Triply Periodic Minimal Surfaces Scaffolds and Their Comparison with Cancellous Bone: Fluid Flow Point of View‎

Document Type : Research Article


Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran


The present study investigated bone growth characteristics, such as permeability, wall shear stress, and surface-to-volume ratio. Then by comparing them with the properties of Cancellous bone, the most desirable scaffolds for bone cell growth have been selected. Nine porous triply periodic minimal surfaces scaffolds in the exact unit cell sizes in four porosities have been designed. Because of the implantation of scaffolds in the body, non-Newtonian fluids can lead to more realistic results. Hence, the non-Newtonian model of the blood has also been examined for comparison with the Newtonian model. The results have shown that the permeability for Newtonian fluids was dependent only on the geometry of the scaffold, and it was intrinsic. Still, in non-Newtonian blood fluid, the permeability has been several times smaller than in the Newtonian model. Also, the average wall shear stress in the non-Newtonian model of blood has been almost twice as large as in the Newtonian model. Finally, by considering the permeability of Cancellous bones ( ), scaffolds which effectively mimicked the characteristics of this type of bone have been identified. The Fischer-Koch S scaffold has the highest permeability among these four scaffolds, and Schwartz Diamond 2 scaffold has the closest permeability to Cancellous bone. This proved that selecting the most desirable scaffold is complex and challenging and should be chosen according to its conditions and application.


