Kemiğin yapısı karmaşık ve heterojendir, bu da boylamasına ve enine yönlerinde farklı mekanik ve biyolojik özelliklere neden olur. Örneğin, trabeküler kemiğin uzunlamasına ve enine yönde elastik modülü ve geçirgenliği birkaç kata kadar değişebilir. Dolaysıyla, implantların tasarımında konuk kemikle uyum sağlaması için bu farklılıkları dikkate almak gerekir. Bu çalışmada, yaygın olarak kemik iskeleleri tasarımında kullanılan gyroid yapısı, izotropik olmayan iskeleler modellemek için modifiye edilmiştir. Bu nedenle, gyroid üçlü periyodik minimal yüzey trigonometrik fonksiyonu manipüle edilerek ve %80 sabit bir gözenekliliğe sahip beş farklı iskele G (-50), G (-25), G (0), G (+25) ve G (+50) modeli elde edilmiştir. Modellerin etkili elastik modülleri sonlu elemanlar analizi kullanılarak hesaplanmıştır. Analiz sonuçları G (-50), G (-25), G (+25) ve G (+50) modellerin boylarınca elastisite modülünün enlerine göre sırasıyla 0.21, 0.62, 1.50 ve 2.23 oranda olduğunu göstermiştir. Ayrıca modellerin geçirgenliği hesaplamalı akışkanlar dinamiği (CFD) analizi kullanılarak hesaplanmıştır. İzotropik olmayan modeller boyuna ve enine yönlerde farklı geçirgenlik göstermiştir. G (-50), G (-25), G (+25) ve G (+50) modellerin geçirgenliği boylarınca enlerine göre oranı sırasıyla 0.67, 0.80, 1.25 ve 1.47 olarak hesaplanmıştır.
The structure of the bone is very complex and heterogeneous; this causes different mechanical and biological properties in its longitudinal and transverse directions. For example, the modulus of elasticity and the permeability of the trabecular bone in a longitudinal and radial direction can vary up to several times. Therefore, implant design that matches these differences is necessary to maximize compliance with the host bone. Given that, in this study, a gyroid structure that generally is used in bone scaffolds was modified to design anisotropic scaffolds. Therefore, the gyroid triply periodic minimal surface trigonometric function was manipulated, and five different architectures were denoted as G(-50), G(-25), G(0), G(+25), and G(+50) with a constant porosity of 80% were developed. The effective elastic moduli of the models were calculated using finite element analysis. The results showed an anisotropicity rate of 0.21, 0.62, 1.50 and 2.23 in elastic moduli for G(-50), G(-25), G(+25) and G(+50) models respectively. As well, the permeability of the models was calculated using computational fluid dynamics (CFD) analysis. Anisotropic models showed different permeability in longitudinal and transverse directions. Longitudinal permeability to lateral direction rate were 0.67, 0.80, 1.25 and 1.47 for G(-50), G(-25), G(+25) and G(+50) models respectively.
 S. Bose, S. Vahabzadeh, and A. Bandyopadhyay, "Bone tissue engineering using 3D printing," Materials Today, 16: 496-504, (2013).
 C. M. Murphy, M. G. Haugh, and F. J. O'Brien, "The effect of mean pore size on cell attachment, proliferation and migration in collagen-glycosaminoglycan scaffolds for bone tissue engineering,"
Biomaterials, 31: 461-466, (2010).
 S. Wu, X. Liu, K. W. K. Yeung, C. Liu, and X. Yang, "Biomimetic porous scaffolds for bone tissue engineering," Materials Science and Engineering: R: Reports, 80: 1-36, (2014).
 K. Bari and A. Arjunan, "Extra low interstitial titanium based fully porous morphological bone scaffolds manufactured using selective laser melting," Journal of the Mechanical Behavior of
Biomedical Materials, 95: 1-12, (2019).
 C. Torres-Sanchez, J. McLaughlin, and A. Fotticchia, "Porosity and pore size effect on the properties of sintered Ti35Nb4Sn alloy scaffolds and their suitability for tissue engineering applications,"
Journal of Alloys and Compounds, 731: 189-199, (2018).
 C. Vyas, G. Ates, E. Aslan, J. Hart, B. Huang, and P. Barto, "Three-Dimensional Printing and Electrospinning Dual-Scale Polycaprolactone Scaffolds with Low-Density and Oriented Fibers to Promote
Cell Alignment," 3d Printing and Additive Manufacturing, 7: 105-113 (2020).
 M. J. Osmond, M. D. Krebs, and M. B. Pantcheva, "Human trabecular meshwork cell behavior is influenced by collagen scaffold pore architecture and glycosaminoglycan composition,"
Biotechnology and Bioengineering, 117: 3150-3159 (2020).
 J. Parthasarathy, B. Starly, S. Raman, and A. Christensen, "Mechanical evaluation of porous titanium (Ti6Al4V) structures with electron beam melting (EBM)," Journal of the Mechanical Behavior of
Biomedical Materials, 3: 249-259, (2010).
