arxiv: 2605.00272 · v1 · submitted 2026-04-30 · 🧬 q-bio.QM

Recognition: unknown

LNODE: latent dynamics reveal the shared spatiotemporal structure of amyloid-β progression

George Biros, Zheyu Wen

Pith reviewed 2026-05-09 19:20 UTC · model grok-4.3

classification 🧬 q-bio.QM

keywords amyloid-betaAlzheimer's diseaseneural ODEPET imaginglatent statesspatiotemporal dynamicsdisease progressionbiomarker modeling

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The pith

A regional neural ODE with latent states captures shared patterns of amyloid-beta buildup and predicts future PET scans years ahead using few parameters per subject.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents LNODE as a mechanism-based model for amyloid beta dynamics in Alzheimer's disease, built as an underparameterized regional neural ODE that is calibrated jointly across entire cohorts of PET scans. It incorporates latent states whose shared temporal evolution allows the model to represent both population trajectories and individual deviations while tracking spatial propagation, proliferation, and clearance of the protein. Despite using only five to ten parameters per subject, the approach fits observed data to R-squared values above 0.99 and successfully forecasts signals in previously unseen scans separated by more than four years. Clustering within the learned latent space further identifies distinct subgroups, suggesting different progression subtypes. If this holds, the model could enable better harmonization of imaging data and more reliable long-term forecasts from limited observations.

Core claim

LNODE is formulated as a regional neural ordinary differential equation model that incorporates a latent-state representation modulating Aβ dynamics, with temporal evolution governed by cohort-shared parameters. When jointly calibrated on 1461 ADNI subjects and 1070 A4 subjects using MUSE and DKT atlases, it captures spatial propagation, proliferation, and clearance of amyloid beta, achieving R² greater than 0.99 on both datasets and accurate predictions on held-out follow-up scans including intervals exceeding four years, while latent-state clustering reveals distinct subgroups consistent with Alzheimer's progression subtypes.

What carries the argument

The latent-state representation within the regional neural ODE, which modulates Aβ dynamics via cohort-shared parameters for temporal evolution while permitting subject-specific deviations.

If this is right

The model enables fusion and harmonization of Aβ PET scans across cohorts for quantitative analysis.
It supports forecasting of amyloid-beta signals in future scans even with multi-year gaps between observations.
Latent-state clustering identifies distinct subgroups consistent with different Alzheimer's progression subtypes.
Strong parameter identifiability and stability properties are supported by synthetic experiments and Hessian analysis.
Intentional underparameterization reduces overfitting and spurious correlations while maintaining high fit accuracy.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The shared-parameter structure could be tested for transferability to other imaging modalities or biomarkers to build integrated progression models.
If the latent clusters remain stable across datasets, they might serve as a basis for stratifying patients in future studies of disease modifiers.
The parsimonious parameterization suggests potential scalability to larger multimodal datasets without proportional increases in subject-specific variables.

Load-bearing premise

The underparameterized regional neural ODE with latent states truly captures the underlying biological spatiotemporal dynamics of amyloid-beta progression instead of merely fitting observed imaging patterns, and the resulting clusters reflect biologically meaningful subtypes.

What would settle it

Application of the calibrated model to an independent cohort with different PET protocols or extended follow-up intervals where predictive accuracy on unseen scans drops substantially below 0.99 or where latent-state clusters fail to align with independent clinical or genetic markers of progression.

Figures

Figures reproduced from arXiv: 2605.00272 by George Biros, Zheyu Wen.

**Figure 1.** Figure 1: Overview of the proposed LNODE method. The workflow comprises four main components: (A) Data preprocessing. We collect T1-weighted MRI and Aβ PET data from the ADNI and A4 Study datasets. PET images are co-registered to each subject’s first T1-weighted MRI scan, and the brain is parcellated into N regions of interest using either the MUSE or DKT atlas. For each scan, we extract a regional Aβ burden, on sca… view at source ↗

**Figure 2.** Figure 2: Quantitative evaluation of the model reconstruction and prediction performance using the DKT atlas. We conduct two experiments to evaluate the model performance on the ADNI cohort: In the first one we reconstruct the data using all cohort scans; in the second one, we use LNODE to predict the second scan using only the first scan to estimate model parameters (defined as the ‘Pred1’ task in the text). The to… view at source ↗

**Figure 3.** Figure 3: Qualitative evaluation of the model reconstruction and prediction performance using the DKT atlas. We perform model inversion using the first scan of each subject as input and predict the next scan (‘Pred1’ task) for subjects in the ADNI cohort. From top to bottom, the three rows correspond to three representative subjects (127_S_5132, 067_S_2169, and 130_S_4660), selected from the CN, MCI, and AD groups, … view at source ↗

**Figure 4.** Figure 4: Prediction results comparison for ADNI dataset when m = 0 and m = 10 for CN, MCI and AD groups. We perform the prediction experiment to predict the next scan for subjects with longitudinal data in ADNI dataset (‘Pred1’ task). We compare the prediction performance when m = 0 and m = 10 for CN, MCI and AD groups in the metrics of R2 scan and R2 cohort. From top to bottom, the three rows correspond to CN, MCI… view at source ↗

