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Abstract

Abeta Positron Emission Tomography (PET) is often used to manage Alzheimer’s disease (AD). To better understand Abeta progression, we introduce and evaluate a mathematical model that couples Abeta at parcellated gray matter regions. We term this model LNODE for ``latent network ordinary differential equations’’. At each region, we track normal Abeta, abnormal Abeta , and m latent states that intend to capture unobservable mechanisms coupled to Abeta progression. LNODE is parameterized by subject-specific parameters and cohort parameters. We jointly invert for these parameters by fitting the model to Abeta -PET data from 585 subjects from the ADNI dataset. Although underparameterized, our model achieves population R-square > 98% compared to R-square > 60% when fitting without latent states. Furthermore, these preliminary results suggest the existence of different subtypes of Abeta progression.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2025/paper/0906_paper.pdf

SharedIt Link: Not yet available

SpringerLink (DOI): Not yet available

Supplementary Material: Not Submitted

Link to the Code Repository

N/A

Link to the Dataset(s)

N/A

BibTex

@InProceedings{WenZhe_LNODE_MICCAI2025,
        author = { Wen, Zheyu and Biros, George},
        title = { { LNODE: Uncovering the Latent Dynamics of Aβ in Alzheimer’s Disease } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15974},
        month = {September},
        page = {316 -- 325}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    This paper introduces LNODE (Latent Network Ordinary Differential Equations) for modeling Amyloid-beta evolution in Alzheimer’s disease. The key innovations are: 1. incorporation of latent states for capturing unobserved mechanisms that are entangled with Amyloid-beta evolution; 2. joint optimization of subject-specific and cohort-level shared parameters on a large cohort; and 3. sparse coupling for identifying disease subtypes. The authors demonstrate that with very limited additional parameters per subject, their model provides remarkable improvement in predictive accuracy. The model also provides a window into potential Amyloid-beta progression subtypes, which could have significant implications for our understanding of disease heterogeneity in Alzheimer’s.

  • 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 designs a latent-state ode sturcture to capture unobservable mechanisms in the amyloid progression.
    2. LNODE leverages information across the entire cohort to learn shared disease dynamics while preserving individual variability.
    3. The model supports the identification of disease subtypes through clustering of the latent state parameters, offering potential for personalized medicine approaches. 4.The paper presents a thorough mathematical formulation with careful attention to parameter estimation, including gradient calculations via adjoint methods.
  • 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. Limited biological interpretation: While the latent states improve model performance significantly, their biological meaning remains unclear. The paper would benefit from deeper discussion of what these latent states might represent physiologically.
    2. Concerns about model complexity vs. meaningful design: The improved performance with latent states (may primarily reflect increased model complexity rather than clinically meaningful design choices. The paper doesn’t sufficiently demonstrate that the latent states capture genuine biological mechanisms rather than just fitting statistical noise.
    3. Insufficient comparison with existing models: The paper only compares against a basic ODE model without latent states. Direct comparisons with other advanced mathematical models and contemporary deep learning approaches would better contextualize the claimed improvements and advantages of LNODE.
    4. Limited novelty in latent variable approach: Several existing works have explored latent variable models and subtyping strategies for disease progression. The paper doesn’t adequately differentiate its contribution from prior latent variable approaches in disease modeling literature, particularly those already applied to neurodegenerative diseases.
    5. Though the paper mentions identifying disease subtypes, it doesn’t explore whether these subtypes correlate with clinical outcomes, progression rates, or treatment responses.
  • 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.

  • 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/2025/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 — could be rejected, dependent on rebuttal

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

    This paper presents LNODE, a mathematical framework modeling Amyloid-beta progression in Alzheimer’s disease using latent states. The approach shows technical merit with its mathematical foundation and improved statistical performance on the ADNI dataset. However, there are several concerns. The dramatical increase of the model performance likely reflect increased model complexity rather than clinically meaningful insights, as the paper doesn’t convincingly demonstrate that latent states capture genuine biological mechanisms. The novelty is limited since similar latent variable approaches and subtyping strategies have been previously explored in disease progression modeling. There’s inadequate comparison with contemporary models, both advanced mathematical approaches and deep learning methods. Additionally, despite identifying potential subtypes, the paper doesn’t investigate whether these correlate with meaningful clinical outcomes or progression rates, leaving clinical relevance uncertain. Additional work addressing biological interpretability, clinical relevance, and positioning relative to existing approaches would significantly strengthen this research.

