cs.CVOct 6, 2026

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

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

Organizations: Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA · Gordon Center for Medical Imaging, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA · Center for Advanced Medical Computing and Analysis, Department of Radiology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, USA

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Abstract

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 R2R^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.

Figures & tables

Figure 1: Uniform linear phase (top) scatters ES across ϕ\phi values; the piecewise linear phase (bottom) aligns ES at ϕ ⁣= ⁣π\phi\!=\!\pi by construction across pathological types.
Figure 2: PhaseFlow3D encodes the ED 3D volume into a latent anchor z0\mathbf{z}_{0} , predicts a phase-conditioned latent velocity via rectified flow matching, and decodes a 3D displacement field through a Radial Contraction Decomposition. The displacement field directly warps the ED volume to synthesize the full 4D cine sequence.
 Image & Video QualityPhysiological Fidelity
MethodPSNR ↑\uparrowSSIM ↑\uparrowLPIPS ↓\downarrowFID ↓\downarrowFVD ↓\downarrowEF MAE ↓\downarrowVol Corr ↑\uparrowVol R2R^{2} ↑\uparrowVol MAE ↓\downarrow
ConvLSTM [ 45 ]19.160.4260.474292.023.31——−- 37.800.734
GAN-cMRI [ 14 ]22.640.5420.409185.819.7039.35%0.308−- 32.910.673
LFDM [ 26 ]28.500.8000.20082.5311.2429.83%0.809−- 5.5470.221
CVAE33.010.8990.06627.954.14132.39%0.781−- 0.5820.179
DragNet [ 7 ]35.610.9280.0305.4501.69037.77%0.757−- 0.4840.175
Table 1: Main results on the combined ACDC and M&Ms test set. Best in bold , second-best underlined . Baselines are evaluated with image-based EF (SegUNet on generated frames), whereas PhaseFlow3D uses warped ED masks; EF under unified measurement protocols is cross-validated in Appendix D (Table 4 ); “—” denotes inapplicable metrics.
 Wilcoxon pp (PhaseFlow3D vs.)
MetricED Rep.ConvLSTMGAN-cMRILFDMCVAEDragNetSimVPDir. Reg.
EF MAE4.5×10−28\mathbf{4.5{\times}10^{-28}}—9.5×10−20\mathbf{9.5{\times}10^{-20}}2.5×10−18\mathbf{2.5{\times}10^{-18}}1.1×10−19\mathbf{1.1{\times}10^{-19}}9.8×10−23\mathbf{9.8{\times}10^{-23}}1.1×10−14\mathbf{1.1{\times}10^{-14}}1.6×10−17\mathbf{1.6{\times}10^{-17}}
Vol Corr——2.2×10−22\mathbf{2.2{\times}10^{-22}}0.840.845.6×10−3\mathbf{5.6{\times}10^{-3}}1.0×10−2\mathbf{1.0{\times}10^{-2}}1.1×10−10\mathbf{1.1{\times}10^{-10}}3.9×10−9\mathbf{3.9{\times}10^{-9}}
Vol R2R^{2}1.3×10−21\mathbf{1.3{\times}10^{-21}}5.4×10−29\mathbf{5.4{\times}10^{-29}}8.4×10−29\mathbf{8.4{\times}10^{-29}}4.7×10−13\mathbf{4.7{\times}10^{-13}}6.7×10−11\mathbf{6.7{\times}10^{-11}}6.1×10−10\mathbf{6.1{\times}10^{-10}}2.5×10−12\mathbf{2.5{\times}10^{-12}}1.3×10−13\mathbf{1.3{\times}10^{-13}}
Vol MAE2.2×10−27\mathbf{2.2{\times}10^{-27}}5.4×10−29\mathbf{5.4{\times}10^{-29}}7.9×10−29\mathbf{7.9{\times}10^{-29}}3.7×10−18\mathbf{3.7{\times}10^{-18}}1.1×10−17\mathbf{1.1{\times}10^{-17}}2.8×10−16\mathbf{2.8{\times}10^{-16}}2.5×10−19\mathbf{2.5{\times}10^{-19}}5.0×10−19\mathbf{5.0{\times}10^{-19}}
Table 2: Paired Wilcoxon signed-rank test ( n=166n{=}166 patients) against all baselines. Every cell is a pp -value; smaller means stronger evidence that PhaseFlow3D is better, and in every significant cell the per-patient means favour PhaseFlow3D. Bold == significant at α=0.05\alpha{=}0.05 . The only non-significant cell is Vol Corr vs. LFDM; “—” marks undefined comparisons (constant or empty predicted volume curves).
Figure 3: Per-patient distribution of image quality (PSNR, SSIM, LPIPS) and physiological fidelity (EF MAE, Vol Corr, Vol R2R^{2} ) on the combined ACDC and M&Ms test set ( n=166n{=}166 ). Each box spans the interquartile range with the median line and 5–95th percentile whiskers. PhaseFlow3D (orange) is compared against the eight baselines (blue); empty slots mark metrics that are undefined for a given method, matching the dashes in Table 1 . Vol R2R^{2} uses a symmetric-log axis to resolve both the high-performing methods near one and the collapsed baselines.
 Image & Video QualityPhysiological Fidelity
VariantPSNR ↑\uparrowSSIM ↑\uparrowLPIPS ↓\downarrowFID ↓\downarrowFVD ↓\downarrowEF MAE ↓\downarrowVol Corr ↑\uparrowVol R2R^{2} ↑\uparrowVol MAE ↓\downarrow
A1: w/o deform decoder35.370.9290.0121.9490.72455.33%—−- 1.7660.250
