Graph theory and its potential in the automatic detection of left bundle branch block

2.1. Data acquisition and cohort definition

2.2. ECG signal preprocessing and representative beat standardization

The raw 12-lead ECG recordings from both the Healthy and LBBB/sLBBB datasets underwent several preprocessing steps to obtain standardized, representative heartbeat signals suitable for subsequent analysis. These steps were performed independently for each subject and each lead.

Baseline Wander Removal: To remove low-frequency baseline wander, an approach equivalent to zero-phase high-pass filtering was implemented. The baseline component was first estimated by applying a 4th-order Butterworth low-pass filter with a cutoff frequency ( f c ) of 0.5 Hz to the raw electrocardiogram signals. Forward-backward digital filtering ensured zero phase distortion in this estimation. The resulting estimated baseline was then subtracted from the original signal, effectively attenuating signal components below 0.5 Hz and yielding the baseline-corrected signal.

R-Peak Detection and Beat Segmentation: Individual heartbeats were extracted from the aforementioned baseline-corrected signals. R-peaks were identified using an established ECG processing toolkit. ⁴⁸ The first and last detected R-peaks in each recording were discarded to avoid boundary effects from incomplete beats. Fixed-size windows were then segmented around each valid R-peak: 400 samples (175 samples pre-R-peak, 225 samples post-R-peak) for the Healthy dataset (originally sampled at 500 Hz), and 800 samples (350 samples pre-R-peak, 450 samples post-R-peak) for the LBBB/sLBBB dataset (originally sampled at 1000 Hz).

Representative Beat Generation via Woody Alignment: To obtain a stable, noise-reduced morphology for each lead, the Woody alignment method ⁴⁹ was applied to the ensemble of segmented beats from that lead. This iterative procedure involves aligning each segmented beat to an evolving template by maximizing their cross-correlation function, and then averaging all aligned beats to update the template for the next iteration. This process was repeated for five iterations. The final averaged template served as the representative heartbeat morphology for that specific lead and subject.

Resampling to Standardized Frequency: Following the generation of representative heartbeats for each of the 12 leads (initially 400 or 800 samples long, reflecting their original sampling rates of 500 Hz and 1000 Hz, respectively), these beats were resampled to a common frequency. This resampling step was intentionally performed after critical preprocessing stages like R-peak detection, beat segmentation, and representative beat alignment. Conducting these initial stages at the original, higher sampling rates leveraged their greater temporal resolution, contributing to more precise morphological characterization and robust representative beat generation.

A target frequency ( f s , f i n a l ) of 200 Hz was chosen for standardization. Downsampling to 200 Hz, rather than standardizing to one of the original higher frequencies, provided a substantial reduction in data dimensionality and subsequent computational demands for the graph-based and machine learning pipelines. This frequency was determined to adequately preserve essential QRS characteristics, which are critical for LBBB analysis, while significantly reducing the computational burden. Fourier-based resampling was utilized for this process. The resampling yielded standardized 12-lead representative beats, each comprising N f i n a l = 160 samples. These 12 × 160 signals (organized as a matrix X ∈ R 12 × 160 per subject) formed the input for the subsequent classification pathways.

2.2.1. Classification pathways overview

Starting from the standardized 12-lead representative beats ( X ), two distinct pathways were investigated for classifying subjects into Healthy, LBBB, or sLBBB categories, as depicted in Figure 1:

Feature extraction using Graph Signal Processing (GSP) followed by traditional Machine Learning (ML) classification.

Transformation of graph connectivity information into image representations for classification by a Convolutional Neural Network (CNN), incorporating explainability analysis.

The subsequent sections detail the specific methods employed within each pathway.

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Figure 1.

Schematic representation of the proposed method.

This pathway focuses on extracting features from the graph spectral domain of the standardized 12-lead representative beats.

Initial Signal Conditioning for Pathway 1: The standardized representative beats X first underwent an additional zero-phase band-pass filtering stage, employing a 4th-order Butterworth filter with a passband of 0.05 − 40 Hz. For connectivity measures known to be sensitive to signal amplitude variations, specifically Pearson correlation and phase difference, the band-pass filtered signals were subsequently subjected to a logarithmic amplitude normalization. Conversely, for cross-correlation analysis, which primarily relies on waveform morphology, the band-pass filtered signals were used directly without this logarithmic transformation. The resulting conditioned signals from this stage are denoted as X ′ for the subsequent GSP steps.

Graph Construction: Adjacency and Laplacian Matrices: Functional connectivity graphs G = ( V , E ) were constructed for each subject, where V represents the 12 ECG leads. Three types of weighted adjacency matrices A ∈ R 12 × 12 were computed using the appropriately conditioned signals X ′ . The specific computations for these adjacency matrices are detailed further in the description of Pathway 2. For each adjacency matrix, the normalized graph Laplacian ( L ) was then derived using the formulation L = I − D − 1 / 2 A D − 1 / 2 , where I is the identity matrix and D is the diagonal degree matrix.

