Paper Info Reviews Meta-Review Author Feedback Post-rebuttal Meta-Reviews

Authors

Ruiliang Gao, Jorg Peters

Abstract

Collecting, stretching and tearing soft tissue is common in surgical procedures. The corresponding repeated deformations have a plastic component that surgeons take into consideration and that surgical simulation should model. Simulated organs and tissues can often be outlined as curved cylinders or planes, offset orthogonally to form thick shells. A pair of primary directions, e.g.\ axial and radial for cylinders, provides a quadrilateral mesh whose offset naturally yields a hexahedral mesh.

To better capture tissue plasticity for hexahedral meshes, this work extends and compares to existing volumetric finite elements. Specifically, we extend the open source simulation framework SOFA leveraged for surgical simulation.

Factoring the deformation gradient, the approach focuses on the challenge of separating symmetric and asymmetric, elastic and plastic deformation components beyond the co-rotational framework – while preserving volume and avoiding re-meshing.

Link to paper

DOI: https://doi.org/10.1007/978-3-030-87202-1_55

SharedIt: https://rdcu.be/cyhRa

Link to the code repository

N/A

Link to the dataset(s)

N/A

Reviews

Review #1

Please describe the contribution of the paper

The study focuses on implementation of algorithms for modelling of soft tissue plasticity in SOFA co-rotational finite element computational framework for surgery simulation. The implementation is done for hexahedral (8-noded) elements. Performance of the newly implemented algorithms is demonstrated through application in modelling of a bar with rectangular cross-section subjected to stretching and twisting.
Please list the main strengths of the paper; you should write about 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.

Accurate/plausible simulation of many surgical procedures (laparoscopic operations, tearing etc.) requires modelling of plasticity of soft tissues. Finite element (FE) algorithms of computational created in the study facilitate such modelling. The study addresses (or discusses) all key issues that need to be taken into account when applying FE analysis in modelling of continua, including incompressibility and deterioration of solution stability due to element distortion. The analytical bases of the proposed algorithms are well explained and sufficiently detailed.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

Novelty and originality of the study is not explained. Almost all commercial finite element codes contain various algorithms for modelling continua undergoing plastic deformations (see proceedings of International Conference on Plasticity, Damage, and Fracture) and it is unclear how the algorithms proposed in the study differ from what is already available in the industrially applied finite element codes? Is the novelty in implementation of plasticity in co-rotational computational mechanics framework?

It has been recognised in the literature that soft tissue constitutive behaviour is best modelled using hyperelastic material models. The manuscript does not explain (or even mentions) how plasticity was combined with hyperelasticity in the proposed algorithms. The statement on page 2 (“extending the linear elastic-plastic FEM…”) seems to indicate that plasticity was combined with lthe inear elastic model. As this is inconsistent with the current knowledge of the constitutive behaviour of soft tissues, explanation/justification is needed.

The manuscript demonstrates the performance of the proposed algorithms through application of bar elongation (stretching) and twisting. However, no quantitative verification that would confirm accuracy and robustness of the proposed algorithms (e.g. through quantitative comparison with the well-established solution methods) is presented.
Please rate the clarity and organization of this paper

Very Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

There is no reason to doubt in reproducibility of the presented results. SOFA is an open-source framework. Will the proposed algorithms be made publically available through the SOFA framework?
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

Clearly state what is the novelty of the study: how the proposed algorithms differ from the existing algorithms for plasticity modelling, what are the advantages of the proposed algorithms in comparison to state-of-the-art.

Justify application of linear elastic-plastic material in soft tissue modelling.

Provide results of quantitative verification of the proposed algorithms (excellent guide for verification of algorithms of computational mechanics is provided ASME PTC 60/V&V 10 Guide for Verification and Validation in Computational Solid Mechanics)
Please state your overall opinion of the paper

borderline reject (5)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The manuscript needs a major revision that requires obtaining additional results (quantitative verification of the proposed algorithms for modelling of soft tissue plasticity).
What is the ranking of this paper in your review stack?