Main Subjects

[1] Y. Lu, L. Cheng, Z. Yang, J. Li, H. Zhu, Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure, PLoS One, 15(9) (2020) e0238471-e0238471.
[2] L. Polo-Corrales, M. Latorre-Esteves, J. Ramirez-Vick, Scaffold Design for Bone Regeneration, Journal of nanoscience and nanotechnology, 14 (2014) 15-56.
[3] M.A. Velasco, C.A. Narváez-Tovar, D.A. Garzón-Alvarado, Design, Materials, and Mechanobiology of Biodegradable Scaffolds for Bone Tissue Engineering, BioMed Research International, 2015 (2015) 729076.
[4] F.S.L. Bobbert, K. Lietaert, A.A. Eftekhari, B. Pouran, S.M. Ahmadi, H. Weinans, A.A. Zadpoor, Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties, Acta Biomaterialia, 53 (2017) 572-584.
[5] Z. Wang, C. Huang, J. Wang, P. Wang, S. Bi, C.A. Abbas, Design and Simulation of Flow Field for Bone Tissue Engineering Scaffold Based on Triply Periodic Minimal Surface, Chinese Journal of Mechanical Engineering, 32(1) (2019) 19.
[6] S. Ma, Q. Tang, Q. Feng, J. Song, X. Han, F. Guo, Mechanical behaviours and mass transport properties of bone-mimicking scaffolds consisted of gyroid structures manufactured using selective laser melting, Journal of the Mechanical Behavior of Biomedical Materials, 93 (2019) 158-169.
[7] A.P.G. Castro, T. Pires, J.E. Santos, B.P. Gouveia, P.R. Fernandes, Permeability versus Design in TPMS Scaffolds, Materials, 12(8) (2019) 1313.
[8] D. Ali, M. Ozalp, S.B.G. Blanquer, S. Onel, Permeability and fluid flow-induced wall shear stress in bone scaffolds with TPMS and lattice architectures: A CFD analysis, European Journal of Mechanics - B/Fluids, 79 (2020) 376-385.
[9] H. Chen, Q. Han, C. Wang, Y. Liu, B. Chen, J. Wang, Porous Scaffold Design for Additive Manufacturing in Orthopedics: A Review, Frontiers in Bioengineering and Biotechnology, 8 (2020).
[10] M.R. Dias, P.R. Fernandes, J.M. Guedes, S.J. Hollister, Permeability analysis of scaffolds for bone tissue engineering, Journal of Biomechanics, 45(6) (2012) 938-944.
[11] S. Ma, Q. Tang, X. Han, Q. Feng, J. Song, R. Setchi, Y. Liu, Y. Liu, A. Goulas, D.S. Engstrøm, Y.Y. Tse, N. Zhen, Manufacturability, Mechanical Properties, Mass-Transport Properties and Biocompatibility of Triply Periodic Minimal Surface (TPMS) Porous Scaffolds Fabricated by Selective Laser Melting, Materials & Design, 195 (2020) 109034.
[12] D. Ali, S. Sen, Finite element analysis of mechanical behavior, permeability and fluid induced wall shear stress of high porosity scaffolds with gyroid and lattice-based architectures, Journal of the Mechanical Behavior of Biomedical Materials, 75 (2017) 262-270.
[13] M. Zhianmanesh, M. Varmazyar, H. Montazerian, Fluid Permeability of Graded Porosity Scaffolds Architectured with Minimal Surfaces, ACS Biomaterials Science & Engineering, 5(3) (2019) 1228-1237.
[14] D. Ali, S. Sen, Permeability and fluid flow-induced wall shear stress of bone tissue scaffolds: Computational fluid dynamic analysis using Newtonian and non-Newtonian blood flow models, Computers in Biology and Medicine, 99 (2018) 201-208.
[15] X.-Y. Zhang, X.-C. Yan, G. Fang, M. Liu, Biomechanical influence of structural variation strategies on functionally graded scaffolds constructed with triply periodic minimal surface, Additive Manufacturing, 32 (2020) 101015.
[16] S.J.P. Callens, C.H. Arns, A. Kuliesh, A.A. Zadpoor, Decoupling Minimal Surface Metamaterial Properties Through Multi-Material Hyperbolic Tilings, Advanced Functional Materials, 31(30) (2021) 2101373.
[17] H.A. Zaharin, A.M. Abdul Rani, F.I. Azam, T.L. Ginta, N. Sallih, A. Ahmad, N.A. Yunus, T.Z.A. Zulkifli, Effect of Unit Cell Type and Pore Size on Porosity and Mechanical Behavior of Additively Manufactured Ti6Al4V Scaffolds, Materials, 11(12) (2018) 2402.
[18] B. Zhang, K. Mhapsekar, S. Anand, Design of Variable-Density Structures for Additive Manufacturing Using Gyroid Lattices, in:  ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2017.
[19] J. Maszybrocka, B. Gapiński, M. Dworak, G. Skrabalak, A. Stwora, The manufacturability and compression properties of the Schwarz Diamond type Ti6Al4V cellular lattice fabricated by selective laser melting, The International Journal of Advanced Manufacturing Technology, 105(7) (2019) 3411-3425.
[20] N. Sreedhar, N. Thomas, O. Al-Ketan, R. Rowshan, H.H. Hernandez, R.K. Abu Al-Rub, H.A. Arafat, Mass transfer analysis of ultrafiltration using spacers based on triply periodic minimal surfaces: Effects of spacer design, directionality and voidage, Journal of Membrane Science, 561 (2018) 89-98.
[21] M.M. Sychov, L.A. Lebedev, S.V. Dyachenko, L.A. Nefedova, Mechanical properties of energy-absorbing structures with triply periodic minimal surface topology, Acta Astronautica, 150 (2018) 81-84.
[22] H.G. von Schnering, R. Nesper, Nodal surfaces of Fourier series: Fundamental invariants of structured matter, Zeitschrift für Physik B Condensed Matter, 83(3) (1991) 407-412.
[23] D. Ali, S. Sen, Computational Fluid Dynamics Study of the Effects of Surface Roughness on Permeability and Fluid Flow-Induced Wall Shear Stress in Scaffolds, Annals of Biomedical Engineering, 46(12) (2018) 2023-2035.
[24] W.C. Chin, Chapter 9 - Transient, Three-Dimensional, Multiphase Pipe and Annular Flow, in: W.C. Chin (Ed.) Managed Pressure Drilling, Gulf Professional Publishing, Boston, 2012, pp. 315-385.