Graph Fourier Transform (GFT): The GFT was used to decompose the conditioned 12-lead signal matrix ( X ′ ) onto the spectral basis defined by the eigenvectors U of the corresponding graph Laplacian L . The eigenvectors U and eigenvalues Λ were obtained from the eigendecomposition L = U Λ U T . The resulting GFT coefficients, forming a matrix X ^ ′ ∈ R 12 × 160 , were computed as X ^ ′ = U T X ′ .

Graph Filtering via Eigenvector Selection: Filtering in the graph spectral domain was performed by selecting a subset of k = 6 eigenvectors, forming a matrix U f i l t ∈ R 12 × 6 . These eigenvectors corresponded to the smallest non-zero eigenvalues (specifically, eigenvalues λ > 10 − 10 ) of the respective Laplacian matrix. This value of k was chosen based on preliminary analyses and common GSP practices, aiming to retain dominant graph spectral components while reducing noise.

Inverse Graph Fourier Transform (iGFT): The signal was reconstructed in the vertex domain using only the GFT coefficients corresponding to the k = 6 selected eigenvectors. Let X ^ f i l t ′ ∈ R 6 × 160 denote these selected GFT coefficients (i.e., the rows of X ^ ′ corresponding to the eigenvectors in U f i l t ). The graph-filtered signal in the vertex domain, X f i l t ′ ∈ R 12 × 160 , was then obtained by applying the iGFT: X f i l t ′ = U f i l t X ^ f i l t ′ . This procedure yielded three distinct sets of graph-filtered signals per subject, one for each connectivity method.

Feature Extraction and Dimensionality Reduction: Each of the 12 × 160 graph-filtered signal matrices ( X f i l t ′ ) was flattened into a 1920-dimensional feature vector. Principal Component Analysis (PCA) was then applied to reduce the dimensionality of these feature vectors to n components = 50 .

Classification Models and Evaluation: Four types of ML classifiers were trained using the 50-dimensional PCA features: Support Vector Machine (SVM) with a Radial Basis Function (RBF) kernel, k-Nearest Neighbors (KNN) with k = 5 neighbors, Gaussian Naive Bayes (GaussianNB), and a Gradient Boosting machine (specifically, LightGBM ⁵⁰ ). Model evaluation was performed using a repeated (200 iterations) stratified train-test split methodology (70% for training, 30% for testing). To handle class imbalance, three strategies were applied exclusively to the training set of each split: random oversampling, random undersampling, or using classifier-inherent class weighting. Performance was primarily reported as the average Balanced Accuracy across the 200 iterations on the test sets.

2.4. Pathway 2: Graph-CNN classification and explainability

This pathway involved transforming inter-lead connectivity information into image representations for classification by a Convolutional Neural Network (CNN), starting from the standardized 12-lead representative beats ( X ∈ R 12 × 160 , each sample at 200 Hz).

Band-Pass Filtering: Initially, each standardized representative beat underwent zero-phase band-pass filtering using a 4th-order Butterworth filter. This filter, with a passband of 0.05 − 40 Hz, was applied to mitigate noise, consistent with standard ECG analysis practices. ⁵¹ Let the output of this step be termed the filtered representative beat.

Connectivity Matrix Calculation with Tailored Normalization: Adjacency matrices ( A ∈ R 12 × 12 ), representing inter-lead connectivity, were computed from the filtered representative beats using three distinct methods, with input signal representation adapted for each:

Pearson Correlation (PC) and Phase Difference (PD): As these methods can be sensitive to amplitude variations, the filtered representative beats first underwent a logarithmic amplitude normalization prior to adjacency matrix calculation. This transformation is defined by preserving the original sign of each signal sample while applying a natural logarithm to one plus its absolute value. The Pearson correlation coefficient ⁵² or the FFT-based average phase difference was then calculated between pairs of these normalized lead signals to form the adjacency matrix A P C or A P D , respectively.

Graph Representation as Image: The calculated adjacency matrix A (from PC, CC, or PD) was transformed into a single-channel grayscale image suitable for CNN input. This involved applying a logarithmic scaling (e.g., log ( 1 + A ) for non-negative A , or log ( 1 + | A | ) more generally if A could contain negative values, followed by appropriate handling to maintain interpretability) to manage potential variations in connectivity strength, followed by min-max normalization to scale values to the range [0, 1]. The resulting 12 × 12 scaled matrix was then resized to 224 × 224 pixels using bilinear interpolation. ⁵³

CNN Architecture: The CNN architecture employed consisted of an input layer accepting 224 × 224 × 1 grayscale images, followed by five convolutional blocks. Each block comprised a 2D convolutional layer ( 3 × 3 kernel, with padding to maintain feature map size, and an increasing number of filters: 32, 64, 128, 256, and 512, respectively for each block), a LeakyReLU activation function (with a negative slope α = 0.1 ), and a max-pooling layer ( 2 × 2 pool size). After the convolutional blocks, the feature maps were flattened. This was followed by a fully connected dense layer (1024 units, ReLU activation), a dropout layer (rate of 0.4 for regularization ⁵⁴ ), and finally an output dense layer (3 units, corresponding to Healthy, LBBB, sLBBB classes) with softmax activation.

