LNODE: latent dynamics reveal the shared spatiotemporal structure of amyloid-β progression
Abstract
We present and analyze LNODE, a mechanism-based phenomenological model for amyloid beta (Aβ) dynamics, calibrated using positron emission tomography (PET) imaging. Aβ is a key biomarker of Alzheimer's disease. LNODE is designed to support the fusion, harmonization, quantitative analysis, and interpretation of Aβ PET scans. We evaluate LNODE on 1461 subjects in the ADNI cohort and 1,070 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 Aβ and incorporates a latent-state representation that modulates Aβ 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 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 cohort 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. Clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes of Alzheimer's disease progression.
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BibTeX
@misc{wen2026lnode,
title = {{LNODE: latent dynamics reveal the shared spatiotemporal structure of amyloid-$β$ progression}},
author = {Zheyu Wen and George Biros},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.00272},
eprint = {2605.00272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00272},
}
RIS
TY - UNPB
TI - LNODE: latent dynamics reveal the shared spatiotemporal structure of amyloid-β progression
AU - Zheyu Wen
AU - George Biros
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.00272
UR - https://arxiv.org/abs/2605.00272
AB - We present and analyze LNODE, a mechanism-based phenomenological model for amyloid beta (Aβ) dynamics, calibrated using positron emission tomography (PET) imaging. Aβ is a key biomarker of Alzheimer's disease. LNODE is designed to support the fusion, harmonization, quantitative analysis, and interpretation of Aβ PET scans. We evaluate LNODE on 1461 subjects in the ADNI cohort and 1,070 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 Aβ and incorporates a latent-state representation that modulates Aβ 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 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 cohort R^2 > 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. Clustering in the learned latent-state space reveals distinct subgroups, consistent with the existence of different subtypes of Alzheimer's disease progression.
ER -