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Abstract
Ischemic stroke is a leading cause of death and disability, in which rapid restoration of blood flow is critical to patient outcome. During embolization, the lodging location of the occluding clot within the cerebral vasculature strongly influences treatment difficulty, as clot stiffness, deformability, and vessel anatomy determine the clot retrievability during endovascular thrombectomy. High-fidelity finite-element method (FEM) simulations can simulate embolization, but their computational cost makes them impractical for real-time clinical use. We propose a fast and data-efficient meshless neural surrogate for simulating Lagrangian embolization dynamics. Our model predicts particle acceleration updates using SE(3)-equivariant neural fields, allowing training from sparsely sampled high-resolution simulations while supporting inference at full spatial resolution. By combining neural dynamics with rotation and translation equivariance, the surrogate generalizes across patient-specific vascular geometries using only 20 training simulations. On held-out test simulations, our approach achieves stable rollouts with a median error of 1.76 mm (Q1–Q3: 0.93–2.82), a median lodging error of 1.27 mm (0.77–1.42), corresponding to a median relative localization error of 1.8%, and a 200–400× speedup over FEM simulations, demonstrating both the accuracy and efficiency of our approach.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/2462_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: https://papers.miccai.org/miccai-2026/supp/2462_supp.zip
Link to the Code Repository
https://github.com/ThijsKuipers1995/neural_clot_sim
Link to the Dataset(s)
N/A
BibTex
@InProceedings{KuiThi_Fast_MICCAI2026,
author = { Kuipers, Thijs P. AND Mojtahedi, Mahsa AND den Haan, Emiel D. AND Konduri, Praneeta R. AND Marquering, Henk A. AND Bekkers, Erik J.},
title = { { Fast Few-Shot Embolization Simulations in Ischemic Stroke Using Equivariant Neural Fields } },
booktitle = {Medical Image Computing and Computer Assisted Intervention -- MICCAI 2026},
year = {2026},
publisher = {Springer Nature Switzerland},
volume = {LNCS 16893},
month = {September},
page = {pending}
}
Reviews
Review #1
- Please describe the contribution of the paper
The authors proposed a surrogate model to simulate the embolization process of clots causing stroke.
- 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 authors used an SE(3)-equivariant representation to train a model to predict the Lagragian motion of the clot. To the reviewer’s knowledge, adaption of this method to simulate clot motion has not been reported before. Clot motion in the vessel undergoes complex forces including hemodynamics, vessel wall friction, and its intrinsic deformation, especially at bifurcations or going from large lumens to small lumens. Traditional FEM methods, such as the Abaqus model used in this manuscript, are well known to be time-consuming and can suffer from numerical instability. The method proposed, although assuming a rigid body motion of the clot, can serve as a potentially useful tool for future clot motion studies.
- 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) oversimplified boundary conditions. The authors assume a constant pressure of 0.002 MPa. This is not commonly seen in the literature; researchers typically use inlet-outlet pressure difference (such as Mirakhorli, F. , Vahidi, B. , Pazouki, M. et al. A Fluid-Structure Interaction Analysis of Blood Clot Motion in a Branch of Pulmonary Arteries. Cardiovasc Eng Tech 14, 79–91 (2023). ), or flow rate boundary conditions as these numbers can be easily measured and verified in the clinical field. Justification of this setting is needed. In addition, friction was also neglected in this study. 2) insufficient validation. Given the aforementioned oversimplification of the physics, the proposed Abaqus models can not be treated as “ground truth”. Validation against phantom experiments should be provided. In addition, human vascular anatomy, especially the neurovasculature, notably has extreme variability in tortuosity. A 10-case test set is statistically insufficient to claim generalizability or robustness of the proposed method. 3) lack of elaboration on collision dynamics. The authors noted that baseline models suffered from “clipping”, they did not provide a rigorous mathematical proof or a loss-term analysis of how their model prevents this. 4) minimum contribution to clinical practice. First, in real-world stoke cases, clots usually formed in other places (heart or carotid) without prior knowledge on its actual location, size and shape since the patients are often without any symptoms. Therefore, it’s unrealistic to apply modeling to “predict” the embolization process. Second, knowing how the clot embolized does no help or has no effect on changing the stoke management workflow. Clinicians use angiography to pinpoint the embolized clot and conduct thrombectomy. That is the gold standard, and no clinicians will seek help from any models to “find” the embolized clot. The reviewer recommends reading the latest clinical guideline (2026 Guideline for the Early Management of Patients With Acute Ischemic Stroke: A Guideline From the American Heart Association/American Stroke Association).
