Segmentation of the aorta in 4D flow MRI using 4D convolutional kernels and learning from sparse annotations

Hinrich Rahlfs; Julio Garcia; Chiara Manini; Markus Hüllebrand; Sebastian Schmitter; Sarah Nordmeyer; Titus Kühne; Heiko Stern

cs.CVSep 3, 2026

Segmentation of the aorta in 4D flow MRI using 4D convolutional kernels and learning from sparse annotations

Authors: Hinrich Rahlfs, Julio Garcia, Chiara Manini, Markus Hüllebrand, Sebastian Schmitter, Sarah Nordmeyer, Titus Kühne, Heiko Stern,

Abstract

Automated aortic segmentation in 4D flow MRI is essential for reproducible hemodynamic assessment but is limited by scarce dense annotations and high computational demands. We developed a fully automated 4D (3D+time) U-Net for segmenting the ascending aorta, arch, and proximal descending aorta, using a parameter-efficient hybrid 4D kernel to capture temporal context and sparse 4D labels derived from existing 2D expert contours and centerlines, thereby avoiding the need for dense 4D annotations. Training comprised 268 scans from 8 centers and 2 vendors, with evaluation on an internal test set (32 scans) and an external post-contrast set (30 scans; different site, protocol, and annotator), compared against frame-wise 3D networks and two semi-automatic references. Against time-resolved annotations, the 4D U-Net achieved Dice scores of 0.927 (internal) and 0.911 (external), versus 0.919/0.847 for the 3D U-Net, 0.893 for static PC-MRA, and 0.808 for registration-based propagation; differences were small in systole but pronounced in diastole. Agreement with expert contours for peak velocity, net flow, axial and circumferential wall shear stress, and diameters was excellent (ICC >=0.954 internal, >=0.980 external), while semi-automatic references performed worse. The method thus provides reproducible, time-resolved aortic segmentation for automated hemodynamic analysis and generalizes across multicenter, multivendor, and independent post-contrast data. The model is publicly available.

Figures & tables

Figure 1: Illustrative example of the segmentation sensitivity of WSS. 4D flow MRI of a subject with bicuspid aortic valve with two segmentations of one cross-section in the ascending aorta. WSS was estimated assuming a constant blood viscosity of $3.2\text{\,}\mathrm{mPa}\text{\,}\mathrm{s}$ . A minor difference in segmentation increases the mean WSS by 25.5%.

Figure 2: Qualitative example of a propagation failure. 3D aortic segmentation and three orthogonal cross-sectional views at peak systole (left) and late systole (right). At peak systole the segmentation was performed with manual oversight, at late systole it was propagated using the Morphon algorithm [ 29 ] . Manual 2D expert annotations (red) and the contour of the 3D segmentation (white) are overlaid. The propagated segmentation underestimates the lumen in the ascending aorta and loses the circular shape in the descending aorta at late systole. See supplementary video 1 for the full cardiac cycle.

Cohort
Characteristic	Training	Test	External test
Scans, $n$	268	32	30
Age, years	$49\pm 18$	$48\pm 18$	$44\pm 16$
Female, %	41	38	40
BAV, $n$	92	13	20
Image acquisition

Table 1: Properties of the training, test, and external test set. Age and plane tilts are given as mean

\pm

standard deviation, all other continuous parameters as range (min-max). The number of annotated 2D contours corresponds to the number of annotated 2D+time cross-sections multiplied by the number of reconstructed cardiac time frames of the respective scan. BAV: bicuspid aortic valve; VENC: velocity encoding.

Figure 3: Study population in the training set, test set, and external test set.

Figure 4: Scan parameters of the training set, test set, and external test set. The FoV and reconstructed voxel size are stated in anterior-posterior (AP), left-right (LR), and superior-inferior (SI) direction.

