# Mechanical Properties of Robocast Glass Scaffolds Assessed through Micro-CT-Based Finite Element Models

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Scaffold Manufacturing, Micro-CT Scans and Defect Identification

#### 2.2. Micro-CT Based Finite Element Modeling

#### 2.2.1. Elastic Analyses

#### 2.2.2. Assessment of Strength

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Roseti, L.; Parisi, V.; Petretta, M.; Cavallo, C.; Desando, G.; Bartolotti, I.; Grigolo, B. Scaffolds for bone tissue engineering: State of the art and new perspectives. Mater. Sci. Eng. C
**2017**, 78, 1246–1262. [Google Scholar] [CrossRef] [PubMed] - Fu, Q.; Saiz, E.; Rahaman, M.; Tomsia, A. Bioactive glass scaffolds for bone tissue engineering: State of the art and future perspectives. Mater. Sci. Eng. C
**2011**, 31, 1245–1256. [Google Scholar] [CrossRef] [PubMed] - Baino, F.; Fiume, E.; Barberi, J.; Kargozar, S.; Marchi, J.; Massera, J.; Verné, E. Processing methods for making porous bioactive glass-based scaffolds—A state-of-the-art review. Int. J. Appl. Ceram. Technol.
**2019**, 16, 1762–1796. [Google Scholar] [CrossRef] - Baino, F.; Caddeo, S.; Novajra, G.; Vitale-Brovarone, C. Using porous bioceramic scaffolds to model healthy and osteoporotic bone. J. Eur. Ceram. Soc.
**2016**, 36, 2175–2182. [Google Scholar] [CrossRef] - El-Rashidy, A.A.; Roether, J.A.; Harhaus, L.; Kneser, U.; Boccaccini, A.R. Regenerating bone with bioactive glass scaffolds: A review of in vivo studies in bone defect models. Acta Biomater.
**2017**, 62, 1–28. [Google Scholar] [CrossRef] [PubMed] - Hench, L. Bioceramics—From Concept to Clinic. J. Am. Ceram. Soc.
**1991**, 74, 1487–1510. [Google Scholar] [CrossRef] - Shahgholi, M.; Oliviero, S.; Baino, F.; Vitale-Brovarone, C.; Gastaldi, D.; Vena, P. Mechanical characterization of glass-ceramic scaffolds at multiple characteristic lengths through nanoindentation. J. Eur. Ceram. Soc.
**2016**, 36, 2403–2409. [Google Scholar] [CrossRef] - Ghorbani, F.; Li, D.; Ni, S.; Zhou, Y.; Yu, B. 3D printing of acellular scaffolds for bone defect regeneration: A review. Mater. Today Commun.
**2020**, 22, 100979. [Google Scholar] [CrossRef] - Eqtesadi, S.; Motealleh, A.; Miranda, P.; Pajares, A.; Lemos, A.; Ferreira, J.M. Robocasting of 45S5 bioactive glass scaffolds for bone tissue engineering. J. Eur. Ceram. Soc.
**2014**, 34, 107–118. [Google Scholar] [CrossRef] - Hollister, S.; Maddox, R.; Taboas, J. Optimal design and fabrication of scaffolds to mimic tissue properties and satisfy biological constraints. Biomaterials
**2002**, 23, 4095–4103. [Google Scholar] [CrossRef] - Zhang, S.; Vijayavenkataraman, S.; Lu, W.F.; Fuh, J.Y.H. A review on the use of computational methods to characterize, design, and optimize tissue engineering scaffolds, with a potential in 3D printing fabrication. J. Biomed. Mater. Res. Part B Appl. Biomater.
**2019**, 107, 1329–1351. [Google Scholar] [CrossRef] [PubMed] - Asadi-Eydivand, M.; Solati-Hashjin, M.; Fathi, A.; Padashi, M.; Abu Osman, N.A. Optimal design of a 3D-printed scaffold using intelligent evolutionary algorithms. Appl. Soft Comput.
**2016**, 39, 36–47. [Google Scholar] [CrossRef] - Barba, D.; Alabort, E.; Reed, R. Synthetic bone: Design by additive manufacturing. Acta Biomater.
**2019**, 97, 637–656. [Google Scholar] [CrossRef] [PubMed] - Scheiner, S.; Sinibaldi, R.; Pichler, B.; Komlev, V.; Renghini, C.; Vitale-Brovarone, C.; Rustichelli, F.; Hellmich, C. Micromechanics of bone tissue-engineering scaffolds, based on resolution error-cleared computer tomography. Biomaterials
**2009**, 30, 2411–2419. [Google Scholar] [CrossRef] [PubMed] - Miranda, P.; Pajares, A.; Guiberteau, F. Finite element modeling as a tool for predicting the fracture behavior of robocast scaffolds. Acta Biomater.
**2008**, 4, 1715–1724. [Google Scholar] [CrossRef] [PubMed] - Entezari, A.; Roohani-Esfahani, S.I.; Zhang, Z.; Zreiqat, H.; Dunstan, C.R.; Li, Q. Fracture behaviors of ceramic tissue scaffolds for load bearing applications. Sci. Rep.
