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One Frame, Full Heartbeat: ECG-Free 4D Cardiac Cine MRI Synthesis via Radial-Decomposed Flow Matching

Shiyi Wang, Ruochen Sun, Xiang Li, Peirong Liu, Fangxu Xing

arXiv:2610.09185v1cs.CV

TL;DR

Standard cine CMR requires ECG gating and repeated breath holds, yet some settings retain only isolated 3D volumes. PhaseFlow3D predicts a full sequence from one ED volume using phase-conditioned latent flow and radial-plus-residual displacement warping. It reports the best EF accuracy and LV volume-curve reconstruction among compared methods, with downstream utility in segmentation and motion analysis.

  • Problem

    Standard cine CMR requires ECG gating and multibreath-hold sequences, while retrospective archives may contain only isolated 3D volumes, making full-cycle synthesis from spatial information alone challenging.

    Source: §1 · pp. 2–3

  • Method

    PhaseFlow3D uses phase-conditioned latent flow and a physics-informed radial-plus-residual displacement field, then warps the real ED volume into each frame.

    Source: §1 · p. 3, §3.4 · p. 6, §3.6 · p. 7

  • Results

    PhaseFlow3D achieves the best EF accuracy and LV volume-curve reconstruction among compared methods, and downstream tests support segmentation, classification, label propagation, and strain-analysis utility.

    Source: §1 · p. 3, §7 · p. 21

  • Takeaways & Limitations

    The synthesized sequences and explicit displacement fields support downstream supervision and quantitative motion analysis from a single ED volume.

    Source: §1 · p. 3, §6 · p. 21

    A single ED volume and canonical phase cannot uniquely determine a patient's true contraction trajectory, so generated dynamics remain model-based predictions rather than observed measurements.

    Source: §6 · p. 21

Abstract

from arXiv · show

Cine cardiovascular magnetic resonance (CMR) captures the cardiac cycle as a four-dimensional (4D) sequence, but standard acquisition requires electrocardiogram (ECG) gating and repeated breath holds. Visual realism alone does not establish accurate patient-specific ejection fraction (EF) or ventricular volumes. We present PhaseFlow3D, a generative framework that synthesizes a complete 4D cine sequence from a single end-diastolic (ED) three-dimensional (3D) volume without ECG. To capture asymmetric systolic and diastolic dynamics, it represents the cardiac cycle as a piecewise linear phase anchored at ED and end-systolic (ES) time points. At inference, a population-level canonical template supplies this phase without patient-specific temporal information. A phase-conditioned rectified flow model generates a cardiac motion trajectory in latent space. Radial Contraction Decomposition converts each latent state into a 3D displacement field, combining a physics-informed radial component for centripetal myocardial contraction with an image-conditioned residual for rotation and out-of-plane motion. Each frame is generated by directly warping the ED volume, bypassing variational autoencoder decoding. On the combined ACDC and M&Ms benchmark, PhaseFlow3D achieves the lowest EF mean absolute error, the only positive left-ventricular volume-curve $R^2$, and the best distributional quality among compared methods. Ablations confirm each component's contribution. Downstream evaluations demonstrate the utility of the synthesized sequences and displacement fields for segmentation, pathology classification, label propagation, and myocardial strain analysis.

1. Introduction

PhaseFlow3D aims to recover a physiologically coherent 4D cine CMR sequence from a single end-diastolic volume without ECG or patient-specific temporal information. It combines phase-conditioned latent motion, radial-plus-residual deformation, and volume-curve supervision to synthesize frames by warping the observed volume.

2. Related Work

  • Prior work includes learning-based registration, ECG-conditioned methods [9], and GAN- and diffusion-based video generators, while visual realism alone does not establish patient-specific EF or LV-volume accuracy.We target single-volume 4D cine synthesis with explicit supervision of EF and the LV volume trajectory.Source: §1 · p. 3

3. Methodology

  • PhaseFlow3D predicts a phase-conditioned latent velocity from a single ED volume and decodes it into 3D displacement fields for ECG-free cine synthesis.At inference, a population-level canonical phase template replaces patient-specific timing; the predicted fields warp the ED volume into each frame.Source: §1 · p. 3, §3 · p. 4

