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Self-Supervised Cardiac Phase Detection via Single-Parameter Latent Orbits
John Bonnici, Matthew Baugh, Aleksandra Kulbaka, Sarah Cechnicka, Bernhard Kainz, Alberto Gomez
TL;DR
Manual ED/ES selection in echocardiography is subjective and variable, motivating annotation-free cardiac phase detection. The paper constrains latent motion to a single-parameter orbit and significantly improves ED localisation while matching ES localisation against prior methods on EchoNet-Dynamic.
Problem
Manual ED/ES selection is subjective and produces substantial inter-operator variability, motivating automated annotation-free detection for reproducible ventricular-function assessment.
Method
A self-supervised autoencoder constrains time-varying motion to a one-dimensional latent orbit whose sinusoidal phase extrema directly identify ED and ES.
Results
ED MAE is 2.36 frames and ES MAE is 2.13 frames, with significantly improved ED localisation and non-significantly improved ES localisation versus LMP.
Takeaways & Limitations
A minimal one-parameter representation can capture cardiac contraction–relaxation dynamics and localise ED/ES without annotations on EchoNet-Dynamic.
Takeaways & Limitations
Evaluation is limited to A4C videos from EchoNet-Dynamic, leaving generalisation of the one-dimensional cardiac-phase assumption to other settings unresolved.
Abstract
from arXiv · showhide
Accurate identification of end-diastole (ED) and end-systole (ES) in echocardiography underpins the quantification of ventricular function, yet manual selection of these key frames is subjective and introduces clinically significant inter-operator variability. Recent self-supervised methods either prescribe strict periodic trajectories or learn an unconstrained low-dimensional motion subspace from reconstruction or registration objectives. The former offers interpretability but imposes restrictive assumptions on temporal progression, whereas the latter leaves cardiac phase implicit and ED/ES must be recovered through post-hoc geometric processing of the learned trajectory. We translate the physiological observation that cardiac phase is a one-dimensional signal into a prior by constraining the latent motion component to a single-parameter latent orbit, i.e., a global linear trajectory in latent space indexed by a bounded scalar phase variable. Mapping this variable through a sinusoidal nonlinearity yields an oscillatory motion signal with consistent temporal ordering, enabling direct identification of ED and ES from the learned phase signal. This inductive bias allows the model to capture an interpretable representation of the cardiac cycle, while maintaining flexibility to capture irregular heartbeats. Trained on EchoNet-Dynamic without annotations, our minimal single-parameter cardiac phase model learns an effective latent orbit, significantly improves upon the previous state of the art in ED localisation and matches it in ES localisation while using a more constrained representation and fewer training epochs. This demonstrates that a principled physiological inductive bias can match or exceed the performance of more complex representations. Code is available at: https://github.com/BonniciJ/OrbitalEcho/
1 Introduction
The paper targets subjective, annotation-free ED/ES frame selection for LVEF estimation by imposing a one-dimensional cardiac-phase prior on disentangled latent motion. Its single-parameter orbit directly identifies ED and ES and improves ED localisation while matching ES localisation on EchoNet-Dynamic with fewer training epochs.
- Motivation: Accurate ED and ES identification is necessary for LVEF estimation, but manual frame selection is subjective and causes substantial inter-operator ejection-fraction variability.Transthoracic echocardiography is widely used because it is portable, low-cost, and acquired in real time.
- Related work: Earlier self-supervised methods recovered cardiac phase from the geometry of an unconstrained low-dimensional motion trajectory without labels [22], but their motion coefficients could span the subspace arbitrarily.The proposed method addresses this limitation by constraining the motion representation to a single parameter.
- Contributions: The model improves ED localisation and matches ES localisation on EchoNet-Dynamic without ED or ES labels, using fewer training epochs and a more constrained representation.The model also achieves strong downstream ejection-fraction prediction performance.
- Contributions: ED and ES are retrieved directly from the minima and maxima of the learned phase signal, avoiding post-hoc geometric phase extraction.The phase is encoded as a cyclic traversal of a one-dimensional trajectory.
- Contributions: The proposed single-parameter latent orbit replaces unconstrained motion coefficients with a one-dimensional trajectory derived from the prior that cardiac phase is a scalar signal.This builds on prior motion-structure decomposition while imposing a stronger physiological constraint directly in the disentangled latent space.
2 Method
The method decomposes echocardiography clips into shared structure and time-varying motion, constraining motion to a one-dimensional sinusoidal latent orbit indexed by a bounded scalar phase. This phase directly supports ED and ES detection through latent extrema while preserving expressive decoding.
