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A machine learning-based multiscale model to predict bone formation in scaffolds


Computational modeling methods combined with non-invasive imaging technologies have exhibited great potential and unique opportunities to model new bone formation in scaffold tissue engineering, offering an effective alternate and viable complement to laborious and time-consuming in vivo studies. However, existing numerical approaches are still highly demanding computationally in such multiscale problems. To tackle this challenge, we propose a machine learning (ML)-based approach to predict bone ingrowth outcomes in bulk tissue scaffolds. The proposed in silico procedure is developed by correlating with a dedicated longitudinal (12-month) animal study on scaffold treatment of a major segmental defect in sheep tibia. Comparison of the ML-based time-dependent prediction of bone ingrowth with the conventional multilevel finite element (FE2) model demonstrates satisfactory accuracy and efficiency. The ML-based modeling approach provides an effective means for predicting in vivo bone tissue regeneration in a subject-specific scaffolding system.

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Fig. 1: Statistical analysis results of predictive accuracy.
Fig. 2: Histogram errors of the ML-based model from months 1 to 12 with respect to the conventional FE2 model.
Fig. 3: Comparison between conventional FE2-based results and ML-based results.
Fig. 4: Comparison of virtual in silico X-ray and in vivo histological images of the implantation site in sheep tibia.
Fig. 5: In vivo X-ray images and the signal densities in ROIs.
Fig. 6: Equivalent von Mises strain distributions for the scaffold.

Data availability

Source data are provided with this paper. Source data for Figs. 1 and 2, training data and raw/processed data required to reproduce these findings are available in a data repository in Zenodo (

Code availability

The related code, neural networks and examples are available to academic researchers at public institutions from Zenodo (


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We acknowledge financial support from the Australian Research Council (ARC) through the Discovery (DP180104200, Q.L. and M.V.S.) and ARC Industrial Transformation Training Centre (IC170100022, Q.L. and H.Z.). The Artemis HPC provided by the Sydney Informatics Hub, a Core Research Facility of the University of Sydney, is acknowledged.

Author information




C.W. and Q.L designed the research plan. C.W. performed the simulations. C.W., A.E., K.Z. and J.F analyzed the data. C.W., A.E. and Q.L. wrote the manuscript. All authors reviewed the final manuscript.

Corresponding author

Correspondence to Qing Li.

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The authors declare no competing interests.

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Peer review information Nature Computational Science thanks Jose A. Sanz-Herrera, Sara Esteban and Zhiyong Li for their contribution to the peer review of this work. Handling editor: Ananya Rastogi, in collaboration with the Nature Computational Science team.

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Supplementary information

Supplementary Information

Supplementary Tables 1–3 and Figs. 1–3.

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Source data

Source Data Fig. 4

Original images for virtual X-ray images at months 3, 6, 9 and 12 and histological image at month 12.

Source Data Fig. 5

In vivo X-ray images taken at months 3, 6, 9 and 12.

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Wu, C., Entezari, A., Zheng, K. et al. A machine learning-based multiscale model to predict bone formation in scaffolds. Nat Comput Sci 1, 532–541 (2021).

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