3.2. Piecewise Linear Cardiac Phase

  • The piecewise linear phase anchors ED and ES at fixed phase positions, accommodating unequal systolic and diastolic durations; a population-average ES fraction supplies the template for blind inference.Frames use a periodic sine-and-cosine phase encoding, aligning ES across subjects without requiring ECG at inference.Source: §1 · p. 3, §3.2 · p. 5

3.5. Radial Contraction Decomposition

  • Radial Contraction Decomposition combines an anatomy-derived radial prior for centripetal LV contraction with an image-conditioned residual for non-radial motion such as rotation, shear, and out-of-plane deformation.The radial branch is ED-anchored, temporally modulated, and localized to the cardiac region; the combined field’s diffeomorphic regularity is assessed numerically rather than guaranteed.Source: §1 · p. 3, §3.5 · p. 7

3.6. Warp-Based 4D Synthesis

  • Each output frame is a direct warp of the real ED volume, bypassing VAE decoding and making temporal variation depend on the predicted displacement field.This anchors image appearance to observed anatomy but does not guarantee anatomically correct motion or eliminate interpolation error.Source: §1 · p. 3, §3.6 · p. 7

3.7. Training Objectives

  • Physiological losses compute EF and volume-curve supervision by warping the ground-truth ED mask through the predicted field, so segmentation runs only on real images.The training objective combines latent flow matching, image-space fidelity, and physiological and anatomical constraints; its folding loss penalizes topology violations without forcing the Jacobian determinant toward unity.Source: §1 · p. 3, §3.7 · p. 8

1. Introduction

  • Five downstream experiments evaluate synthesized sequences and displacement fields for segmentation, pathology classification, label propagation, and blind myocardial strain analysis.The paper states that synthetic supervision can largely substitute for real supervision in segmentation and pathology classification.Source: §1 · p. 3

3.3. CineVAE3D: Per-Frame 3D Encoding

  • A frozen CineVAE3D encodes frames independently, while phase-conditioned rectified flow models temporal transport; folding compressed depth into channels enables 4D reasoning with a 3D network.At inference, the velocity network is evaluated once at the ED-conditioned anchor, without iterative ODE integration.Source: §3.3 · pp. 5–6, §3.4 · p. 6

3.7. Training Objectives

  • ED supervision requires zero displacement at ED, while ES endpoint supervision anchors contraction magnitude using mask overlap, LV volume, and EF terms.Predicted volumes and EF are computed by warping the ground-truth ED segmentation mask through the predicted displacement field, without running a segmentation network on generated images.Source: §3.7 · p. 8
  • The volume-curve loss supervises normalized per-frame error, curve R^2, amplitude, and bias using warped soft ED masks; frozen SegUNet processes only real images, avoiding domain shift.Gradients flow through the differentiable warp to the velocity network.Source: §3.7 · p. 8

3.8. Network architecture and implementation

  • The architecture combines an ED latent anchor and phase-conditioned latent velocity with physics-informed radial contraction and an image-conditioned residual displacement to warp the ED volume into cine frames.The CineVAE3D encoder is frozen, while the phase projector and VelocityUNet4D provide phase-conditioned latent motion.Source: Figure 2 · p. 9, §3.8 · p. 9

4. Experiments and Results

On the combined ACDC and M&Ms benchmark, PhaseFlow3D improved physiological fidelity and sequence-level distributional quality over the compared methods. Ablations, phase-template validation, deformation checks, and qualitative results examine its components and outputs.

4.1. Experiment Setup

  • Training used 255 combined ACDC and M&Ms subjects, with evaluation on their combined test sets; the model was trained in two progressive stages.The two-stage schedule took approximately 29 hours on one NVIDIA RTX A6000 GPU.Source: §4.1 · p. 10

4.2. Comparison to Baselines

  • 12.85% EF MAE versus the best competing method’s 27.03%, and Vol R2 of 0.05 was the only positive result; FID was 2.02 and FVD was 0.68.The reported image-quality comparison also notes that some methods had higher per-frame PSNR.Source: §4.2 · pp. 10–11, Table 1 · p. 11