2
Number of papers in your stack

2
Reviewer confidence

Very confident

Review #2

Please describe the contribution of the paper

The authors propose a method for incorporation of hexahedral FEM-based plasticity in surgical simulation. This is achieved by factoring the deformation gradient into plastic and elastic components, i.e., by factoring it into elastic rotation, plastic rotation, elastic stretch, and plastic stretch. The method also separates the symmetric and asymmetric parts of the deformation gradient. Other important aspects of the proposed method include material hardening (to prevent distortion) and volume preservation. The proposed methodology is incorporated into the open-source SOFA simulation framework.
Please list the main strengths of the paper; you should write about 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 proposed methodology is novel in that it incorporates hexahedral meshes and an improved framework for plasticity which also incorporates symmetry into the surgical simulator. (Currently, the only plasticity simulations that are performed in SOFA are based on tetrahedral meshes which are less realistic due to their unnatural stiffness and asymmetry.) (2) The simulations of surgical tearing are volume preserving and do not require remeshing.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

(1) Only academic test cases have been shown in the paper, whereas it would have been beneficial to see results from at least one more realistic test case. (2) No run times or assessment of the computational cost for the proposed methodology have been included.
Please rate the clarity and organization of this paper

Very Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

The code would need to be made available to ensure reproducibility of the results. If it has been incorporated into the version of SOFA that is found online, then the code has been made accessible. This is not been explicitly statement in the reproducibility statement. The dataset has been made available by the authors.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

This is an interesting paper on improving a surgical simulator via incorporation of hexahedral meshes and symmetry to simulate plasticity more accurately. A more accurate surgical simulator will be useful for surgeons in training, as more realistic results will be produced (particularly in response to tearing motions). The paper could be improved through the addition of a single, more realistic test case from the surgical simulator. It would also benefit from the incorporation of either run times or an assessment of the computational cost. It could also be improved through the addition of quantitative results concerning the accuracy of the simulation results (when compared to the previous tetrahedral version). Finally, it would be helpful to include a discussion as to how physically realistic it is to switch to a purely elastic simulation when the hexahedral elements invert in the plasticity simulation. Some work is needed on the References section. For example, the capitalization of the titles of journals and conference proceedings are inconsistently capitalized. Reference 17 does not include a complete set of bibliographic details. There are also several places in which the writing could be improved: “for small changes the enclosing surface” should be “for small changes to the enclosing surface”; “preservation of volume tricky” should be “the preservation of the volume is tricky”. There are also a few grammatical corrections/typos which should be addressed: “hex-elements” should be “hex elements”. Similarly, “hex-meshes” and “tet-meshes” should be “hex meshes” and “tet meshes”, respectively. In addition, “unnaturally stiffness” should be “unnatural stiffness” or “unnaturally stiff”; “extendinglinear” should be “extending linear”; “central face on end of the bar” should be “central face on the end of the bar”, and “handles inverted element robustly” should be “handles inverted elements robustly”. Also, “ie” should be “i.e.,” and “e.g.” should be “e.g.,”.
Please state your overall opinion of the paper

Probably accept (7)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The proposed methodology advances the state-of-the-art in surgical simulation of stretching and tearing of soft tissue and will be useful to surgeons in training. This is an important contribution. The simulations are volume preserving and do not require remeshing. The former is required for the mechanics. The latter is an excellent aspect of their simulations which helps decrease the complexity of the simulation, as well as its run time. Although only academic test cases have been provided, it is still clear that the state-of-the-art has been advanced in surgical simulation. The incorporation of run times or an assessment of the computational cost would have been useful to have been included.
What is the ranking of this paper in your review stack?