 Serpooshan, V., M. Julien, O. Nguyen, H. Wang, A. Li, N. Muja, J. E. Henderson and S. N. Nazhat, "Reduced hydraulic permeability of three-dimensional collagen scaffolds attenuates gel contraction
and promotes the growth and differentiation of mesenchymal stem cells," Acta Biomaterialia, 6: 3978-3987 (2010).
 Y. Guyot, F. P. Luyten, J. Schrooten, I. Papantoniou, and L. Geris, "A three-dimensional computational fluid dynamics model of shear stress distribution during neotissue growth in a perfusion
bioreactor," Biotechnology and Bioengineering, 112: 2591-2600, (2015).
 Y. Guyot, I. Papantoniou, F. P. Luyten, and L. Geris, "Coupling curvature-dependent and shear stress-stimulated neotissue growth in dynamic bioreactor cultures: a 3D computational model of a
complete scaffold," Biomechanics and Modeling in Mechanobiology, 15: 169-180, (2016).
 Ó. L. Rodríguez-Montaño, C. J. Cortés-Rodríguez, A. E. Uva, M. Fiorentino, M. Gattullo, G. Monno, et al., "Comparison of the mechanobiological performance of bone tissue scaffolds based on
different unit cell geometries," Journal of the Mechanical Behavior of Biomedical Materials, 83: 28-45, (2018).
 V. Weißmann, R. Bader, H. Hansmann, and N. Laufer, "Influence of the structural orientation on the mechanical properties of selective laser melted Ti6Al4V open-porous scaffolds," Materials &
Design, 95: 188-197, (2016).
 P. F. Egan, V. C. Gonella, M. Engensperger, S. J. Ferguson, and K. Shea, "Computationally designed lattices with tuned properties for tissue engineering using 3D printing," Plos One, 12: 1-20, (2017).
 S. C. Kapfer, S. T. Hyde, K. Mecke, C. H. Arns, and G. E. Schröder-Turk, "Minimal surface scaffold designs for tissue engineering," Biomaterials, 32: 6875-6882, (2011).
 L. Y. Zhu, L. Li, Z. A. Li, J. P. Shi, W. L. Tang, J. Q. Yang, et al., "Design and biomechanical characteristics of porous meniscal implant structures using triply periodic minimal surfaces," Journal of
Translational Medicine, 17: 1-10, (2019).
 C. Yan, L. Hao, A. Hussein, and P. Young, "Ti–6Al–4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting," Journal of the Mechanical Behavior of
Biomedical Materials, 51: 61-73, (2015).
 S. Gómez, M. D. Vlad, J. López, and E. Fernández, "Design and properties of 3D scaffolds for bone tissue engineering," Acta Biomaterialia, 42: 341-350, (2016).
 Zhu, Y. L., R. Q. Zhu, J. Ma, Z. Q. Weng, Y. Wang, X. L. Shi, Y. C. Li, X. D. Yan, Z. Dong, J. K. Xu, C. Z. Tang and L. Jin., "In vitro cell proliferation evaluation of porous nano-zirconia scaffolds with different
porosity for bone tissue engineering," Biomedical Materials, 10: 055009, (2015).
 A. Arjunan, M. Demetriou, A. Baroutaji, and C. Wang, "Mechanical performance of highly permeable laser melted Ti6Al4V bone scaffolds," Journal of the Mechanical Behavior of Biomedical
Materials, 102: 103517,(2020).
 A. A. Abdel-Wahab, K. Alam, and V. V. Silberschmidt, "Analysis of anisotropic viscoelastoplastic properties of cortical bone tissues," Journal of the Mechanical Behavior of Biomedical Materials, 4:
 K. Hasegawa, C. H. Turner, and D. B. Burr, "Contribution of collagen and mineral to the elastic anisotropy of bone," Calcified Tissue International, 55: 381-386, (1994).
 M. Asgari, J. Abi-Rafeh, G. N. Hendy, and D. Pasini, "Material anisotropy and elasticity of cortical and trabecular bone in the adult mouse femur via AFM indentation," Journal of the Mechanical Behavior of Biomedical Materials, 93: 81-92, (2019).
 C. Daish, R. Blanchard, K. Gulati, D. Losic, D. Findlay, D. J. E. Harvie, P.Pivonka, "Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations," Bone Reports, 6: 129-139, (2017).
 G. Baroud, R. Falk, M. Crookshank, S. Sponagel, and T. Steffen, "Experimental and theoretical investigation of directional permeability of human vertebral cancellous bone for cement infiltration," Journal of Biomechanics, 37: 189-196, (2004).
 A. Ataee, Y. Li, D. Fraser, G. Song, and C. Wen, "Anisotropic Ti-6Al-4V gyroid scaffolds manufactured by electron beam melting (EBM) for bone implant applications," Materials & Design, 137: 345-354, (2018).
 G. Falvo D'Urso Labate, F. Baino, M. Terzini, A. Audenino, C. Vitale-Brovarone, P. Segers, R. Quarto, G. Catapano, "Bone structural similarity score: a multiparametric tool to match properties of biomimetic bone substitutes with their target tissues," J Appl Biomater Funct Mater, 14: 277-289, (2016).