4.3. Ablation Study

  • Removing the deformation decoder left image metrics nominally strong but yielded 55.33% EF MAE and undefined Vol Corr, while removing the radial head worsened EF MAE from 12.85% to 15.00% and Vol R2 from 0.05 to −0.24.The decoder ablation produced essentially no ventricular contraction; the radial-head ablation left contraction amplitude and its temporal curve unreliable.Source: §4.3 · p. 13
  • Removing the residual reduced PSNR to 33.14 dB and raised FVD to 1.06, while removing volume-curve loss raised EF MAE to 14.66% and lowered Vol Corr to 0.78.A radial-only field cannot represent rotation, twist, or out-of-plane motion; endpoint terms alone do not constrain the full temporal course.Source: §4.3 · p. 13
  • Replacing piecewise phase with uniform phase kept EF MAE similar (12.60% vs. 12.85%) but worsened Vol Corr (0.74 vs. 0.84) and Vol R2 (−0.20 vs. 0.05).The piecewise phase distinguishes rapid systolic descent from slower diastolic recovery.Source: §4.3 · p. 13

4.4. Phase Template Validation

  • The canonical ES fraction of 0.38 approximated the training population mean of 0.398 ± 0.076; its pooled phase RMSE was 3.8% of the cycle versus 6.2% for uniform phase.Group-mean oracle templates improved only slightly over the canonical template in every group, without requiring pathology labels at inference.Source: §4.4 · p. 13

4.5. Deformation Regularity Evaluation

  • Folding voxels averaged 0.0005% and stayed below 0.002% per patient; these whole-volume statistics do not isolate myocardium or establish tissue incompressibility.A representative HCM subject showed displacement localized to the myocardium and positive Jacobian determinants throughout.Source: §4.5 · pp. 14–15

4.6. Qualitative Results

  • Qualitative results show sharp, coherent synthesized frames with systolic thickening and diastolic expansion, while predicted LV volume curves reflect pathology-specific contraction patterns.Reconstruction error concentrated near the myocardial boundary and peaked around end systole.Source: §4.6 · p. 15

5. Downstream Applications

The frozen generator is evaluated in blind single-ED-volume settings for downstream utility, including synthetic supervision, label propagation, strain analysis, and perceptual realism. Results show strong retention for segmentation supervision, useful but reduced classification performance, and pathology-ordered strain estimates.

5. Downstream Applications

  • Inference uses a single real ED volume and canonical phase template without an ES image, ECG, or pathology label; the generated deformation is localized to myocardium and fold-free.Figure 8 shows positive Jacobian determinants throughout the displayed deformation.Source: §5 · p. 15, Figure 7 · p. 16

5.1. Synthetic Supervision for Segmentation

  • 0.887 ± 0.002 Dice under fully synthetic supervision retains 99.2% of the all-real pipeline A baseline of 0.894±0.005.At up to 75% substitution, pipeline A stays within the all-real baseline’s seed-noise band; pipeline B retains 96.9% under full substitution.Source: §5.1 · p. 16, Figure 11 · p. 18

5.2. Synthetic Supervision for Pathology Classification

  • 0.711±0.048 balanced accuracy with one-quarter synthetic training samples is about two points below the all-real 0.733±0.048; full substitution retains 72.7%.At full substitution balanced accuracy is 0.533 ± 0.018, more than 2.5× the 0.2 chance level.Source: §5.2 · p. 16, Figure 12 · p. 19

5. Downstream Applications

  • PhaseFlow3D produces sharp, anatomically coherent frames, with reconstruction error concentrated in a thin myocardial-boundary band and peaking near ES.The VAE-decoded variant exhibits reconstruction blur, while errors remain near zero in the static background.Source: Figure 8 · p. 17, Figure 9 · p. 17

5.3. Label Propagation Through the Displacement Field

  • 0.712 ± 0.129 LV Dice from blind ED-to-ES label propagation recovers most of the interval between the no-motion floor and two-frame Demons oracle.The floor is 0.622 ± 0.177 and the oracle is 0.738 ± 0.138; propagation exceeds the oracle in NOR and ARV, while myocardium Dice is 0.572 versus 0.700 for Demons.Source: §5.3 · pp. 17–18, Figure 13 · p. 19

5.4. Myocardial Strain Analysis

  • NOR has the strongest peak-systolic GCS (−11.3 ± 2.7%) and DCM the weakest (−3.3 ± 0.3%), with significant separation across ACDC groups (H= 14.9, p= 0.005).Strain magnitudes are smaller than clinically reported values, so the authors interpret this result as validating group separation and ordering rather than absolute strain values.Source: §5.4 · p. 18, Figure 14 · p. 20

