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Article

Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites

1
TECNALIA, Basque Research and Technology Alliance (BRTA), Mikeletegi Pasealekua 2, 20009 Donostia-San Sebastián, Spain
2
Department of Engineering, Public University of Navarra, 31006 Pamplona, Spain
3
Complex Tissue Regeneration Department, MERLN Institute for Technology-Inspired Regenerative Medicine, University of Maastricht, 6211 LK Maastricht, The Netherlands
4
Department of Physics and Astronomy, Padova University, Via Marzolo 8, 35131 Padova, Italy
5
Materials Physics Center (MPC), Centro de Fisica de Materiales (CSIC, UPV/EHU), Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastián, Spain
*
Authors to whom correspondence should be addressed.
Academic Editor: Mauro Malvè
Mathematics 2021, 9(15), 1746; https://doi.org/10.3390/math9151746
Received: 2 June 2021 / Revised: 6 July 2021 / Accepted: 7 July 2021 / Published: 24 July 2021
(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering)
Additive manufacturing (AM) of scaffolds enables the fabrication of customized patient-specific implants for tissue regeneration. Scaffold customization does not involve only the macroscale shape of the final implant, but also their microscopic pore geometry and material properties, which are dependent on optimizable topology. A good match between the experimental data of AM scaffolds and the models is obtained when there is just a few millimetres at least in one direction. Here, we describe a methodology to perform finite element modelling on AM scaffolds for bone tissue regeneration with clinically relevant dimensions (i.e., volume > 1 cm3). The simulation used an equivalent cubic eight node finite elements mesh, and the materials properties were derived both empirically and numerically, from bulk material direct testing and simulated tests on scaffolds. The experimental validation was performed using poly(ethylene oxide terephthalate)-poly(butylene terephthalate) (PEOT/PBT) copolymers and 45 wt% nano hydroxyapatite fillers composites. By applying this methodology on three separate scaffold architectures with volumes larger than 1 cm3, the simulations overestimated the scaffold performance, resulting in 150–290% stiffer than average values obtained in the validation tests. The results mismatch highlighted the relevance of the lack of printing accuracy that is characteristic of the additive manufacturing process. Accordingly, a sensitivity analysis was performed on nine detected uncertainty sources, studying their influence. After the definition of acceptable execution tolerances and reliability levels, a design factor was defined to calibrate the methodology under expectable and conservative scenarios. View Full-Text
Keywords: finite element modelling; bone tissue engineering; 3D scaffold; additive manufacturing finite element modelling; bone tissue engineering; 3D scaffold; additive manufacturing
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MDPI and ACS Style

Calderon-Uriszar-Aldaca, I.; Perez, S.; Sinha, R.; Camara-Torres, M.; Villanueva, S.; Mota, C.; Patelli, A.; Matanza, A.; Moroni, L.; Sanchez, A. Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites. Mathematics 2021, 9, 1746. https://doi.org/10.3390/math9151746

AMA Style

Calderon-Uriszar-Aldaca I, Perez S, Sinha R, Camara-Torres M, Villanueva S, Mota C, Patelli A, Matanza A, Moroni L, Sanchez A. Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites. Mathematics. 2021; 9(15):1746. https://doi.org/10.3390/math9151746

Chicago/Turabian Style

Calderon-Uriszar-Aldaca, Iñigo, Sergio Perez, Ravi Sinha, Maria Camara-Torres, Sara Villanueva, Carlos Mota, Alessandro Patelli, Amaia Matanza, Lorenzo Moroni, and Alberto Sanchez. 2021. "Size Effects in Finite Element Modelling of 3D Printed Bone Scaffolds Using Hydroxyapatite PEOT/PBT Composites" Mathematics 9, no. 15: 1746. https://doi.org/10.3390/math9151746

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