CNN Training and Evaluation with Cross-Validation: A 5-fold stratified cross-validation strategy was employed for robust model evaluation. Within each fold, the data was split into training and testing sets. The training set was balanced using random oversampling. The CNN model was compiled using the Adam optimization algorithm (learning rate 1 × 10 − 4 ) and categorical cross-entropy loss. Models were trained for a maximum of 40 epochs with a batch size of 64, using early stopping and learning rate reduction on plateau to optimize training and prevent overfitting. Performance was evaluated on the unseen test set of each fold, and results were aggregated.

Explainability using Grad-CAM: To enhance clinical interpretability, the Gradient-weighted Class Activation Mapping (Grad-CAM) technique ³⁷ was applied. Grad-CAM produces heatmaps highlighting image regions (i.e., pairwise lead interactions in the graph image) most influential for a given class prediction.

Baseline Spectrogram Model for Comparison: To contextualize the graph-CNN performance, a baseline model using a CNN on single-lead ECG spectrograms was developed. For each subject, the representative beat from Lead I (160 samples at 200 Hz) was transformed into a spectrogram via Short-Time Fourier Transform (STFT), using a Hann window of 64 samples and 50% overlap to provide adequate time-frequency resolution for QRS complex morphology. The resulting spectrogram was resized to 224 × 224 pixels and fed into a simplified CNN architecture. This model was trained and evaluated using the same 5-fold cross-validation and balancing strategies as the graph-CNNs.

2.5. Model evaluation metrics

The performance of both classification pathways was evaluated on their respective test sets using a comprehensive set of standard metrics suitable for multi-class classification, including: Accuracy, Balanced Accuracy, Precision, Recall (Sensitivity), F1-score, Confusion Matrix, and Area Under the Receiver Operating Characteristic Curve (AUC). Balanced Accuracy was chosen as the primary metric for comparison in Pathway 1 due to its robustness in the presence of class imbalance.

Accuracy: The overall proportion of correctly classified instances.

3.1. Pathway 1: Graph-based filtering and machine learning classification

The first pathway employed graph signal processing (GSP) for robust feature extraction from 12-lead ECGs, followed by classification using established machine learning (ML) algorithms. This approach aims to harness the inter-lead relationships to build discriminative feature sets.

Graph Construction and Spectral Basis. For both pathways explored in this work, functional connectivity graphs were constructed to model the interactions between the 12 ECG leads. Three distinct methods were utilized to compute the weighted adjacency matrices ( A ∈ R 12 × 12 ): Pearson Correlation (PC), which measures linear correlation; Cross-Correlation (CC), which identifies temporal shifts and morphological similarities; and Phase Difference (PD), ⁵⁵ which captures phase synchrony between lead signals.

The graph structures derived from these adjacency matrices are visualized in Figure 2. These graphs depict the ECG leads as nodes and the computed inter-lead connectivity strengths (weights of the adjacency matrix A ) as weighted edges. For illustrative purposes in these visualizations (Figure 2), connections with weights surpassing a predefined threshold (e.g., 0.4) are highlighted (e.g., in red) to emphasize dominant interactions, while weaker connections are also shown (e.g., in gray). It is important to clarify that this threshold-based highlighting of edges is solely for visualization purposes in Figure 2 and does not influence the subsequent processing steps; the full, unthresholded adjacency matrices (after setting the diagonal to zero and appropriate handling of negative values based on the connectivity method) are used for the computation of the graph Laplacian in Pathway 1. The considerable structural differences observed in the graphs generated by PC, CC, and PD reiterate that each method offers a distinct perspective on inter-lead dynamics. Compared to approaches like using mutual information for adjacency, ³⁵ our chosen methods (PC, CC, PD) specifically target linear correlation, waveform similarity including time lags, and phase relationships, respectively. These aspects are particularly pertinent for characterizing the conduction delays and altered activation sequences inherent in LBBB and sLBBB.

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Figure 2.

Graphs Representing ECG Lead Interactions for Different Patient Groups (Healthy, LBBB, sLBBB) and Connectivity Methods (PC, CC, PD). Connections with weights exceeding 0.4 are highlighted in red, general connections in gray. The structure varies significantly based on the group and the chosen connectivity metric.

