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

Authors

Daniel H. Pak, Minliang Liu, Theodore Kim, Liang Liang, Raymond McKay, Wei Sun, James S. Duncan

Abstract

Volumetric meshes with hexahedral elements are generally best for stress analysis using finite element (FE) methods. With recent interests in finite element analysis (FEA) for Transcatheter Aortic Valve Replacement (TAVR) simulations, fast and accurate generation of patient-specific volumetric meshes of the aortic valve is highly desired. Yet, most existing automated image-to-mesh valve modeling strategies have either only produced surface meshes or relied on simple offset operations to obtain volumetric meshes, which can lead to undesirable artifacts. Furthermore, most recent advances in deep learning-based meshing techniques have focused on watertight surface meshes, not volumetric meshes. To fill this gap, we propose a novel volumetric mesh generation technique using template-preserving distortion energies under the deep learning-based deformation framework. Our model is trained end-to-end for image-to-mesh prediction, and our mesh outputs have good spatial accuracy and element quality. We check the FEA-suitability of our model-predicted meshes using a valve closure simulation. Our code is available at \url{https://github.com/danpak94/Deep-Cardiac-Volumetric-Mesh}.

Link to paper

DOI: https://doi.org/10.1007/978-3-030-87231-1_47

SharedIt: https://rdcu.be/cyhV4

Link to the code repository

https://github.com/danpak94/Deep-Cardiac-Volumetric-Mesh

Link to the dataset(s)

N/A private dataset, will have some images from MM-WHS in the code repo because those are publicly available.

Reviews

Review #1

Please describe the contribution of the paper

The authors proposed a novel strategy for deep learning-based volumetric finite element mesh generation for aortic valves. Their method uses a template-preserving distortion energy in addition to a deep-learning based distortion framework. The authors discuss the suitability of their hexahedral volumetric meshes for use in a finite element simulation of aortic valve closure. Their learned volumetric meshes exhibited good spatial accuracy and mesh quality.
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) A novel method has been proposed for the deep learning of a volumetric hexahedral mesh of the aortic valves. Such a method is novel in that other deep learning-based mesh generation techniques have focused on watertight surface meshes. Whereas, techniques that are not based on deep learning either produce surface meshes or generated a volume mesh based on simple offset operations. (2) The hexahedral meshes that have been learned exhibit good spatial accuracy and mesh quality. (3) The authors discuss the suitability of their learned volumetric meshes for a finite element-based valve closure simulation.
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) The method requires that two volumetric mesh templates be included as input. (2) The proposed method is computationally expensive (e.g., the deep learning method took around 24 hours of training time. More details regarding the computational cost are needed to determine the total run time of the method and whether the computational expense can be reduced.)
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 authors will share the code and the parameters used to generate the results if the paper is accepted. However, they are not able to share their dataset, as it is not a public one. This is acceptable given the nature of their study.
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 which is focused on the development of a deep-learning based method for generation of volumetric finite element meshes with hexahedral elements. The learned meshes model the aortic valves and have been utilized in a simulation of valve closure. The resulting meshes are of good spatial accuracy and mesh quality. This is a very good paper with only minor flaws. One limitation (as noted by the authors) is the requirement that two volumetric mesh templates be used as input. In addition, the method appears to be computationally expensive, although the traditional image to mesh pipeline is also expensive. Hopefully in due time, the authors will be able to reduce or remove both these limitations. This will be important for generating patient-specific volumetric meshes of the aortic valves for use in TAVR simulations which requires the generation of patient-specific meshes in a fast and accurate manner. The paper could be improved by incorporating more mathematics and decreasing the amount of machine learning terminology that is used without definition. This will make the methodology more accessible to the reader. The paper would also benefit from a more detailed discussion on the various types of deformations under consideration. In addition, the authors should add a discussion as to whether element inversion ever occurred for the deforming mesh elements. If not, what was done to prevent mesh tangling? The authors also mention ablation and weighting ablation in conjunction with L_{arap} and L_{warap}. I don’t understand what is meant here, as the authors are not performing simulations of cardiac ablations or even considering patients with heart arrhythmias. Perhaps a mistake has been made here with respect to the terminology/notation? The References also need some work. In particular, the titles of the journals and conference proceedings seem to utilize random capitalization. In addition, proper nouns such as CT, MRI, and TEE need o be capitalized. Other: “mesb deformation task” should be “The mesh deformation task”. “sampling on mesh surface” should be “sampling on the mesh surface”. “points on surface” should be “points on the surface”.
Please state your overall opinion of the paper

