1.69	0.92– 3.09	0.09
Complexity Score (per quartile)	1.67	1.22– 2.30	0.001	1.93	1.27– 2.93	0.002

^*LVEDV and LVESV were collinear and the stronger of the 2 associations (LVESV) was included in the multivariable model. Since total scar is derived from core+gray, it was not included in the models.

CI= Confidence interval; CM = cardiomyopathy; LVEDV = left ventricular end diastolic volume; LVEF = left ventricular ejection fraction; LVESV = left ventricular end systolic volume; OR = odds ratio

On univariate Cox time-to-event regression analysis (Table 3), the following variables were significantly associated with VA: LVEF (by quartiles, HR = 0.7 [0.5– 1.0]; p = 0.02), left ventricular end systolic volume (by quartiles, HR = 1.8 [1.3– 2.5]; p < 0.001), left ventricular end diastolic volume (by quartiles, HR = 1.6 [1.2– 2.1]; p = 0.003), core scar mass (by quartiles, HR = 1.5 [1.1– 2.0]; p = 0.009), gray scar mass (by quartiles, HR = 1.6 [1.2– 2.2]; p = 0.002), duration of cardiomyopathy (by quartiles, HR = 1.3 [1.0– 1.8]; p = 0.045), and CS (by quartiles, HR = 1.6 [1.2– 2.0]; p = 0.001). Notably, Shannon entropy was not found to be associated with VA events (by quartiles, HR 0.9 [0.7– 1.2], p = 0.57). The CS was independently associated with VA events on a time-to-event basis in a multivariable Cox regression analysis (by quartiles, HR = 1.5 [1.2– 2.0]; p= 0.002) and showed a stronger association than any other variable. (Figure 3) The only other variable that remained significantly different in patients with VA events compared to those without on multivariable analysis was duration of cardiomyopathy (HR = 1.5 [1.1– 2.0]; p= 0.02). Figure 4 demonstrates SCC analysis for 2 patients, one with a high CS who had a VA event, and one with a low CS who did not have a VA event.

Table 3.

Risk factors for earlier time to VA event in univariable and adjusted multivariable Cox regressions models.

	Univariable Cox Model			Multivariable Cox Model
	HR	95% CI	p-Value	HR	95% CI	p-Value
Age (per quartile)	0.98	0.74– 1.29	0.86	0.99	0.71– 1.39	0.97
Male sex (vs. female)	0.89	0.37– 2.13	0.80	0.77	0.30– 1.99	0.59
Caucasian race (vs. non-Caucasian)	1.07	0.47– 2.42	0.87	0.70	0.28– 1.73	0.44
Hypertension (presence vs. absence)	1.31	0.66– 2.57	0.44
Diabetes (presence vs. absence)	0.90	0.45– 1.81	0.77
Hyperlipidemia (presence vs. absence)	0.85	0.41– 1.73	0.65
Duration of CM (per quartile)	1.35	1.01– 1.80	0.045	1.47	1.06– 2.04	0.02
QRS Duration (per quartile)	1.29	0.98– 1.71	0.07
LVEF (per quartile)	0.71	0.53– 0.96	0.02	0.80	0.56– 1.14	0.22
LVESV* (per quartile)	1.81	1.32– 2.48	<0.001	1.36	0.93– 2.00	0.12
LVEDV (per quartile)	1.56	1.17– 2.10	0.003
Core Scar (per quartile)	1.47	1.10– 1.98	0.009	1.14	0.76– 1.71	0.53
Gray Zone (per quartile)	1.61	1.19– 2.19	0.002	1.35	0.92– 1.98	0.13
Complexity Score (per quartile)	1.56	1.20– 2.02	0.001	1.52	1.17– 1.98	0.002

^*LVEDV and LVESV were collinear and the stronger of the 2 associations (LVESV) was included in the multivariable model. Since total scar is derived from core+gray, it was not included in the models.