2
Number of papers in your stack

3
Reviewer confidence

Very confident

Review #3

Please describe the contribution of the paper

The work was focused on the improvement of real-time simulation of soft tissue undergoing plastic deformation for medical training. It was implemented within the SOFA (Simulation Open Framework Architecture) environment. This is an interesting topic. This contribution uses a multiplicative decomposition of the deformation gradient into elastic and plastic components, while separating the symmetrical and asymmetrical, elastic and plastic deformations beyond the corotational FEM. Some capabilities and limitations of the introduced method are highlighted.
Please list the main strengths of the paper; you should write about 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 presented method is interesting. It relies on a multiplicative decomposition of the deformation gradient into plastic and elastic deformation and handles both rotational and stretching plasticity. The work presents a sufficient amount of novelty, including the extension of the linear co-rotational elasto-plastic FEM to hexagonal meshes, and the comparison of the blended vertex approach and the piecewise constant cell-centered approach to the plastic rotational deformation. Particular attention is paid to preserving the volume in the case of relatively large deformations.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

The paper is well written and the mathematical formulation of the problem is quite clear. Some numerical experiments are presented. However, my main concern is the assessment of the performances of the numerical approach (convergence and stability). While some numerical experiments are presented, it would be more beneficial if the authors present a quantitative validation of the approach, for instance in comparison with known results or regarding the temporal evolution of the stress components and a comparison with a reference solution obtained with a very fine mesh.
Please rate the clarity and organization of this paper

Excellent
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

The plasticity decomposition and the method are well explained. Authors should specify whether the presented algorithm will be available to the scientific community in a future release of the SOFA environment.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html
- The authors should provide further insights on why/how the multiplicative stress decomposition of the deformation gradient into elastic and plastic components features more stability than the additive strain decomposition? This is an important topic of discussion for other elasticity problems (e.g. the active strain and active stress formulations for active anisotropic elasticity).
- How this methodology provides a faster performance for large displacements. A comparison with known results or available benchmarks would support this point.
- I suggest writing the stress-strain relationship for clarity.
- It is not clear if the incompressibility of the material is assumed in the elasticity component and how this is enforced numerically.
- If an element is about to be inverted, this work disables the plasticity. What is the difficulty of considering instead a local mesh adaptation within SOFA?
- What is the advantage of using hexahedral finite elements instead of tetrahedral elements for such simulations? Please justify.
- In the numerical experiments, I propose to provide the temporal evolution of the total stress components.
- When large structural deformations occur, traditional Lagrangian methods generally suffer from stability and require high computational costs and robust remeshing strategies. However, an Eulerian formulation is usually more suitable due to its ability to handle arbitrary deformation regardless of its magnitude, but requires the resolution of additional equations. It would be useful if the authors can comment on the adequacy of their method compared to a fully Eulerian formalism.
- The reader would prefer to see a quantitative validation of the approach, for example a comparison between the stress-strain paths and results available in the published literature. Can we say that the current tool within SOFA is more appropriate than the other frameworks available?
- I recommend to highlight the main changes of the formalism in the 2D case, eg. for plastic stretching.
Please state your overall opinion of the paper

strong accept (9)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The work presents a sufficient amount of novelty to be published in the MICCAI conference. The idea is interesting and the method is promising. I just have a few concerns about numerical validation that could be further investigated in a separate paper.
What is the ranking of this paper in your review stack?

1
Number of papers in your stack

5
Reviewer confidence

Very confident

Primary Meta-Review

Please provide your assessment of this work, taking into account all reviews. Summarize the key strengths and weaknesses of the paper and justify your recommendation. 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 a simulation method for soft tissue in the surgical environment with SOFA. While R2 and R3 recommend acceptance, R1 recommends rejection. Use the rebuttal to address the criticism of R1, in particular regarding the novelty of the proposed model wrt existing models, not just SOFA. Also discuss the possibility and method to obtain new comparison and validation results.
What is the ranking of this paper in your stack? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

4

Author Feedback

ADDED COMPARISONS We added a comparison of FEM beam simulations using (1) our 8-node hex corotational elasticity + higher-order plasticity (Y5200 P.45) (2) Abaqus 8-node hex C3D8R linear elasto-plasticity, (3) Abaqus 8-node hex C3D8R hyperelasto-plasticity (Moon-Rivlin, C10=1765, C01=43, D1=1E-05)

The linear Abaqus model (2) stretches locally and visibly less realistic in the `eyeball norm’ of real-time simulation. By contrast, (1) and (3) fully agree on the location of highest deformation and agree within 5% in the stretch during temporal evolution.