**Figure 5.** Figure 5: Prediction of unseen Aβ scans for ADNI and A4 subjects. The trained simple binary classifier is applied to A4 Study subjects to identify individuals with potential diagnostic transitions from CN to AD. For ADNI dataset, we use provided ground-truth longitudinal diagnosis labels to identify subjects with diagnostic transitions. For both datasets, we train the LNODE model using status-stable subjects and sub… view at source ↗

**Figure 6.** Figure 6: Synthetic experiment results. We generate synthetic data using the proposed LNODE model with m = 1 latent state and randomly sampled, known cohort-shared and subject-specific parameters. We then apply the LNODE inversion procedure to recover the synthetic scans and model parameters. Model performance is evaluated in terms of reconstruction accuracy and stability of the estimated parameters. With fixed obse… view at source ↗

**Figure 7.** Figure 7: The most frequent Aβ initial condition (IC) locations identified by the algorithm for the MUSE and DKT atlases in the ADNI and A4 cohorts. We perform model inversion to reconstruct Aβ scans for all subjects in the ADNI and A4 datasets using either the MUSE or DKT atlas. From the inversion results, we extract the estimated initial condition (IC) locations and compute the occurrence frequency of each ROI acr… view at source ↗

**Figure 13.** Figure 13: As we increase the number of subjects in the cohort inversion, the condition number of the Hessian [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗

**Figure 8.** Figure 8: Latent states parameters analysis when m = 3, 5, 10. A) We show the cohort-shared latent state parameters ϕ3,k for different numbers of latent states, m = 3, 5, 10. B) For each latent state k, we quantify the sparsity of the subject-specific weights wh,i[k] using the ratio ∥wh∥∞/∥wh∥2. Larger values of this ratio indicate greater sparsity. This analysis is performed for the cases m = 3, 5, 10. (C) For a gi… view at source ↗

**Figure 9.** Figure 9: Latent state trajectory as a function of disease age. We compute the mean and standard deviation of the latent state trajectories hi,k(t) across subjects i for different latent states. From top to bottom, the five rows correspond to the five latent states under m = 5. The first ten columns display the mean latent state trajectory at disease ages t = 0, 0.25, 0.5, 0.75, 1, with two brain views shown for eac… view at source ↗

**Figure 10.** Figure 10: Quantitative evaluation of reconstruction and prediction using the MUSE atlas. We assess model performance on the ADNI cohort through two tasks: reconstruction using all scans and prediction of the next scan using only the first scan for parameter estimation. The top row shows reconstruction with m = 10, the middle row shows next-scan prediction with m = 10, and the bottom row compares prediction performa… view at source ↗

**Figure 11.** Figure 11: Qualitative evaluation of the model reconstruction and prediction performance using the MUSE atlas. We perform model inversion using the first scan of each subject as input and predict the next scan for subjects in the ADNI cohort and we use MUSE atlas here. From top to bottom, the three rows correspond to three representative subjects, selected from the CN, MCI, and AD groups, respectively. These subject… view at source ↗

**Figure 12.** Figure 12 [PITH_FULL_IMAGE:figures/full_fig_p037_12.png] view at source ↗

**Figure 13.** Figure 13: We compute the condition number of the whole Hessian matrix H. We explore the changes of the condition number versus number of subjects. The condition number decreses as the number of subjects increases, indicating improved identifiability and stability of parameter estimation. 38 [PITH_FULL_IMAGE:figures/full_fig_p038_13.png] view at source ↗

read the original abstract

We introduce LNODE, a mechanism-based phenomenological model for amyloid beta (A$\beta$) dynamics, calibrated using positron emission tomography (PET) imaging. A$\beta$ is a key biomarker of Alzheimer's disease. LNODE is designed to support the fusion, harmonization, quantitative analysis, and interpretation of Abeta PET scans. We evaluate LNODE on 1461 subjects in the ADNI cohort and 1070 subjects in the A4 Study, using MUSE and DKT anatomical atlases. LNODE is formulated as a regional neural ordinary differential equation (ODE) model that is jointly calibrated on all available scans within a cohort. The model captures the spatial propagation, proliferation, and clearance of A$\beta$ and incorporates a latent-state representation that modulates A$\beta$ dynamics. The temporal evolution of these latent states is governed by cohort-shared parameters, enabling LNODE to represent both population-level trajectories and subject-specific deviations. The proposed model demonstrates strong parameter identifiability and stability properties, supported by synthetic experiments and analytical analysis of the Hessian condition number. To mitigate overfitting and reduce spurious correlations, LNODE is intentionally underparameterized, employing approximately five to ten parameters per subject. Despite this parsimonious parameterization, LNODE achieves $R^2 > 0.99$ in both the ADNI and A4 datasets. LNODE exhibits strong predictive performance: in the A4 cohort, it accurately forecasts the A$\beta$ PET signal in previously unseen follow-up scans, including cases with inter-scan intervals exceeding four years. Clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes of Alzheimer's disease progression.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

LNODE gives a fresh neural ODE setup for amyloid PET that fits tightly and predicts future scans, but the latent clusters as disease subtypes rest on unvalidated assumptions.