Figure 5: Sparse cross-section annotations and label for vessel segmentation in 4D flow MRI. On the left, the velocity magnitude and the averaged PC-MRI magnitude are shown for the systolic and the end-systolic time points. The expert annotation was created for all time points and is shown in red. In the middle, the twelve cross-section positions are shown, spanning the ascending aorta, aortic arch, and proximal descending aorta. The right part illustrates a schematic of the corresponding sparse label: background (black) and lumen (gray) voxels are used to compute the loss during network training, while ignore voxels (shown in white) are excluded from the loss calculation.

Figure 6: Network architecture of the proposed 4D U-Net. The Conv4D is performed either using the hybrid kernel or the hypercube kernel. The 3D cube, which is common for 3D CNNs, is shown for reference.

Figure 7: Transformations used to evaluate automatic 4D segmentation against time-resolved 2D contours. Left: pixelated expert annotation shown within the annotation plane. Right: a single time point of the automatic 4D label with the corresponding annotation plane overlaid. A multiplanar reconstruction (MPR) is extracted along this plane for model evaluation. Trilinear interpolation with thresholding at 0.5 is applied to produce smoother label boundaries compared to nearest-neighbor interpolation.

Kernel	Temp.	Chan.	DSC	HD	ACD	Failed	$\boldsymbol{\Delta t_{\text{train}}}$	$\boldsymbol{\Delta t_{\text{inf}}}$
shape	res.			$\mathrm{mm}$	$\mathrm{mm}$	$\mathrm{\%}$	fold 0	$\mathrm{s}$
3D cube	No	$32$	$0.9157$ 0.064	$2.658$ 1.327	$0.806$ 0.582	$0.231$	07:55:56	$21.2$
hybrid	Yes	$32$	0.9251 0.054	$2.435$ 1.205	0.718 0.519	$0.154$	07:59:32	12.3
hybrid	No	$32$	$0.9236$ 0.061	$2.449$ 1.114	$0.722$ 0.499	$0.259$	08:02:42	$15.9$
hypercube	Yes	$10$	$0.9236$ 0.060	$2.440$ 1.110	$0.720$ 0.491	$0.240$	08:56:17	$15.5$
hypercube	Yes	$32$	$0.9250$ 0.054	2.423 1.133	$0.720$ 0.507	0.149	11:00:54	$17.5$

Table 2: Ablation study evaluating the impact of the convolution kernel shape, temporal resampling (Temp. res.), and the number of channels in the first network layer (Chan.), evaluated on the 5-fold cross-validation of the internal training set. Label creation is fixed to an extrusion thickness of

6\text{\,}\mathrm{mm}

and a centerline radius of

4\text{\,}\mathrm{mm}

. Values are reported as mean

\pm

standard deviation over all time points and cross-sections. Best values are in bold .

Extrusion thickness	Centerline radius	DSC	HD	ACD	Failed
$\mathrm{mm}$	$\mathrm{mm}$		$\mathrm{mm}$	$\mathrm{mm}$	$\mathrm{\%}$
$2$	$2$	$0.920$ 0.067	$2.476$ 1.120	$0.755$ 0.540	$0.311$
$2$	$4$	$0.920$ 0.063	$2.542$ 1.229	$0.762$ 0.532	$0.270$
$4$	$2$	$0.923$ 0.065	$2.426$ 1.060	$0.724$ 0.496	$0.312$
$4$	$4$	$0.923$ 0.063	$2.461$ 1.158	$0.727$ 0.500	$0.282$
$6$	$2$	$0.924$ 0.063	2.413 1.099	0.717 0.492	$0.292$

Table 3: Ablation over the sparse-annotation creation parameters: extrusion thickness of the cross-section annotation and radius of the centerline, evaluated on the 5-fold cross-validation of the internal training set with the 4D hybrid kernel and temporal resampling. Values are reported as mean

\pm

standard deviation over all time points and cross-sections. Best values are in bold .

