Conditional Neural ODE for Longitudinal Parkinson's Disease Progression Forecasting

TL;DR

CNODE tackles irregularly sampled, heterogeneous PD progression by learning continuous brain morphometry trajectories in a shared latent space conditioned on patient-specific onset $\tau_i$ and progression speed $\gamma_i$. It models vertex-wise medial thickness features and subcortical volumes to construct a shared trajectory and uses a metadata-aware contrastive loss to align visits across subjects. An encoder–ODE–decoder architecture evolves latent states along aligned times $\tilde{t}$ via $z_i(\tilde{\mathbf t}_i) = \texttt{ODESolve}(g_\vartheta, z_{i,0}, \tilde{\mathbf t}_i)$ and reconstructs $X_{i,k}$. On the PPMI dataset, CNODE outperformed baselines in MSE, RMSE, and $R^2$ (e.g., MSE $0.0258 \pm 0.0001$, RMSE $0.1606 \pm 0.0003$, $R^2 = 0.8260 \pm 0.0006$), supporting its potential for personalized disease monitoring and digital-twin forecasting.

Abstract

Parkinson's disease (PD) shows heterogeneous, evolving brain-morphometry patterns. Modeling these longitudinal trajectories enables mechanistic insight, treatment development, and individualized 'digital-twin' forecasting. However, existing methods usually adopt recurrent neural networks and transformer architectures, which rely on discrete, regularly sampled data while struggling to handle irregular and sparse magnetic resonance imaging (MRI) in PD cohorts. Moreover, these methods have difficulty capturing individual heterogeneity including variations in disease onset, progression rate, and symptom severity, which is a hallmark of PD. To address these challenges, we propose CNODE (Conditional Neural ODE), a novel framework for continuous, individualized PD progression forecasting. The core of CNODE is to model morphological brain changes as continuous temporal processes using a neural ODE model. In addition, we jointly learn patient-specific initial time and progress speed to align individual trajectories into a shared progression trajectory. We validate CNODE on the Parkinson's Progression Markers Initiative (PPMI) dataset. Experimental results show that our method outperforms state-of-the-art baselines in forecasting longitudinal PD progression.

Figures (2)

• Figure 1: Overview of CNODE. (a) Firstly, we extract vertex-wise medial thickness from MRI, with subcortical structure volumes. (b) Secondly, we construct a shared progression trajectory. (c) Then we employ contrastive learning to align time distributions. Finally, we model the continuous evolution with Neural ODE.
• Figure 2: Effect of $\lambda_1/\lambda_2$ on CNODE performance.