Mechanobiology-guided machine learning models for predicting long bone fracture healing across diverse scenarios

Background

Fracture healing is a complex, time-dependent process governed by biological and mechanical factors, including implant properties. While finite element (FE) modeling provides detailed mechanobiological insights into this process, its computational cost remains a major limitation for widespread clinical or research use. In this study, we developed and validated a machine learning (ML) framework as a rapid alternative for a previously validated 21-day mechanoregulation-based FE model of femoral fracture healing in rodents.

Methods

We trained and compared seven ML algorithms (SVR, RF, XGBoost, MLP, CNN, RNN, LSTM) using 648 simulated healing trajectories from a validated FE mechanobiological model, varying implant, loading, and biological parameters. Hyperparameters were optimized via Bayesian search with repeated validation. Generalizability was tested on 100 unseen scenarios (interpolation), and robustness was assessed by reducing training data. Extrapolation tests evaluated predictions beyond the training timeline, and SHAP analysis was used to interpret feature contributions.

Results

The sequence-to-sequence LSTM model consistently outperformed other algorithms, achieving up to 98 % error reduction compared to baseline methods in predicting central, intermediate, and outer callus stiffness, as well as total strain energy. SHAP analysis revealed biologically meaningful patterns: screw number strongly increased central stiffness, while excessive loading negatively impacted outer callus formation, aligning with established mechanobiological principles. The model generalized well to unseen (interpolated) input combinations and maintained strong performance even when trained on as little as 50 % of the data, highlighting its robustness and data efficiency. In time-step forecasting, the model accurately predicted future healing outcomes from partial early-stage data, though predictive accuracy declined with increasing extrapolation distance.

Conclusion

This study presents a computationally efficient and explainable ML-enhanced surrogate modeling framework that preserves the mechanistic fidelity of FE-based healing simulations while offering near-instantaneous predictions. This approach lays the groundwork for real-time decision support tools in orthopedic research, implant design, and personalized fracture management by enabling rapid scenario testing, sensitivity analysis, and forecasting.