  • 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



Review #2

  • Please describe the contribution of the paper

    This paper proposes LNODE, a cohort-based ODE model incorporating latent states to model Aβ progression in Alzheimer’s disease (AD), trained using Aβ-PET imaging data. The conclusions include:

    • Introduces a novel latent-variable ODE framework that models the dynamics of Aβ accumulation across brain regions.
    • Jointly estimates subject-specific and cohort-shared parameters from cohort data, achieving strong performance (significant R² improvement) compared to existing mechanistic models.
    • Reveals potential new subtypes of Aβ progression by analyzing the learned latent structure.
    • Demonstrates robustness and generalization across both synthetic and real clinical datasets (ADNI), including analysis of latent state dimensionality.
  • 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.
    • Novelty: The introduction of latent ODEs (LNODE) to model Aβ dynamics in a cohort-shared yet individualized manner is innovative.
    • Methodological Rigor: The paper provides a detailed and clear formulation of the ODE systems, with a careful inverse problem setup incorporating regularization and sparsity constraints.
    • Promising Results: The method shows significant improvement over baselines, achieving a 45.9% R² uplift compared to the state-of-the-art.
    • Subtype Discovery: The use of latent variables to reveal subtypes is interesting and presented in an interpretable manner.
  • 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.
    • Data Usage: While ADNI is a strong dataset, the work would be strengthened by demonstrating robustness across additional datasets that also include Aβ data (e.g., AIBL, OASIS), although this is understandably future work.
    • Subtype Validation: Subtypes are identified via k-means clustering on the wiw_iwi vectors; however, there is limited biological or clinical validation (e.g., MMSE trends, tau-PET differences).
    • Clarity and Readability: The paper is quite dense and mathematical. While technical depth is necessary, it would benefit from clearer explanations and higher-level intuition, particularly in Section 2 (mid-page 5) and Section 3 (mid-page 6). The heavy concentration of equations interwoven with text reduces overall readability.
  • 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.

  • 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/2025/en/REVIEWER-GUIDELINES.html
    • In Figure 1, panels (A), (B), and (C) could be visually separated more clearly.
    • You use both the terms “latent state” and “hidden state” in the paper, but it is unclear whether they refer to the same concept.
  • 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 — could be accepted, dependent on rebuttal

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

    Accept with minor revisions. This work presents a novel and methodologically sound modeling framework with promising results in modeling Aβ progression in Alzheimer’s disease. Improvements in presentation, minor clarifications, and additional validation of the discovered subtypes would further strengthen the paper.

  • 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



Review #3

  • Please describe the contribution of the paper

    In this paper, the authors propose a latent network ordinary differential equation based framework to model the progression of Amyloid Beta (Abeta) proteins in Alzheimer’s disease.

  • 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.

    Major strength of the paper is in its novel theoretical formulation that is biologically inspired. It incorporates sparse initial conditions for abnormal Abeta, network-based spread of Abeta, clearance of abnormal Abeta, and latent states that account for disease subtypes (each of which are biologically motivated) in a unified mathematical framework.

  • Please list the major weaknesses of the paper. Please provide details: for instance, if you state that a formulation, way of using data, demonstration of clinical feasibility, or application is not novel, then you must provide specific references to prior work.

    The main weaknesses of the paper are enlisted below:

    1. The latent states that correspond to different subtypes have been mentioned in pages 3 and 5 to take values k = 1,…,m with m being 1,2,3. Yet, the result in Figure 2b shows no latent states as the baseline result. It is not clear why a condition of “no subtype” be chosen for evaluation or if it is biologically meaningful.
    2. The criteria for choosing 3 subtypes as the optimum result is not clear and appear subjective. The authors state in page 8 (Section 3) that m=4 was also tested, which is inconsistent with previous assertions in Section 2 that m = 1,2,3 were tested.
    3. The detected subtypes have not been clinically characterized, nor have other subtyping techniques been used for testing the validity or clinical usefulness of the detected subtypes.
    4. The authors introduce 2 evaluation metrics R^2{cohort} and \sum{R^2{scan}} to quantify the proportion of the variance explained by the model in the cohort, and for a subject respectively. While R^2{cohort} has been reported for the training set and the independent test-set, \sum{R^2{scan}} has not been reported for the test-set. It is also unclear how many follow-up scans (on average) for each subject are used to obtain this.
    5. It appears that while the model explains the average Abeta progression in different subtypes, a substantially lower \sum{R^2_{scan}} indicates that per-subject differences remain that cannot be explained by the model. A brief discussion on this would help the readers in interpreting the model.
  • 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.

