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Abstract
Ultrasound microvascular vector flow imaging (VFI) is essential for analyzing microvascular hemodynamics. Existing methods typically utilize angular-wise Doppler velocities combined with the least-squares (LS) optimization to estimate the vector flow field. However, the effectiveness of LS-VFI is limited due to the intrinsic instability of LS in multi-angle ultrafast beamforming. Motivated by the characteristics of microvasculature, this paper summarizes two fundamental assumptions for microvascular blood flow and proposes a novel method for microvascular vector flow imaging. Our method leverages the morphological features and angular-wise Doppler velocities to estimate the direction vector field. Then our method recovers the microvascular vector flow field by backprojecting the Doppler velocities onto the direction vector field. Particularly, the estimation of the direction vector field employs a layer-wise peeling on the microvascular networks, like peeling an onion. The backprojection is realized via a weighted global optimization. Extensive 2D and 3D experiments demonstrate that our method resolves the vector flow fields that better align with the microvascular networks compared to LS-VFI. Notably, our method achieves improvements in flow rates of approximately 3.2% to 38.4% in the Doppler phantom experiments.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/0989_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{FeiZet_Peeling_MICCAI2026,
author = { Fei, Zetao AND Ye, Chuling AND Wang, Liansheng AND Chen, Yinran},
title = { { Peeling an Onion: Layer-Wise Doppler-Backprojected Ultrasound Microvascular Vector Flow Imaging } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16888},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The authors propose a novel method for microvascular vector flow imaging. Their approach applies a layer-wise peeling strategy to microvascular networks, integrating morphological features with angular Doppler velocity information to estimate the flow direction vector field. The method is evaluated on both 2D and 3D phantom datasets, as well as on in vivo liver data, and shows promising performance.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The two fundamental assumptions underlying microvascular blood flow are physiologically plausible.
The layer-wise peeling scheme, inspired by the process of peeling an onion, performs well and demonstrates improved results compared to existing methods in both in silico and in vivo experiments.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
The method description focuses on vessels with a uniform diameter. It is unclear how the method can be applied to vessels with varying diameters.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
- In Section 2.1, the mask image is obtained using a threshold of 15 dB. How was this threshold selected?
- Could you provide more details on how the method is implemented for vessels with varying diameters?
- In the caption of Fig. 2, the value is reported as “1.17 ml/s,” which does not match the “1.67 ml/s” stated in the main text. Please clarify this discrepancy.
- In Table 1, the Direction nRMSE values for the proposed method appear to be identical across different setups. Is this correct?
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper is well organized and effectively highlights the novelty of the proposed method, and the experimental design is sound. However, the implementation of the method for vessels with varying diameters or branching structures remains unclear.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The authors have successfully clarified the mask generation process and the algorithm’s adaptability.
Review #2
- Please describe the contribution of the paper
This paper proposes a new method for ultrasound microvascular vector flow imaging (VFI) that leverages vessel morphology and angular-wise Doppler velocities. The method is built on two assumptions about microvascular flow: (1) flow direction aligns with the vessel axis, and (2) flow exhibits spatial continuity within branches. The technical contributions include a Hessian-based direction estimator (HDE) applied at vessel boundaries, a layer-wise peeling strategy that alternates centripetal edge and centrifugal centerline paths to estimate direction vectors throughout the vessel interior, and a weighted global optimization for backprojecting Doppler velocities onto the estimated direction field. The method is validated in 2D Doppler phantom experiments, in-vivo liver imaging, and 3D simulated helical flow phantoms, showing improvements over least-squares VFI (LS-VFI).
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.The two fundamental assumptions are well-justified by microvascular hemodynamics (low Reynolds number, viscous-dominated laminar flow). The idea of leveraging vessel morphology, information that is already available from power Doppler imaging, to constrain the direction field is sensible and elegant. This represents a departure from purely algebraic LS-VFI approaches by incorporating geometric prior knowledge. 2.The dual-path peeling scheme is a clever engineering solution to the problem of estimating direction vectors in the vessel interior. By combining boundary-derived Hessian information with centerline-derived skeleton information, the method achieves robust coverage of the entire vascular cross-section. 3.The confidence-weighted backprojection addresses a real practical problem, the numerical instability of direct Doppler-to-velocity inversion near orthogonal beam-flow angles. The weighting scheme gracefully suppresses unreliable projections while preserving spatial continuity. 4.The paper evaluates in 2D phantom, 2D in-vivo, and 3D simulation settings, demonstrating the versatility of the approach. The 3D helical flow phantom results are particularly compelling, with dramatic improvements in azimuthal angle estimation (nRMSE from 23.21% to 0.76%).