From these adjacency matrices, the normalized graph Laplacians ( L = I − D − 1 / 2 A D − 1 / 2 ) were derived. The Laplacian matrix is fundamental in GSP as its eigendecomposition provides the spectral basis (eigenvectors and eigenvalues) for graph-based filtering and analysis.^32,56 Figure 3 illustrates representative Laplacian matrices computed using PC, CC, and PD for subjects from the Healthy, LBBB, and sLBBB cohorts. Visual inspection of these Laplacians reveals distinct patterns across groups and connectivity methods. For instance, the Healthy group often exhibits patterns (e.g., predominantly yellow tones in the provided visualization scheme) suggestive of synchronized and temporally aligned cardiac conduction. Conversely, LBBB and sLBBB groups tend to show patterns (e.g., more green and blue tones) indicative of desynchronization, temporal misalignments, and phase instability, which are characteristic of conduction abnormalities. These qualitative differences underscore that each connectivity metric, as reflected in both the adjacency-based graph structures and their corresponding Laplacians, captures unique aspects of inter-lead electrophysiological relationships, forming a diverse basis for subsequent feature extraction.

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Figure 3.

Laplacian Matrices of ECG Lead Relationships for Healthy, LBBB, and sLBBB Groups. Visual differences (e.g., color patterns indicated by red dots signifying strong connections or overall hues) reflect varying levels of synchronization and temporal alignment captured by different connectivity methods (Pearson Correlation, Cross-Correlation, Phase Difference).

Graph filtering, a core GSP technique, transforms signals by leveraging the relational structure of the graph. For ECG analysis, this means that the filtering process considers not only the individual lead morphologies but also how these leads are interconnected (Figure 2), as defined by the Laplacian (Figure 3). Filtering operators, designed based on the Laplacian’s spectral properties (eigenvectors and eigenvalues), ⁵⁶ can selectively attenuate or amplify signal components based on their variation across the graph. This allows, for example, low-pass graph filtering to emphasize smooth, global patterns and reduce noise, or high-pass filtering to enhance localized variations.

GSP-ML Pipeline Implementation and Classification Outcomes. The GSP-ML pipeline for Pathway 1 was implemented in Python, primarily utilizing libraries such as NumPy, ⁵² SciPy, ⁵⁷ Scikit-learn, ⁵⁸ and Imbalanced-learn. ⁵⁹ The process for each subject’s 12-lead representative beat ( X ∈ R 12 × 160 ) involved:

Computing the Graph Fourier Transform (GFT) of X using the eigenvectors of the corresponding Laplacian L , i.e., X ^ = U T X . ⁵⁶

For robust performance evaluation, this dataset underwent N = 200 iterations of stratified random 70%/30% train/test splitting. Stratification ensured that class proportions were maintained in both training and testing sets across iterations. Four distinct ML classifiers were evaluated: Support Vector Machine (SVM) with a Radial Basis Function (RBF) kernel, k-Nearest Neighbors (KNN, with k = 5 ), Gaussian Naive Bayes (NB), and Gradient Boosting (GB, implemented via LightGBM ⁵⁰ ). Given the inherent class imbalance in the dataset, three balancing strategies were applied exclusively to the training set of each iteration: random oversampling of minority classes, random undersampling of majority classes, and classifier-inherent class weighting (i.e., class_weight=’balanced’ for SVM and GB; for KNN and NB, this was termed ’no_balance’ as it represented training without explicit over/undersampling).

Table 1 summarizes the classification performance, reporting the Mean Balanced Accuracy (BalAcc) ⁶¹ and its Standard Deviation (SD) over the 200 iterations. BalAcc was chosen as the primary performance metric due to its suitability for imbalanced datasets. Each entry in the table reflects the performance achieved using the best-performing balancing strategy for that specific combination of connectivity method and classifier. The overall best-performing combination is highlighted in bold.

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Table 1.

Classification results for pathway 1 (GSP-ML).

Conn. Method	Clsf.	Mean BalAcc	SD	Best Bal. Strat.
Pearson Corr.	SVM	0.8000	0.0226	CW
	KNN	0.7682	0.0246	OS
	GB	0.7691	0.0249	CW
	NB	0.7253	0.0270	NoBal
Cross Corr.	SVM	0.8220	0.0231	CW
	KNN	0.7714	0.0249	OS
	GB	0.7777	0.0221	OS
	NB	0.7200	0.0283	NoBal
Phase Diff.	SVM	0.8317	0.0214	CW
	KNN	0.7855	0.0248	OS
	GB	0.7917	0.0226	CW
	NB	0.7461	0.0279	NoBal

Balanced accuracy (mean ± SD) is reported for each connectivity method and classifier, using its best-performing balancing strategy over 200 iterations.

Abbreviations: SVM: Support Vector Machine; KNN: K-Nearest Neighbors; GB: Gradient Boosting; NB: Naive Bayes; CW: class_weight; OS: oversampling; NoBal (Strategy): no_balance.