5.5. Perceptual Realism

  • 0.639 ± 0.011 discriminator AUC indicates mild real-versus-synthetic separability above the 0.5 chance level.AUC peaks at 0.718 in mid-systole and falls to 0.574 late in the cycle; shared temporal resampling makes this a conservative upper bound on synthesis-attributable separability.Source: §5.5 · p. 19, Figure 15 · p. 20

6. Discussion

The discussion argues that physiological accuracy and image/distributional quality require distinct evaluation, and ties the model’s performance to its radial and phase priors. It also identifies prediction, cohort, acquisition, and motion-pattern boundaries that warrant validation.

6. Discussion

  • PSNR can favor SimVP and Direct Reg despite their larger EF errors and lower volume-curve R^2; physiological metrics address a different question from pixel and distributional metrics.The radial decomposition’s removal costs the most physiological accuracy, whereas removing the residual costs the most image quality.Source: §6 · p. 20
  • The canonical phase template supports blind inference from one ED volume, but a population timing template only approximates individual ES timing and clinical utility requires separate validation.Ablation A5 indicates the asymmetric phase preserves volume-curve shape better than uniform phase.Source: §6 · p. 21
  • The displacement fields support motion analysis, missing-frame recovery, downstream supervision, registration benchmarks, and in-silico trials within the evaluated synthesis setting.Segmentation supervision has near-lossless retention, while classification incurs a moderate cost.Source: §6 · p. 21
  • A single ED volume and canonical phase cannot uniquely determine true patient dynamics, so generated motion remains a model-based prediction rather than an observed measurement.The study also uses ECG-gated cine resampled to 16 slices; free-breathing, non-ED anchors, broader cohorts, and pronounced non-radial motion remain validation or extension needs.Source: §6 · p. 21

7. Conclusion

PhaseFlow3D synthesizes 4D cine CMR from a single ED volume without ECG and generates more physiologically accurate ventricular dynamics than the compared methods. Its sequences and displacement fields are proposed for motion analysis, missing-frame recovery, downstream data augmentation, and deformation-algorithm validation.

7. Conclusion

  • PhaseFlow3D synthesizes cine CMR from one ED volume without ECG and achieves the best EF accuracy and LV volume-curve reconstruction among compared methods.The resulting sequences and displacement fields are proposed for cardiac motion analysis, missing-frame recovery, downstream segmentation and disease-classification augmentation, and registration validation.Source: §7 · p. 21

A. Excluded Baselines

The excluded baseline families require inference information or modality adaptations that differ from PhaseFlow3D’s single-ED-volume CMR setting. The authors therefore describe direct comparisons as mismatched or unfair under the reported setups.

Registration methods

  • VoxelMorph aligns two observed images, so its required target frame is unavailable in the single-ED-volume inference setting.Source: A. Excluded Baselines · p. 21

ECG-conditioned methods

EchoLVFM

  • EchoLVFM [24] uses 2D ultrasound and target EF conditioning, so comparison would require modality adaptation and harmonized conditioning unavailable to PhaseFlow3D.Providing target EF adds information unavailable at PhaseFlow3D inference; removing it changes EchoLVFM’s reported setup.Source: A. Excluded Baselines · p. 22

B. Implementation Details

The implementation separates per-frame 3D encoding from temporal flow modeling, then converts latent states into image-conditioned displacement fields for direct warping of the ED volume.

B. Implementation Details

  • CineVAE3D encodes each frame independently into a (B, 4, 4, 16, 16) latent, leaving all temporal reasoning to the flow model.The VAE uses 3D spatial attention at its two coarsest levels and is frozen after 100 pretraining epochs.Source: B. Implementation Details · p. 22
  • VelocityUNet4D uses a 3D U-Net with a D′-fold channel trick, flow-time AdaGN conditioning, and per-frame phase cross-attention at both levels.The backbone has base channels 128, multipliers, and two residual blocks per level.Source: B. Implementation Details · p. 22
  • The deformation decoder upsamples latent features with image-encoder skip connections, and training proceeds in two stages with physiology-only losses followed by all losses.The image encoder processes the ED volume; the decoder uses three upsampling steps, while the two training stages last 50 and 100 epochs.Source: B. Implementation Details · p. 22
  • The RadialContractionHead combines a global contraction amplitude, an LV-ROI-normalized spatial modulation, and a peak-normalized temporal profile with ED subtraction.Its GlobalNet predicts A_pat; LocalNet modulates contraction distribution, while TemporalNet predicts per-frame values.Source: B. Implementation Details · p. 22
  • Each frame is generated by independently applying its displacement field to a broadcast ED volume using differentiable trilinear 3D warping with border padding.The displacement field has shape 3 × D × H × W.Source: B. Implementation Details · p. 22