accept (8)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

This is the first method to propose a deep learning technique for the generation of volumetric finite element methods. Given the level of interest in transcatheter aortic valve replacement (TAVR) simulations, fast and accurate generation of patient-specific volumetric meshes of the aortic valve is of importance. The results obtained by the authors indicate that they were able to learn hexahedral volume meshes of good spatial accuracy and mesh quality. And they demonstrated their use in a finite element valve closure simulation. The method is rather successful despite requiring two volumetric mesh templates as input. With time, they should be able to address this limitation and to reduce the computational expensive of their method.
What is the ranking of this paper in your review stack?

1
Number of papers in your stack

3
Reviewer confidence

Very confident

Review #2

Please describe the contribution of the paper

The authors present a volumetric mesh generation approach using a model-preserving distortion energy under a deep learning-based deformation method for a clinically relevant application.
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 authors present a deep learning image-to-mesh model using distortion energy for volumetric hexahedral meshes of aortic valves. Two effective deformation strategies are considered.
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.
- Better explain how the valve thickness is set.
- In the case of a healthy aortic valve, the cusps are very thin structures that can be assumed to be elastic membranes. It would be interesting to know if it is possible to use the presented method to model such extremely slender structures.
- It is not known whether the method can take into account the calcified aortic valve, where the thickness is not homogeneous along the cusps.
- Unlike hexahedral meshes, tetrahedral meshes are known to be more suitable for representing complex geometric shapes and are more general. Better to explain why the hexahedral elements are more accurate for the valve problem.
- A basic validation test is presented to study the stresses when closing the valve. Provide details on how to handle contact between cusps.
- A family of existing Eulerian valve models is not cited. The valve is described using a fully Eulerian immersed surface formalism and FEM simulations are then performed using reduced order models to follow the deformations of the leaflets.
- Is it possible to extend the formalism developed to model the fibrous and anisotropic structure of cusps? This is a very important aspect to develop a high fidelity valve model for FSI simulations.
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 dataset is not public and cannot be shared. The code is available.
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 approach is interesting. Address the points in 4/.
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?

A novel method is developed for an interesting heart valve problem. The presentation is clear. I vote for accepting this submission.
What is the ranking of this paper in your review stack?

2
Number of papers in your stack

5
Reviewer confidence

Confident but not absolutely certain

Review #3

Please describe the contribution of the paper

Authors propose a novel volumetric mesh generation technique using a template-preserving distortion energy for volumetric aortic valve meshes. Previous valve modeling strategies focus on surface meshes or volumetric meshes generated by simple offset operations. This paper aims to learn an image-to-mesh model that directly outputs optimized volumetric meshes.
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 paper tackles an important and difficult problem. I particularly appreciate the effort to develop nice and detailed figures. I also like the FEA evaluation, which highlights the potential clinical relevance to perform biomechanics studies.
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 main weakness of this work is the lack of comparison against other methods. The presented evaluation considers only variants of the main method. While ablation is important, it cannot be considered as a complete comparison against the state of the art. A comparative study with the methods mentioned in Section 1 would definitely make the contributions stronger, even if those methods apply simpler strategies to reconstruct/deform the volumes (like deformation along surface normals).
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

I believe it could be reproduced from the paper.
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

Beyond the aspects mentioned in relation to the evaluation, it seems to me that the work is well motivated and nicely presented. The contribution is rather limited, but overall I enjoyed reading the paper.
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?

I believe the paper could be accepted if the other reviewers are not concerned with the limited evaluation.
What is the ranking of this paper in your review stack?

