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

Mandibular reconstruction with vascularized bone grafts is complicated by donor-host nonunion, and current virtual surgical planning produces a geometric plan rather than a configuration that explicitly promotes bone union. We present OsteoOpt++, an image-to-decision planning loop for patient-specific mandibular reconstruction. A pre-operative computed tomography (CT) is converted into a personalized digital twin through template-to-patient registration and CT-derived updates of the muscle and temporomandibular-joint parameters. Bayesian optimization with an expected-improvement-plus acquisition rule then searches six clinically controllable cut-plane and donor-positioning variables under an apposition-driven objective and a safety-factor-regularized variant. The workflow was evaluated on three generic defects (body, symphysis, and ramus-body) and a total of 3+1 patient-specific cases, with 3 used for optimization and 1 for validation. In the generic cases, against a common surgical approach, cycle-averaged donor-mandible apposition increased by up to 29 percentage points (329% relative); in the patient-specific cases, against the surgeon-implemented day-5 post-operative configuration, by up to 26 percentage points. A 10% sensitivity analysis over eleven modeling parameters capped the change in the apposition-driven objective at 3% for generic cases and 4% for patient-specific cases, and the longitudinal case showed Dice overlap of 0.70 and 0.76 between predicted apposition and year-1 bone formation. Clinically, this provides surgeons with a pre-operative, image-driven recommendation for cut-plane orientation and donor placement that is predicted to improve union conditions over the configurations currently delivered in the operating room. The optimization and patient-specific modeling code is open source at https://github.com/hamidreza-aftabi/OsteoOpt.

Cranial implant generation is an important task in medical imaging. Recent point cloud based generative methods, particularly flow matching, offer strong reconstruction quality and efficient sampling, but still require multiple neural function evaluations during inference. This limits rapid generation of multiple plausible implant candidates. We propose Teacher-guided Endpoint Distillation (TED), a simple one-step distillation framework for conditional cranial implant generation on point clouds. TED trains a one-step student using teacher-guided endpoint supervision and geometric matching losses, while avoiding explicit path straightening. We evaluate TED on the SkullFix and SkullBreak benchmarks. TED achieves the best overall performance on the SkullBreak dataset, remains competitive on SkullFix, and provides the strongest Chamfer distance performance among the compared one-step methods. In addition, TED generates implants in approximately 0.04s per sample. These results show that one-step distillation can substantially accelerate conditional point cloud implant generation without sacrificing reconstruction quality.

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to $256 \times 256$. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a $12\times$ inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by $23.1\%$ in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.