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.While Assumptions 1 and 2 are reasonable for straight or gently curved microvessels, their validity at bifurcations, confluences, and regions with recirculation zones is questionable. The paper briefly acknowledges that secondary flows are negligible at microvascular scale, but does not experimentally validate this claim. The in-vivo liver results show bifurcations, but no quantitative assessment is provided for these specific regions. A dedicated analysis of performance at branch points would be valuable. 2.The entire method depends on a high-quality binary mask derived from power Doppler with a 15 dB threshold. In practice, microvascular segmentation from power Doppler is noisy and threshold-dependent. The paper mentions “morphological filtering and image optimization (e.g., Gaussian smoothing)” but provides no details on these steps. The sensitivity of the overall VFI accuracy to segmentation quality is not analyzed. What happens when vessels are partially occluded, when small vessels are missed, or when noise creates false vessel detections? 3.The in-vivo liver experiment provides only qualitative comparisons. While it is understood that ground truth is unavailable for in-vivo cases, the authors could have provided quantitative metrics such as flow profile smoothness, angular consistency along vessel segments, or conservation of mass at bifurcations. Without any quantitative measure, the claim that the method “better aligns with the morphology” remains subjective. 4.The method is compared only against LS-VFI. While LS-VFI is indeed the standard baseline, recent learning-based approaches for vector flow estimation exist and could provide additional context. Furthermore, no comparison is made against model-based regularization strategies that also exploit vessel geometry but through different formulations (e.g., divergence-free constraints, Stokes flow priors). 5.The parameter ε in Eq. 8 is described as “empirically determined within [0, 0.1],” but no sensitivity analysis is provided. Given that this parameter controls the trade-off between stability and fidelity near orthogonal flow-beam angles, its impact on the results should be documented.
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not mention open access to source code or data, but provides a clear and detailed description of the algorithm to ensure reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
N/A
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(4) Weak Accept — marginally above the acceptance threshold, but would not mind if rejected, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper presents a creative and physically motivated approach to microvascular VFI that effectively integrates geometric priors from vessel morphology with Doppler velocity measurements. The layer-wise peeling strategy and weighted global optimization are technically sound contributions. The 3D simulation results are particularly impressive. However, the evaluation has notable gaps: no quantitative metrics for in-vivo data, limited comparison scope (LS-VFI only), idealized phantom geometries, and unanalyzed sensitivity to segmentation quality and key parameters. The method’s practical utility hinges on assumptions and preprocessing steps whose robustness in realistic clinical scenarios is not demonstrated. A rebuttal addressing the segmentation sensitivity and providing quantitative in-vivo metrics would strengthen the case for acceptance.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Accept
- [Post rebuttal] Please justify your final decision from above.
The rebuttal partially addresses the major concerns. The new mass conservation measurement at the Y-bifurcation (4.26% vs. 14.88% for LS-VFI) is the most meaningful addition and provides quantitative in-vivo evidence that was missing from the manuscript, though it remains a single measurement at a single bifurcation. The explanation of ε-insensitivity in (0, 0.2] and the condition number argument (15.38 in 2D, 69.73 in 3D) clarifying the core advantage over LS-VFI are helpful and should have appeared in the paper. The justification for limited baselines (model-based methods require elaborate adaptation, learning-based methods lack training data for contrast-free microvascular VFI) is understandable, though this remains a limitation. The reference-based argument for Assumption 2 is acceptable but experimental validation at bifurcations would have been stronger. The direction nRMSE truncation explanation is satisfactory. Overall, the rebuttal demonstrates the authors understand the concerns and provide reasonable responses. I maintain my score of 4 (Weak Accept), as the method’s core contribution (bypassing the LS condition number problem via morphological priors) is sound, the 3D results are strong, and the remaining limitations are acknowledged rather than deflected.
Review #3
- Please describe the contribution of the paper
The primary contribution of this paper is the proposal of a novel ultrasound microvascular vector flow imaging (VFI) method that leverages both the morphological features of microvessels and angular-wise Doppler velocities. Specifically, the authors introduce: a layer-wise peeling strategy that iteratively peels the microvascular network from the edges toward the centerlines to estimate the direction vector field of blood flow; a Hessian-based direction estimation (HDE) method applied within each peeled layer to determine blood flow direction candidates, which are then resolved using Doppler velocities to eliminate directional ambiguity; and a weighted global optimization framework designed to backproject the multi-angle Doppler velocities onto the estimated direction vector field, thereby recovering a complete and accurate microvascular vector flow field.
