# Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data arXiv: https://arxiv.org/abs/2211.04234 ยท HTML: https://mlsanity.com/paper/2211.04234/ ## Key facts - Cited by 19 papers in the map (data through 14 Oct 2026). - Builds on 17 of its 58 references that are in the map. - First posted on arXiv 8 Nov 2022. ## Builds on (most cited first, 17 of 17) - [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017) - [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015) - [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018) - [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016) - [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016) - [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016) - [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019) - [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020) - [FastSurfer -- A fast and accurate deep learning based neuroimaging pipeline](https://mlsanity.com/paper/1910.03866/) (2019) - [TADPOLE Challenge: Accurate Alzheimer's disease prediction through crowdsourced forecasting of future data](https://mlsanity.com/paper/2001.09016/) (2020) - [Neural Ordinary Differential Equation based Recurrent Neural Network Model](https://mlsanity.com/paper/2005.09807/) (2020) - [Neural parameters estimation for brain tumor growth modeling](https://mlsanity.com/paper/1907.00973/) (2019) - [Deep Probabilistic Modeling of Glioma Growth](https://mlsanity.com/paper/1907.04064/) (2019) - [MinimalRNN: Toward More Interpretable and Trainable Recurrent Neural Networks](https://mlsanity.com/paper/1711.06788/) (2017) - [Projective Skip-Connections for Segmentation Along a Subset of Dimensions in Retinal OCT](https://mlsanity.com/paper/2108.00831/) (2021) - [Continuous-Time Deep Glioma Growth Models](https://mlsanity.com/paper/2106.12917/) (2021) - [Longitudinal modeling of MS patient trajectories improves predictions of disability progression](https://mlsanity.com/paper/2011.04749/) (2020) ## Built on by (most cited first, 19 of 19) - [ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Images](https://mlsanity.com/paper/2406.14794/) (2024) - [OmniBrainBench: A Comprehensive Multimodal Benchmark for Brain Imaging Analysis Across Multi-stage Clinical Tasks](https://mlsanity.com/paper/2511.00846/) (2025) - [Longitudinal Flow Matching for Trajectory Modeling](https://mlsanity.com/paper/2510.03569/) (2025) - [LaTiM: Longitudinal representation learning in continuous-time models to predict disease progression](https://mlsanity.com/paper/2404.07091/) (2024) - [Temporal Flow Matching for Learning Spatio-Temporal Trajectories in 4D Longitudinal Medical Imaging](https://mlsanity.com/paper/2508.21580/) (2025) - [Longitudinal Self-supervised Learning Using Neural Ordinary Differential Equation](https://mlsanity.com/paper/2310.10431/) (2023) - [TimeFlow: Temporal Conditioning for Longitudinal Brain MRI Registration and Aging Analysis](https://mlsanity.com/paper/2501.08667/) (2025) - [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024) - [Forecasting Disease Progression with Parallel Hyperplanes in Longitudinal Retinal OCT](https://mlsanity.com/paper/2409.20195/) (2024) - [CRONOS: Continuous Time Reconstruction for 4D Medical Longitudinal Series](https://mlsanity.com/paper/2512.16577/) (2025) - [Anatomy-DT: A Cross-Diffusion Digital Twin for Anatomical Evolution](https://mlsanity.com/paper/2509.25280/) (2025) - [Diagnostic-Guided Longitudinal Modeling for Forecasting Retinal Atrophy Progression](https://mlsanity.com/paper/2604.16955/) (2026) - [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026) - [DiffSight-Former: Modeling Structural Differences and Temporal Dynamics for Glaucoma Progression Prediction](https://mlsanity.com/paper/2606.09140/) (2026) - [SMART: A Flexible, Interpretable, and Scalable Spatio-temporal Brain Atlas from High-Resolution Imaging Data](https://mlsanity.com/paper/2606.18753/) (2026) - [Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory](https://mlsanity.com/paper/2606.28630/) (2026) - [When Is a Conformal Guarantee Fair? Auditing Silent Subgroup Under-Coverage in Alzheimer's Disease Longitudinal Prediction](https://mlsanity.com/paper/2608.04254/) (2026) - [Modelling Geographic Atrophy Progression using Implicit Neural Representations](https://mlsanity.com/paper/2608.10807/) (2026) - [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026) ## Abstract (arXiv) Robust forecasting of the future anatomical changes inflicted by an ongoing disease is an extremely challenging task that is out of grasp even for experienced healthcare professionals. Such a capability, however, is of great importance since it can improve patient management by providing information on the speed of disease progression already at the admission stage, or it can enrich the clinical trials with fast progressors and avoid the need for control arms by the means of digital twins. In this work, we develop a deep learning method that models the evolution of age-related disease by processing a single medical scan and providing a segmentation of the target anatomy at a requested future point in time. Our method represents a time-invariant physical process and solves a large-scale problem of modeling temporal pixel-level changes utilizing NeuralODEs. In addition, we demonstrate the approaches to incorporate the prior domain-specific constraints into our method and define temporal Dice loss for learning temporal objectives. To evaluate the applicability of our approach across different age-related diseases and imaging modalities, we developed and tested the proposed method on the datasets with 967 retinal OCT volumes of 100 patients with Geographic Atrophy, and 2823 brain MRI volumes of 633 patients with Alzheimer's Disease. For Geographic Atrophy, the proposed method outperformed the related baseline models in the atrophy growth prediction. For Alzheimer's Disease, the proposed method demonstrated remarkable performance in predicting the brain ventricle changes induced by the disease, achieving the state-of-the-art result on TADPOLE challenge.