Leveraging an ECG Beat Diffusion Model for Morphological Reconstruction from Indirect Signals

[1] Golany, Tomer, et al. "12-lead ecg reconstruction via Koopman operators." International Conference on Machine Learning. PMLR, 2021.

[2] Chen, Jintai, et al. "ME-GAN: Learning panoptic electrocardio representations for multi-view ECG synthesis conditioned on heart diseases." International Conference on Machine Learning. PMLR, 2022.

[3] Douedi S, Douedi H. P wave. [Updated 2023 Jul 24]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-. Available from: https://www.ncbi.nlm.nih.gov/books/NBK551635/

[4] Goldenberg, I. L. A. N., Arthur J. Moss, and Wojciech Zareba. "QT interval: how to measure it and what is “normal”." Journal of cardiovascular electrophysiology 17.3 (2006).

[5] Song, Yang, and Stefano Ermon. "Generative modeling by estimating gradients of the data distribution." Advances in neural information processing systems 32 (2019).

We thank the reviewer for the feedback and the appreciation of our effort to apply and propose new methods to use diffusion models (DDM) in ECG. We now address the points raised by the reviewer.

• Authors reimplement EkGAN, DeScoD, SSSD, WGAN on the PhysioNet...: We thank the reviewer their comment, we will clarify the following in the supplementary material. The pretrained weights were not available for the baselines or minor adaptation was needed to extend the networks to our case, so we had to retrain the models from scratch on the PhysionNet dataset. Our code and weights are available to ensure reproducibility and fair comparison.
• There are two common baselines ...: [1] and [2] are indeed important contributions to the generative ECG community, and we regret overlooking them in our introduction. We will rectify this oversight. For the numerical comparison, we compare our work with that of Joo et al. (2023) (EkGAN in our paper), which is a more recent work that aligns with [2] as it also uses a GAN to generate 12-lead ECGs from a single lead. Unlike [2], the code for the experiments is available
• ..to preprocess all ECGs from 10-second signals to single beat... and Normally, ECG is 10 seconds ... Could the authors explain the reasons?:
  • In this work, we focus on analyzing the morphology of heartbeats, a task that is distinct from the general ECG analysis. While the methods we present for ECG restoration and anomaly detection from partial observations can be applied, it would be necessary to define a new, presumably more complex, DDM and train it on a much larger dataset. This work is very interesting, but it differs from the work carried out in this paper.
  • However, we want to emphasize that heartbeat analysis is an important aspect which is extremely relevant to all diseases related to the morphology of the ECG (see references [64], [65], [19], [38] in the paper). Other generative models have previously focused on a single beat, such as WGAN. Furthermore, centralizing the data is a common practice in generative models. A well known illustration is the CelebA dataset, one of the most used benchmarks in image generation tasks, where the generative models are always trained in the version of the dataset obtained by first centering all faces.
  • We have absolutely no doubts about the contribution of the general methodology we present in the context of long ECGs [rather than heartbeats]. However, it is quite clear that a special study should be carried out to build a relevant DDM on the one hand, and to adapt the parameters of EMBeat-Diff to this new context on the other. Larger models allow smaller batches for parallel evaluation and thus a smaller number of maximum particles that can be used in the particle filter. However, since the distribution is more complex, we need a larger number of particles at the same time to achieve reasonable posterior sampling.
  • We have nevertheless provided a proof of concept in those lines. We trained a DDM to produce 5-second slices instead of 10 seconds due to time and GPU constraints. We then applied "EMBeat-diff" to reconstruct 12-lead ECGs from limb leads only and I, II, III + V2 + V4 (similar to the Kardia12L mentioned by reviewer UDMo). We found that the reconstruction of the 12 leads becomes more complex when we use multi-beat ECGs, and we also need precordial leads to generate reasonable ECGs (see attached figure). We will include an improved version of this new experiment in the supplementary material to demonstrate that the inference methods we presented also apply to the analysis of 10-second segments, even though this was not the immediate aim of our study.
• In Table 1, the inference time of the baseline WGAN is ...: It is well known that DDM are slower than GAN models, as they require more than one neural function evaluation (NFE). The great value of DDMs is that one can make a trade-off between quality and inference time and thereby achieve better sample quality than some state-of-the-art GAN models, as is the case in the field of computer vision [5]. In our work, we show that this is also the case for the heartbeat morphology generation of the ECG. We show that the proposed DDM outperforms WGAN in equalising a dataset (Table 1) and that it achieves a lower Earth Mover's Distance (EMD) even when performing relatively few NFEs (Figure 1). Furthermore, DDMs are easier to train and show better theoretical convergence results. GANs, on the other hand, are notoriously difficult to train and suffer from mode collapse. We would also like to point out that the WGAN has a small number of parameters. Although in principle it should be possible to obtain a better GAN network with a larger number of parameters, we consider the development of a more efficient GAN network to be outside the scope of the present work.
• In data preprocessing, authors claim ...:We used the annotation from the dataset to select patients with the labels "NSR" (normal sinus rhythm), "ST" (sinus tachycardia) and "SA" (sinus arrhythmia). Thank you for pointing this out, we add a sentence in the appendix B.1.1.
• From B1.1, authors use [R -192 ms, R + 512 ms] ...: Thank you for your question. We chose the window [R-192ms, R+512ms] for single beat analysis because a normal PR interval is between 120ms and 200ms (see [3]), and a normal QT interval is less than 450ms (see [4]). Anything outside this interval should not correspond to cardiac activity during a normal heartbeat. Additionally, the 5s ECG experiment can be considered an ablation study of the window size. It shows that reconstructing 12 leads from 5s crops is more complex and requires precordial leads for reasonable results. We will include this discussion on the choice of the window in the supplementary material.