- 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
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.
(2) Reject — should be rejected, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
As stated above, the authors should be congratulated on developing a surrogate model to predict clot motion in a fairly quick and (debatably) accurate manner; however, the problem formulation is not realistic, and the result does not address any clinical needs or offer a path to improved interventional outcomes.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #2
- Please describe the contribution of the paper
A method is proposed to simulate the progression of a clot in blood vessels during an ischemic stroke event. The blood vessels are assumed to be rigid, which makes this method applicable to the neuro cases. A Lagrangian approach is followed where a neural network is trained to infer the velocity of query points. An neural network architecture is described to be equivariant to rigid transforms by transforming coordinate vector features by all rotations in a platonic subgroup (tetrahedral group in practice), and designing an equivariant kernelized cross-attention operator to encode the current, input state. The method was compared with FEM simulations in Abaqus on complex cerebral vessel geometries, as well as out of domain geometries to demonstrate generalizability. The method is compared with two state of the art methods.
- 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.
- easy to read, illustrations and videos in supplementary materials are informative
- the method is original as far as I know, and efficient. It leverages recent and relevant techniques.
- experiments are performed against ground truth FEM and compare with two SOTA methods. Dispersion measures are provided. Full rigid equivariance is assessed compared to simple translation invariance. Complex and realistic geometries are used.
- the approach could be generalized to other Lagrangian simulation with rigid contacts
- 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.
- some details are missing and no code is announced. Reproducibility is not warranted.
- it seems only one set of mechanical parameters were used for the clot. Other settings would have been interesting
- the pressure field seems independent of the clot progress, whereas the clot should influence it. It is unclear how this field is managed.
- 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
- details on the diversity of cerebral vessel geometries would be appreciated. Reference 1 is anonymous and should have been attached to the submission
- some more ablation would have been interesting, especially on M, the number of downsampled points
Minor comments:
- p. 3, caption of figure 1: furthest is used, and farthest elsewhere
- p.4, paragraph starting with “Importantly”: kernalized -> kernelized; This weight-sharing constraints -> constrains; Eq. 5 reduces to the self-attention -> to self-attention
- p.8, second paragraph of the discussion: low per-step errors on both the simple tube. -> no both
- 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.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The method is original and timely. Though it is applied to clot simulation, the general method can be generalized to the simulation of a moving soft object in a rigid vasculature. Experimentations are rather well designed. More settings, closer to the clinic, would be appreciated, though determining boundary conditions is always a complicated.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Review #3
- Please describe the contribution of the paper
The authors propose a neural surrogate for simulating blood clot dynamics which is based on cross-attention. The model is SE(3)-equivariant by the use of the Platonic transformer formalism. The proposed approach is validated on two datasets of realistic vessels and idealised tubes, respectively. The authors find that their model achieves improved lodging error over two baselines.
- 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 proposed method is well developed and well explained. The work represents an impressive amount of work considering the finite element simulations and model ablations. Cross-validation alleviates the small dataset size and the out-of-domain evaluation makes for an important stress test of the method.
- 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.
A figure of the idealised, synthetic dataset would have been nice. The authors do not mention if they plan on publishing the datasets and / or their implementation. For my understanding, the title of the manuscript does not map to the content.
- 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
- Fig. 1: Consider annotating in the cross-attention blocks which input are the keys / values and which one are the queries for additional clarity.
- Complex Vessel Dataset: Is Abaqus the simulation software? If yes please make this clear, e.g., by citing a reference.
- 2.3 SE(3)-Equivariant Neural Dynamics:
- Out of curiosity, have you considered using geometric algebra transformers (GATr)? If yes, what were the reasons you went with the option you chose?
- Are the equivariant linear projections $\phi_q$ and $\phi_c$ learnable? Please clarify.