read the letter

The main point is that this paper puts forward LNODE, a regional neural ODE with latent states and cohort-shared parameters, to model how amyloid beta progresses across brain regions in PET data. It reports very high fits and some multi-year forecasts on held-out scans from the A4 cohort, plus synthetic checks for identifiability. That combination is new for this specific biomarker and application, and the choice to stay underparameterized with only five to ten subject-specific values is a reasonable guard against overfitting. The high R-squared numbers and the forward prediction test are the concrete strengths here, and the joint calibration across large cohorts like ADNI and A4 shows the model can handle real-scale data without blowing up. The soft spots are around validation and comparison. The abstract gives no baselines against simpler growth models or standard longitudinal methods, and no error bars or uncertainty on the predictions, so it is hard to judge how much the performance actually improves on existing tools. More importantly, the clustering of latent states is presented as revealing distinct Alzheimer's subtypes, yet there is no reported check against independent markers such as APOE status, cognitive scores, or other biomarkers. Without that link, the clusters could reflect statistical patterns in the fitted data rather than true biological pathways. The joint fitting on all scans within a cohort also raises a mild circularity risk for the reported predictive accuracy, even if future scans are held out. This paper is aimed at researchers who build or use quantitative models for Alzheimer's imaging biomarkers. A reader working on harmonization, subtype discovery, or longitudinal forecasting in PET would get practical ideas from the architecture and the results, even if they end up adapting parts of it. It deserves a serious referee because the core modeling idea is coherent and the predictive experiments are specific enough to be worth expert review on the methods and the missing validation steps.

Referee Report

4 major / 1 minor

Summary. The paper introduces LNODE, a regional neural ODE model with a latent-state representation for modeling the spatiotemporal dynamics of amyloid-β (Aβ) progression from PET scans. It is jointly calibrated on cohorts from ADNI (1461 subjects) and A4 (1070 subjects) using MUSE and DKT atlases, claims R² > 0.99 despite using only 5–10 parameters per subject, demonstrates predictive accuracy on held-out future scans (including intervals >4 years), and uses clustering in latent space to identify subgroups consistent with distinct AD progression subtypes. Synthetic experiments and Hessian analysis are cited to support identifiability and stability.

Significance. If the central claims hold after addressing evaluation concerns, LNODE could provide a parsimonious, mechanism-based framework for harmonizing Aβ PET data and forecasting progression, with potential utility in subtype stratification. The intentional underparameterization and reported synthetic validation for identifiability are methodological strengths that distinguish it from purely data-driven approaches.

major comments (4)

[Abstract] Abstract: the claim that LNODE 'accurately forecasts the Aβ PET signal in previously unseen follow-up scans' is at risk of circularity because the model is 'jointly calibrated on all available scans within a cohort'; the manuscript must explicitly describe the train/test split, how subject-specific parameters are estimated without future data, and whether predictions are truly out-of-sample for each subject.
[Abstract] Abstract and results: no quantitative error bars, confidence intervals, or explicit baseline comparisons (e.g., to linear mixed-effects models, standard neural ODEs without latent states, or existing Aβ progression models) are reported despite R² > 0.99 and multi-year predictive claims; this omission makes it impossible to assess whether the performance exceeds what simpler models achieve.
[Abstract] Abstract: the statement that 'clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes' lacks any description of the clustering algorithm, robustness checks (e.g., stability across initializations or subsamples), or correlation with independent markers such as APOE genotype, cognitive scores, or other biomarkers; without this, the biological interpretation remains unsupported.
[Abstract] Abstract: the assertion of 'strong parameter identifiability and stability properties, supported by synthetic experiments' is load-bearing for the underparameterized claim, yet the manuscript provides no quantitative metrics (e.g., recovery error, condition numbers across noise levels) or tests that directly address whether the latent dynamics recover ground-truth subtypes versus statistical artifacts in the PET data.

minor comments (1)

[Abstract] Abstract: the roles of the MUSE and DKT atlases are mentioned without indicating whether results are consistent across atlases or if one is primary.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. These have identified important areas where the manuscript can be clarified and strengthened. We address each major comment point by point below, with commitments to specific revisions.

read point-by-point responses

Referee: [Abstract] Abstract: the claim that LNODE 'accurately forecasts the Aβ PET signal in previously unseen follow-up scans' is at risk of circularity because the model is 'jointly calibrated on all available scans within a cohort'; the manuscript must explicitly describe the train/test split, how subject-specific parameters are estimated without future data, and whether predictions are truly out-of-sample for each subject.

Authors: We agree that the abstract phrasing risks implying circularity and will revise it for precision. The shared cohort-level parameters are estimated jointly, but the predictive evaluation holds out future scans per subject: subject-specific latent states and parameters are fit using only scans up to the start of the prediction window, after which the model is integrated forward without access to the held-out data. We will add an explicit Methods subsection detailing the train/test split, the per-subject hold-out protocol, and confirmation that all reported multi-year forecasts are out-of-sample. revision: yes
Referee: [Abstract] Abstract and results: no quantitative error bars, confidence intervals, or explicit baseline comparisons (e.g., to linear mixed-effects models, standard neural ODEs without latent states, or existing Aβ progression models) are reported despite R² > 0.99 and multi-year predictive claims; this omission makes it impossible to assess whether the performance exceeds what simpler models achieve.

Authors: We concur that error bars and baselines are necessary to interpret the reported performance. In revision we will add bootstrap-derived confidence intervals for all R² and prediction-error metrics. We will also include quantitative comparisons against linear mixed-effects models and standard neural ODEs (without latent states) on identical held-out prediction tasks, reporting mean errors, statistical significance, and results in a new table and figure in the Results section. revision: yes
Referee: [Abstract] Abstract: the statement that 'clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes' lacks any description of the clustering algorithm, robustness checks (e.g., stability across initializations or subsamples), or correlation with independent markers such as APOE genotype, cognitive scores, or other biomarkers; without this, the biological interpretation remains unsupported.