(1) executes at 25-33 hex/ms whereas (3) was computed without real-time considerations (at ca 7ms per hex). Since we compute the deformation gradient at more locations, the time increase of (1) above SOFA’s elastic-only corotational code is up to 20% during the most expensive computational time steps, immediately after release.

A figure illustrating plasticity in Nissen-Fundoplication has been added as additional test case.

VERIFICATION We plead guilty to using SOFA’s fast large displacement co-rotational code rather than attempting to add a real-time suitable hyperelastic hex code to SOFA (the existing hyperelastic tetrahedra-based code is brittle). Implementation of and comparison with hyperelastic hex code for SOFA are on our to-do list. (Yes, we intend to add hex plasticity to the SOFA distribution.) Since tissue is by default better modeled as hyperelastic material, the agreement of (1) and (3) is remarkable. We currently do not have a formal analysis why our hex-extension of the 3rd-order accurate blended-vertex deformation of [2] works well without the more sophisticated nonlinear elastic model. The typically high Poisson ratio certainly helps. We have added a corresponding remark in the paper.

Refining our default coarse hex mesh once and twice for quantitative verification reproduces the same deformation shapes. Of course, the shape is locally smoothed commensurate with the higher resolution. Execution time scales linearly with the number of hex-elements since there is no explicit matrix built or inverted.

NOVELTY Currently no hex-FEM codes exist that model plasticity in an interactive environment suitable for surgery simulation. Extending the blended-vertex approach to hex elements makes this possible. By contrast, engineering analysis softwares do not (need to) obey real-time constraints. SPH-like approaches do not take advantage of the available regular quad-offset structure.

HEX vs TET Coarse hex-meshes naturally model thick shells and free-form deformation of models in laparoscopic surgery. Our auto-generation from quad-surface models is predictable and immediate. By contrast, auto-generated tet-models need to be much denser (or use higher degree elements), change under small perturbations of the input and so lack the symmetry and feature alignment of hex elements.

SWITCH TO PURE ELASTIC, REMESHING Twist torques due to rotation of lap surgery instrument heads are extremely low [Surg End 14 pp 791–798]. Switching to a purely elastic simulation when hexahedral elements are about to invert favors robustness over physics during flawed, unrealistic high-torque interactions.

Remeshing (adaptation) or a partially Eulerian MPM approach compatible with real-time performance may in the future mitigate also these extreme scenarios.

MULTIPLICATIVE DECOMPOSITION We point out that the additive decomposition of the deformation gradient into elastic and plastic components fails for large deformations and, unlike multiplicative stress decomposition, does not lend itself to easily model incompressibility.

We fixed the detailed typographical recommendations. Thank you for all the good feedback!

Post-rebuttal Meta-Reviews

Meta-review # 1 (Primary)

Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

The rebuttal convincingly addresses the issues raised by the reviewers and AC. The authors are encouraged to improve their paper for the camera ready version, especially to clarify the contributions and add the new experiments performed.
After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Accept
What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

4

Meta-review #2

Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

Since the paper focuses on simulation, it does not use real data. This would have been fine as long as the authors showed validation and testing on simulated data. The reviewers appreciated the novelty of the paper. However, the experimental results section is lacking.
After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Reject
What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

7

Meta-review #3

Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.

R2 and R3 were in favor of acceptance to begin with. The rebuttal contains additional detail on the proposed method’s benefit compared to existing approaches, which had been asked for by R1.
After you have reviewed the rebuttal, please provide your final rating based on all reviews and the authors’ rebuttal.

Accept
What is the rank of this paper among all your rebuttal papers? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

3

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Improving hexahedral-FEM-based plasticity in surgery simulation