- Please list the major strengths of the paper: you should highlight a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
1.By utilizing the fundamental assumption that microvascular blood flow aligns with the vessel’s local geometric tangent, the method successfully overcomes the intrinsic instability and inaccuracies of traditionalmethods. 2.The authors tested their method across multiple scenarios, including 2D controlled-flow phantom experiments, an in-vivo human liver scan, and 3D helical flow phantom simulations. 3.The experimental results demonstrates clear numerical superiority over the LS-VFI baseline, improving flow rate accuracy by approximately 3.2% to 38.4% in phantom experiments.
- Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.
1.The algorithm requires the initial morphology to be extracted from power Doppler images using a fixed 15 dB threshold. If the initial mask is fragmented or inaccurate due to high noise, weak signals or split-vassel , the subsequent “layer-wise peeling” process could fail or propagate errors. 2.The entire methodology relies heavily on the assumption that blood flow is uniformly aligned with the vessel axis and exhibits spatial continuity. This assumption may not always be valid under conditions such as complex bifurcations, local disturbances, pathological flow, or out-of-plane motion. 3.The baseline for comparison is limited, the authors only compare with LS-VFI, making it difficult to demonstrate that their method is truly superior across a broader range of microvascular flow estimation tasks. Additionally, the experimental results lack statistical analysis, particularly involving multi-subject in-vivo statistics. 4.The authors describe their innovations with excessive confidence, which may lead readers to believe that they have completely overcome the limitations of LS-VFI. In fact, the final recovery step remains a weighted least-squares type optimization. A more accurate description would be that the introduction of morphological priors makes the solution more stable.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.
The submission does not provide sufficient information for reproducibility.
- Based on your review and your understanding of the MICCAI Scientific Code of Ethics, do you believe this submission may involve a potential ethics concern or violation?
N/A
- Optional: If you have any additional comments to share with the authors, please provide them here. Please also refer to our Reviewer’s guide on what makes a good review and pay specific attention to the different assessment criteria for the different paper categories: https://conferences.miccai.org/2026/en/REVIEWER-GUIDELINES.html
1.Some results in Table 1 appear slightly questionable. For example, under four different flow rates, the authors’ method gives direction estimates of approximately 27.2 ± 0.7° in almost all cases, and the corresponding directional nRMSE values are also nearly identical. This might be because the geometric direction is inherently a fixed 30° , but it also indicates a stable systematic bias, and the authors do not explain why the estimates are not closer to 30°.
- Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making.
(3) Weak Reject — marginally below the acceptance threshold, but would not mind if accepted, dependent on rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The innovative use of vascular morphology to guide velocity estimation is brilliant and yields excellent results, heavily outweighing the limitations regarding parameter tuning and limited clinical data. The proposed method is effective and has been validated across multiple different experiments. The paper conveys the general idea, but many implementation details remain unclear, such as the specifics of centerline extraction, inter-layer stopping criteria, and morphological operation settings. The validation on in-vivo data is simplistic, and some experimental results still raise confusions.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
Reject
- [Post rebuttal] Please justify your final decision from above.
I thank the authors for their rebuttal. The response has addressed my main questions, and I am satisfied with the clarifications regarding my concerns. I still view the paper as a borderline but acceptable contribution.