A2: w/o radial head34.480.9240.0172.1550.76515.00%0.851−- 0.2440.114
A3: radial only (w/o residual)33.140.9220.0203.0981.05818.48%0.823−- 0.4150.132
A4: w/o vol curve loss34.330.9240.0203.0630.99814.66%0.785−- 0.6430.143
A5: linear phase34.910.9270.0171.8530.69712.60%0.741−- 0.1980.126
Table 3: Ablation study on the combined ACDC and M&Ms test set. Best in bold , second-best underlined .
Figure 4: Group-mean piecewise phase templates (coloured; ACDC pathology groups and pooled M&Ms) vs. the canonical template used at inference (black) and the uniform linear baseline (grey dashed). Each template reaches ϕ=π\phi=\pi (ES) at the group-mean ES fraction, encoding pathology-specific systole–diastole timing.
Figure 5: Per-frame phase RMSE (% of cycle) of the canonical template (solid blue), the group-mean oracle template (dotted green), and the uniform linear baseline (grey dashed), per ACDC pathology group and for the pooled M&Ms cohort. Shaded region: error saved by the canonical template over the linear baseline.
Figure 6: det⁡(Jφ)\det(\mathbf{J}_{\varphi}) distribution of the composed 3D displacement field (radial and scaling-and-squaring residual, K=7K=7 ) on the ACDC ++ M&Ms test set. Left : global histogram (log scale); red dashed: fold boundary ( det⁡=0\det=0 ). Right : per-group mean ±\pm std. Folding voxels are 0.0005%0.0005\% on average ( <0.002%<0.002\% per patient), indicating a low measured folding rate.
Figure 7: Spatial view of deformation regularity for a representative HCM subject (patient036, mid-ventricular slice) at six frames across the cardiac cycle. Rows: ground-truth cine, PhaseFlow3D generation, displacement magnitude ∣φ∣|\boldsymbol{\varphi}| , and Jacobian determinant det⁡(Jφ)\det(\mathbf{J}_{\boldsymbol{\varphi}}) . The deformation is localized to the myocardium; det⁡(Jφ)<1\det(\mathbf{J}_{\boldsymbol{\varphi}})<1 (blue) marks local contraction and >1>1 (red) local expansion, and it stays strictly positive everywhere, confirming a fold-free diffeomorphic mapping.
Figure 8: Qualitative comparison (MINF and NOR, mid-ventricular slice). Rows 1–3: ground truth, the VAE-decoded variant (A1), and PhaseFlow3D at ED, mid-systole, ES, and mid-diastole. Row 4: predicted displacement magnitude ∣φ∣|\boldsymbol{\varphi}| . PhaseFlow3D produces sharp, anatomically coherent frames; the VAE-decoded variant exhibits characteristic reconstruction blur.
Figure 9: Per-pixel absolute reconstruction error ∣Gen−GT∣|\mathrm{Gen}-\mathrm{GT}| for three representative subjects (rows) across six frames spanning the cardiac cycle (columns), on the mid-ventricular slice. The error stays near zero over the static background and concentrates in a thin band at the myocardial boundary, peaking around ES where motion is largest.
Figure 10: LV volume curves (% of ED volume). Ground-truth (solid) vs. PhaseFlow3D-predicted (dashed) trajectories for one representative patient per ACDC pathology group.
Figure 11: Segmentation substitution. Test Dice (LV and myocardium mean, 3-seed mean) vs. the fraction of real supervision replaced by synthetic supervision, for phase-aligned substitution (pipeline A, blue) and full-cycle substitution (pipeline B, red). Dashed lines: each pipeline’s all-real baseline. Right edge: retention, the ratio of fully synthetic to all-real Dice.
Figure 12: Classification substitution. Balanced accuracy and macro-F1 (3-seed mean ±\pm std) vs. the fraction of real geometry samples replaced by synthetic ones. Dashed line: all-real balanced accuracy; dotted line: 5-class chance. Right edge: balanced-accuracy retention.
Figure 13: Label propagation. LV Dice of the ED annotation warped to ES, per ACDC pathology group and pooled (All), for the no-motion floor, our blind single-frame propagation, and the Demons two-frame oracle that sees the real ES image. Bars: patient mean; error bars: patient std.
Figure 14: Peak-systolic GCS from the synthesized motion, by ACDC pathology group (blue) and for the pooled M&Ms cohort (grey). Bars: group mean; error bars: patient standard deviation. The Kruskal–Wallis test is computed across the five ACDC groups.
Figure 15: Perceptual realism. Left: pooled out-of-fold ROC of the real-vs-synthetic discriminator (3-seed mean, shaded band: seed std); the dotted diagonal is chance. Right: AUC by cycle third; mid-systole carries most of the residual separability.
Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