The classification results obtained via the GSP-ML pathway (Table 1) demonstrate the utility of integrating graph theory with machine learning for automated LBBB and sLBBB detection from 12-lead ECGs. ³² The performance metrics provide several key insights.

Impact of Connectivity Metrics. A notable finding is the differential performance associated with the choice of connectivity metric, a distinction also visually suggested by the diverse graph structures in Figures 2 and 3. Graphs derived from Phase Difference (PD) and Cross-Correlation (CC) consistently outperformed those based on Pearson Correlation (PC). The highest overall Mean Balanced Accuracy of 0.8317 ± 0.0214 was achieved using PD-derived graph features classified by an SVM. CC-based features also yielded strong performance (Mean BalAcc 0.8220 ± 0.0231 with SVM), while the best PC-based result was slightly lower (Mean BalAcc 0.8000 ± 0.0226 with SVM).

This suggests that metrics capturing temporal dynamics and synchrony—such as phase relationships (PD) or time-lagged similarities (CC)—are more effective in distinguishing LBBB and sLBBB conduction patterns than simpler linear correlation (PC). These observations are consistent with the pathophysiology of LBBB, which involves significant electrical dyssynchrony and altered ventricular activation sequences,^3,45 potentially leading to mechanical dyssynchrony. ⁷

Classifier Performance Comparison. Among the ML algorithms evaluated on the GSP-PCA features, SVM with an RBF kernel consistently delivered the highest Balanced Accuracy across all three connectivity types. This underscores SVM’s capability in handling complex, potentially high-dimensional feature spaces and defining effective non-linear decision boundaries. ⁵⁸ Gradient Boosting (GB), an ensemble learning technique known for its robustness,^25,50 was generally the second most effective classifier. In contrast, KNN and Gaussian NB yielded comparatively lower performance for this specific task and feature set.

Importance of Handling Class Imbalance. The investigation into balancing strategies confirmed their critical role in achieving optimal performance with imbalanced datasets. ⁵⁹ For SVM and GB, applying some form of balancing, particularly the class_weight=’balanced’ option, generally led to improved Mean Balanced Accuracy compared to training on the imbalanced data directly. This strategy was part of the top-performing models (Table 1). Recent advancements in handling imbalanced multi-label classification also offer potential avenues for exploration. ²³

Persistent Challenge: LBBB versus sLBBB Discrimination. Despite the promising overall accuracies, effectively distinguishing between the LBBB and sLBBB classes remains the most significant challenge for this pathway. Figure 4 displays typical ECG morphologies for Healthy, LBBB, and sLBBB subjects in leads V4, V5, and V6. While the Healthy group shows normal QRS duration (<120ms, highlighted by a red circle), both LBBB and sLBBB exhibit prolonged QRS duration (>120ms). Critical differentiating features, such as QRS notching (marked by red circles), are subtle and vary in presentation, as per criteria like Strauss et al. ⁹ .

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Figure 4.

Temporal and Morphological Analysis of Electrocardiographic Signals in Healthy, LBBB, and sLBBB Groups. Examples shown for leads V4, V5, and V6. Red circles highlight key features: normal QRS duration (¡120ms) in Healthy vs. prolonged QRS (¿120ms) in LBBB/sLBBB, and characteristic QRS notches in LBBB/sLBBB.

The graph-based approach aims to capture these complex inter-lead relationships (Figure 2) to better detect conduction delays and accentuate morphological differences by analyzing synchrony.

However, for the best-performing model in this pathway (PD + SVM + class_weight=’balanced’), further analysis of the detailed per-class metrics reveals a mean F1-score for the LBBB class of 0.6822 . This is considerably lower than the F1-score for the Healthy class ( 0.9881 ) and the sLBBB class ( 0.8299 ). Similarly, the mean Area Under the ROC Curve (AUC) for the LBBB class ( 0.8959 ) was lower than for Healthy ( 0.9987 ) and sLBBB ( 0.9332 ). This difficulty is quantitatively detailed in the aggregated confusion matrix from the 200 test splits, presented in Table 2.

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Table 2.

Aggregated confusion matrix for the top-performing model in pathway 1 (PD-SVM).

	Pred. Healthy	Pred. LBBB	Pred. sLBBB
True Healthy	17926	74	0
True LBBB	354	7210	3436
True sLBBB	5	2841	15354

Rows represent true labels and columns predicted labels over 200 test splits.