2
Number of papers in your stack

3
Reviewer confidence

Not Confident

Review #4

Please describe the contribution of the paper

The study addresses automated generation of hexahedral finite element meshes of aortic valves. The proposed method relies on deformation of a template mesh. The deformation field is determined through minimisation of the mesh distortion energy using convolutional neural network while enforcing spatial accuracy (measured as distance to the surface). The proposed method is show-cased by conducting aortic valve stress analysis (using finite element method) for 10 patient data-sets.
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.

Fast (automated) generation of hexahedral patient-specific finite element meshes is one of the unsolved challenges in computational biomechanics. The study presents a possible solution to overcome this challenge. Although the scope is limited to aortic valves, it may be anticipated that the proposed approach can be applied also to other body organs.
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.

Rather strong statement about advantages of hexahedral (over tetrahedral meshes) are made in the manuscript. Although in general correct, they are presented as facts/”truths” without providing any specific supporting arguments/evidence and without explicitly stating that advantages of hexahedral elements are particularly evident for soft incompressible (nearly incompressible) continua such as soft tissues.

For mesh quality evaluation, only Jacobian determinant and skew metric are used. Nothing wrong with these measures/criteria, but it is unclear why other commonly used metrics, such as warpage and aspect ratio have not been used.

The manuscript contains section about the limitations of the proposed method. However, it remains unclear what are the limits of the proposed template-based approach (i.e. what are the limits of the differences between the template and given valve geometry for the proposed mesh “warping” to still work). This would be one of the key limitations of the proposed template-based meshing approach.

FE stress analysis: the description is extremely brief without any information about the mesh used (how many nodes and elements in the meshes), analysis type (static or transient, linear of nonlinear), material models used, and finite element code/solver used. Figure 4: No units are provided for the computed stress (is stress in kPa?).

There is no information about the time required to generate the meshes from the template using the proposed method — such information would likely be of importance and interest for potential users.

There are many unclear/vague and possibly erroneous statements in the manuscript (e.g. “deformation can be defined more flexibly”, “we used deformation gradient for calculation of various distortion energies” — there is only one definition of distortion energy density in the manuscript in Eq. 7). “Computing F for hexahedral elements involves using quadrature points, but we were able to obtain just as accurate results in less training time by simply splitting each hexahedron into 6 tetrahedra and using the above formulation.” – this statement does not appear to be correct. For hexahedral meshes, the deformation gradient does not have to be calculated at Gauss points.
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

Appears to be sufficient. Datasets are not provided, but sufficient description of the data used is included. If the Authors could consider releasing template meshes and patient-specific meshes generated in the study, it would help to improve confidence in the methods proposed in the study.
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

Provide more convincing justification (references, more specific evidence) for preference for hexahedral rather than tetrahedral meshes.

Expand the section on limitations of the proposed method.

Add stress units used in Fig. 4. Provide more specific information about the FE analysis used (static or transient, linear of nonlinear, material model, number of nodes and elements, finite element code/solver used).
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?

Fast/automated generation of patient-specific hexahedral meshes is a formidable challenge. The study proposes a possible solution to this challenged. Revision is clearly required, but it would be limited to providing additional information about the study (without any need for obtaining more results) and clarification of the statements/formulations in the manuscript
What is the ranking of this paper in your review stack?

3
Number of papers in your stack

3
Reviewer confidence

Somewhat 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.

This paper proposes a deep-learning based generation of a volumetric mesh for FEM. It fills the gaps between existing methods that generates only surfacic FEM meshes and preserves of distorsion energy into the learned generation. This work is relevant for stress analysis of aortic valves in cardiac imaging.

One reviewer notes the novelty of genereting full volumetric FEM meshes instead of current surfacic meshes from images, and appreciates the discussion on its application to aortic valve simulations. It notes “a very good paper with only minor flaws”. It hihglights the potential impact of this approach for TAVR and other applications relying on FEM meshes.

A second reviewer appreciates the use of a learning approach to generate volumetric FEM meshes using distorsion energy. Questions on methodological motivations are raised.

A third reviewer mentions the “difficult challenge” of volumetric mesh generation, but indicate a lack of comparison with mesh-based methods.