	Method	Dyn.	Labels	Architecture	DSC	HD	ACD	Failed
						$\mathrm{mm}$	$\mathrm{mm}$	$\mathrm{\%}$
Test set	PCMRA3D	✗	—	—	$0.893$ 0.055	$4.003$ 2.479	$1.104$ 0.755	0.00
	ManReg4D	✓	—	—	—	—	—	—
	nnU3D-syn	✓	Synth. [ 33 ]	nnU-Net 3D [ 13 ]	$0.552$ 0.412	$4.376$ 2.741	$1.700$ 1.343	$34.82$
	nnU3D-syn+	✓	Synth.+ [ 33 ]	nnU-Net 3D [ 13 ]	$0.754$ 0.291	$4.284$ 2.620	$1.668$ 1.369	$11.73$
	UTR3D-sp	✓	Sparse (ours)	UNETR 3D [ 12 ]	$0.885$ 0.149	$3.029$ 1.670	$0.926$ 0.663	$2.45$

Table 4: Segmentation performance on the test set and the external test set for different volumetric aortic segmentation methods. We state whether a method produces a dynamic (4D) segmentation, which training labels were used, and which network architecture was employed. Values are reported as mean

\pm

standard deviation over all time points and cross-sections. Best values per test set are in bold .

Figure 8: Comparison of 3D U-Net and 4D U-Net with hybrid kernel and hypercube kernel for different cardiac phases. The graphs show the Dice similarity coefficient (DSC) over time, evaluated using 5-fold cross-validation on the internal training set. The solid line shows the mean DSC, and the dashed lines represent the 5th and 95th percentiles. Below, the 3D U-Net and the 4D U-Net are shown for a cross-section in the A3.1 plane at end diastole ( $t=0$ $\mathrm{ms}$ ), systole, and late diastole; for the time-resolved 3D segmentation and all time points see supplementary video 2.

Parameter	Unit	Method	Bias	$1.96\sigma$	ICC (95 % CI)	Bias	$1.96\sigma$	ICC (95 % CI)
			Test set			External test set
$v_{\max}$	$\frac{\mathrm{m}}{\mathrm{s}}$	nnU4D-sp	0.009	0.130	0.991 (0.99-0.99)	0.000	0.000	1.000 (1.00-1.00)
		nnU3D-sp	0.009	$0.133$	0.991 (0.99-0.99)	0.000	0.000	1.000 (1.00-1.00)
		PCMRA3D	$-0.065$	$0.502$	0.881 (0.85-0.91)	–	–	–
		ManReg4D	–	–	–	$0.003$	$0.031$	0.999 (0.998-1.00)
Net Flow	mL	nnU4D-sp	$0.53$	$7.25$	0.985 (0.98-0.99)	$0.91$	7.42	0.990 (0.99-0.99)

Table 5: Agreement of the extracted quantitative parameters with the expert annotation on the test set and the external test set. Lowest absolute bias, lowest

1.96\sigma

, and highest ICC(2,1) (95 % CI) per parameter within each test set are highlighted in bold. “–” indicates that a method was not applicable to that set. Only the three methods with the lowest failure rate of the respective test set are included, and all values are computed on the cross-sections that were successfully segmented by all included methods.

Figure 9: Qualitative evaluation on the test set. The cases with the lowest and the median DSC are shown. For each case, the 3D segmentation at the systolic time point and at the time point with the lowest DSC are displayed. The expert annotation is overlaid on the automatic segmentation in the ascending aorta, aortic arch, and descending aorta. Supplementary videos 3-5 for these cases and for the 25th DSC percentile case are provided and additionally show the results of the comparison methods.

Figure 10: Qualitative evaluation on the external test set. The cases with the lowest and the median DSC are shown. For each case, the 3D segmentation at the systolic time point and at the time point with the lowest DSC are displayed. The expert annotation is overlaid on the automatic segmentation in the ascending aorta, aortic arch, and descending aorta. Supplementary videos 6-8 for these cases and for the 25th DSC percentile case are provided and additionally show the results of the comparison methods.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