Authors: We will expand the subtype analysis description. The revised manuscript will specify the clustering algorithm, cluster-number selection criterion, and provide robustness checks (stability across random initializations and bootstrap subsamples). We will also report correlations of the resulting clusters with APOE genotype, cognitive scores, and additional biomarkers, accompanied by a new supplementary figure. revision: yes
Referee: [Abstract] Abstract: the assertion of 'strong parameter identifiability and stability properties, supported by synthetic experiments' is load-bearing for the underparameterized claim, yet the manuscript provides no quantitative metrics (e.g., recovery error, condition numbers across noise levels) or tests that directly address whether the latent dynamics recover ground-truth subtypes versus statistical artifacts in the PET data.

Authors: The synthetic recovery experiments and Hessian analysis appear in the Supplementary Information. We will move key quantitative results into the main text, adding tables of parameter recovery error across noise levels, Hessian condition numbers, and explicit tests on synthetic data with known ground-truth subtypes. These additions will directly address recovery of structure versus artifacts. revision: yes

Circularity Check

1 steps flagged

Joint calibration on all scans risks making 'unseen follow-up' forecasts reduce to in-sample interpolation rather than independent extrapolation.

specific steps

fitted input called prediction [Abstract]
"LNODE is formulated as a regional neural ordinary differential equation (ODE) model that is jointly calibrated on all available scans within a cohort. [...] Despite this parsimonious parameterization, LNODE achieves R² > 0.99 in both the ADNI and A4 datasets. LNODE exhibits strong predictive performance: in the A4 cohort, it accurately forecasts the Aβ PET signal in previously unseen follow-up scans, including cases with inter-scan intervals exceeding four years."

The model parameters and latent states are calibrated jointly to the entire set of scans; the subsequent claim of forecasting 'previously unseen follow-up scans' therefore reduces to evaluating the same fitted dynamics on held-in data rather than demonstrating out-of-sample extrapolation.

full rationale

The paper's central modeling step is a regional neural ODE with latent states that is explicitly jointly calibrated to the full cohort data. The abstract then presents R² > 0.99 and 'strong predictive performance' on previously unseen follow-up scans as evidence of generalization. Because the calibration description encompasses all available scans and no separate hold-out protocol is quoted in the provided text, the reported forecasts cannot be shown to be fully independent of the fitted quantities. This constitutes a moderate instance of fitted-input-called-prediction without invalidating the overall mechanistic formulation or the R² fit itself. No self-citation chains, self-definitional equations, or ansatz smuggling are present.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on the validity of modeling Aβ as regional neural ODEs modulated by latent states whose dynamics are governed by shared parameters; these elements are introduced without independent biological validation beyond the fit to PET data.

free parameters (2)

subject-specific parameters
Approximately five to ten parameters per subject calibrated to individual PET scans to capture deviations from population trajectories.
cohort-shared parameters
Parameters governing the temporal evolution of the latent states, fitted jointly across the cohort.

axioms (2)

domain assumption Aβ dynamics can be represented by a system of regional neural ordinary differential equations
Core modeling choice stated in the abstract as the basis for LNODE.
domain assumption Latent states modulate Aβ dynamics with temporal evolution governed by cohort-shared parameters
Enables the separation of population-level trajectories from subject-specific deviations.

invented entities (1)

latent-state representation no independent evidence
purpose: Modulates regional Aβ dynamics and captures subject-specific deviations while sharing temporal parameters across the cohort
New component introduced to represent heterogeneity in progression patterns.

pith-pipeline@v0.9.0 · 5602 in / 1740 out tokens · 43262 ms · 2026-05-09T19:20:33.817045+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

61 extracted references · 1 canonical work pages

[1]

Amyloid beta deposition, neurodegeneration, and cognitive decline in sporadic Alzheimer’s disease: a prospective cohort study

Villemagne, Victor L et al. Amyloid beta deposition, neurodegeneration, and cognitive decline in sporadic Alzheimer’s disease: a prospective cohort study. The Lancet Neurology12, 357 - 367 (2013)

2013
[2]

Rosenberg, Yun Zhou, Anil Kumar, Vanessa Raymont, Hayden T

Wong, Dean F., Paul B. Rosenberg, Yun Zhou, Anil Kumar, Vanessa Raymont, Hayden T. Ravert, Robert F. Dannals et al. In vivo imaging of amyloid deposition in Alzheimer disease using the radioligand 18F-AV-45 (flobetapir F 18). Journal of nuclear medicine51, 913-920 (2010)

2010
[3]

Pereira, Jesse A

Vogel, Jacob W., Nick Corriveau-Lecavalier, Nicolai Franzmeier, Joana B. Pereira, Jesse A. Brown, Anne Maass, Hugo Botha et al. Connectome-based modelling of neurodegenerative diseases: towards precision medicine and mechanistic insight. Nature Reviews Neuroscience24, 620-639 (2023)

2023
[4]

Knopman, William J

Jack, Clifford R., David S. Knopman, William J. Jagust, Ronald C. Petersen, Michael W. Weiner, Paul S. Aisen, Leslie M. Shaw et al. Tracking pathophysiological processes in Alzheimer’s disease: an updated hypothetical model of dynamic biomarkers. The lancet neurology12, 207-216 (2013)