MethodImage-basedMask propagation
GAN-cMRI [ 14 ]38.68±18.0738.68\pm 18.07—
LFDM [ 26 ]29.67±15.7629.67\pm 15.76—
CVAE31.70±18.5531.70\pm 18.55—
DragNet [ 7 ]36.49±16.4336.49\pm 16.4337.73±16.8037.73\pm 16.80
SimVP [ 25 ]26.22±18.0826.22\pm 18.08—
Direct Reg29.71±17.6629.71\pm 17.66—
Appendix
Table 4: EF MAE (%, patient mean ±\pm std, n=166n{=}166 ) under the two unified measurement protocols, both referenced against the expert annotations. “—”: the method exposes no pixel-space displacement field, so mask propagation is undefined. ConvLSTM is omitted because its EF is undefined under either protocol (cf. Table 1 ). For GAN-cMRI, 3838 cases whose generated frames yield an empty LV cavity are excluded ( n=128n{=}128 ).
MetricMean ±\pm StdMedian [IQR]
Image quality
PSNR (dB)34.97±3.2434.97\pm 3.2434.6734.67 [32.66, 37.32][32.66,\,37.32]
SSIM0.927±0.0120.927\pm 0.0120.9260.926 [0.917, 0.936][0.917,\,0.936]
LPIPS0.017±0.0060.017\pm 0.0060.0150.015 [0.013, 0.021][0.013,\,0.021]
Physiological fidelity
EF MAE (%)12.85±11.0312.85\pm 11.039.499.49 [4.58, 18.41][4.58,\,18.41]
Appendix
Table 5: Per-patient dispersion of PhaseFlow3D on the joint ACDC ++ M&Ms test set ( n=166n{=}166 patients), reported as mean ±\pm standard deviation and as median with interquartile range.
QuantityTrain ( n=255n{=}255 )Val ( n=49n{=}49 )
σ\sigma of z1\mathbf{z}_{1}0.8000.794
σ\sigma of anchor Evae(xED)E_{\mathrm{vae}}(\mathbf{x}_{\mathrm{ED}})0.7980.793
σ\sigma of z1−repeatT(⋅)\mathbf{z}_{1}-\mathrm{repeat}_{T}(\cdot)0.1310.122
α/σ(z1)\alpha/\sigma(\mathbf{z}_{1})12.5%12.6%
α/σ(z1−repeatT(⋅))\alpha/\sigma(\mathbf{z}_{1}-\mathrm{repeat}_{T}(\cdot))76.6%82.1%
Appendix
Table 6: Empirical latent statistics ( σ\sigma = per-element standard deviation, averaged over patients). The two splits agree closely, indicating the latent scale is a stable property of the frozen encoder rather than a split artifact.
Figure 16: Per-pathology qualitative results (one representative patient per group). Top row : ground truth; bottom row : PhaseFlow3D synthesis. ED frame ( t=0t=0 , leftmost) is the sole model input.
Synthetic fractionPipeline APipeline B
0%0\%0.894±0.0050.894\pm 0.0050.891±0.0080.891\pm 0.008
25%25\%0.898±0.0030.898\pm 0.0030.898±0.0050.898\pm 0.005
50%50\%0.900±0.0010.900\pm 0.0010.885±0.0030.885\pm 0.003
75%75\%0.896±0.0000.896\pm 0.0000.890±0.0060.890\pm 0.006
90%90\%0.890±0.0030.890\pm 0.0030.868±0.0110.868\pm 0.011
100%100\%0.887±0.0020.887\pm 0.0020.863±0.0090.863\pm 0.009
Appendix
Table 7: Segmentation substitution: test Dice (LV and myocardium mean, 3-seed mean ±\pm std) at each synthetic supervision fraction.
Synthetic fractionBalanced accuracyMacro-F1
0%0\%0.733±0.0480.733\pm 0.0480.731±0.0520.731\pm 0.052
25%25\%0.711±0.0480.711\pm 0.0480.705±0.0520.705\pm 0.052
50%50\%0.600±0.0650.600\pm 0.0650.593±0.0670.593\pm 0.067
75%75\%0.570±0.0550.570\pm 0.0550.551±0.0640.551\pm 0.064
90%90\%0.526±0.0100.526\pm 0.0100.489±0.0090.489\pm 0.009
100%100\%0.533±0.0180.533\pm 0.0180.492±0.0210.492\pm 0.021
Appendix
Table 8: Classification substitution: five-class balanced accuracy and macro-F1 (3-seed mean ±\pm std) at each synthetic substitution fraction.
StructureNo-motion floorOurs (single-frame)Demons (oracle)
LV0.622±0.1770.622\pm 0.1770.712±0.1290.712\pm 0.1290.738±0.1380.738\pm 0.138
Myocardium0.486±0.1640.486\pm 0.1640.572±0.1210.572\pm 0.1210.700±0.0930.700\pm 0.093
Appendix
Table 9: Label propagation on the ACDC test set ( n=30n{=}30 ): Dice of the ED annotation warped to ES (patient mean ±\pm std) per structure and arm.

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