		Performance				Runtime ( $\mathrm{s}$ / case)			Localization ( $\mathrm{\%}$ )
	Crop	DSC	HD	ACD	Failed	ROI	4D	Total	Under-	Over-
			$\mathrm{mm}$	$\mathrm{mm}$	$\mathrm{\%}$	steps	seg.		crop	crop
Test set	✗	$0.921$	$2.623$	$0.793$	$0.00$	–	$40.81$	$40.81$	–	–
Test set	✓	0.927	2.460	0.723	$0.00$	$6.09$	12.29	18.38	$0.00$	$0.00$
Ext. test set	✗	$0.894$	$3.175$	$0.955$	$1.25$	–	$113.37$	$113.37$	–	–
Ext. test set	✓	0.911	2.630	0.757	0.73	$8.44$	38.55	46.99	$0.00$	$36.67$

Appendix

Table 6: Post-hoc evaluation of the ROI cropping (bounding box of the 3D time-averaged segmentation with a

5

-voxel margin) on the test set and the external test set. The cropping was fixed before any test-set evaluation. The comparison against processing the full field of view was performed post-hoc and was not used for any model or parameter selection. Runtimes are given per case. Best values per test set are in bold .

DSC	HD95 [mm]	ASD [mm]
$0.904\pm 0.069$	$7.56\pm 8.48$	$1.45\pm 1.34$

Appendix

Table 7: Performance of the 3D localization nnU-Net on the time-averaged PC-MRA, evaluated against the manual PC-MRA segmentations in the subject-wise five-fold cross-validation of the internal training set (all folds combined,

n=268

scans). Values are mean

\pm

standard deviation over scans and are computed in the original image geometry. DSC: Dice similarity coefficient; HD95: 95th-percentile Hausdorff distance; ASD: average surface distance.

Step	Search axis	Temp. res.	Chan.	DSC	HD	ACD	Failed
	configuration				$\mathrm{mm}$	$\mathrm{mm}$	$\mathrm{\%}$
1	$3\!\times\!3\!\times\!3$ (3D)	No	$32$	$0.9136$ 0.068	$2.702$ 1.395	$0.826$ 0.601	$0.270$
	$3\!+\!3\!\times\!3\!\times\!3$ (hybrid)	Yes	$32$	$0.9230$ 0.063	$2.461$ 1.158	$0.727$ 0.500	$0.282$
	$3\!+\!3\!\times\!3\!\times\!3$ (hybrid)	No	$32$	$0.9229$ 0.060	$2.472$ 1.140	$0.730$ 0.510	$0.240$
	$3\!\times\!3\!\times\!3\!\times\!3$ (hypercube)	Yes	$10$	$0.9228$ 0.059	$2.465$ 1.120	$0.729$ 0.503	$0.235$
	$\boldsymbol{3\!\times\!3\!\times\!3\!\times\!3}$ (hypercube)	Yes	32	0.9236 0.058	2.444 1.165	0.731 0.509	0.207

Appendix

Table 8: All four steps of the coordinate-descent selection of model configuration and sparse-label parameters. All values were obtained on the subject-wise 5-fold cross-validation of the internal training set and are reported as mean

\pm

standard deviation over all

90354

annotated 2D contours (

2954

cross-sections

\times

the number of reconstructed time frames of the respective scan). The configuration selected in each step is in bold . Step 1 was performed with

\text{et}=

4\text{,}\mathrm{mm}

and $\text{cr}=$4\text{\,}\mathrm{mm}

, step 2 with the hypercube kernel, 32 channels and temporal resampling, step 3 with

\text{et}=

6\text{,}\mathrm{mm}

and $\text{cr}=$4\text{\,}\mathrm{mm}

, and step 4 with the hybrid kernel, 32 channels and temporal resampling. In step 4 the label configuration selected in step 2 was re-selected, i.e. the coordinate descent converged.

