Stress analysis in bone scaffold geometries under compression loads with the mechanical properties of a Hydroxyapatite/lactic acid material


bone geometry
bone injert
scaffolding simulation
human bone
elastic modulus
cubic model geometría ósea
injerto óseo
simulación de andamios
hueso humano
módulo elástico
modelo cúbico

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Díaz León, J. L., Hernández Navarro, C., Martínez Valencia, M. I., & Vázquez López, J. A. (2023). Stress analysis in bone scaffold geometries under compression loads with the mechanical properties of a Hydroxyapatite/lactic acid material . Nova Scientia, 15(30), 1–15.


The relationship between the strength of the material and the geometry of bone scaffolds ensures that the scaffold pores remain intact while bone cells develop through them. In this study, mechanical simulations of two geometries of bone scaffolds are presented using the mechanical properties of Hydroxyapatite (HAp) mixed with lactic acid. First, compression tests were performed on the HAp to determine its mechanical properties. Then, two geometries of bone scaffolds were modeled based on the porosity and size suitable for cell regeneration as reported in the literature, and the mechanical properties values were used for FEM simulations. The elastic modulus of 253.4 MPa, yield stress of 7.53 MPa, and Poisson's ratio of 0.33 were found. The porosities calculated for the cubic and cylindrical CAD models are 43.83% and 50.51%, respectively. It was found that the cubic model supported a force of 21 N in versus the cylindrical model, which supported a force of 19 N; these forces were applied in the simulations not to exceed the maximum permissible stress of 4.5 MPa of the HAp.


Adachi, T., Osako, Y., Tanaka, M., Hojo, M., & Hollister, S. J. (2006). Framework for optimal design of porous scaffold microstructure by computational simulation of bone regeneration. Biomaterials, 27(21), 3964–3972.

Asadi-Eydivand, M., Solati-Hashjin, M., Fathi, A., Padashi, M., & Abu Osman, N. A. (2016). Optimal design of a 3D-printed scaffold using intelligent evolutionary algorithms. Applied Soft Computing, 39, 36–47.

Babis, G. C., & Soucacos, P. N. (2005). Bone scaffolds: The role of mechanical stability and instrumentation. Injury, 36(4), S38–S44.

Barbieri, C. H., & Garcia-Mandarano Filho, L. (2019). Biomechanics of bone block graft models of different geometry. Acta Ortopédica Brasileira, 27(3), 136–140.

Boccaccio, A., Ballini, A., Pappalettere, C., Tullo, D., Cantore, S., & Desiate, A. (2011). Finite Element Method (FEM), Mechanobiology and Biomimetic Scaffolds in Bone Tissue Engineering. International Journal of Biological Sciences, 7(1), 112–132.

C28 Committee. (2015). Test Method for Monotonic Compressive Strength of Advanced Ceramics at Ambient Temperature (Núm. C1424). ASTM International.

Cheah, C. M., Chua, C. K., Leong, K. F., & Chua, S. W. (2003). Development of a Tissue Engineering Scaffold Structure Library for Rapid Prototyping. Part 2: Parametric Library and Assembly Program. The International Journal of Advanced Manufacturing Technology, 21(4), 302–312.

Chumnanklang, R., Panyathanmaporn, T., Sitthiseripratip, K., & Suwanprateeb, J. (2007). 3D printing of hydroxyapatite: Effect of binder concentration in pre-coated particle on part strength. Materials Science and Engineering: C, 27(4), 914–921.

Coelho, P. G., Hollister, S. J., Flanagan, C. L., & Fernandes, P. R. (2015). Bioresorbable scaffolds for bone tissue engineering: Optimal design, fabrication, mechanical testing and scale-size effects analysis. Medical Engineering & Physics, 37(3), 287–296.

Doyle, H., Lohfeld, S., & McHugh, P. (2015). Evaluating the effect of increasing ceramic content on the mechanical properties, material microstructure and degradation of selective laser sintered polycaprolactone/β-tricalcium phosphate materials. Medical Engineering & Physics, 37(8), 767–776.

Egan. (2019). Integrated Design Approaches for 3D Printed Tissue Scaffolds: Review and Outlook. Materials, 12(15), 2355.

Egan, P. F., Shea, K. A., & Ferguson, S. J. (2018). Simulated tissue growth for 3D printed scaffolds. Biomechanics and Modeling in Mechanobiology, 17(5), 1481–1495.

Elsayed, Y., & Lekakou, C. (2016). Designing and modeling pore size distribution in tissue scaffolds. En Characterisation and Design of Tissue Scaffolds (pp. 23–43). Elsevier.

Esmaeili, S., Akbari Aghdam, H., Motififard, M., Saber-Samandari, S., Montazeran, A. H., Bigonah, M., Sheikhbahaei, E., & Khandan, A. (2020). A porous polymeric–hydroxyapatite scaffold used for femur fractures treatment: Fabrication, analysis, and simulation. European Journal of Orthopaedic Surgery & Traumatology, 30(1), 123–131.

Fang, Z., Starly, B., & Sun, W. (2005). Computer-aided characterization for effective mechanical properties of porous tissue scaffolds. Computer-Aided Design, 37(1), 65–72.

García, E., Louvier-Hernández, J. F., Mendoza-Leal, G., Flores-Martínez, M., & Hernández-Navarro, C. (2020). Tribological study of HAp/CTS coatings produced by electrodeposition process on 316L stainless steel. Materials Letters, 277, 128336.