- Architecture: The autoencoder decomposes each clip into a patient-specific, time-invariant structure latent and a time-varying motion latent constrained to a one-dimensional parametrised orbit.Clips contain T consecutive grayscale frames sampled with a random starting frame.
- Architecture: Each frame is independently convolutionally encoded, then a lightweight temporal convolution with kernel size 5 incorporates local context without a heavy sequence model.The temporal mixer produces features h_t in R^C from the independently encoded frames.
- Latent decomposition: Temporal averaging yields the structure latent, while subtracting the clip mean removes stationary content and leaves motion, cardiac phase, and high-frequency features.This separation assumes cardiac phase appears as a zero-mean oscillation that is cancelled by averaging.
- Latent orbit: A phase MLP predicts a bounded scalar phase, which a cosine basis and one global learned direction map into motion m_t = a cos(ϕ_t) along a single latent axis.The unconstrained direction coordinates changes across anatomical features, while sharing it across samples promotes cycle consistency.
- Phase identification: The decoder reconstructs each frame from the sum z_t = s + m_t, while ED and ES are hypothesised to occur at extrema farthest from the average latent state.These extrema represent maximal relaxation and contraction of the left ventricle, corresponding to its largest and smallest states.
3 Experiments and Results
Experiments on EchoNet-Dynamic evaluate unsupervised ED/ES detection and downstream EF prediction using withheld annotations during training. The 1D orbit model achieves the lowest unsupervised localization errors and improves EF prediction over LMP with substantially fewer pre-training epochs.
- Experimental setup: The model is evaluated on EchoNet-Dynamic’s 10,030 A4C videos using the official split, with annotations withheld during training and results reported after 50 epochs.ED/ES localization is reported using mean absolute error in frames and milliseconds.
- Detection performance: 2.36 frames (46.0 ms) ED MAE and 2.13 frames (41.6 ms) ES MAE are the lowest among unsupervised methods, improving ED over LMP by 0.74 frames.The ED improvement has 95% bootstrap CI [0.57, 0.92] and p ≪0.001 after Bonferroni-corrected Wilcoxon testing.
- Qualitative results: Figure 2 qualitatively compares predicted phase signals and ED/ES frames for regular and irregular heartbeats, alongside reconstructions and orbit-position histograms.The reconstructions are generated purely from the learned latent orbit and decoder.
- Ejection Fraction: 6.02% MAE versus 6.27% MAE demonstrates improved EF prediction over LMP using one-tenth as many pre-training epochs.The MLP prediction head is trained supervised with frozen base-model weights on concatenated structure and motion features.
ED MAE ES MAE
The learned representation retains low-frequency cardiac motion and produces cycle-consistent phase values that separate ED and ES across patients. Ablations show that temporal mixing and the single-parameter orbit are important for performance and disambiguation.
- The reconstructions retain low-frequency cardiac motion while purposefully excluding speckle and noise, making cardiac phase clearly represented.The reconstructions are used solely for pre-training.
- ED and ES labels cluster at consistent, well-separated phase values on the latent orbit across patients.Figure 2(C) shows little overlap between the ED and ES histograms.
- Ablation study: Removing temporal mixing degrades performance on all metrics, while removing Gaussian blur reduces ED accuracy but slightly improves ES accuracy.
- Extension to two parameters: Extending the model to two parameters removes cycle consistency and ED/ES clustering, making ED/ES disambiguation impossible.The elliptical formulation requires monotonic phase increments; without this constraint, the model collapses to zero motion or an oscillatory arc.
4 Discussion
The discussion supports a one-dimensional cardiac-phase representation that enables unsupervised ED/ES localisation and lightweight EF regression, while identifying systematic bias between predicted extrema and clinical annotations. The authors conclude that the minimal orbital model outperforms baselines for ED/ES detection with substantially shorter training.
- Discussion: The results support the hypothesis that A4C cardiac phase is intrinsically one-dimensional, with a single parameter and learned linear projection capturing contraction–relaxation dynamics and localising ED and ES.The learned orbital motion also supports training a lightweight EF regression MLP head.
- Bias Correction: Predicted phase extrema do not exactly coincide with clinically annotated ED and ES frames on average, but correcting this systematic bias improves performance.This limitation affects methods that identify ED and ES as extrema of predicted or derived phase signals, or their proxies.
- Conclusion: The proposed self-supervised method constrains cardiac phase to a one-dimensional parametrised orbit, enabling unambiguous ED/ES prediction without supervision after a fraction of the training time.The method is based on the physiological prior that the cardiac cycle is governed by a single mechanical degree of freedom.
- Conclusion: Experiments on EchoNet-Dynamic show that the minimal representation outperforms baselines for ED/ES detection.The conclusion presents this result as evidence for the effectiveness of the constrained representation.