We are afraid that the reviewer may have misunderstood the focus of our paper and the rebuttal.

The goal of our paper is not merely the "analysis of single beats", but rather to investigate morphological heartbeat anomalies, such as Long QT syndrome (LQT) or Myocardial Infarction (MI), and to develop a white-box tool for detecting these localized anomalies. For example, LQT is only visible on the QT segment, and MI may only be visible on the precordial leads. Currently, there is no sufficiently large public dataset to train generative models for these conditions. We have developed a flexible method based on the reconstruction of 12 leads from a partial ECG, that allows us to generate the healthy counterpart of a heartbeat associated with localized MI or LQT (see Section 4). In addition to outputting an abnormality score, our approach is also able to highlight where the patient’s signal is abnormal, allowing cardiologists to rule out non-relevant abnormalities, thereby limiting the risk of hallucination.

Moreover, we demonstrate that the proposed approach can be used to solve several important ECG analysis problems, such as baseline wander removal, electrode motion removal, and missing lead reconstruction. We have thoroughly evaluated the proposed technique and compared it with state-of-the-art approaches.

As mentioned in the answer to UDMo’s question "how easily would it be to generate 10s ECG signals" and in the last paragraph of the rebuttal to the current reviewer TuvT, our method can be directly applied to 10-second ECGs. We have done this for healthy ECGs and ECGs with Atrial Fibrillation (see the attached PDF in the rebuttal). Furthermore, it is important to note that applying a 12 lead ECG reconstruction to arrhythmias such as Premature Ventricular Contractions (PVCs) has limited added value beyond visualization, as arrhythmia detection can be done directly by analyzing a single lead, as mentioned below.

The reviewer's argument about heartbeat segmentation is unconvincing. The detection of PVC is a well-established topic, and methods for detecting PVCs have existed since 1979 (Murthy et al., Transactions on Biomedical Engineering, 1979). Today, there are methods with a sensitivity of 99.91% and specificity of 99.37% (Mazidi et al., Cluster Computing, 2020). In fact, devices like AliveCor’s KardiaMobile1L already integrate PVC detection by default. Therefore, it is straightforward to apply our heartbeat analysis to PVCs: one simply needs to detect PVCs prior to studying the heartbeats.

Murthy, Ivaturi SN, and Mandayam R. Rangaraj. "New concepts for PVC detection." IEEE Transactions on Biomedical Engineering 7 (1979): 409-416.

Mazidi, Mohammad Hadi, Mohammad Eshghi, and Mohammad Reza Raoufy. "Detection of premature ventricular contraction (PVC) using linear and nonlinear techniques: an experimental study." Cluster Computing 23 (2020): 759-774.

We thank the reviewer for their detailed feedback.

• There is a shortcoming in the selection of comparison models. Although performance evaluations were conducted on various tasks, different models were used for each task. The model should be comparable regardless of the task. A comprehensive comparison is needed. It would be beneficial to separate the diffusion-based and GAN-based models and compare their performance in detail.

Comparison methods are specialized for specific tasks and cannot be used interchangeably. For example, the DeScoD model is designed for baseline-wander removal and cannot be used for ECG reconstruction or ECG anomaly detection, while EkGAN and AAE are not suitable for baseline-wander removal. To our knowledge, EM-BeatDiff is the only one capable of addressing all these tasks. For each task, we have taken care to use the most appropriate comparison methods and to compare our results with the state-of-the-art for the corresponding task. Could you please specify how you envision comparing all of these methods regardless of the task?