Author Feedback
We thank all the reviewers for their valuable comments and for recognizing the novelty of our paper. Our feedback is as follows. Q1: Sensitivity of the masks. (R1, R2, R3) A: We admit that the microvascular mask is important for the success of our method. If vessels are occluded or missed, the Doppler signals are absent, then no VFI method can work. Otherwise, our method performs well given the high sensitivity of current PDI methods. The 15 dB threshold was used based on PDI results and visual inspection. For improvement, Doppler variances could be combined with power Doppler for mask generation because noise-induced masks yield much higher variances than blood flow signals. Q2: Feasibility of Assumption 2.(R2, R3) A: Since conducting complex flow phantom experiments is non-trivial, we refer to Refs. [9, 10, 21] to support Assumption 2.In particular, Ref. [21] states that “the flow structure is still dominated by a Poiseuille flow without a secondary flow” in microvascular cases. The microvascular pathological flow mainly exhibits variations in flow rate, velocity gradient, and/or wall shear stress, rather than the flow patterns. Therefore, the assumption remains valid even in complex cases. Q3: Limited comparison. (R2, R3) A: Currently, we only use LS-VFI for comparison because (i) model-based methods are mainly applied to large-scale and fast ventricle flows, whereas their adaptation to microvascular imaging requires elaborate modification, and (ii) learning-based methods require massive datasets for training and testing. Moreover, the learning-based method for contrast-free microvascular VFI is currently missing. Q4: In-vivo quantification. (R2, R3) A: We follow the comments of the reviewers and calculated the mass conservation at a Y-bifurcation reported in Fig. 3.Our method has a flow conservation error of 4.26%, which is lower than that of LS-VFI (14.88%). Statistical analysis on multiple subjects/organs is our future focus. Q5: Parameter details. (R2, R3) A: Parameter ε in (0, 0.1] corresponds to an unreliable beam-flow angles of [84°, 90°]. We empirically determined the value of ε since our method is insensitive to ε in the range of (0, 0.2] according to the experiments. The centerline extraction and morphology/image optimization were applied with built-in MATLAB functions with default settings. For example, the sigma σ of the Gaussian kernel was 0.55, whereas the erosion/dilation used a disk with a 1-pixel radius. Q6: Identical nRMSE of directions. (R1, R3) A: Our direction estimates (Tab. 1) appear identical because our method resolves very similar masks at various flow rates. The differences (e.g., 27.2069° at 1.67 ml/s vs. 27.2131° at 1.17 ml/s) were truncated to one decimal place. The gap between 27.2° and 30° is due to the local operation of the Hessian estimator (a Gaussian convolution kernel with σ = 1) under a pixel size of half-wavelength. Q7: Innovations description. (R3) A: We agree that our method cannot overcome all limitations of LS-VFI, e.g., the Doppler variances still impact the vector flow fields. However, our method overcomes the most intrinsic limitation of LS-VFI, i.e., the high condition number of the LS model under small-angle transmit plane waves. In the 2D (3D) experiments, the LS condition number is 15.38 (69.73), meaning that 1% Doppler perturbation causes at least 15.38% (69.73%) vector errors. Our method bypasses this limitation through the morphological prior. The weighted global optimization is not related to LS-VFI, but rather to reducing the “divide-by-zero” risk of backprojection. Q8: Vessel diameter variation. (R1) A: Our method can handle varying-diameter vessels. The peeling scheme is adaptive, and the procedure will not stop until the mask is fully covered (see Fig. 1). The varying vessel diameters in the in-vivo case validated the feasibility of this scheme. Q9: Caption error of Fig. 2.(R1) A: We thank the reviewer for pointing out this error. It should be 1.67 ml/s.
Meta-Review
Meta-review #1
- Your recommendation
Invite for Rebuttal
- Please justify your decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
Please provide justifications and clarifications for the concerns raised by the reviewers.
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This paper proposes a microvascular vector flow imaging method that integrates vessel morphology with angular Doppler velocities via a layer-wise peeling strategy.
Reviewers broadly agree that the core idea is novel and well-motivated, combining vessel morphology with Doppler velocity as a principled alternative to purely algebraic LS-VFI is elegant and grounded in physiologically plausible assumptions. The 3D helical flow results are particularly compelling, and the multi-scenario validation across 2D phantom, in-vivo liver, and 3D simulation settings demonstrates the versatility of the approach.
The shared concerns are the limited baseline comparison, the lack of in-vivo quantification, and sensitivity to segmentation quality. The rebuttal provides a meaningful addition, a mass conservation measurement at a Y-bifurcation showing 4.26% error vs 14.88% for LS-VFI, which partially addresses the in-vivo quantification concern. The justification for limited baselines is reasonable given the lack of training data for learning-based microvascular VFI and the difficulty of adapting model-based methods. The sensitivity to segmentation quality and the validity of the core assumptions at complex bifurcations remain incompletely addressed.
The core contribution is sound and the results are convincing. I recommend acceptance.
Meta-review #2
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
Although the paper remains somewhat borderline and has limitations regarding limited bifurcation validation, restricted baselines, and the need for clearer numerical precision in the final manuscript, the rebuttal provides meaningful quantitative evidence, clarifies the method’s core advantage over LS-VFI, and supports the soundness of the main contribution. Therefore, the AC recommends acceptance.
Meta-review #3
- After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.
Accept
- Please justify your recommendation.
This is a borderline paper, with 2 accept and 1 reject, yet, the reviewer recommending rejection also mentioned that their concerns are resolved after reading rebutaal and they would not mind if this paper gets accepted, given its current merit. I read the paper and think it meets the publishing bar at MICCAI, therefore I recommend accept.