- In (6) does RoPE break SO(3) equivariance? What happens if X is rotated in 3D?
- There is a typo in “weight-sharing constraints the operator” (“constrains”).
- Decoder and Implicit Neural Dynamics: Even though it might be too late at this point, consider reformulating “implicit neural representation”. What exactly is implicit here? If I understand correctly, the network enables zero-shot super-resolution, as is common in neural operators. Some authors refer to this as possessing the “neural field property”.
- 4 Discussion and Conclusion: “[…] low per-step errors on both the simple tube.”
- 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.
(5) Accept — should be accepted, independent of rebuttal
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed method is well developed and well explained. The work represents an impressive amount of work considering the finite element simulations and model ablations. Cross-validation alleviates the small dataset size and the out-of-domain evaluation makes for an important stress test of the method.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the authors’ rebuttal, please state your final opinion of the paper.
N/A
- [Post rebuttal] Please justify your final decision from above.
N/A
Author Feedback
We thank all the reviewers for their time and feedback.
Clinical relevance (R1): We agree that embolization simulation in isolation has limited direct clinical utility. We note that our goal is not to predict or localize the clot for diagnosis per se, which we agree is the role of angiography. Rather, accurate embolization is a necessary component of full in-silico thrombectomy treatment models, establishing initial conditions for clot retrieval simulation and patient-specific digital twins. We acknowledge this motivation is present in the introduction but not made sufficiently explicit. The paper is an early proof of concept wherethe core contribution is an efficient neural surrogate capturing embolization dynamics from limited training data, as a first stepping stone toward fast, full treatment simulation. Deployment in a clinical context would require rigorous validation studies, probably including more realistic boundary conditions, and phantom experiments, well beyond the scope of this paper. We will make this framing more explicit in the introduction.
Simulation setup (R1): The constant pressure boundary condition was chosen to match prior computational thrombectomy studies. We agree this is a simplification and will acknowledge it more explicitly. Clot-vessel friction is modeled through the contact and material formulation of the clot and vessel.
Test set size (R1): Each of the 10 test trajectories contains 195 timesteps, yielding approximately 1950 per-step evaluations (measured by the per-step error). While these states are not fully independent as they come from sequential trajectories, they are also not fully dependent either for the model, as the model receives no temporal context and processes each state in isolation. The 10 test cases cover distinct patient-specific geometries, and the out-of-domain evaluation demonstrates generalization to qualitatively different tubular shapes. Combined with the five-fold cross-validation on the development set, we believe this forms a sufficient basis for assessing model performance and see generalization behaviour to unseen vessel geometries.
Collision dynamics (R1): We do not apply physics-informed losses or hard constraints to prevent clipping, and make no formal claims about collision prevention. We empirically observe an absence of the severe instabilities seen in the baselines, such as large-scale clipping through the vessel wall and clot fragmentation.
Code/dataset release (R1-2-3): Code will be released upon acceptance and a link will be provided in the manuscript. We will investigate options for data sharing.
Pressure field independence (R2): Since blood pressure is constant, the flow field is precomputed on the empty vessel and does not update as the clot moves, consistent with current thrombectomy simulation models.
RoPE and SO(3) equivariance (R3): RoPE does not break equivariance. Node positions are lifted to all group elements ‘g in G’ alongside features, so relative positions are consistently rotated across all group frames.
‘phi_q’ and ‘phi_c’ (R3): These are indeed learnable equivariant linear layers.
GATr (R3): We chose platonic transformers as equivariance is induced via weight-sharing across group elements without modifying the computation graph of a regular performer model, preserving the efficient kernelized attention formulation. But GATr would have definitely been an interesting baseline as well.
Single clot parameter set (R2): Agreed, varying clot mechanical properties is an important next step.
‘Implicit neural representation’ (R3): The decoder queries arbitrary spatial locations at inference time, allowing for full-resolution inference from a subsampled latent state. We agree the terminology is potentially confusing as this property is also referred to as the neural field property in the literature.
We thank all the reviewers for their comments and feedback on typos, figures, and annotations.
Meta-Review
Meta-review #1
- Your recommendation
Provisional Accept
- 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.
High variance of ranking across 3 reviewers, but two advocated acceptance.