  • 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/2025/en/REVIEWER-GUIDELINES.html

    I found the description to be too dense for it to be useful for reproducibility just based on the shared information.

  • 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.

    (5) Accept — should be accepted, independent of rebuttal

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

    Inspite of the weaknesses mentioned above, the elegant mathematical formulation introduced in this paper explaining Abeta progression in Alzheimer’s disease offers a promising way to investigate disease mechanisms.

  • 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 sincerely appreciate reviewers’ thorough review of our manuscript and the valuable feedback provided. We focus on the main points raised by the reviewers.

Response to Reviewer 1:

Comments 1: It is not clear why a condition of ”no subtype” be chosen for evaluation or if it is biologically meaningful?

Response: In the literature, the most popular model corresponds to one special case of our proposed LNODE model, where there is no latent states. Our proposed LNODE model is a generalization of this model with more powerful performance using very limited additional parameters. We take “no latent states” as the baseline model which is equivalent to compare our model with the SOTA model in the literature under comparable number of parameters.

Comments 2: The detected subtypes have not been clinically characterized, nor have other subtyping techniques been used for testing the validity or clinical usefulness of the detected subtypes.

Response: It is our future work to validate the subtypes using other subtyping techniques. In this paper, we focus on the methodology and preliminary results.

Comments 3: It appears that while the model explains the average Abeta progression in different subtypes, a substantially lower R2scan indicates that per-subject differences remain that cannot be explained by the model.

Response: In the literature, R2cohort is one of the most popular metrics to evaluate the model performance. The R2cohort in the SOTA model on Abeta is lower than 0.7 while our model achieves numbers above 0.98. Regarding to R2scan, the literature seldom reports this metric since this number is always much lower than R2cohort. We report both of them to show the performance of our model. Even though the R2scan is lower than R2cohort, we still show the power of the proposed model.

Response to Reviewer 3:

Comments 1: The paper would benefit from deeper discussion of what these latent states might represent physiologically.

Response: The latent states corresponds to the common progression trajectories of the disease across the population. They are used to identify subtypes of patients with similar disease progression patterns.

Comments 2: Concerns about model complexity vs. meaningful design: The improved performance with latent states may primarily reflect increased model complexity rather than clinically meaningful design choices.

Response: As what we mentioned in the paper, the model complexity increase very little but the performance improves significantly. As far as we know, more complex models exist in the literature, but they never achieve a R2cohort like ours.

Comments 3: Limited novelty in latent variable approach: Several existing works have explored latent variable models and subtyping strategies for disease progression.

Response: We proposed the “latent network” ODE model which means that the latent states are generated from the network perspective. The latent states are not directly derived from the image data (e.g. using auto-encoder scheme) but inferred from both the network model and longitudinal Abeta abnormality defined in the paper. The novelty is sufficient and quite different from the existing works.

Response to Reviewer 8:

Comments 1: While ADNI is a strong dataset, the work would be strengthened by demonstrating robustness across additional datasets that also include Abeta data (e.g., AIBL, OASIS), although this is understandably future work.

Response: Thanks the reviewer’s suggestion. We will explore the robustness of our model on other datasets in the future.

Comments 2: Subtypes are identified via k-means clustering on the wi vectors; however, there is limited biological or clinical validation.

Response: This belongs to the future work. We will conduct further validation of the subtypes using other subtyping techniques and explore the clinical characteristics of the detected subtypes.



Meta-Review

Meta-review #1

  • Your recommendation

    Provisional Accept

  • If your recommendation is “Provisional Reject”, then summarize the factors that went into this decision. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. You do not need to provide a justification for a recommendation of “Provisional Accept” or “Invite for Rebuttal”.

    Major strength of the paper is in its novel theoretical formulation that is biologically inspired. The approach shows technical merit with its mathematical foundation. There are some improvement (validation) and clarification points mentioned by the reviewers.



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