C. Data Preprocessing

Preprocessing fixes patient-level splits and applies consistent spatial, temporal, and intensity transforms to each sample, without augmentation or registration.

C. Data Preprocessing

  • The stratified ACDC split and M&Ms subset partitions are reused unchanged across all main and baseline models, ensuring an identical evaluation protocol; patient-level splits are fixed offline before per-sample transforms run on the fly inside the Dataset.Source: C. Data Preprocessing · p. 22
  • Preprocessing uses only an isotropic in-plane resize and center depth pad/crop; no intensity augmentation, cropping, or registration is applied. Intensities are normalized per patient so all frames share one range, preserving relative temporal contrast.Source: C. Data Preprocessing · p. 22
  • A single per-patient intensity range is shared across frames, preserving relative temporal contrast.The resampled sequence is min–max normalized to [−1, 1].Source: C. Data Preprocessing · p. 22

D. Evaluation Metrics

The evaluation combines image- and video-quality measures with physiological volume metrics, and includes unified EF protocols to check whether measurement pathways affect method rankings.

D. Evaluation Metrics

  • Preprocessing resamples each sequence to 30 frames, assigns a piecewise-linear phase from ED = 0 through ES = π to the last frame = 2π, and encodes phase as sine and cosine.M&Ms sequences are shifted so ED is frame 0; the pipeline also resizes slices to 128 × 128 and pads or crops depth to 16.Source: D. Evaluation Metrics · p. 23
  • The primary physiological protocol warps the ED segmentation mask through PhaseFlow3D's displacement field, whereas baselines are evaluated by segmenting generated frames with the same frozen SegUNet.Unified image-based EF uses SegUNet on every method's generated frames; unified mask propagation is defined only for methods exposing an image-space displacement field.Source: D. Evaluation Metrics · pp. 23–24
  • EF MAE measures absolute ejection-fraction error, while Vol Corr measures volume-curve shape and Vol MAE measures normalized per-frame volume error.Vol Corr is independent of scale; Vol MAE is normalized by ED volume.Source: D. Evaluation Metrics · p. 23
  • Vol R^2 penalizes bias and variance in the volume curve, with negative values indicating predictions worse than the mean.The supplied metric description also identifies PSNR as a pixel-fidelity measure, LPIPS as a deep-feature perceptual measure, FID as frame-distribution realism, and FVD as sequence-level temporal coherence and motion statistics.Source: D. Evaluation Metrics · p. 23
  • 14.55% versus 26.22% EF MAE under the unified image-based protocol favors PhaseFlow3D over the best baseline, so the Table 1 advantage is not an artifact of the measurement pathway.For DragNet, the two protocols give 37.73% versus 36.49%; the segmentation network alone has EF MAE 5.48% ± 5.33% on real frames.Source: Table 4 · p. 24, D. Evaluation Metrics · p. 24

E. Metric Variability

The reported patient-level performance comes from one fixed-seed run; image metrics vary little, while physiological metrics are more dispersed and heavy-tailed.

E. Metric Variability

  • SSIM is tightly concentrated at 0.927 ± 0.012 across patients.The paper contrasts this with greater dispersion in physiological metrics.Source: E. Metric Variability · p. 24
  • Vol R^2 has median 0.567 and IQR [−0.058, 0.797]; its unbounded lower tail lets a few outliers pull the mean toward zero.The authors attribute the spread to between-patient variation in cardiac motion and pathology severity rather than estimator noise.Source: E. Metric Variability · p. 24
  • Table 5 summarizes PhaseFlow3D across 166 joint ACDC+M&Ms test patients using mean ± standard deviation and median with IQR.All reported numbers come from a single training run with seed 42.Source: E. Metric Variability · p. 24, Table 5 · p. 25

F. Latent Scale and Anchor Perturbation

The section characterizes the frozen encoder’s latent scale and examines whether anchor noise disrupts motion supervision. It finds that the perturbation changes the starting point while preserving the target, making it usable as augmentation.