2013
[5]

R. C. Petersen, P. S. Aisen, L. A. Beckett, M. C. Donohue, A. C. Gamst, D. J. Harvey, C. R. Jack, W. J. Jagust, L. M. Shaw, A. W. Toga, J. Q. Trojanowski, & M. W. Weiner. Alzheimer’s disease neuroimaging initiative (ADNI) clinical characterization. Neurology74, 201-209 (2010)

2010
[6]

Rentz, Keith A

Sperling, Reisa A., Dorene M. Rentz, Keith A. Johnson, Jason Karlawish, Michael Donohue, David P. Salmon, & Paul Aisen. The A4 study: stopping AD before symptoms begin? Science translational medicine6, 228fs13-228fs13 (2014)

2014
[7]

Staging beta- amyloid pathology with amyloid positron emission tomography

Mattsson, Niklas, Sebastian Palmqvist, Erik Stomrud, Jacob Vogel, & Oskar Hansson. Staging beta- amyloid pathology with amyloid positron emission tomography. JAMA neurology76, 1319-1329 (2019)

2019
[8]

Villemagne, Pierrick Bourgeat, Jurgen Fripp, Oscar Acosta, Gael Chetelat, Luping Zhou et al

Dore, Vincent, Victor L. Villemagne, Pierrick Bourgeat, Jurgen Fripp, Oscar Acosta, Gael Chetelat, Luping Zhou et al. Cross-sectional and longitudinal analysis of the relationship between Abeta deposition, cortical thickness, and memory in cognitively unimpaired individuals and in Alzheimer disease. JAMA neurology70, (2013)

2013
[9]

Vogel, Alexa Pichet Binette, Travis B

Chaggar, Pavanjit, Jacob W. Vogel, Alexa Pichet Binette, Travis B. Thompson, Olof Strandberg, Niklas Mattsson-Carlgren, Linda Karlsson et al. Personalised regional modelling predicts tau progression in the human brain. PLoS Biology23, e3003241 (2025)

2025
[10]

Young, Neil P

Vogel, Jacob W., Alexandra L. Young, Neil P. Oxtoby, Ruben Smith, Rik Ossenkoppele, Olof T. Strandberg, Renaud La Joie, Leon M. Aksman, Michel J. Grothe, & Yasser Iturria-Medina. Four distinct trajectories of tau deposition identified in Alzheimer’s disease. Nature medicine27, 871-881 (2021). 25

2021
[11]

Sotero, Paule J

Iturria-Medina, Yasser, Roberto C. Sotero, Paule J. Toussaint, Alan C. Evans, & Alzheimer’s Disease Neuroimaging Initiative. Epidemic spreading model to characterize misfolded proteins propagation in aging and associated neurodegenerative disorders. PLoS computational biology10, e1003956 (2014)

2014
[12]

Correlating tau pathology to brain atrophy using a physics-based Bayesian model

Schafer A, Chaggar P, Goriely A, Kuhl E, & Alzheimer’s Disease Neuroimaging Initiative. Correlating tau pathology to brain atrophy using a physics-based Bayesian model. Engineering with Computers38, 3867-3877 (2022)

2022
[13]

Marinescu, Neil P

Young, Alexandra L., Razvan V. Marinescu, Neil P. Oxtoby, Martina Bocchetta, Keir Yong, Nicholas C. Firth, David M. Cash et al. Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with Subtype and Stage Inference. Nature communications9, 4273 (2018)

2018
[14]

101 labeled brain images and a consistent human cortical labeling protocol

Klein, Arno & Jason Tourville. 101 labeled brain images and a consistent human cortical labeling protocol. Frontiers in neuroscience6, 171 (2012)

2012
[15]

A kernel two-sample test

Gretton A, Borgwardt KM, Rasch MJ, Scholkopf B & Smola A. A kernel two-sample test. J Mach Learn Res.13, 723-773 (2012)

2012
[16]

MUSE: MUlti-atlas region segmentation utilizing ensembles of registration algorithms and parameters, and locally optimal atlas selection

Doshi J, Erus G, Ou Y, Resnick SM, Gur RC, Gur RE, Satterthwaite TD, Furth S, Davatzikos C & Alzheimer’s Neuroimaging Initiative. MUSE: MUlti-atlas region segmentation utilizing ensembles of registration algorithms and parameters, and locally optimal atlas selection. NeuroImage127, 186-195 (2016)

2016
[17]

A single-snapshot inverse solver for two-species graph model of tau pathology spreading in human Alzheimer’s disease

Wen, Zheyu, Ali Ghafouri, George Biros & Alzheimer’s Disease Neuroimaging Initiative. A single-snapshot inverse solver for two-species graph model of tau pathology spreading in human Alzheimer’s disease. Brain Informatics18(2025)

2025
[18]

Aligning personalized biomarker trajectories onto a common time axis: a connectome-based ODE model for Tau-Amyloid beta dynamics

Wen, Zheyu, George Biros & Alzheimer’s Disease Neuroimaging Initiative. Aligning personalized biomarker trajectories onto a common time axis: a connectome-based ODE model for Tau-Amyloid beta dynamics. Medical Image Analysis, 103757 (2025)

2025
[19]

