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Abstract

Predicting patient-specific facial soft-tissue deformation is critical for iterative orthognathic surgery planning. However, current computational methods face a strict accuracy-efficiency trade-off: high-fidelity Finite Element Methods (FEM) are computationally prohibitive, whereas pure deep learning models often produce biomechanically inconsistent results. While Physics-Informed Neural Networks (PINNs) offer a promising avenue, learning the complex heterogeneous mechanics of bone–soft-tissue interactions with only partial clinical supervision (i.e., outer facial surfaces) remains highly unstable. To overcome these challenges, we present PINNOCHIO, a novel physics-informed framework for facial soft-tissue simulation. PINNOCHIO introduces a hybrid sequential decomposition that explicitly decouples discontinuous bone–soft-tissue interface movements from continuous volumetric hyperelastic deformation. This structural separation enables stable training and facilitates a physics-enabled sim-to-real adaptation strategy, ensuring internal biomechanical consistency without requiring volumetric ground truth. Evaluated on a 40-patient clinical cohort, PINNOCHIO outperforms existing baselines in both surface accuracy and physical validity. Furthermore, it achieves a substantial speedup over FEM, successfully resolving the accuracy-efficiency trade-off to provide a highly reliable and practical tool for interactive surgical planning. Source code is available at https://github.com/RPIDIAL/PINNOCHIO.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2026/paper/1982_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

https://github.com/RPIDIAL/PINNOCHIO

Link to the Dataset(s)

N/A

BibTex

@InProceedings{LeeJun_PINNOCHIO_MICCAI2026,
        author = { Lee, Jungwook AND Kim, Daeseung AND Gu, Kevin AND Hu, Zhangfeng AND Kuang, Tianshu AND Hopeman, Finn AND Liebschner, Michael A. K. AND Gateno, Jaime AND Yan, Pingkun},
        title = { { PINNOCHIO: Physics-Informed Neural Network for Coupled Hyperelastic Interface-Volume Simulation in Orthognathic Surgery } },
        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 propose a framework for simulating the deformation of facial structures after bone repositioning in orthognathic surgery. The framework is strongly rooted in physics-based principles, implementing a two-step methodology decoupling movement of bone-tissue interface after bone repositioning and volumetric soft-tissue deformation. The authors evaluate their proposed framework on a large dataset of 40 clinical orthognathic surgery cases, obtaining convincing results above concurrent methods from the state-of-the-art.

  • 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 the novel hybrid boundary displacement prediction coupled to the physics-constrained volumetric propagation for simulation of orthognathic surgery. The choice of Graph Neural Network with attention layers seems particularly well-fitted for this problem, specially when combined with physics-based unsupervised training that effectively preserves physical plausibility of the output deformations. Further, the evaluation protocol is convincing, both using a large dataset of 40 real surgical data, and comparing with competitive methods from the state-of-the-art.

  • 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, there are no major methodological weaknesses to this work. However, the clarity of the text can be improved in various ways:

    • It is unclear whether re-training is needed for every new case. My understanding is that the flexibility of the framework allows for population training, but this should be explicitly clarified.
    • Although Sec. 2 introduces very well the notion of fixed, moving and sliding interfaces, Sec. 3.1 and Sec. 3.2 introduce two anatomical layers, with a rather confusing subsequent description of intra-layer and layer-bone interfaces. In Sec. 3.2, it is no longer clear which are the interfaces that are moving, sliding or fixed.
    • Related to the point above, it would be useful to illustrate these layers and interfaces.
    • It is unclear how the FEM data was generated. Does it correspond to the FEM-RLSE baseline ? Please clarify.
    • Consider adding details of the training procedure: what do you need to stabilize the optimization ? Is this related to the non-linearity of the physical term ? How much time does the training take ?
    • For reproducibility purposes, consider adding details of the networks’ architectures
    • Ethical considerations on the dataset acquisition are lacking.
  • 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 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?

    Clinical data used but no details on ethical evaluation by an appropriate committee was given.

  • 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 is methodologically sound, the evaluation protocol is convincing, and the results are compelling. I believe this paper should be accepted, but the text could still be considerably improved.

  • 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 provided critical details that were lacking in the initial submission, specifically regarding the training protocol, the absence of per-case retraining, and the application of FEM-RLSE as both a baseline and part of the sim-to-real pre-training strategy.

    Furthermore, the authors have committed to releasing clinical trial and implementation data, which addresses my previous concerns regarding reproducibility.

    Provided that these details and clarifications are fully integrated into the final manuscript, I recommend this work for acceptance.