• It would be beneficial to separate the diffusion-based and GAN-based models and compare their performance in detail.

Some of the methods we have included in our study, such as the Adversarial Autoencoder (AAE), do not fall into either of these categories. Would you mind providing more details on how you envision the separation of these methods?

• There are many different ECG generation models available. What are the advantages of using a diffusion model?

Section 4 of the paper provides the advantages of using a diffusion model. In Table 1 and in Figure 1 of the paper, we provide comparisons of BeatDiff with various ECG generation models in terms of size, inference time, and different evaluation metrics. As stated on line 214, "Diffusion-based models BeatDiff and SSDM outperform WGAN, with BeatDiff being 400 times faster than SSDM".

• A performance comparison with existing models for each task is necessary. If a comparison is difficult, it would be helpful to specify the exact reasons why only the respective models were used for each task.

We already provide an exhaustive comparison of our BeatDiff model with existing ECG generation models such as SSDM or WGAN (which to the best of our knowledge are currently the state of the art). We also extensively compare our EM-BeatDiff algorithm on multiple tasks with multiple approaches that are respectively the state of the art on their tasks (such as DeScoD for baseline-wander removal, EkGAN for missing lead reconstruction, and AAE for anomaly detection). For each task, we merely selected the baseline approach which was the state-of-the-art method for this task. To better address your concerns, we are happy to provide additional comparison. Please let us know if there is a specific method that you think we should include, and on which specific task.

• The paper proposes EM-BeatDiff based on BeatDiff. Is it obvious that EM-BeatDiff performs better than using BeatDiff alone? A comparative analysis is needed.

BeatDiff and EM-BeatDiff serve different purposes and are not directly comparable. BeatDiff is a diffusion model trained to generate ECGs, while EM-BeatDiff is a sampling algorithm that utilizes BeatDiff as a prior to address various challenges in heartbeat morphology reconstruction from partial observations. As stated in the paper (line 63), "we show how BeatDiff can be used as a prior to address various challenges in heartbeat morphology reconstruction from partial observations." Therefore, BeatDiff alone cannot be used to solve the same tasks as EM-BeatDiff. BeatDiff serves as the generative prior for EM-BeatDiff, and the two are not meant to be compared directly. EM-BeatDiff leverages the generative capabilities of BeatDiff to perform downstream tasks such as heartbeat morphology reconstruction, which a diffusion model alone cannot accomplish.

• Conditional options such as age, gender, and RR were used. However, only the effect of RR is confirmed in the actual paper. Can other conditions not be utilized?

Age, sex, and RR all have an impact on ECG morphology. However, although age and sex have a significant impact on ECG morphology, there is no known formula in the literature that represents this correlation in a closed form. The RR interval has a more subtle impact, but it is still significant and well established in the ECG literature under the Fridericia formula (QT linearly correlated with RR^(1/3)). Furthermore, the effect of the sex variable is visible in the classifier improvement score given in Table 1. We will clarify this in the updated version of the paper. Thank you for pointing this out.

• The rationale for choosing diffusion models and their advantages are not clearly articulated. The paper lacks a thorough comparison with other state-of-the-art generative models, which would provide a more convincing argument for the selection of diffusion

c.f. response to above question on the justification of using diffusion models.

• The dataset used in the study may be limited to specific conditions or environments. Therefore, the generalization ability of the model across diverse patient populations and different clinical settings may not be fully validated.

We used the PhysioNet Challenge dataset, comprising 43k 12-lead ECGs. This dataset contains the largest and most diverse database of 12-leads ECGs publicly available. Building a larger ECG database is beyond the scope of this paper.

We would like to first thank the reviewer for taking the time to review our work.

Regarding the question formulated in the weakness section, indeed, it is generally accepted that increasing the number of parameters can improve model accuracy. However, in our case, we found that increasing the size of the GAN compared to the WGAN proposed in the literature made the training strategy much more complex. We did not manage to achieve better results with a larger GAN. It is possible that a different architecture and an adapted training procedure could make a larger GAN competitive with BeatDiff, but this was not the main purpose of our work. We plan to explore this avenue in subsequent work.

I will retain my score.

