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Abstract
Accurate motion management via patient-specific motion models is critical for motion compensation and tumor tracking in 4D radiotherapy. Existing approaches typically rely on a two-step pipeline combining deformable image registration (DIR) and linear surrogate-based regression, limiting their ability to capture complex, nonlinear surrogate-to-motion relationships. We propose a novel implicit neural representation (INR) motion model that jointly optimizes DIR and surrogate regression, directly predicting continuous deformation vector fields from arbitrary surrogate states. The framework simultaneously learns forward and backward motion models with enforced cyclic consistency, and adapts the SIREN architecture with anisotropic frequency scaling to account for the differing spatial and temporal dynamics of the input. Evaluated on the DIR-Lab 4DCT dataset, our method achieves a mean TRE of 1.08 mm and DSC of 0.625, outperforming classical and INR-based two-step baselines while yielding strictly zero folding across all cases. Source code is available at https://github.com/IPMI-ICNS-UKE/INR-Motion-Modeling.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/5263_paper.pdf
SharedIt Link: Not yet available
SpringerLink (DOI): Not yet available
Supplementary Material: Not Submitted
Link to the Code Repository
https://github.com/IPMI-ICNS-UKE/INR-Motion-Modeling
Link to the Dataset(s)
BibTex
@InProceedings{GebJoh_Nonlinear_MICCAI2026,
author = { Gebauer, Johannes B. AND Büttgen, Laura E. AND Sentker, Thilo AND Werner, René},
title = { { Non-linear INR-Based Motion Modeling for 4D Radiotherapy } },
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 paper proposes an INR based respiratory motion model. The model takes 4DCT images and corresponding surrogate signal values as input and uses a SIREN architecture to map the 5D coordinates (3 spatial and 2 surrogate signal values) to 3D deformations. The generated DVFs will map the reference image (the EE phase of the 4DCT) to each of the other images. The model uses two SIRENs to generate the forward and backward mappings, which are constrained to be inverse consistent to each other. The framework is evaluated on the open DIR-LABs dataset, achieving good results.
- 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.
Although INRs have been used for respiratory motion modelling before, this has been for CBCT and MRI (I think), and as far as I am aware they have not been used to build motion models from 4DCT before. The INR framework proposed here seems very sensible and well suited to modelling breathing motion from 4DCT, where the motion is parameterised by a small number (in this case 2) of surrogate signal. The method achieves good results on the DIR-LABs datasets, with better results than the comparison methods, and good TRE values compared to other methods in the literature.
- 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.
In my opinion the major weakness of this paper is that it is not addressing the real problems with trying to model and compensate for breathing motion in RT. The authors are correct that simple linear models will not be able to capture non-linear surrogate-motion relationships (although I disagree that this means they cannot represent spatially varying hysteresis and tissue deformation, and the linear models do vary spatially, and so can represent both of these), and the results presented in the paper show that the proposed method is indeed more accurate than the simple linear model they evaluated. However, the reason that motion models built from 4DCT are not used clinically is not because the simple linear models are not accurate enough – it is that the 4DCT itself does not provide a good estimate of the motion that actually occurs during treatment. There are a number of reasons for this: 4DCT assumes reproducible motion so it cannot capture breath-to-breath variability in the motion, and such motion causes artefacts in the 4DCT; there can also be day-to-day variations in the motion, so even if the 4DCT captures the motion well on the day it is acquired, it may not represent the motion on another day; 4DCT and surrogate based motion models also rely on having surrogate signals that have a strong and consistent relationship with the motion, and can be acquired both during imaging and treatment, which in practice can be difficult to obtain. This is why many works on modelling breathing motion for RT in recent years have focussed on how to build models that can account for breath-to-breath variations (e. g. by using unsorted 4DCT as in ref 8), can account for day-to-day variations (e. g. by building models from CBCT projections, or MR data for the MR-Linac), or can account for imperfect surrogate signals (e. g. ref 8). Related to the previous comment, although the propose method achieves good results on the DIR-LABs datasets that it is evaluated on, this does not really give any indication of how accurate it would be in clinical practice. That is, evaluating the models on the same data they are fitted to just measures how well the model can be made to fit the data, it doesn’t evaluate how well it can predict unseen data, which is ultimately what it needs to do – although the results do show that it can fit the data better than the other models (which is a good start!).
- 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 has provided an anonymized link to the source code, dataset, or any other dependencies.
- 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
As mentioned above, I think the SIREN based framework presented here is good for surrogate based motion models, and it could in principle be used with unsorted 4DCT data (as in 8) rather than sorted data (if the surrogate signals corresponding to the unsorted data are available) or could be applied to CBCT (or MRI) data – and this could be an interesting direction for future work.
- 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 proposed method seems like a good sensible framework for surrogate-driven motion models. However, I think the data used to build and evaluate the framework (i.e. 4DCT) currently limits the clinical applicability of the method and results
- 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
The paper extends prior work on motion modelling (with surrogate signals) and connects it to neural implicit functions for providing stable, accurate and inverse consistent predictions.