LNODE: Uncovering the Latent Dynamics of Aβin Alzheimer’s Disease

Wen, Zheyu & George Biros. LNODE: Uncovering the Latent Dynamics of Aβin Alzheimer’s Disease. In International Conference on Medical Image Computing and Computer-Assisted Intervention Cham: Springer Nature Switzerland, 313-322 (2025)

2025
[20]

Harvard aging brain study: dataset and accessibility

Dagley, Alexander, Molly LaPoint, Willem Huijbers, Trey Hedden, Donald G. McLaren, Jasmeer P. Chatwal, Kathryn V. Papp et al. "Harvard aging brain study: dataset and accessibility." Neuroimage 144, 255-258 (2017)

2017
[21]

Spread of pathological tau proteins through communicating neurons in human Alzheimer’s disease

Vogel JW, Iturria-Medina Y, Strandberg OT, Smith R, Levitis E, Evans AC & Hansson O. Spread of pathological tau proteins through communicating neurons in human Alzheimer’s disease. Nat Commun. 11, 2612 (2020). 26

2020
[22]

Advances in functional and structural MR image analysis and implementation as FSL

Smith SM, Jenkinson M, Woolrich MW, Beckmann CF, Behrens TE, Johansen-Berg H, Bannister PR, De Luca M, Drobnjak I, Flitney DE & Niazy RK. Advances in functional and structural MR image analysis and implementation as FSL. NeuroImage23, S208-S219 (2004)

2004
[23]

Hong, J., Kang, S.K., Alberts, I. et al. Image-level trajectory inference of tau pathology using variational autoencoder for Flortaucipir PET. Eur J Nucl Med Mol Imaging49, 3061-3072 (2022)

2022
[24]

Bayesian physics-based modeling of tau propagation in Alzheimer’s disease

Schafer, Amelie, Mathias Peirlinck, Kevin Linka, Ellen Kuhl, & Alzheimer’s Disease Neuroimaging Initiative (ADNI). Bayesian physics-based modeling of tau propagation in Alzheimer’s disease. Frontiers in physiology12, 702975 (2021)

2021
[25]

Mormino, & Ellen Kuhl

Schafer, Amelie, Elizabeth C. Mormino, & Ellen Kuhl. Network diffusion modeling explains longitudinal tau PET data. Frontiers in neuroscience14, 566876 (2020)

2020
[26]

Thompson, Alain Goriely, Ellen Kuhl, & Alzheimer’s Disease Neuroimaging Initiative

Schafer, Amelie, Pavanjit Chaggar, Travis B. Thompson, Alain Goriely, Ellen Kuhl, & Alzheimer’s Disease Neuroimaging Initiative. Predicting brain atrophy from tau pathology: a summary of clinical findings and their translation into personalized models. Brain Multiphysics2, 100039 (2021)

2021
[27]

Understanding the complex interplay between tau, amyloid and the network in the spatiotemporal progression of Alzheimer’s Disease

Raj, Ashish, Justin Torok, and Kamalini Ranasinghe. Understanding the complex interplay between tau, amyloid and the network in the spatiotemporal progression of Alzheimer’s Disease. Progress in Neurobiology, 102750 (2025)

2025
[28]

Senjem, Christopher G

Sintini, Irene, Jonathan Graff-Radford, Matthew L. Senjem, Christopher G. Schwarz, Mary M. Machulda, Peter R. Martin, David T. Jones et al. Longitudinal neuroimaging biomarkers differ across Alzheimer’s disease phenotypes. Brain143, 2281-2294 (2020)

2020
[29]

Stuss, & Sandra E

Lam, Benjamin, Mario Masellis, Morris Freedman, Donald T. Stuss, & Sandra E. Black. Clinical, imaging, and pathological heterogeneity of the Alzheimer’s disease syndrome. Alzheimer’s research & therapy5, 1 (2013)

2013
[30]

Sharp, & Roger N

Whittington, Alex, David J. Sharp, & Roger N. Gunn. Spatiotemporal distribution of beta-amyloid in Alzheimer disease is the result of heterogeneous regional carrying capacities. Journal of Nuclear Medicine 59, 822-827 (2018)

2018
[31]

Toledo, Nicolas Honnorat, Jimit Doshi, Erdem Varol, Aristeidis Sotiras, David Wolk, John Q

Dong, Aoyan, Jon B. Toledo, Nicolas Honnorat, Jimit Doshi, Erdem Varol, Aristeidis Sotiras, David Wolk, John Q. Trojanowski, Christos Davatzikos, & Alzheimer’s Disease Neuroimaging Initiative. Heterogeneity of neuroanatomical patterns in prodromal Alzheimer’s disease: links to cognition, progression and biomarkers. Brain140, 735-747 (2017)

2017
[32]

A multiscale model to explain the spatiotemporal progression of amyloid beta and tau pathology in Alzheimer’s disease

Xu, Chunrui, Enze Xu, Yang Xiao, Defu Yang, Guorong Wu, & Minghan Chen. A multiscale model to explain the spatiotemporal progression of amyloid beta and tau pathology in Alzheimer’s disease. International Journal of Biological Macromolecules310, 142887 (2025). 27

2025
[33]

Protein-protein interactions in neurodegenerative diseases: A conspiracy theory

Thompson, Travis B., Pavanjit Chaggar, Ellen Kuhl, Alain Goriely, & Alzheimer’s Disease Neuroimag- ing Initiative. Protein-protein interactions in neurodegenerative diseases: A conspiracy theory. PLoS computational biology16, e1008267 (2020)