**2016**, 6, 28816. [Google Scholar] [CrossRef] - Genet, M.; Houmard, M.; Eslava, S.; Saiz, E.; Tomsia, A.P. A two-scale Weibull approach to the failure of porous ceramic structures made by robocasting: Possibilities and limits. J. Eur. Ceram. Soc.
**2013**, 33, 679–688. [Google Scholar] [CrossRef] - Farina, E.; Gastaldi, D.; Baino, F.; Vernè, E.; Massera, J.; Orlygsson, G.; Vena, P. Micro computed tomography based finite element models for elastic and strength properties of 3D printed glass scaffolds. Acta Mech. Sin.
**2021**, 37, 292–306. [Google Scholar] [CrossRef] - Baino, F.; Barberi, J.; Fiume, E.; Orlygsson, G.; Massera, J.; Verné, E. Robocasting of Bioactive SiO2-P2O5-CaO-MgO-Na2O-K2O Glass Scaffolds. J. Healthc. Eng.
**2019**, 2019, 5153136. [Google Scholar] [CrossRef] - Barberi, J.; Baino, F.; Fiume, E.; Orlygsson, G.; Nommeots-Nomm, A.; Massera, J.; Verné, E. Robocasting of SiO2-based bioactive glass scaffolds with porosity gradient for bone regeneration and potential load-bearing applications. Materials
**2019**, 12, 2691. [Google Scholar] [CrossRef] [Green Version] - Tulyaganov, D.U.; Fiume, E.; Akbarov, A.; Ziyadullaeva, N.; Murtazaev, S.; Rahdar, A.; Massera, J.; Verné, E.; Baino, F. In Vivo Evaluation of 3D-Printed Silica-Based Bioactive Glass Scaffolds for Bone Regeneration. J. Funct. Biomater.
**2022**, 13, 74. [Google Scholar] [CrossRef] [PubMed] - Otsu, N. A Threshold Selection Method from Gray-Level Histograms. IEEE Trans. Syst. Man Cybern.
**1979**, 9, 62–66. [Google Scholar] [CrossRef] - Barberi, J.; Nommeots-Nomm, A.; Fiume, E.; Verné, E.; Massera, J.; Baino, F. Mechanical characterization of pore-graded bioactive glass scaffolds produced by robocasting. Biomed. Glasses
**2019**, 5, 140–147. [Google Scholar] [CrossRef] - Flaig, C. A Highly Scalable Memory Efficient Multigrid Solver for μ-Finiteelement Analyses. Ph.D. Thesis, ETH, Zürich, Switzerland, 2012. [Google Scholar]
- Tagliabue, S.; Rossi, E.; Baino, F.; Vitale-Brovarone, C.; Gastaldi, D.; Vena, P. Micro-CT based finite element models for elastic properties of glass-ceramic scaffolds. J. Mech. Behav. Biomed. Mater.
**2017**, 65, 248–255. [Google Scholar] [CrossRef] [PubMed] - Munz, D.; Fett, T. Ceramics, Mechanical Properties, Failure Behaviour, Materials Selection; Springer: Berlin/Heidelberg, Germany, 1999. [Google Scholar]
- Miranda, P.; Pajares, A.; Saiz, E.; Tomsia, A.P.; Guiberteau, F. Fracture modes under uniaxial compression in hydroxyapatite scaffolds fabricated by robocasting. J. Biomed. Mater. Res. Part A
**2007**, 83A, 646–655. [Google Scholar] [CrossRef] - Petit, C.; Meille, S.; Maire, E.; Gremillard, L.; Adrien, J.; Lau, G.Y.; Tomsia, A.P. Fracture behavior of robocast HA/β-TCP scaffolds studied by X-ray tomography and finite element modeling. J. Eur. Ceram. Soc.
**2017**, 37, 1735–1745. [Google Scholar] [CrossRef] - Hollister, S.J.; Kikuchi, N. Homogenization Theory and Digital Imaging—A Basis for Studying the Mechanics and Design Principles of Bone Tissue. Biotechnol. Bioeng.
**1994**, 43, 586–596. [Google Scholar] [CrossRef] - Bendsøe, M.P.; Sigmund, O. Material interpolation schemes in topology optimization. Arch. Appl. Mech.
**1999**, 69, 635–654. [Google Scholar] [CrossRef] - Hamdia, K.M.; Ghasemi, H.; Zhuang, X.; Rabczuk, T. Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties. Eng. Anal. Bound. Elem.
**2022**, 134, 412–418. [Google Scholar] [CrossRef] - Stipsitz, M.; Zysset, P.K.; Pahr, D.H. Efficient materially nonlinear μFE solver for simulations of trabecular bone failure. Biomech. Model. Mechanobiol.
**2020**, 19, 861–874. [Google Scholar] [CrossRef] [Green Version] - Chen, Q.; Baino, F.; Spriano, S.; Pugno, N.; Vitale-Brovarone, C. Modelling of the strength-porosity relationship in glass-ceramic foam scaffolds for bone repair. J. Eur. Ceram. Soc.
**2014**, 34, 2663–2673. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Micro-CT reconstruction of two scaffolds. Geometric imperfections are described: (