- 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 paper is extremely well written and presented with exceptionally clear concept figures, tables and result visualisations.
- The method is novel and nicely integrates the benefits of continuous INR fitting to “hyper”linear surrogate regression, in addition some minor adjustment (anisotropic frequency scaling and
- The DIRlab validation results clearly demonstrate the high accuracy in terms of TRE making this a very practical new tool for clinical adoption in radiotherapy
- The authors clearly describe the implementation and promise to release source code for reproducibility
- 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.
- There are no major weaknesses, but rather a few suggestions that I provided in the detailed comments - my only minor concern is that parameter sharing of the INR across phases could be slightly more clearly explained.
- 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 authors claimed to release the source code and/or dataset upon acceptance of the submission.
- 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
As mentioned above, please clarify the parameter sharing across phases more explicitly. The sampling of coordinates (plus jitter) during patient-specific INR training follows prior work principles but may lead to noisy gradients wrt regularity and similarity loss - an ablation study on this batch-size could be interesting. Could a B-spline transformation model be considered? The simulated surrogate signal is mentioned to be 2D and based on lung volumes, how accurate and/or realistic is this? Please slightly exand hear if space permits. The SOTA comparisons are a bit limited (please report std-dev for TRE over cases), while the ablation disentangles INR optimisation and motion modelling at least one other SOTA 4D approach (e.g https://doi.org/10.1016/j.media.2010.10.003 or more recently https://doi.org/10.1002/mp.70248) could be included.
- 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.
(6) Strong Accept — must be accepted due to excellence
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
High level of technical contribution paired with solid experimental validation and exceptionally high quality presentation.
- 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 #3
- Please describe the contribution of the paper
The authors propose a registration framework for motion compensation during lung radiotherapy. The framework leverages an Implicit Neural Representation (INR) formulation, which relies on 4DCT images along with surrogate respiratory signals for training, and outputs displacement fields from surrogate signals alone at inference time. The authors evaluate the proposed framework on the publicly available DIR-Lab dataset and synthetic surrogate respiratory signals, and report encouraging results.
- 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 main strength of this work is the parametrization of the INR with surrogate respiratory signals, which allows for a compact representation of the full respiratory cycle using a low-dimensional, time-varying signal. Further, using appropriate frequency scaling parameters, smooth time-varying deformation transitions within the respiratory cycle can be obtained.
In addition, the text is very well written and clear overall, with nice illustrations accompanying the methodological descriptions and results.
- 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 main weakness is the relatively limited comparison to other works in the state-of-the-art. The authors do compare the performance of their proposed framework against a classical method for 4D motion compensation based on surrogate signals (along some ablation variants), but no comparison is given against top performant methods on the DIR-Lab dataset, defeating the purpose of using such publicly available dataset. This is naturally not possible for the full respiratory cycle, but comparing TREs at the two extreme configurations against DIR-Lab public results could already provide information on the proposed framework’s registration accuracy.
An additional problem is the fact that the surrogate signal is artificially generated from the image itself. Although understandable given that such data is lacking from the DIR-Lab dataset, there is no guarantee that this corresponds to a real, measurable surrogate signal. I would have expected some sort of robustness analysis by evaluating how noise in the surrogate signal can affect overall registration performance.
An additional consideration: it is a bit surprising that the regularization term enforces a spatial jacobian of 1 (volume preserving deformation), since respiratory motion is mostly driven by large volume changes. I believe a physically inspired regularization term would be more appropriate [A].
[A] Z. Min et al., “Biomechanics-informed Non-rigid Medical Image Registration with Elasticity Theories,” in IEEE Transactions on Medical Imaging, doi: 10.1109/TMI.2026.3665279
- 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 has provided an anonymized link to the source code, dataset, or any other dependencies.
- 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 is not referenced on the text
- Sec. 2.2, the first paragraph after “Ablation Models” should be rephrased as difficult to understand
- Sec. 2.3, consider adding the definition of the temporal regularization terms
- Consider specifying the strategy used for tuning-in all the lambda hyper-parameters
- 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 proposed registration framework is sound, bears high clinical potential, and demonstrates encouraging results. However, a discussion on registration accuracy with respect to other publicly available methods’ performances (from DIR-Lab) is lacking, and could improve this work’s positioning with respect to state-of-the-art lung registration algorithms. Further, there is no guarantee of good performance in a real scenario, and the authors may have overlooked a simple, yet efficient way of testing robustness to perturbations of the surrogate signal.
- 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
N/A
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.
The paper proposes an INR-based respiratory motion model using a SIREN architecture to map 5D inputs to 3D deformations, with inverse-consistent forward and backward mappings, and demonstrates good performance on the DIR-LAB dataset. Overall, it is technically strong with promising clinical potential and solid validation, though some minor limitations in benchmarking and robustness analysis leave some uncertainty about real-world performance. This paper received three positive ratings. The AC concurs with the reviewers’ evaluations and recommends an “acceptance”.