The matrix clearly shows a higher rate of confusion between LBBB and sLBBB (e.g., 3436 LBBB instances misclassified as sLBBB, and 2841 sLBBB instances misclassified as LBBB). This difficulty likely arises from the inherent morphological similarities between LBBB and sLBBB (Figure 4), suggesting that the GSP-PCA features, while informative, may not fully encapsulate all subtle differentiating characteristics defined by strict criteria. ⁹

Furthermore, the heterogeneity in data sources (Healthy controls from a general ECG database versus LBBB/sLBBB patients from the MADIT-CRT trial who had heart failure ¹⁰ ) is a potential confounding factor. The model might inadvertently learn population-level differences beyond pure LBBB electrophysiology, which could affect its generalization to other LBBB populations. Accurate LBBB vs. sLBBB differentiation is clinically crucial for optimizing Cardiac Resynchronization Therapy (CRT) patient selection. ⁶²

Robustness and Comparative Significance. The cross-validation strategy involving 200 stratified train-test splits indicates good robustness for the top-performing models, as evidenced by the relatively small standard deviations in Balanced Accuracy (e.g., ± 0.0214 for the best model, Table 1).

The achieved Balanced Accuracy of up to 0.8317 demonstrates the potential of the GSP-ML pipeline for differentiating these ECG categories. While the distinction from the Healthy class benefits overall accuracy, this aspect should be interpreted in light of the aforementioned dataset differences. Nevertheless, this performance represents a substantial improvement over simpler heuristic baselines relying solely on QRS duration or basic morphology criteria. ⁹ However, a comprehensive assessment of this pathway’s true standing requires direct benchmarking against a wider range of contemporary state-of-the-art LBBB/sLBBB detection algorithms reported in the literature.^12,63

Contribution of GSP Feature Extraction. This pathway effectively demonstrates the benefit of explicitly modeling inter-lead electrophysiological relationships as graph structures. ³² The application of GSP-based filtering, particularly with connectivity defined by PD and CC, appears successful in extracting physiologically relevant features reflecting cardiac synchrony and dyssynchrony. The low-pass graph filtering (retaining N modes = 6 components) likely emphasizes global activation patterns and coherent variations across leads, rather than focusing on purely local, single-lead features. ⁵⁶

Limitations of the GSP-ML Pathway. While promising, this pathway has several limitations. The primary one, as discussed, is the residual difficulty in robustly discriminating LBBB from sLBBB. Secondly, the features generated through GFT followed by PCA, while effective, offer limited direct clinical interpretability; understanding precisely which electrophysiological phenomena are captured by the top principal components can be challenging. Thirdly, while the 200-split validation demonstrates robustness on the current dataset, generalization to entirely new, unseen datasets from different clinical settings or demographics requires further investigation. The aforementioned dataset heterogeneity is a key aspect of this limitation.

Concluding Remarks and Future Directions for Pathway 1. The GSP-ML pathway proves to be a viable and robust method for automated LBBB/sLBBB classification, achieving a Mean Balanced Accuracy of up to 0.8317 . The results highlight the superiority of connectivity measures that capture temporal and phase dynamics (PD, CC) and the effectiveness of SVM classifiers for this task. Future research for this pathway should focus on several areas:

Enhanced Feature Engineering: Exploring combinations of features derived from different connectivity methods (PC, CC, PD) simultaneously, or incorporating other graph-theoretical measures.

The second pathway investigated in this study involved transforming the inter-lead functional connectivity information into 2D image representations, which were subsequently classified using a Convolutional Neural Network (CNN). This approach aimed to harness the potent hierarchical feature extraction capabilities of CNNs for graph-derived images ⁶⁴ and to enhance model transparency through established explainability techniques. The dataset specifically utilized for this pathway, after ensuring valid adjacency matrix generation for all subjects across the three connectivity methods (Pearson Correlation, Cross-Correlation, and Phase Difference), comprised 786 recordings (Healthy: 300, LBBB: 184, sLBBB: 302). The performance of CNNs operating on these graph-derived images was evaluated against a baseline CNN that processed single-lead spectrogram images, representing a direct ECG segment-to-image conversion strategy.

Image Representation of Graph Connectivity. A critical step in this pathway was the conversion of the 12 × 12 weighted adjacency matrix for each subject ( A P C , A C C , or A P D ), derived from appropriately preprocessed 12-lead representative beats (using log-normalized signals for PC/PD and band-pass filtered signals for CC, as detailed in the Connectivity Matrix Calculation paragraph within Section 2.4), into a single-channel grayscale image. This transformation was performed as follows:

Logarithmic Scaling: The transformation A ′ = log ( 1 + A ) was applied to each adjacency matrix. This is a common technique to manage skewed data, stabilize variance, and reduce the disproportionate impact of very high connectivity values, thereby making relative differences in connectivity strengths more apparent before subsequent normalization for image generation. ³²

Performance of Graph-CNN Models and Baseline. The classification efficacy of Pathway 2 was rigorously evaluated using a 5-fold stratified cross-validation strategy. The detailed performance metrics for the CNNs operating on images derived from Pearson Correlation (PC), Cross-Correlation (CC), and Phase Difference (PD) adjacency matrices, alongside the baseline spectrogram CNN, are presented in Table 3. The CNN architecture employed for the graph-image classifiers is detailed in Section 2.4 (under the CNN Architecture paragraph).

