Physics-Grounded Disentangled Flow Modeling for Brain Disease Progression Trajectory

2026-06-26

AI Summary

Existing methods for predicting longitudinal brain lesion evolution often fail to explicitly model underlying physical mechanisms, leading to entangled representations of structural deformation and image intensity changes, which compromises the model’s physical plausibility, generalizability, and interpretability. This work proposes the PDF framework, which, for the first time, decouples lesion evolution into two distinct physical processes—morphological deformation and intensity variation—and models each using flow-matching networks. To ensure physically consistent morphological dynamics, the framework incorporates a partial differential equation (PDE)-based regularized loss derived from diffusion–reaction–advection dynamics. Evaluated on three public longitudinal neuroimaging datasets, the method achieves state-of-the-art performance, demonstrating that disentangled representation learning combined with PDE-based constraints effectively enhances both interpretability and generalization in longitudinal lesion modeling.

Abstract

Forecasting longitudinal brain lesion evolution is critical for disease monitoring and treatment planning. Existing approaches typically learn a direct mapping from a baseline image to a future observation, without explicitly modeling the physical mechanisms underlying the lesion progression. Such an entangled modeling of structural deformation and image intensity variation limits physical plausibility, model generalization, and interpretability. To address this, we propose PDF, a Physics-grounded Disentangled Flow matching framework for longitudinal brain disease forecasting. We explicitly decompose the longitudinal modeling of lesion growth into two processes, each learned by a dedicated flow matching network: morphology evolution, which captures lesion growth and structural deformation; and intensity evolution, which models signal changes driven by variations in lesion concentration. To enforce physics-grounded constraints, we introduce a PDE-regularized loss based on lesion growth dynamics, that enforces a diffusion-reaction-advection formulation for morphological evolution. Experiments on three public longitudinal datasets spanning diverse brain diseases demonstrate state-of-the-art performance, validating the effectiveness of the disentangled modeling framework and physics-grounded learning design. Code is publicly available at https://github.com/jhuldr/PDF.

Problem

• longitudinal brain lesion evolution
• physical plausibility
• disentangled modeling
• structural deformation
• intensity variation

Innovation

• disentangled flow modeling
• physics-grounded learning
• lesion progression forecasting
• PDE-regularized loss
• longitudinal brain imaging