A fourth reviewer also mentions a “formidable challenge”, has minor clarifications.

All reviewers convergence on the one same positive contribution of learning a volumetric mesh generation for FEM aortic valve simulations. Learning based approaches currently fails in providing only surfacic meshes or derived from surfaces, whereas this paper should have good impact in the cardiac community. The evaluation appears solid, although irreproducible, with meshes described as of improved accuracy. Improvement could be on clarifying statements on hexahedral vs tetrahedral meshes, and descriptions on experiments.

For all these reasons, the paper should be a clear contribution to the field which could enable new straightforward FEM applications. Recommendation is towards Early Acceptance.

Oral: All three reviewers have recommended Oral, and two recommends a young scientists award. This is supported by the “formidable / difficult challenge” the authors have faced and its high impact in cardiac imaging.
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).

1

Author Feedback

Thank you to all reviewers and the meta-reviewer for the helpful comments. Here, we would like to take the opportunity to answer questions and address potential confusions.

R1: “The method appears to be computationally expensive… This will be important for generating patient-specific volumetric meshes… in a fast and accurate manner.” – We would like to emphasize that most of the computational burden only pertains to the training phase. Our inference step takes ~20ms per image (Section 3.2). “What was done to prevent mesh tangling?” – For space deformation, we used “a dense topology-preserving smooth field” (Section 2.1.1), which effectively prevents meshes from folding or tearing after deformation. For node-specific displacements, we have no such method of topology-preservation, and thus space deformation is preferred. In both formulations, distortion minimization discourages mesh tangling at a local scale because mesh tangling would require significant distortion of multiple neighboring elements. “The authors also mention ablation… I don’t understand what is meant here” – We simply meant experiments with and without the weighting strategy of Section 2.3 (i.e. ablation studies in machine learning).

R2: “Explain how the valve thickness is set” – We used a leaflet thickness of ~0.8mm, which was based on representative parameters from the literature and our co-authors’ extensive experience in working with aortic valve simulations. Can we use “the presented method to model such extremely slender structures” – Our proposed method aims to keep consistent leaflet thickness before and after template deformation. Based on the uniformity of the ~0.8mm thickness in our predicted meshes, we believe the method can model thinner structures. For modeling the “calcified aortic valve,” we plan to develop a separate non-template-deformation method for incorporating calcification as a separate entity because (1) it has random location and amount in each patient and (2) it has vastly different geometry and material properties from the valve. For tetra vs hexahedra, the Abaqus documentation specifies that first-order tetrahedra “should not be used except as filler elements in noncritical areas,” one explanation of which is due to volumetric locking when modeling incompressible continua such as soft tissues. Furthermore, “a good mesh of hexahedral elements usually provides a solution of equivalent accuracy at less cost” compared to second-order tetrahedra. We thank the reviewer for other suggestions on the details of FEM (e.g. contact handling, Eulerian models, fibrous and anisotropic structure). Due to limited space, we omitted most FEM info because we only meant to validate our meshes’ suitability as FEM geometry inputs, not provide extensive biomechanics insight. We will address these points in future works.

R3: “A comparative study with the methods mentioned in Section 1 would definitely make the contributions stronger” – We agree, but unfortunately none of the non-deep-learning cited works had public code available. Furthermore, most deep learning methods are variations of our implemented baseline experiments, usually with modifications to the network architecture. For proper evaluation of distortion minimization, we used a consistent network architecture for each deformation strategy.

R4: For the “limits of differences between the template and given valve geometry”, we believe that our method will work as long as the patient does not have a congenital valve abnormality (i.e. the patient has three leaflets). “For hexahedral meshes, the deformation gradient does not have to be calculated at Gauss points” – We are unaware of such a method, and we would be delighted to explore this further. We based our calculation of F on the cited literature. The number of nodes and elements were specified in Section 3.1. We thank the reviewer for many other comments. We believe we provided an explanation for most of them in previous responses.

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Distortion Energy for Deep Learning-based Volumetric Finite Element Mesh Generation for Aortic Valves