Among the CNNs leveraging graph-derived images, the model utilizing images from Cross-Correlation (CC) adjacency matrices demonstrated the highest Mean Balanced Accuracy ( 0.7646 ± 0.0475 ). This performance was marginally superior to the Pearson Correlation (PC) based CNN ( 0.7616 ± 0.0261 ). The Phase Difference (PD) based CNN exhibited a comparatively lower Mean Balanced Accuracy ( 0.7233 ± 0.0360 ).

The baseline model, which employed a simpler CNN architecture on spectrograms generated from a single ECG lead (Lead I), achieved a Mean Balanced Accuracy of 0.7358 ± 0.0285 . This baseline is representative of fiducial-free, direct ECG segment-to-2D image conversion methods, an increasingly explored strategy in automated ECG analysis that avoids reliance on precise wave delineation and has shown promise in various studies. ⁶⁵ The graph-CNNs, particularly those based on CC and PC, showed competitive, and in terms of balanced accuracy, slightly superior performance compared to this specific single-lead spectrogram baseline, indicating that the encoded inter-lead relationship patterns within the graph-derived images provide valuable discriminative information.

Analysis of Classification Performance and Comparison with Pathway 1. The best-performing graph-CNN model (Cross-Correlation CNN) yielded a Mean Accuracy of 0.7938 ± 0.0485 . While this model identified the Healthy class with high efficacy (F1-score: 0.9721 ), the accurate differentiation between LBBB and sLBBB classes remained the most significant challenge, as reflected by their respective F1-scores of 0.5742 for LBBB and 0.7383 for sLBBB. This difficulty is further detailed by the aggregated confusion matrix for the Cross-Correlation CNN model presented in Figure 5.

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Figure 5.

Performance of the Cross-Correlation CNN model detailed via an aggregated confusion matrix from 5-fold cross-validation (total N=786 subjects: 300 Healthy, 184 LBBB, 302 sLBBB). The matrix displays absolute counts for true versus predicted labels. Corresponding True Positive Rates (TPR) and False Negative Rates (FNR) for each class are also presented graphically.

The confusion matrix highlights considerable overlap between the LBBB and sLBBB classes. Specifically, 76 out of 184 LBBB instances (summed across the 5 test folds) were misclassified as sLBBB, while 69 out of 302 sLBBB instances were misclassified as LBBB. This underscores that the subtle distinctions underpinning the strict LBBB criteria ⁹ are not fully resolved by the CNN when operating on these image-based representations of graph connectivity.

When juxtaposing the outcomes of Pathway 2 with those of Pathway 1 (GSP-ML), the latter’s optimal model (PD + SVM) achieved a notably higher Mean Balanced Accuracy ( 0.8317 ± 0.0214 ) compared to the best Graph-CNN model from Pathway 2 (CC-CNN, 0.7646 ± 0.0475 ). This disparity suggests that, for the current dataset and chosen model configurations, the features extracted via GSP and classified by a conventional SVM were more effective in overall class discrimination. Nevertheless, Pathway 2 offers a distinct methodological paradigm, particularly concerning the potential for visual interpretation of the CNN’s learned features.

Explainability using Grad-CAM. To address the critical need for model interpretability in clinical AI applications, Gradient-weighted Class Activation Mapping (Grad-CAM) ³⁷ was implemented. Grad-CAM generates heatmaps that visually identify the regions within an input image—in this context, the specific inter-lead connectivities within the 12 × 12 graph image–that were most influential in the CNN’s decision-making process for a given class. Figure 6 illustrates representative Grad-CAM heatmaps (rendered using a JET colormap as per the analysis script) for correctly classified examples from the Healthy, LBBB, and sLBBB groups, across the three graph connectivity methods. The use of such saliency mapping techniques is increasingly recognized as valuable for introspecting deep learning models in medical image analysis and related fields. ²⁰

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Figure 6.

Grad-CAM heatmaps of CNN activation zones. Columns define subject class (Healthy, LBBB, sLBBB); rows define the connectivity metric (Pearson Correlation, Cross-Correlation, or Phase Difference) for the input graph image. Displayed examples are correctly classified instances with high prediction confidence. JET colormap (red indicates high importance, blue low) on 12 × 12 inter-lead connectivity images (axes: standard ECG leads I-V6).

Qualitatively, these heatmaps visually indicate which pairwise lead interactions the CNN focused on. For Healthy subjects, the activations across all methods are generally diffuse, possibly reflecting the overall coherence of normal cardiac conduction without strong localized points of discriminative stress for the CNN. However, for LBBB and sLBBB classifications, more distinct patterns emerge (Figure 6).