CI= Confidence interval; CM = cardiomyopathy; HR = hazard ratio; LVEDV = left ventricular end diastolic volume; LVEF = left ventricular ejection fraction; LVESV = left ventricular end systolic volume

Figure 3.

Results of Multivariable Cox Regression Model. In a multivariable Cox regression analysis, the CS was independently associated with VA events on a time-to-event basis and showed a stronger association than any other variable.

Figure 4.

Example SCC analysis from 2 patients. Panel A shows the LGE-CMR-derived scar pattern from a patient with a low scar burden (12.1 g) but a high CS (0.99) who ultimately had a VA event. Panel B shows the LGE-CMR-derived scar pattern from a patient with a high scar burden (84 g) but a low CS (0.00) who did not have a VA event.

Competing risk regression analysis using non-arrhythmic death as the competing event was additionally performed. As in the original multivariable Cox analysis, the CS was independently associated with VA events on a time-to-event basis using competing risk regression analysis (by quartiles, HR = 1.5 [1.2– 1.9]; p= 0.001) and showed a stronger association than any other variable. Also as in the original multivariable Cox analysis, the only other variable that remained significantly different in patients with VA events compared to those without a VA event using competing risk regression analysis was duration of cardiomyopathy (HR = 1.5 [1.1– 2.1]; p= 0.01). Finally, multi-variable Cox regression using all-cause mortality as the outcome was performed. Both LVEF (HR 0.7 [0.5– 1.0]; p = 0.47) and LV end systolic volume (HR 0.7 [0.5– 1.0]; p = 0.03) were associated with all-cause mortality, but CS was not (HR 1.1 [0.8– 1.4]; p = 0.4).

Discussion

In this study, we developed and tested a novel ML approach for assessing myocardial substrate spatial complexity and demonstrated that this method accurately predicted the risk of VA events in patients with ICM and LV systolic dysfunction with overall accuracy of 81% and high negative predictive value of 91%. We additionally showed that, using this method, a scar CS ranging from 0 to 1 can be generated, where 0 indicates low SSC and 1 represents high SSC; and that this score was strongly and independently associated with both occurrence of VA events and time to VA event in multivariable models that adjusted for LV ejection fraction, scar mass, and gray zone mass. The SSC analysis in general, and the CS specifically, therefore provided incremental prognostic information when added to known risk factors for VA in this population.

Several electrophysiologic mechanisms underlie VA in the structurally abnormal heart, the most well-characterized of which is macro re-entry. Re-entry requires specific substrate properties, including an area of anatomic or functional block, one pathway with unidirectional block, and a second pathway with slow conduction.¹⁸ Regions of transition from healthy myocardium to scar may satisfy these requirements and provide an appropriate substrate for sustaining ventricular re-entry.¹¹ Based on this, we hypothesized that the propensity for a specific region of admixed viable myocardium and scar to give rise to a VA may relate to the degree of spatial complexity within or around that region.

In patients with ICM, the presence, volume, and transmural extent of LGE on CMR imaging provide important prognostic information about the risk of VA and death.^5,6,19 Furthermore, on LGE-CMR, SI values can be used to discriminate dense scar from ‘gray’ zones of transition from healthy myocardium to scar.¹⁰ Such gray zones may harbor critical components of the circuits that are necessary to sustain re-entrant arrhythmias.^8,11 The extent of gray zone has been shown to be an important marker of risk for VA and death following MI.⁶ However, attempts to further characterize substrate heterogeneity in the ischemic substrate have been limited.