2020
[34]

Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer’s disease

Pal, Swadesh, and Roderick Melnik. Nonlocal models in the analysis of brain neurodegenerative protein dynamics with application to Alzheimer’s disease. Scientific Reports12, 7328 (2022)

2022
[35]

Maini, Daniel J

Liu, Yue, Kevin Suh, Philip K. Maini, Daniel J. Cohen, and Ruth E. Baker. Parameter identifiability and model selection for partial differential equation models of cell invasion. Journal of the Royal Society Interface21, 20230607 (2024)

2024
[36]

Browning, Alexander P., Maria Tasca, Carles Falco, and Ruth E. Baker. Structural identifiability analysis of linear reaction-advection-diffusion processes in mathematical biology. Proceedings of the Royal Society A480, 20230911 (2024)

2024
[37]

Data-driven modelling of neurodegenerative disease progression: thinking outside the black box

Young AL, Oxtoby NP, Garbarino S, Fox NC, Barkhof F, Schott JM, & Alexander DC. Data-driven modelling of neurodegenerative disease progression: thinking outside the black box. Nat. Rev. Neurosci. 25, 111-130 (2024)

2024
[38]

Blazey, Yi Su, Amrita Hari-Raj, Aylin Dincer, Shaney Flores, Jon Christensen et al

Gordon, Brian A., Tyler M. Blazey, Yi Su, Amrita Hari-Raj, Aylin Dincer, Shaney Flores, Jon Christensen et al. Spatial patterns of neuroimaging biomarker change in individuals from families with autosomal dominant Alzheimer’s disease: a longitudinal study. The Lancet Neurology17, 241-250 (2018)

2018
[39]

Lee, Shaney Flores et al

Fan, Shuyang, Maria Rosana Ponisio, Pan Xiao, Sung Min Ha, Satrajit Chakrabarty, John J. Lee, Shaney Flores et al. AmyloidPETNet: classification of amyloid positivity in brain PET imaging using end-to-end deep learning. Radiology311, e231442 (2024)

2024
[40]

Kowshik, Shreyas Puducheri, Michael F

Jasodanand, Varuna H., Sahana S. Kowshik, Shreyas Puducheri, Michael F. Romano, Lingyi Xu, Rhoda Au, and Vijaya B. Kolachalama. AI-driven fusion of multimodal data for Alzheimer’s disease biomarker assessment. Nature Communications16, 7407 (2025)

2025
[41]

Knopman et al

Gottesman, Rebecca F., Andrea LC Schneider, Yun Zhou, Josef Coresh, Edward Green, Naresh Gupta, David S. Knopman et al. Association between midlife vascular risk factors and estimated brain amyloid deposition. Jama317, 1443-1450 (2017)

2017
[42]

Roe, Chengjie Xiong, Anne M

Morris, John C., Catherine M. Roe, Chengjie Xiong, Anne M. Fagan, Alison M. Goate, David M. Holtzman, and Mark A. Mintun. APOE predicts amyloid-beta but not tau Alzheimer pathology in cognitively normal aging. Annals of neurology67, 122-131 (2010)

2010
[43]

Visualizing data using t-SNE

Maaten, Laurens van der, & Geoffrey Hinton. Visualizing data using t-SNE. Journal of machine learning research9, 2579-2605 (2008). 28

2008
[44]

and Gu, Y

Moscoso, A., Heeman, F., Raghavan, S., Costoya-Sánchez, A., Van Essen, M., Mainta, I., Camacho, V., Rodríguez-Fonseca, O., Silva-Rodríguez, J., Perissinotti, A. and Gu, Y. Frequency and clinical outcomes associated with tau positron emission tomography positivity. JAMA334, 229-242 (2025)

2025
[45]

and Vissel, B

Kepp, K.P., Robakis, N.K., Hoilund-Carlsen, P.F., Sensi, S.L. and Vissel, B. The amyloid cascade hypothesis: an updated critical review. Brain146, 3969-3990 (2023)

2023
[46]

and Dietrich, P.Y

Frisoni, G.B., Altomare, D., Thal, D.R., Ribaldi, F., van der Kant, R., Ossenkoppele, R., Blennow, K., Cummings, J., van Duijn, C., Nilsson, P.M. and Dietrich, P.Y. The probabilistic model of Alzheimer disease: the amyloid hypothesis revised. Nature Reviews Neuroscience23, 53-66 (2022)

2022
[47]

Jorge Cardoso, Sebastien Ourselin, and Lauge Sorensen

Ghazi, Mostafa Mehdipour, Mads Nielsen, Akshay Pai, Marc Modat, M. Jorge Cardoso, Sebastien Ourselin, and Lauge Sorensen. Robust parametric modeling of Alzheimer’s disease progression. NeuroIm- age225, 117460 (2021)

2021
[48]

Chen, Guo-fang, Ting-hai Xu, Yan Yan, Yu-ren Zhou, Yi Jiang, Karsten Melcher, and H. Eric Xu. Amyloid beta: structure, biology and structure-based therapeutic development. Acta pharmacologica sinica38, 1205-1235 (2017)

2017
[49]

and Rao, P.P

Mohamed, T., Shakeri, A. and Rao, P.P. Amyloid cascade in Alzheimer’s disease: Recent advances in medicinal chemistry. European journal of medicinal chemistry113, 258-272 (2016)

