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An explainable machine learning-based probabilistic framework for the design of scaffolds in bone tissue engineering

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Abstract

Recently, 3D-printed biodegradable scaffolds have shown great potential for bone repair in critical-size fractures. The differentiation of the cells on a scaffold is impacted among other factors by the surface deformation of the scaffold due to mechanical loading and the wall shear stresses imposed by the interstitial fluid flow. These factors are in turn significantly affected by the material properties, the geometry of the scaffold, as well as the loading and flow conditions. In this work, a numerical framework is proposed to study the influence of these factors on the expected osteochondral cell differentiation. The considered scaffold is rectangular with a 0/90 lay-down pattern and a four-layered strut made of polylactic acid with a 5% steel particle content. The distribution of the different types of cells on the scaffold surface is estimated through a scalar stimulus, calculated by using a mechanobioregulatory model. To reduce the simulation time for the computation of the stimulus, a probabilistic machine learning (ML)-based reduced-order model (ROM) is proposed. Then, a sensitivity analysis is performed using the Shapley additive explanations to examine the contribution of the various parameters to the framework stimulus predictions. In a final step, a multiobjective optimization procedure is implemented using genetic algorithms and the ROM, aiming to identify the material parameters and loading conditions that maximize the percentage of surface area populated by bone cells while minimizing the area corresponding to the other types of cells and the resorption condition. The results of the performed analysis highlight the potential of using ROMs for the scaffold design, by dramatically reducing the simulation time while enabling the efficient implementation of sensitivity analysis and optimization procedures.

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Acknowledgements

This research work is supported by the Hellenic Foundation for Research and Innovation (HFRI) under the “First Call for HFRI. Research Projects to support Faculty members and Researchers and the procurement of high-cost research equipment grant” (Project Number: 2060).

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Author notes

  1. Efstratios Polyzos, Stephanos Tsinopoulos, Lincy Pyl, and Demosthenes Polyzos have contributed equally to this work.

Authors and Affiliations

  1. Department of Mechanical Engineering and Aeronautics, University of Patras, 26504, Rio, Greece

    George Drakoulas, Theodore Gortsas & Demosthenes Polyzos

  2. Department of Mechanical Engineering, University of Peloponnese, 26334, Patras, Greece

    Theodore Gortsas & Stephanos Tsinopoulos

  3. Department of Mechanics of Materials and Constructions, Vrije Universiteit Brussel (VUB), 1050, Brussels, Belgium

    Efstratios Polyzos & Lincy Pyl

Authors
  1. George Drakoulas
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  2. Theodore Gortsas
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  3. Efstratios Polyzos
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  4. Stephanos Tsinopoulos
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  5. Lincy Pyl
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  6. Demosthenes Polyzos
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Contributions

GD performed conceptualization, methodology, software, visualization, investigation, validation, and writing—original draft; TG provided conceptualization, methodology, software, investigation, writing—original draft, and writing—review and editing; SP analyzed software, investigation, and writing—review and editing; ST conducted software and supervision; LP revised supervision and writing—review and editing; DP approved funding acquisition, methodology, supervision, and writing–review and editing.

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Correspondence to George Drakoulas or Theodore Gortsas.

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Drakoulas, G., Gortsas, T., Polyzos, E. et al. An explainable machine learning-based probabilistic framework for the design of scaffolds in bone tissue engineering. Biomech Model Mechanobiol (2024). https://doi.org/10.1007/s10237-024-01817-7

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