Metric pair	Bias	95 % LoA	ICC(2,1) [95 % CI]	Pearson $r$	Spearman $\rho$
$\text{mean}(\text{DSC}_{\text{2Dt}})$ vs. $\text{DSC}_{\text{4D}}$	$0.012$	$[-0.048,0.072]$	$0.985$ [ $0.97$ , $0.99$ ]	$0.986$	$0.848$
$\text{mean}(\text{ACD}_{\text{2Dt}})$ vs. $\text{ASD}_{\text{4D}}$	$-0.153$	$[-0.869,0.562]$	$0.741$ [ $0.53$ , $0.86$ ]	$0.785$	$0.803$
$\max(\text{HD}_{\text{2Dt}})$ vs. $\text{HD95}_{\text{4D}}$	$-7.06$	$[-62.27,48.15]$	$0.156$ [ $-0.16$ , $0.45$ ]	$0.398$	$0.780$

Appendix

Table 9: Agreement between case-wise 2D+time cross-sectional and 4D volumetric evaluation metrics, assessed on

n=36

automatic segmentations (6 methods

\times

6 cases). Bias and limits of agreement (LoA) are reported as

\text{metric}_{\text{2Dt}}-\text{metric}_{\text{4D}}

Figure 11: Agreement between case-wise 2D+time cross-sectional and 4D volumetric evaluation metrics, assessed on $n=36$ automatic segmentations (6 methods $\times$ 6 cases of the internal test set for which a 4D expert annotation was available). Colors indicate the segmentation method (see legend). The six cases were deliberately selected to span the full range of segmentation quality and are therefore not representative.

Figure 12: Dice similarity coefficient (DSC) of the proposed 4D U-Net over the cardiac cycle, stratified by dataset characteristics. The solid line shows the mean DSC and the dashed lines the 5th and 95th percentiles.

Figure 13: Bland-Altman analysis of the quantitative parameters on the test set. Colors indicate valve configuration (see legend). The solid and dashed lines mark the bias and the $\pm 1.96$ standard deviations of the differences of the proposed nnU4D-sp. Each point corresponds to one annotated 2D+time cross-section. Only the three methods with the lowest failure rate of the respective test set are shown, and all values are computed on the cross-sections that were successfully segmented by all shown methods.

Figure 14: Bland-Altman analysis of the quantitative parameters on the external test set. Plot layout, parameters, and inclusion criteria are identical to Figure 13 . Note that $v_{\max}$ is identical for the compared methods in most cross-sections, because the location of the peak through-plane velocity lies well inside the lumen and is therefore insensitive to the boundary differences between the segmentations.

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Magnetic Resonance Imaging Cardiac MRI Image Denoising

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This work introduces an unsupervised Divergence and Aliasing-Free neural network (DAF-FlowNet) for 4D Flow Magnetic Resonance Imaging (4D Flow MRI) that jointly enhances noisy velocity fields and corrects phase wrapping artifacts. DAF-FlowNet parameterizes velocities as the curl of a vector potential, enforcing mass conservation by construction and avoiding explicit divergence-penalty tuning. A cosine data-consistency loss enables simultaneous denoising and unwrapping from wrapped phase images. On synthetic aortic 4D Flow MRI generated from computational fluid dynamics, DAF-FlowNet achieved lower errors than existing techniques (up to 11% lower velocity normalized root mean square error, 11% lower directional error, and 44% lower divergence relative to the best-performing alternative across noise levels), with robustness to moderate segmentation perturbations. For unwrapping, at peak velocity/velocity-encoding ratios of 1.4 and 2.1, DAF-FlowNet achieved 0.18% and 5.2% residual wrapped voxels, representing reductions of 72% and 18% relative to the best alternative method, respectively. In scenarios with both noise and aliasing, the proposed single-stage formulation outperformed a state-of-the-art sequential pipeline (up to 15% lower velocity normalized root mean square error, 11% lower directional error, and 28% lower divergence). Across 10 hypertrophic cardiomyopathy patient datasets, DAF-FlowNet preserved fine-scale flow features, corrected aliased regions, and improved internal flow consistency, as indicated by reduced inter-plane flow bias in aortic and pulmonary mass-conservation analyses recommended by the 4D Flow MRI consensus guidelines. These results support DAF-FlowNet as a framework that unifies velocity enhancement and phase unwrapping to improve the reliability of cardiovascular 4D Flow MRI.

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