Review #2

  • Please describe the contribution of the paper

    This paper presents PINNOCHIO, a physics-informed framework for predicting soft-tissue deformation in orthognathic surgery. To address the limitations of conventional finite element methods, which are accurate but computationally expensive, and purely deep learning-based approaches, which are efficient but often lack biomechanical consistency, the proposed method adopts a sequential decomposition strategy consisting of boundary displacement prediction followed by physics-constrained volumetric propagation. This design explicitly decouples the discontinuous motion at the bone–soft tissue interface from the continuous hyperelastic deformation within the soft-tissue volume. In addition, the framework incorporates physics-based regularization derived from a Neo-Hookean hyperelastic material model, together with a sim-to-real adaptation scheme that combines FEM-based pretraining with fine-tuning under real clinical surface supervision. As a result, the method improves both surface prediction accuracy and the physical plausibility of internal deformation without requiring volumetric ground-truth annotations, thereby enabling patient-specific preoperative simulation that jointly balances accuracy, efficiency, and biomechanical reliability.

  • 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 paper addresses a clinically important problem in orthognathic surgery, namely patient-specific facial soft-tissue simulation for iterative surgical planning, with a clear motivation to balance biomechanical fidelity and computational efficiency. 2.The method design is meaningful for this task because it explicitly handles heterogeneous mechanics, i.e., discontinuous sliding at the bone–soft-tissue interface and continuous volumetric deformation inside the tissue. 3.The paper proposes a practical sim-to-real adaptation strategy that allows fine-tuning on real clinical cases using only postoperative outer facial surface supervision, which is important given the lack of dense internal ground truth.

  • 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.Although the method is physics-informed, real clinical supervision is still restricted to postoperative outer facial surfaces, so the physical plausibility of the internal volumetric deformation on real data is not directly validated with internal ground truth. 2.The comparison setting is somewhat limited. The paper compares against FEM-RLSE and two learning-based baselines, but it does not include a broader range of recent physics-aware or deformation-constrained methods, which makes the strength of the empirical claim less complete. 3.The ablation study is useful, but it is still relatively narrow. More analysis on hyperparameter sensitivity, material parameter selection, and the contribution of each architectural component would make the technical claims more convincing.

  • 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 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.

    (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?

    This work addresses an important clinical problem with a technically meaningful method and shows encouraging empirical results. In particular, the proposed sequential physics-informed framework is a clear methodological contribution, and the reported performance suggests a good balance between biomechanical validity and computational efficiency. However, the overall evidence is still somewhat limited by the relatively small clinical cohort, the lack of direct validation of internal deformation on real cases, and limited reproducibility details.

  • 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 authors have addressed most of my concerns in their rebuttal.



Review #3

  • Please describe the contribution of the paper

    The paper introduces PINNOCHIO, a physics-informed neural network for facial soft-tissue simulation in orthognathic surgery. The main contributions are: 1.A hybrid sequential architecture that explicitly decouples the discontinuous sliding mechanics at the bone-soft-tissue interface from the continuous hyperelastic deformation of the tissue volume. 2.A physics-enabled “sim-to-real” training strategy that pre-trains the model on synthetic FEM data and fine-tunes it on clinical data using only outer facial surface supervision, relying on physical constraints to regularize the internal volume. 3.A practical resolution to the traditional accuracy-efficiency trade-off, demonstrating that the model can achieve inference times of 3.24 seconds while incorporating biomechanical constraints, compared to hours required for traditional FEM.

  • 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 addresses patient-specific facial soft-tissue simulation for orthognathic surgery planning, a clinically important and computationally demanding task where current FEM-based approaches are too slow for interactive use.
    • The separation into boundary displacement prediction and volumetric propagation is a reasonable and well-motivated architectural choice, explicitly addressing the differing physical nature of bone–tissue interaction versus volumetric tissue deformation.
    • The method achieves a substantial reduction in runtime compared to FEM-based simulation (seconds vs hours)
  • 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 description of FEM-based pretraining lacks clarity regarding whether synthetic simulations are generated independently of the 40-patient cohort used for evaluation.
    • Although geometry is patient-specific, are fixed across all subjects. This limits true patient personalization.
    • The ablation study reveals that adding the complex Physics Loss only improves the Chamfer Distance from 1.02 mm to 0.98 mm. This 0.04 mm gain is clinically imperceptible (well below CT resolution), raising the question of whether the computational complexity of the physics constraint is empirically justified for surface accuracy
  • 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 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.

    (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?

    Although the paper tackles a critical clinical problem with an elegant and efficient hybrid architecture, I recommend a Weak Reject due to unresolved risks of pre-training data leakage and marginal empirical gains from the complex physics loss.