 G. F. D. Labate, G. Catapano, C. Vitale-Brovarone, and F. Baino, "Quantifying the micro-architectural similarity of bioceramic scaffolds to bone," Ceramics International, 43: 9443-9450, (2017).
 X. Wang, S. Xu, S. Zhou, W. Xu, M. Leary, P. Choong, M. Qian, M. Brandt, M. Xie, "Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A
review," Biomaterials, 83: 127-141, (2016).
 D. Ali, M. Ozalp, S. B. Blanquer, and 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: 376-385, (2020).
 D. Ali, "Effect of scaffold architecture on cell seeding efficiency: A discrete phase model CFD analysis," Computers in biology and medicine, 109: 62-69, (2019).
 Z. Qin, G. S. Jung, M. J. Kang, and M. J. Buehler, "The mechanics and design of a lightweight three-dimensional graphene assembly," Science Advances, 3: e1601536, (2017).
 G. S. Jung and M. J. Buehler, "Multiscale Mechanics of Triply Periodic Minimal Surfaces of Three-Dimensional Graphene Foams," Nano Letters, 18 : 4845-4853, (2018).
 M. Burkhard, P. Fürnstahl, and M. Farshad, "Three-dimensionally printed vertebrae with different bone densities for surgical training," European Spine Journal, 28: 798-806, (2019).
 M. Yakout, M. A. Elbestawi, and S. C. Veldhuis, "Density and mechanical properties in selective laser melting of Invar 36 and stainless steel 316L," Journal of Materials Processing Technology,
266: 397-420, (2019).
 P. Vossenberg, G. A. Higuera, G. van Straten, C. A. van Blitterswijk, and A. J. B. van Boxtel, "Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue
engineering," Biomechanics and Modeling in Mechanobiology, 8, : 499-507, (2009).
 A. C. Marin and D. Lacroix, "The inter-sample structural variability of regular tissue-engineered scaffolds significantly affects the micromechanical local cell environment," Interface Focus, 5:
 X. Xue, M. K. Patel, M. Kersaudy-Kerhoas, M. P. Y. Desmulliez, C. Bailey, and D. Topham, "Analysis of fluid separation in microfluidic T-channels," Applied Mathematical Modelling, 36: 743-755,
 S. Truscello, G. Kerckhofs, S. Van Bael, G. Pyka, J. Schrooten, and H. Van Oosterwyck, "Prediction of permeability of regular scaffolds for skeletal tissue engineering: A combined computational
and experimental study," Acta Biomaterialia, 8: 1648-1658, (2012).
 D. Egger, M. Fischer, A. Clementi, V. Ribitsch, J. Hansmann, and C. Kasper, "Development and Characterization of a Parallelizable Perfusion Bioreactor for 3D Cell Culture," Bioengineering, 4: 1-
 J. W. Gooch, "Hagen-Poiseuille Equation," in Encyclopedic Dictionary of Polymers, J. W. Gooch, Ed., ed New York, NY: Springer New York,: 355-355, (2011).
 R. Voronov, S. VanGordon, V. I. Sikavitsas, and D. V. Papavassiliou, "Computational modeling of flow-induced shear stresses within 3D salt-leached porous scaffolds imaged via micro-CT,"
Journal of Biomechanics, 43: 1279-1286, (2010).
 A. Lesman, Y. Blinder, and S. Levenberg, "Modeling of Flow-Induced Shear Stress Applied on 3D Cellular Scaffolds: Implications for Vascular Tissue Engineering," Biotechnology and
Bioengineering, 105: 645-654, (2010).
 S. Sohrabi, J. D. Zheng, E. A. Finol, and Y. L. Liu, "Numerical Simulation of Particle Transport and Deposition in the Pulmonary Vasculature," Journal of Biomechanical Engineering-Transactions of
the Asme, 136: 1-11 (2014).
 D. Ali and 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: 262-270, (2017).
 D. W. Abueidda, R. K. Abu Al-Rub, A. S. Dalaq, D.-W. Lee, K. A. Khan, and I. Jasiuk, "Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces," Mechanics of
Materials, 95: 102-115, (2016).
 S. Vijayavenkataraman, L. Zhang, S. Zhang, J. Y. Hsi Fuh, and W. F. Lu, "Triply Periodic Minimal Surfaces Sheet Scaffolds for Tissue Engineering Applications: An Optimization Approach toward
Biomimetic Scaffold Design," ACS Applied Bio Materials, 1: 259-269, (2018).
 M. Zhianmanesh, M. Varmazyar, and H. Montazerian, "Fluid Permeability of Graded Porosity Scaffolds Architectured with Minimal Surfaces," ACS Biomaterials Science & Engineering, 5: 1228-
 R. Oftadeh, M. Perez-Viloria, J. C. Villa-Camacho, A. Vaziri, and A. Nazarian, "Biomechanics and mechanobiology of trabecular bone: a review," Journal of biomechanical engineering, 137:
 E. A. Nauman, K. E. Fong, and T. M. Keaveny, "Dependence of Intertrabecular Permeability on Flow Direction and Anatomic Site," Annals of Biomedical Engineering, 27: 517-524, (1999).