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Abstract
The crucial role in diagnosing ischemic coronary artery disease is played by fractional flow reserve evaluation. Machine learning based fractional flow reserve evaluation has become the most important method due to it effectiveness and high computation efficiency. However, it still suffers from lacking of the proper description for the coronary artery fluid. This study presents a variational field constraint learning method for assessing fractional flow reserve from digital subtraction angiography images. Our method offers a promising approach by integrating governing equations and boundary conditions as unified constraints. Moreover, we also provide a multi-vessels neural network for the prediction of FFR for coronary artery. By leveraging a holistic consideration of the fluid dynamics, our method achieves more accurate fractional flow reserve prediction compared to existing methods. Our VFCLM is evaluated over 8000 virtual subjects produced by 1D hemodynamic models and 180 in-vivo cases. VFCLM achieves the MAE of 1.17 mmHg and MAPE of 1.20% for quantification.
Links to Paper and Supplementary Materials
Main Paper (Open Access Version): https://papers.miccai.org/miccai-2024/paper/0134_paper.pdf
SharedIt Link: https://rdcu.be/dV1Xm
SpringerLink (DOI): https://doi.org/10.1007/978-3-031-72384-1_72
Supplementary Material: N/A
Link to the Code Repository
N/A
Link to the Dataset(s)
N/A
BibTex
@InProceedings{Zha_Variational_MICCAI2024,
author = { Zhang, Qi and Liu, Xiujian and Zhang, Heye and Xu, Chenchu and Yang, Guang and Yuan, Yixuan and Tan, Tao and Gao, Zhifan},
title = { { Variational Field Constraint Learning for Degree of Coronary Artery Ischemia Assessment } },
booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2024},
year = {2024},
publisher = {Springer Nature Switzerland},
volume = {LNCS 15003},
month = {October},
page = {768 -- 778}
}
Reviews
Review #1
- Please describe the contribution of the paper
This paper describes a new framework using variational formulations for the estimation of fractional flow reserve. The framework reformulate the problem of estimating fractional flow reserve from angiograms by integrating the constitutive equations of Navier-Stokes with the problem of finding the patient-specific boundary conditions into a single variational formulation.
- 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 overcomes one of the limitation of physic-informed neural networks which require introducing a prior on the boundary condition. The method presented in this paper propose a strong coupling of the boundary conditions with the constitutive equations in the training loss instead, increasing accuracy by better leveraging the available data. The proposed method decreases the error on both a virtual and real dataset by as much as half the MAE compared to other state-of-the-art methods.
- 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 quality of the writing makes understanding difficult at times. Incorrect references to Murray’s law (first paragraph page 4). Several important variables/parameters are not described in the text (e.g., N, \mu, \nu). Figure 2 isn’t clear, with some of its components not appearing in the text. The paper lacks critique on the limitations of the study. There are some many typos to pa attention.
- Please rate the clarity and organization of this paper
Poor
- 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.
- Do you have any additional comments regarding the paper’s reproducibility?
Parts of the pipeline are unclear, e.g., in Figure 2 “Network calculating in single vessel” and how is fractional flow reserve effectively calculated.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
Parts of the pipeline are unclear, e.g., in Figure 2 “Network calculating in single vessel” and how is fractional flow reserve effectively calculated.
- 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
Weak Accept — could be accepted, dependent on rebuttal (4)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The paper’s overall structure is good. The algorithm seems novel and shows good performance. The method is described in some detail but lack clarity at times. Parts of the framework is not described in enough details. However, many references are given to make up for this. Language mistakes and typos make the understanding difficult at times.
- Reviewer confidence
Very confident (4)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
N/A
Review #2
- Please describe the contribution of the paper
This study introduces a variational field constraint learning method for assessing fractional flow reserve (FFR) from digital subtraction angiography images, addressing the challenge of lacking proper description for coronary artery fluid dynamics. By integrating governing equations and boundary conditions as unified constraints, along with a multi-vessel neural network for FFR prediction, the method achieves more accurate FFR prediction compared to existing methods, with promising results evaluated across virtual and in-vivo cases.
- 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.
- VFCLM to obtain physical information within the temporal and spatial domains of the coronary artery and accurately assess FFR from digital subtraction angiography images,
- VFCLM introduces a variational form integrally taking into account the Navier-stokes equations and boundary conditions,
- VFCLM uses a multi-vessel network structure and adds Murray’s law as the hard constraint to satisfy the fluid properties in the vascular tree.
- The extensive experiments on the 8000 synthetic coronary and digital sub- traction imaging images of 180 cases. The performance of VFCLM demonstrates advantages over existing methods.
- 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.
Limited evaluation of clinical studies.
- Please rate the clarity and organization of this paper
Very 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.
- Do you have any additional comments regarding the paper’s reproducibility?
N/A
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
The performance of VFCLM demonstrates advantages over existing methods. Further evaluation of clinical studies is important.
- 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
Weak Accept — could be accepted, dependent on rebuttal (4)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The performance of VFCLM demonstrates advantages over existing methods. Further evaluation of clinical studies is important.
- Reviewer confidence
Somewhat confident (2)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
N/A
Review #3
- Please describe the contribution of the paper
Injects biophysical priors via Navier-Stokes to modeling blood flow as a way to improve FFR (a diagnostic). It uses a variational form to allow computational solution of the biophysical constraints.
- 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.
It leverages biophysical priors to improve a model. This is a fundamentally strong approach, and is a valuable contribution (assuming, as others can verify much better than myself, that the details of the method are coherent). It addresses a concrete use case (increasing usability of FFR).
- 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.