  • 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



Author Feedback

We thank the reviewers for recognizing our method’s clear methodological contribution (R1, R2, R3), convincing empirical results (R1, R2), and resolution of the accuracy-efficiency trade-off (R2, R3). Below, we address key concerns grouped into categories for clarity and brevity.

  • Physics Loss & Internal Validity (R2, R3) In iterative orthognathic planning, surgeons evaluate not only the outer face but also how soft tissue deforms internally: how muscle/fat redistribute and whether the deformation pattern is physically plausible. This internal behavior allows surgeons to reason about and adjust each candidate bone plan. A simulation matching outer surface but producing invalid internal deformation cannot support this reasoning. Direct validation against patient-specific ground truth would be ideal but is infeasible: post-OP imaging lacks dense pre/post-OP correspondence, so per-voxel displacement cannot serve as a validation target. This is precisely why physics-informed framework is needed: to enforce internal plausibility through governing equation rather than direct supervision. Physics loss ensures this internal validity. As shown in Table 2 & Fig. 3-b, removing it degrades the Equilibrium Residual and produces physically implausible meshes. Chamfer Distance is reported only as a sanity check that surface accuracy is preserved; the 0.04 mm change confirms this preservation, with the actual contribution in the physical validity metrics. Beyond this, we are pursuing complementary strategies: surgeon-based reader studies and interface sliding pattern analysis against biomechanically expected behavior.

  • Training Protocol & No Data Leakage (R1, R3) PINNOCHIO is trained in a population-wise manner: once trained, model is applied to new cases without per-case re-training. FEM-based pretraining (generated using FEM-RLSE [13], the same simulator as our FEM baseline) and clinical fine-tuning are conducted under the same 5-fold split with strict patient-level separation, ensuring no data leakage between pretraining and fine-tuning.

  • Baseline Selection (R2) Recent physics-aware methods (e.g., SIMM [16], PhysSFI-Net) do not enforce physics explicitly but learn it implicitly from FEM-simulated supervision, which makes FEM-simulated performance their upper bound by construction. We therefore include FEM-RLSE [13] as the representative of this family, since no FEM-supervised method can structurally surpass it. Conversely, ACMT-Net [6] and DGCFP [11] represent the SOTA surface-only methods trained on post-OP surfaces. The chosen baselines therefore span both paradigms.

  • Patient Personalization & Extended Analysis (R2, R3) We agree that patient-specific material parameters would enhance personalization. However, such properties cannot be obtained from routine clinical imaging, and we therefore adopted literature-supported values per tissue type. Our framework is not restricted to uniform parameters: the Lamé parameters μ and λ are spatially assigned, so any patient-specific estimation (e.g., from ultrasound elastography) can be incorporated without architectural change. The ablations in Table 2 are designed to isolate two main methodological contributions (sequential decomposition and physics regularization). Further sensitivity analyses on hyperparameters and material parameters are part of our ongoing study.

  • Clarifications & Reproducibility (R1) Mechanical (fixed/moving/sliding) and anatomical (muscular/superficial) partitions are independent: every interface contains all three node types. Training stabilization involves two choices: (1) each module is trained sequentially then combined for end-to-end fine-tuning, avoiding joint-optimization instability (2) FEM-pretraining provides a physics-consistent initialization, so Neo-Hookean term acts as regularizer. Full training takes ~4h pretraining + 2h fine-tuning on a 24 GB GPU. Network architectures, hyperparameters, IRB number, and source code will be released upon acceptance.



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.

    This work proposes a sequential physics-informed framework for coupled hyperelastic interface-volume simulation in orthognathic surgery and received mixed scores. The authors emphasize the clinical importance of the results, for example, justify the marginal improvement in Chamfer distance (1.02 mm to 0.98 mm) and provide evidence of generalization. Please also refer to the reviewers’ comments for additional feedback.

  • 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.

    The author has provided clarification about the data leakage and baseline selection. Two reviewers are happy with the rebuttal and agree to accept it.



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.

    I believe the rebuttal adequately addressed the major concerns raised during the review process. The authors also outlined clear future plans for a surgeon-based reader study, acknowledging the current limitations of the work while presenting a solid strategy for further validation and improvement. In addition, the planned public release of the code is an important strength that will support reproducibility and benefit the research community.

    Overall, this is a strong CAI+MIC contribution that is well aligned with the scope of the MICCAI Conference. Although some weaknesses remain, I believe the work is sufficiently strong to warrant 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.

    Reviewers’ praised the clinical motivation, methodological contribution of physics-informed NNs, and empirical results. The rebuttal provided missing details, addressed concerns, and commited to data release for reproducibility. Post-rebuttal reviews all agree on acceptance.



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