One emerging approach utilizes the concept of Shannon entropy. Simplistically, the Shannon entropy of a set of elements is the average number of yes-or-no questions that must be asked in order to determine the identity of an unknown element in the set. Applied to SI values in an LGE-CMR image dataset, Shannon entropy is a measure of the uncertainty involved in predicting whether a specific pixel will have a specific SI value. Androulakis and colleagues recently assessed the utility of Shannon entropy, as applied to LGE-CMR imaging, for the prediction of VA events in patients with ICM, and showed that Shannon entropy is independently associated with risk of VA events.²⁰ Similarly, Muthalaly and colleagues assessed the utility of Shannon entropy, as applied to LGE-CMR, for the prediction of VA events in patients with non-ischemic cardiomyopathy and showed that Shannon entropy was independently associated with risk of VA events.²¹ Lastly, Gould and colleagues showed that, among patients with ischemic and non-ischemic cardiomyopathy and ICDs in situ, increased mean entropy on LGE-CMR is associated with risk of appropriate ICD therapies.²² However, Shannon entropy does not account for 3D spatial relationships that may be important to the underlying electrophysiologic properties of a substrate.²³ Therefore, alternative approaches that focus on 3D spatial relationships may provide complementary information, as our results suggest here.

Our SSC analytic method demonstrated better accuracy for identifying patients who were VA-free by 5 year follow-up, with a negative predictive value of 91%, than for identifying patients who experienced VA events. This suggests that the CS could therefore be most useful in identifying a low-risk subgroup of patients with ICM who is much less likely to benefit from ICD insertion in the ensuing 5 years. The poor positive predictive capacity of this technique may be related to the fact that ventricular arrhythmias not only require the appropriate substrate but also sufficient triggers. It may be more biologically feasible to identify a substrate that is not capable of sustaining an arrhythmia than to identify one that is, since arrhythmic events rely on both structural and functional triggering factors, the latter of which may fluctuate over time.

Finally, computing advances offer many promising yet accessible opportunities for developing sophisticated and precise approaches to image analysis. The method we developed and described in this paper requires minimal computing capabilities, can be performed on standard personal computing machines, and analysis can be completed within the span of several hours. Furthermore, although the number of patients included in this study was small for a ML analysis, the number of data points generated from each patient’s imaging was large, enabling a robust ML result.

Limitations

The current study has several limitations. The cohort represented a predominantly male and Caucasian population. The number of clinical events was small. While patients were enrolled over a long period of time during which ICD programming may have varied, the incidence rates of ICD firing remained relatively stable at 2–4% per year across all years for the whole cohort. However, there was a decline over time in inappropriate ICD therapies, possibly due to changes in device programming. In order to optimize the statistical ML process, we utilized a Monte-Carlo cross validation approach in which a given patient would be used, on alternate runs, both as part of the training data set and the validation data set. Accordingly, a major limitation of the current study is that the results have not been validated in an independent cohort. Furthermore, the 12 eigenvector frequencies included in our protocol were chosen based on initial performance with pilot test runs. Therefore, proof that these 12 frequencies are a robust component of the classification apparatus will ultimately require validation in an independent cohort.

Conclusions

Incrementally to multiple known risk factors for VA in patients with ICM, the CS derived from our 3D SSC analysis of LGE-CMR images was significantly and independently associated with VA events in a multivariable time-to-event analysis. Therefore, SSC analysis of LGE-CMR images may be a promising tool to refine VA risk assessment in patients with ICM.

What is Known

• The cardiac magnetic resonance imaging technique of late gadolinium enhancement enables the non-invasive detection of potentially arrhythmogenic substrate and is a strong predictor of ventricular arrhythmia events in patients with ischemic cardiomyopathy.

What the Study Adds

• Incrementally to multiple known risk factors for ventricular arrhythmias in patients with ischemic cardiomyopathy, substrate spatial complexity analysis of late gadolinium enhancement cardiac magnetic resonance imaging is significantly and independently associated with ventricular arrhythmia events.

Non-standard Abbreviations and Acronyms:

CMR

Cardiac magnetic resonance imaging

CS

Complexity score

ICD

Implantable cardioverter-defibrillator

ICM

Ischemic cardiomyopathy

LGE

Late gadolinium enhancement

LVEF

Left ventricular ejection fraction

ML

Machine learning

SSC

Substrate spatial complexity

SI

Signal intensity

VA

Ventricular arrhythmia