OsteoFlow: Lyapunov-Guided Flow Distillation for Predicting Bone Remodeling after Mandibular Reconstruction

TL;DR

OsteoFlow is a flow-based model that predicts long-term bone remodeling after mandibular reconstruction by distilling continuous trajectories, significantly improving accuracy over existing methods.

Contribution

The paper introduces Lyapunov-guided trajectory distillation for flow models, enhancing long-term prediction accuracy in bone remodeling tasks.

Findings

Reduces mean absolute error in resection zone by ~20%.

Outperforms state-of-the-art baselines on 344 paired regions.

Enforces geometric correspondence without sacrificing generative capacity.

Abstract

Predicting long-term bone remodeling after mandibular reconstruction would be of great clinical benefit, yet standard generative models struggle to maintain trajectory-level consistency and anatomical fidelity over long horizons. We introduce OsteoFlow, a flow-based framework predicting Year-1 post-operative CT scans from Day-5 scans. Our core contribution is Lyapunov-guided trajectory distillation: Unlike one-step distillation, our method distills a continuous trajectory over transport time from a registration-derived stationary velocity field teacher. Combined with a resection-aware image loss, this enforces geometric correspondence without sacrificing generative capacity. Evaluated on 344 paired regions of interest, OsteoFlow significantly outperforms state of-the-art baselines, reducing mean absolute error in the surgical resection zone by ~20%. This highlights the promise of trajectory distillation for long-term prediction. Code is available on GitHub: OsteoFlow.