**a**) fibers interruption identified by red arrows and (

**b**) fibers detaching between two adjacent printing planes.

**Figure 2.**3D representation of the macroscopic stiffness of the scaffolds: (

**a**) cubic symmetry scaffolds, (

**b**) low porosity scaffolds and (

**c**) scaffolds exhibiting detaching of fibers.

**Figure 4.**Best fitting curve of ideal scaffolds (black line) from Farina et al. and best fitting curve also considering real scaffolds (purple line).

**Figure 5.**Crack pattern upon compressive load: (

**a**) the load is orthogonal to both families of fibers and (

**b**) the load is directed along the x-fibers.

**Figure 6.**Section of the scaffold in the xz-plane, under compressive load along the z-direction (vertical). Cracks are highlighted in dark blue.

${\mathit{E}}_{\mathit{x}}/{\mathit{E}}_{0}$ | ${\mathit{E}}_{\mathit{y}}/{\mathit{E}}_{0}$ | ${\mathit{E}}_{\mathit{z}}/{\mathit{E}}_{0}$ | ${\mathit{G}}_{\mathbf{xy}}/{\mathit{E}}_{0}$ | ${\mathit{G}}_{\mathbf{yz}}/{\mathit{E}}_{0}$ | ${\mathit{G}}_{\mathbf{xz}}/{\mathit{E}}_{0}$ | |
---|---|---|---|---|---|---|

graded | 0.28 ± 0.02 | 0.27 ± 0.03 | 0.15 ± 0.08 | 0.03 ± 0.01 | 0.06 ± 0.01 | 0.06 ± 0.02 |

monoporous | 0.19 ± 0.02 | 0.17 ± 0.04 | 0.44 ± 0.14 | 0.07 ± 0.02 | 0.11 ± 0.03 | 0.11 ± 0.03 |

${\mathit{\sigma}}_{\mathit{x}}$ | ${\mathit{\sigma}}_{\mathit{z}}$ | |
---|---|---|

graded | 0.24 ± 0.05 | 0.08 ± 0.09 |

monoporous | 0.08 ± 0.02 | 0.31 ± 0.14 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

D’Andrea, L.; Gastaldi, D.; Verné, E.; Baino, F.; Massera, J.; Örlygsson, G.; Vena, P.
Mechanical Properties of Robocast Glass Scaffolds Assessed through Micro-CT-Based Finite Element Models. *Materials* **2022**, *15*, 6344.
https://doi.org/10.3390/ma15186344

**AMA Style**

D’Andrea L, Gastaldi D, Verné E, Baino F, Massera J, Örlygsson G, Vena P.
Mechanical Properties of Robocast Glass Scaffolds Assessed through Micro-CT-Based Finite Element Models. *Materials*. 2022; 15(18):6344.
https://doi.org/10.3390/ma15186344

**Chicago/Turabian Style**

D’Andrea, Luca, Dario Gastaldi, Enrica Verné, Francesco Baino, Jonathan Massera, Gissur Örlygsson, and Pasquale Vena.
2022. "Mechanical Properties of Robocast Glass Scaffolds Assessed through Micro-CT-Based Finite Element Models" *Materials* 15, no. 18: 6344.
https://doi.org/10.3390/ma15186344