Specifically, images derived from Pearson Correlation and Phase Difference tend to elicit CNN activations that emphasize widespread, global connections, particularly highlighting interactions between frontal plane (limb) leads and precordial leads, as well as strong inter-limb lead activations. Phase Difference, consistent with its sensitivity to temporal phase shifts, generally shows broader and more intense activation patterns across these connections compared to Pearson Correlation, potentially capturing more extensive alterations in electrical synchrony. In contrast, images from Cross-Correlation appear to guide the CNN to focus on patterns that include strong inter-precordial lead relationships (e.g., within V1-V3 or V4-V6, and between these groups), alongside significant interactions between these precordial leads (especially V4-V6) and lateral limb leads like I and aVL. This might reflect the CNN leveraging CC’s strength in identifying morphological similarities and temporal shifts, which are key in localizing altered ventricular activation sequences in LBBB and sLBBB. ⁴⁵ These observed differences in activation foci across connectivity metrics underscore that each method provides a unique electrophysiological perspective that the CNN learns to utilize for discrimination. This visual feedback, while requiring careful interpretation, is a valuable step towards demystifying the CNN’s decision process for this complex classification task.

Discussion of Pathway 2 Strengths, Limitations, and Broader Context. Pathway 2’s methodology of transforming graph structures into an image domain for CNN-based classification represents an innovative strategy. A primary strength of this approach is its inherent potential for direct visual interpretability of model decisions through techniques like Grad-CAM, thereby addressing the crucial requirement for transparency in AI models intended for clinical settings. The adoption of a 5-fold stratified cross-validation scheme for the 786 subjects (Healthy: 300, LBBB: 184, sLBBB: 302) provides an initial measure of the models’ robustness and generalization capability on the available data. Standard practices such as data augmentation (RandomOversampling of the training sets within each fold) and regularization methods (Dropout, Early Stopping with restoration of best weights) were implemented to mitigate the risk of overfitting, a common challenge in the training of complex neural networks, especially with moderate-sized datasets. ¹⁸

Despite these strengths, Pathway 2 exhibits several limitations. Firstly, the overall classification performance, particularly in the challenging task of distinguishing LBBB from sLBBB, did not surpass that achieved by Pathway 1. This suggests that the conversion to an image format, while enabling the use of CNNs, might lead to a loss of some nuanced graph topological information that GSP-ML could exploit, or that the chosen CNN architecture could be further optimized for this specific type of image data. Secondly, the transformation of a compact 12 × 12 adjacency matrix into a much larger 224 × 224 image via bilinear interpolation, while standard for many CNN inputs, could potentially introduce interpolated artifacts or obscure very fine-grained structural details. The performance of the CNN is also intrinsically linked to the discriminative quality of the input graph images; if the underlying connectivity metric does not effectively capture class-specific patterns, the subsequent CNN classification will invariably be constrained.

Furthermore, as with Pathway 1, the heterogeneity of the data sources (Healthy controls from a general ECG database versus LBBB/sLBBB patients with pre-existing heart failure from the MADIT-CRT trial ¹⁰ ) constitutes a potential confounding factor that could impact the models’ generalization to different patient populations. Although class imbalance was addressed during the training phase through oversampling and class weighting strategies, its residual impact on multi-class performance, especially when dealing with subtly different subclasses like LBBB and sLBBB, warrants continuous consideration. Advanced techniques, such as those employing fuzzy deep neural networks for imbalanced multi-label classification problems, might offer further improvements in such scenarios. ²³

A comprehensive comparative analysis against a broader spectrum of state-of-the-art LBBB/sLBBB detection methodologies, particularly those employing deep learning, is still an essential future step. Our baseline (single-lead spectrogram CNN) offers one point of reference, aligning with fiducial-free ECG imaging approaches. ⁶⁵ The observation that graph-CNNs (notably CC-CNN and PC-CNN) achieved competitive or slightly improved balanced accuracy over this specific baseline suggests the added value of incorporating multi-lead inter-relationships, even when transformed into an image.

Concluding Remarks and Future Directions for Pathway 2. The Graph-CNN pathway (Pathway 2) successfully demonstrated the feasibility of classifying LBBB and its strict variant by translating inter-lead cardiac electrophysiological connectivity into an image format suitable for CNNs, achieving a peak Mean Balanced Accuracy of 0.7646 with Cross-Correlation derived images. Although this performance was quantitatively lower than the GSP-ML approach of Pathway 1, Pathway 2 offers significant advantages in terms of providing visual insights into model decision-making via Grad-CAM, thereby enhancing interpretability. The precise differentiation between LBBB and sLBBB remains the primary area for improvement. Future research avenues for this pathway include:

Advanced CNN Architectures and Training Strategies: Investigating more sophisticated CNN architectures, potentially incorporating attention mechanisms or transformer-based models adapted for image data. Furthermore, Self-Supervised Learning (SSL) techniques could be explored for pre-training the CNN component on larger, unlabeled ECG datasets, which may lead to more robust and generalizable feature representations.^27,28