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

Hamidreza Aftabi, Faye Yu, Brooke Switzer, Zachary Fishman, Eitan Prisman, Antony Hodgson, Cari Whyne, Sidney Fels, Michael Hardisty

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.

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

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.
Paper Structure (9 sections, 6 equations, 2 figures, 3 tables, 1 algorithm)

This paper contains 9 sections, 6 equations, 2 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Experiments and Results
  4. Dataset and Augmentation Pipeline
  5. Implementation Details and Metrics
  6. Results and Ablation Studies
  7. Conclusion

Figures (2)

  • Figure 1: Illustration of the preprocessing steps and the teacher–student Lyapunov-guided distillation framework for guiding the student velocity field.
  • Figure 2: Model predictions for three representative cases (union, partial union, and nonunion), shown on the resection plane and two other central orthogonal slices. The purple circle shows the partial union near the resection site, while the pink ellipsoid depicts the nonunion.