… detect pathologies (such as MI) from the reconstructed precordial leads. In our study, we show that it's possible to generate precordial leads from limb leads for healthy patients. This is because healthy patients have correct electrical signal conduction, and our model, trained on numerous healthy ECGs, can capture this information. However, challenges arise with conduction issues like Myocardial Infarctions (MI), where part of the heart is necrotic. If the necrosis is highly localized, predicting the ECG shape in precordial leads accurately becomes difficult. To address this, the model would need to be trained on ECGs with MI. Unfortunately, there are only 500 MI patients in Physionet, which is insufficient to cover all possible MI localizations. We are currently training a generative model on 600,000 patients from a partner hospital's cardiology service to evaluate if our algorithm can generate precordial leads for patients with localized MI or Long QT. This is a future task as the data is not yet publicly available due to anonymization reasons.

AliveCor recently develop a new system based… Many thanks for the reference to Kardia12L from AliveCor. Their AI model for 12-lead reconstruction includes two precordial leads. This is likely because they reconstruct multiple beats of higher dimension than in our case. We found that generating higher-dimensional signals with our approach requires at least two precordial leads (see below). Regarding MI detection from limb leads, this is an interesting question but requires a dataset of MI to develop an accurate model. To our knowledge, there is no large public dataset of ischemia (Physionet has less than 1k, insufficient for training a diffusion model), but this would be valuable for future work. It is worth noting that our approach has a distinct advantage over AliveCor's AI: We do not need to know which leads should be used to reconstruct the signal before training the model. Therefore, signals acquired by an AliveCor system with two precordial leads or signals acquired with smartwatches (where we can acquire I, II, III, V1, V3 and V6 depending on the placement of the smartwatch [van der Zande, Sensors 2023]) can be used.

How easily would it be to generate 10s ECG signals? Thank you for this interesting question. Although our study focused on heartbeat morphology, we found that our approach can generate 10-second ECG signals. We trained a diffusion model to produce 5-second slices due to time and GPU constraints. We then applied our sampling algorithm to reconstruct 12-lead ECGs from limb leads only and limb leads + V2 + V4 (similar to Kardia12L). We found that reconstructing 12 leads from multi-beat ECGs is more complex and requires precordial leads for reasonable results (see attached figure). We will include an improved version of this experiment in the supplementary material to show that our methods apply to 10-second segments, though our main focus remains on heartbeat morphology and pathology detection.

It would be interesting to be able to generate arrhythmic data such as AF Thank you for the question. While we have focused on the reconstruction of heart beats for morphologic analysis, it is important to point out that testing the ability to reconstruct arrhythmic ECGs is valuable for testing the method in a controlled environment, even if it is not necessarily of direct clinical interest. Indeed, arrhythmias like atrial fibrillation (AF) and premature ventricular contractions (PVC) can be detected from lead I alone (e.g., with an Apple Watch or Kardia), unlike morphological abnormalities such as MI or long QT, which require examining heartbeat characteristics. We trained a diffusion model on 5-second ECGs with AF from Physionet and successfully predicted a reasonable 12-lead ECG from limbs+V2+V4 (Kardia12L setting). A larger AF dataset (not yet publicly available) would yield more interesting results, but this experiment shows the method's potential for generating rhythmic abnormalities. We will include this study in the supplementary material.

discuss the ability to generate precordial leads for limb leads only…

• Healthy heartbeats: Our paper focuses on generating 12-lead healthy heartbeats from partial measurements (e.g., limb leads only). We show that our approach can also classify abnormal heartbeats. In Section 4, we generate healthy counterparts of abnormal heartbeats and use the distance as an anomaly score. The flexibility of our method allows the detection of various heart conditions (MI, LQT, LAD, LAE) by reconstructing 12 leads from limb leads only, QRS only, or ST only (see Table 12).
• Unhealthy heartbeats case: Generating unhealthy heartbeats from incomplete heartbeat (e.g., limb leads) requires a large dataset of ECGs with morphological abnormalities, which is not yet publicly available. However, this would enable the use of additional simulated leads for abnormality detection from portable devices such as Smartwatch or AliveCor products.
• 10s ECG: Generating 10s 12-lead ECGs from limb leads only, by solving an inverse problem, is non-trivial. Our current algorithm requires precordial leads (as observed by AliveCor). A special study is needed to build a relevant diffusion model and adapt the algorithm's parameters. This adaptation is complex due to the need for larger models and more particles for posterior sampling.

risk of hallucination Our anomaly detection tool is semi-white-box: rather than outputting an abnormality score, our approach is also able to show the healthy counterparts of an abnormal signal and highlight where they differ from the patient's signals. This could theoretically enable cardiologists to rule out abnormalities that are not relevant. However, there is still a risk of hallucinations. We have shown that the generated signals are close to the real signals for healthy patients, a clinical study must be performed before clinical use. We'll mention this in the final paper.