2016
[50]

Functional brain architecture is associated with the rate of tau accumulation in Alzheimer’s disease

Franzmeier, Nicolai, Julia Neitzel, Anna Rubinski, Ruben Smith, Olof Strandberg, Rik Ossenkoppele, Oskar Hansson, and Michael Ewers. Functional brain architecture is associated with the rate of tau accumulation in Alzheimer’s disease. Nature communications11, 347 (2020)

2020
[51]

and Rowe, C.C

Klunk, W.E., Koeppe, R.A., Price, J.C., Benzinger, T.L., Devous Sr, M.D., Jagust, W.J., Johnson, K.A., Mathis, C.A., Minhas, D., Pontecorvo, M.J. and Rowe, C.C. The Centiloid Project: standardizing quantitative amyloid plaque estimation by PET. Alzheimer’s & dementia,11, 1-15 (2015)

2015
[52]

TauGenNet: Plasma-Driven Tau PET Image Synthesis via Text-Guided 3D Diffusion Models

Gong, Yuxin, Se-in Jang, Wei Shao, Yi Su, and Kuang Gong. TauGenNet: Plasma-Driven Tau PET Image Synthesis via Text-Guided 3D Diffusion Models. arXiv preprint arXiv:2509.04269 (2025)

work page arXiv 2025
[53]

Learning patient-specific spatial biomarker dynamics via operator learning for Alzheimer’s disease progression

Wang, Jindong, Yutong Mao, Xiao Liu, Wenrui Hao, and Alzheimer’s Disease Neuroimaging Initiative. Learning patient-specific spatial biomarker dynamics via operator learning for Alzheimer’s disease progression. ArXiv arXiv-2507 (2025)

2025
[54]

Uncover Governing Law of Pathology Propagation Mechanism Through A Mean-Field Game

Dan, Tingting, Zhihao Fan, and Guorong Wu. Uncover Governing Law of Pathology Propagation Mechanism Through A Mean-Field Game. In The Thirty-ninth Annual Conference on Neural Information Processing Systems. 29
[55]

Sorensen, and Chao Yang

Lehoucq, Richard B., Danny C. Sorensen, and Chao Yang. ARPACK users’ guide: solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods. Society for Industrial and Applied Mathematics, (1998). Acknowledgements Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) databa...

1998
[56]

initial conditionpi: ∂xi(T) ∂pi =Z TP⊺ b, Ji,pi =P bZTP⊺ b

Jacobian w.r.t. initial conditionpi: ∂xi(T) ∂pi =Z TP⊺ b, Ji,pi =P bZTP⊺ b
[57]

···

Jacobian w.r.t.wij: ∂Mi ∂wij =   κjΛ+ρjI 0···0 I(j) 0···0 0 0···0 0 0···0 ... ...···... ... ...···... 0 0···0 0 0···0   , ∂xi(T) ∂wij = ∂ZT ∂wij (xi0 + ¯ZTgi) +ZT ∂¯ZT ∂wij gi, Ji,wij =P b ∂xi(T) ∂wij . 32
[58]

diffusion coefficientsκj: ∂Mi ∂κj =   wijΛ 0···0 0 0···0

Jacobian w.r.t. diffusion coefficientsκj: ∂Mi ∂κj =   wijΛ 0···0 0 0···0 ... ... ... ... 0 0···0   , ∂xi(T) ∂κj = ∂ZT ∂κj (xi0 + ¯ZTgi), Ji,κj =P b ∂xi(T) ∂κj
[59]

growth ratesρj: ∂Mi ∂ρj =   wijI 0···0 0 0···0

Jacobian w.r.t. growth ratesρj: ∂Mi ∂ρj =   wijI 0···0 0 0···0 ... ... ... ... 0 0···0   , ∂xi(T) ∂ρj = ∂ZT ∂ρj (xi0 + ¯ZTgi), Ji,ρj =P b ∂xi(T) ∂ρj
[60]

couplingϕ1: ∂Mi ∂ϕ1 =   0 0···0 Λ 0···0

Jacobian w.r.t. couplingϕ1: ∂Mi ∂ϕ1 =   0 0···0 Λ 0···0 ... ... ... ... Λ 0···0   , ∂xi(T) ∂ϕ1 = ∂ZT ∂ϕ1 (xi0 + ¯ZTgi), Ji,ϕ1 =P b ∂xi(T) ∂ϕ1
[61]

bias termϕ2: ∂gi ∂ϕ2 =   0 I

Jacobian w.r.t. bias termϕ2: ∂gi ∂ϕ2 =   0 I ... I   , ∂xi(T) ∂ϕ2 =Z T ¯ZT ∂gi ∂ϕ2 , Ji,ϕ2 =P bZT ¯ZT ∂gi ∂ϕ2 . 33 Full Hessian matrix. H=   Hˆp1ˆp1 Hˆp1w1 0···0 0 0 H ˆp1κ Hˆp1ρ Hˆp1ϕ 1 Hˆp1ϕ 2 Hw1ˆp1 Hw1w1 0···0 0 0 H w1κ Hw1ρ Hw1ϕ 1 Hw1ϕ 2 0 0 H ˆp2ˆp2 Hˆp2w2 ···0 0 H ˆp2κ Hˆp2ρ Hˆp2ϕ 1 Hˆp2ϕ 2 0 0 H w2ˆp2 H...