F. Latent Scale and Anchor Perturbation

  • The full sequence latent has dimension 122,880, computed as 4 × 30 × 4 × 16 × 16.The latent is taken as the posterior mode of the frozen CineVAE3D encoder.Source: F. Latent Scale and Anchor Perturbation · p. 25
  • Empirical latent statistics agree closely across the training and validation splits, indicating a stable encoder latent scale rather than a split artifact.Source: Table 6 · p. 25
  • 42.70±9.70 was the validation transport distance, while the anchor-noise norm was 35.04±0.07 and perturbed directions differed by 40.2°±6.2°.The noise projection onto the motion direction was 0.073±0.056, or 0.18% of transport distance.Source: F. Latent Scale and Anchor Perturbation · p. 25
  • The large orthogonal noise component changes the anchor but leaves the endpoint fixed, so each draw supplies a valid training pair and acts as anchor augmentation.The authors consider α=0.1 a safe choice.Source: F. Latent Scale and Anchor Perturbation · p. 25

G. Extended Qualitative Results

The extended qualitative examples compare synthesized cine sequences with ground truth across ACDC pathology groups. They show pathology-specific motion signatures from a single ED input.

G. Extended Qualitative Results

  • Figure 16 shows six evenly spaced frames across the cardiac cycle, with ground truth above PhaseFlow3D synthesis for one representative patient per group.Source: G. Extended Qualitative Results · p. 25
  • The ED frame at t=0 is the only inference-time input; subsequent frames are synthesized using the canonical phase template and predicted 3D displacement field.Source: G. Extended Qualitative Results · p. 26
  • PhaseFlow3D captures normal wall-thickening in NOR, large-cavity contraction in DCM, asymmetric septal hypertrophy in HCM, regional wall-motion abnormality in MINF, and preserved right ventricular dynamics in ARV.Source: G. Extended Qualitative Results · p. 26

H. Downstream Experiment Protocols and Full Results

The appendix details downstream evaluation protocols and their full-result tables. The experiments use the frozen main checkpoint under blind canonical-phase inference, with distinct procedures for substitution, label propagation, strain analysis, and realism discrimination.

H. Downstream Experiment Protocols and Full Results

  • All downstream experiments use the frozen main checkpoint with blind canonical-phase inference; substitution experiments report means and standard deviations over seeds 42, 43, and 44.Source: H. Downstream Experiment Protocols and… · p. 26
  • Segmentation substitution replaces ES supervision pairs or intermediate-phase slices with synthesized frames and warped real ED annotations, then evaluates on real ACDC test ED and ES frames.Table 7 reports test Dice for LV and myocardium across synthetic supervision fractions.Source: H. Downstream Experiment Protocols and… · p. 26, Table 7 · p. 26
  • Classification substitution compares real ED/ES feature vectors with eight synthesized intermediate-phase vectors per patient, using patient-stratified five-fold cross-validation and real test annotations.Table 8 reports five-class balanced accuracy and macro-F1 across substitution fractions.Source: H. Downstream Experiment Protocols and… · p. 26, Table 8 · p. 26
  • Label propagation warps the multiclass ED annotation to canonical ES through the recovered displacement field and compares Dice by structure with a Demons-registration oracle.Table 9 reports results on 30 ACDC test patients.Source: H. Downstream Experiment Protocols and… · p. 27, Table 9 · p. 27
  • Strain analysis selects the synthesized frame with minimum warped LV volume, derives the forward deformation gradient, and computes circumferential Green–Lagrange strain.Radial and longitudinal projections are computed but not reported.Source: H. Downstream Experiment Protocols and… · p. 27
  • The realism discriminator is a four-block strided CNN trained on 128×128 slices, with patient-level folds and AUC from pooled out-of-fold predictions.Source: H. Downstream Experiment Protocols and… · p. 27
  • Figure 16 presents one representative patient per pathology group, with ground truth on top and PhaseFlow3D synthesis below; the ED frame is the sole model input.Source: Figure 16 · p. 28
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