In-Silico Prediction of Mechanical Behaviour of Uniform Gyroid Scaffolds Affected by Its Design Parameters for Bone Tissue Engineering Applications
Abstract
:1. Introduction
2. Materials and Methods
2.1. Design of Scaffolds
2.1.1. Implicit Description of TPMS
2.1.2. Signed Distance Field
2.1.3. Design of a Scaffold with an External Shape
2.1.4. Design of Scaffolds Based on User-Desired Pore Size (PS) and Strut Size (SS)
- (i.)
- Calculate level constant (C) based on PS and SS:
- (ii.)
- Calculate pore size (P2π) and strut size (S2π) for the period coefficient No = 2π:
- (iii.)
- Calculate the scale factor (SF) from either giving the desired pore or strut size;
- (iv.)
- Calculate suitable period coefficient (N).
- (i.)
- PS200 (Pore Size 200 µm and Strut Size 200 µm);
- (ii.)
- PS350 (Pore Size 350 µm and Strut Size 200 µm);
- (iii.)
- PS550 (Pore Size 550 µm and Strut Size 200 µm);
- (iv.)
- PS750 (Pore Size 750 µm and Strut Size 200 µm);
- (v.)
- PS1000 (Pore Size 1000 µm and Strut Size 200 µm).
2.2. Creation of FE Volume Meshes
2.2.1. Meshing
2.2.2. Converting the Implicit Body (Gyroid Lattice) into the Surface Mesh
2.2.3. Converting the Surface Mesh into a Volume Mesh
2.2.4. Converting the Volume Mesh into a FE Volume Mesh
2.3. Simulation
2.3.1. FE Model
2.3.2. Simulation Method and Static Analysis
3. Results and Discussion
3.1. Design and Morphological Parameters
3.2. FE Simulation—Von Mises Stress and Deformation Prediction
3.3. Discussion
3.4. Limitations
4. Conclusions
- (i.)
- The advantage of having TPMS with the SDF method is that the end user can give the desired pore and strut sizes and porosity to achieve the required architecture of scaffolds for effective mechanical and degradation properties.
- (ii.)
- In the design of scaffolds, the level constant plays a vital role in tuning their interconnected architecture by deciding how many parts are to be solid (strut) or void (pores). This level constant influences the morphological parameters such as pore and strut sizes so that the pore–strut ratio decides the level constant variation, whereby a positive value results in more solid regions and a decrease in the level constant results in more solid regions and large pore sizes.
- (iii.)
- The porosity of scaffolds can be controlled by modifying the pore size of the scaffolds, keeping a constant strut size. Thus, these morphological properties affect the architecture of the lattice, which in turn alters the total mechanical properties.
- (iv.)
- The visual stress and deformation distributions are achieved using FE simulations, from which the values of mechanical responses are predicted.
- (v.)
- The maximum von Mises stress and the maximum deformation increase due to decreased volume fraction and increased porosity.
- (vi.)
- The effective elastic modulus of the scaffolds decreases with increased pore size and porosity. It was also predicted that the effective elastic moduli were in the 0.05 to 1.93 GPa range, matching that of trabecular bone.
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Appendix B. Creation of a Gyroid Scaffold in nTopology Software
Appendix C. Creation of FE Volume Mesh in nTopology
Appendix D. Static Structural Analysis
References
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Label | Element Count | Node Count | Edge Count | Vertex Count |
---|---|---|---|---|
PS200 | 7,052,136 | 11,570,625 | 9,867,119 | 1,703,506 |
PS350 | 8,386,979 | 12,702,213 | 10,945,522 | 1,756,691 |
PS550 | 2,576,201 | 4,442,317 | 3,753,745 | 688,572 |
PS750 | 1,794,654 | 3,107,398 | 2,623,529 | 483,869 |
PS1000 | 1,155,452 | 2,032,425 | 1,711,706 | 320,719 |
Material | Young’s Modulus (E) | Poisson Ratio (ν) | Yield Strength |
---|---|---|---|
Titanium Grade 5 (Ti-6Al-4V) | 114 GPa | 0.34 | 883 MPa |
Label | PS (µm) | SS (µm) | C | N | Surface Area of Scaffold (mm2) | Volume of Scaffold (mm3) | Porosity (%) | Volume Fraction (%) | SA:V (mm−1) |
---|---|---|---|---|---|---|---|---|---|
PS200 | 200 | 200 | 0.01 | 13.52 | 1831.62 | 126.09 | 49.56 | 50.44 | 14.53 |
PS350 | 350 | 200 | −0.62 | 9.90 | 1191.99 | 74.18 | 70.33 | 29.67 | 16.07 |
PS550 | 550 | 200 | −1.01 | 7.27 | 720.39 | 41.50 | 83.40 | 16.60 | 17.36 |
PS750 | 750 | 200 | −1.18 | 5.72 | 469.93 | 26.75 | 89.30 | 10.70 | 17.57 |
PS1000 | 1000 | 200 | −1.30 | 4.54 | 295.11 | 15.56 | 93.78 | 6.22 | 18.97 |
Pore size ↓, Relative density of the lattice ↑, Volume Fraction ↑ Pore size ↑, Relative density of the lattice ↓, Volume Fraction ↓ |
Label | Reactive Force (×10−2 N) | Max. Deformation (µm) | Max. Von Mises Stress (GPa) | Strain (µm/m) | Stress (N/m2) | Effective Elastic Modulus (GPa) | Relative Elastic Modulus (×10−3) |
---|---|---|---|---|---|---|---|
PS200 | 2.69 | 5.58 | 0.23 | 558.00 | 1075.40 | 1.93 | 16.92 |
PS350 | 3.03 | 10.90 | 0.35 | 1089.53 | 1212.00 | 1.11 | 9.74 |
PS550 | 4.35 | 63.35 | 1.34 | 6335.41 | 1740.00 | 0.27 | 2.37 |
PS750 | 7.91 | 186.34 | 2.21 | 18,633.80 | 3164.00 | 0.17 | 1.49 |
PS1000 | 9.40 | 725.57 | 6.82 | 72,557.00 | 3760.00 | 0.05 | 0.44 |
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N. Musthafa, H.-S.; Walker, J.; Rahman, T.; Bjørkum, A.; Mustafa, K.; Velauthapillai, D. In-Silico Prediction of Mechanical Behaviour of Uniform Gyroid Scaffolds Affected by Its Design Parameters for Bone Tissue Engineering Applications. Computation 2023, 11, 181. https://doi.org/10.3390/computation11090181
N. Musthafa H-S, Walker J, Rahman T, Bjørkum A, Mustafa K, Velauthapillai D. In-Silico Prediction of Mechanical Behaviour of Uniform Gyroid Scaffolds Affected by Its Design Parameters for Bone Tissue Engineering Applications. Computation. 2023; 11(9):181. https://doi.org/10.3390/computation11090181
Chicago/Turabian StyleN. Musthafa, Haja-Sherief, Jason Walker, Talal Rahman, Alvhild Bjørkum, Kamal Mustafa, and Dhayalan Velauthapillai. 2023. "In-Silico Prediction of Mechanical Behaviour of Uniform Gyroid Scaffolds Affected by Its Design Parameters for Bone Tissue Engineering Applications" Computation 11, no. 9: 181. https://doi.org/10.3390/computation11090181