Insufficient descriptions of some items (eg equations dropped in without motivation) Substantial grammar and typo problems detract from the value of the content. The paper requires a thorough proofing to maximize its impact on readers. Without this proofing, it will likely not be taken seriously.
- 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.
- Do you have any additional comments regarding the paper’s reproducibility?
Applying Navier Stokes in this context is a highly interesting approach. Except for grammar, the exposition is clear. Bottom of pg 1: is there a ref, esp review, for the last claim “promising method”)? Pg 2 “Because they use a integral…” Good insight Fig 1 caption: “uniformed form”? “prepossessing” - typo will not get caught by spellcheck Pg 4: “father” - “parent” is more standard Murray’s law: Give definition Fig 2: why no outlet conditions? Is there any “in == out” condition? Eqn 1: What is N? a scalar, function? Pg 5: what is a “pure impedance boundary” Eqns 4 and 5: do these equations have derivations or intuitive motivations? They drop in with no way to verify correctness. Put something in an Appendix? Pg 6: “towards the true solution”: “towards a true solution” I assume, since non-unique. Can you briefly discuss uniqueness of solutions, what guarantee of reaching a biologically realistic solution, etc? Fig 3: Please, more explanation in the caption, especially what the four subplots are showing. “PINN, GPGNN, and 1D-Comp…”: please add brief summaries and references for all these. Bibliography formatting: many capitalized terms are lower case, eg “mri”. You can use braces {MRI} to protect upper case letters.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html
Applying Navier Stokes in this context is a highly interesting approach. Except for grammar, the exposition is clear. Bottom of pg 1: is there a ref, esp review, for the last claim “promising method”)? Pg 2 “Because they use a integral…” Good insight Fig 1 caption: “uniformed form”? “prepossessing” - typo will not get caught by spellcheck Pg 4: “father” - “parent” is more standard Murray’s law: Give definition Fig 2: why no outlet conditions? Is there any “in == out” condition? Eqn 1: What is N? a scalar, function? Pg 5: what is a “pure impedance boundary” Eqns 4 and 5: do these equations have derivations or intuitive motivations? They drop in with no way to verify correctness. Put something in an Appendix? Pg 6: “towards the true solution”: “towards a true solution” I assume, since non-unique. Can you briefly discuss uniqueness of solutions, what guarantee of reaching a biologically realistic solution, etc? Fig 3: Please, more explanation in the caption, especially what the four subplots are showing. “PINN, GPGNN, and 1D-Comp…”: please add brief summaries and references for all these. Bibliography formatting: many capitalized terms are lower case, eg “mri”. You can use braces {MRI} to protect upper case letters.
- 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
Accept — should be accepted, independent of rebuttal (5)
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The approach brings in new structural information to narrow the search space for the model. My recommendation assumes that the grammar gets fully corrected.
- Reviewer confidence
Confident but not absolutely certain (3)
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
N/A
- [Post rebuttal] Please justify your decision
N/A
Author Feedback
We are immensely thankful to AC and all the Reviewers for their thorough review of this manuscript and for their valuable suggestions. We note that both reviewers provided comments on the syntax of the writing of this manuscript as well as the description of the equations. Therefore, we have made improvements in response to reviewer comments.
- Section of introduction: We’ve added a reference to promising method on page 1. What makes ML a promising method for obtaining FFR is that compared with CFD method, ML method overcomes the experience requirements and time consumption caused by tedious pre-processing and grid rendering. For the comment of Reviewer #3, we are deeply sorry for the misuse of the word “preprogressing”, so we change it to “progressing”.
- Section of Method: We would like to thank Reviewers #1 and #3 for their comments on the details of the method, which we believe are very helpful in improving the quality of the manuscript. As the comment of Reviewer #1 for Murray’s law, we add the references to explain what it means. According to Reviewer #3’s opinion, we have revised “father” to “parents”. For the outlet boundary condition, we used the impendence, which build the relationship of velocity and pressure in boundary, which has been widely used. The parameter N represents the pressure dropping caused by stenosis, which could be found in the Ref. [14]. The parameter \mu and \rho represents the viscosity and density with the value of 0.003 Pa.s and 1060 Kg/m^3. The Eq. (5) represents the energy functional and it was preliminarily obtained in article titled “Outflow boundary conditions for one-dimensional finite element modeling of blood flow and pressure waves in arteries”, and we discretized it and added stenosis model coupling to obtain the updated format (suitable for PINN) in this study.
- Section of Experiment and Result: As the “true solution” in page 6, it refers to the numerical solution that satisfies the clinical measurement, which should be unique in the determined discrete format and under the certain clinical measurements. We have retained the description of the numerical solution. We note that reviewer #5 believes that the validation of the clinical application of this study is insufficient, but we still want to state that this study first generated a virtual dataset with fluid mechanics methods, and the method proposed in this study achieved good results on this dataset, which proves that the proposed method can obtain physical information satisfying NS equation and boundary conditions. Later, the method was used in clinical data sets to verify the possibility of clinical application of this study, and good results were obtained, and this clinical dataset consists of 180 cases. We believe is sufficient to explain the feasibility of this study in clinical application.
- Section of Figure: For Figure 1, the caption” uniformed form” represents a uniform practice for the rest of PINN-related research in dealing with the Navier-stokes equation and boundary condition. So, we keep this word to exhibit the correctness of this method. For Figure 2, the details of the elements were shown in page 3 and 4, but as the Reviewer thought that our supplementary explanation to Figure 2 was insufficient, we added some details in page 4, including the details about neural networks.
Meta-Review
Meta-review not available, early accepted paper.