Hastings, G. W., & Ducheyne, P. (Eds.). (2017). Natural and Living Biomaterials. CRC Press.

Helguero, C. G., Mustahsan, V. M., Parmar, S., Pentyala, S., Pfail, J. L., Kao, I., Komatsu, D. E., & Pentyala, S. (2017). Biomechanical properties of 3D-printed bone scaffolds are improved by treatment with CRFP. Journal of Orthopaedic Surgery and Research, 12(1), 195.

Iwasashi, M., Sakane, M., Suetsugu, Y., & Ochiai, N. (2009). Bone Regeneration at Cortical Bone Defect with Unidirectional Porous Hydroxyapatite In Vivo. Key Engineering Materials, 396–398, 11–14.

Jasemi, A., Kamyab Moghadas, B., Khandan, A., & Saber-Samandari, S. (2022). A porous calcium-zirconia scaffolds composed of magnetic nanoparticles for bone cancer treatment: Fabrication, characterization and FEM analysis. Ceramics International, 48(1), 1314–1325.

Karageorgiou, V., & Kaplan, D. (2005). Porosity of 3D biomaterial scaffolds and osteogenesis. Biomaterials, 26(27), 5474–5491.

Kumar, A., Kargozar, S., Baino, F., & Han, S. S. (2019). Additive Manufacturing Methods for Producing Hydroxyapatite and Hydroxyapatite-Based Composite Scaffolds: A Review. Frontiers in Materials, 6, 313.

Kwon, S.-H., Jun, Y.-K., Hong, S.-H., Lee, I.-S., Kim, H.-E., & Won, Y. Y. (2004). Calcium Phosphate Bioceramics with Various Porosities and Dissolution Rates. Journal of the American Ceramic Society, 85(12), 3129–3131.

Lee, E.-J., Koh, Y.-H., Yoon, B.-H., Kim, H.-E., & Kim, H.-W. (2007). Highly porous hydroxyapatite bioceramics with interconnected pore channels using camphene-based freeze casting. Materials Letters, 61(11–12), 2270–2273.

Ma, P. X., Zhang, R., Xiao, G., & Franceschi, R. (2000). Engineering new bone tissue in vitro on highly porous poly (hydroxyl acids)/hydroxyapatite composite scaffolds. 10.<284::aid-jbm16>;2-w.

Miranda, P., Pajares, A., & Guiberteau, F. (2008). Finite element modeling as a tool for predicting the fracture behavior of robocast scaffolds. Acta Biomaterialia, 4(6), 1715–1724.

Navarro, C. H., Moreno, K. J., Arizmendi-Morquecho, A., Chávez-Valdez, A., & García-Miranda, S. (2012). Preparation and tribological properties of chitosan/hydroxyapatite composite coatings applied on ultra high molecular weight polyethylene substrate. Journal of Plastic Film & Sheeting, 28(4), 279–297.

Olivares, A. L., Marsal, È., Planell, J. A., & Lacroix, D. (2009). Finite element study of scaffold architecture design and culture conditions for tissue engineering. Biomaterials, 30(30), 6142–6149.

Pilkey, W. D., Pilkey, D. F., & Bi, Z. (2020). Peterson’s Stress Concentration Factors. John Wiley & Sons.

Ramakrishna, S., Mayer, J., Wintermantel, E., & Leong, K. W. (2001). Biomedical applications of polymer-composite materials: A review. Composites Science and Technology, 61(9), 1189–1224.

Rho, J.-Y., Kuhn-Spearing, L., & Zioupos, P. (1998). Mechanical properties and the hierarchical structure of bone. Medical Engineering & Physics, 20(2), 92–102.

Sandino, C., Planell, J. A., & Lacroix, D. (2008). A finite element study of mechanical stimuli in scaffolds for bone tissue engineering. Journal of Biomechanics, 41(5), 1005–1014.

Voyiadjis, G. Z., & Yaghoobi, M. (2019a). Chapter 1 - Introduction: Size effects in materials. En G. Z. Voyiadjis & M. Yaghoobi (Eds.), Size Effects in Plasticity (pp. 1–79). Academic Press.

Voyiadjis, G. Z., & Yaghoobi, M. (2019b). Size effects in plasticity: From macro to nano. Elsevier, Academic Press, an Imprint of Elsevier.

Wang, W. G., Chiang, W. H., & Bartolo, P. J. (2016). Design, fabrication and evaluation of PCL/Graphene scaffolds for bone regeneration. 7.

Yang Chen, Ma, H. T., Li Liang, Chaoyang Zhang, Griffith, J. F., & Ping-Chung Leung. (2015). A simulation study on marrow fat effect on biomechanics of vertebra bone. 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 3921–3924.

Yousefi, A.-M., Hoque, M. E., Prasad, R. G. S. V., & Uth, N. (2015). Current strategies in multiphasic scaffold design for osteochondral tissue engineering: A review: Current Strategies in Multiphasic Scaffold Design. Journal of Biomedical Materials Research Part A, 103(7), 2460–2481.

Zadpoor, A. A. (2015). Bone tissue regeneration: The role of scaffold geometry. Biomaterials Science, 3(2), 231–245.

Zhang, S., Vijayavenkataraman, S., Lu, W. F., & Fuh, J. Y. H. (2019). A review on the use of computational methods to characterize, design, and optimize tissue engineering scaffolds, with a potential in 3D printing fabrication. 107(5), 23.

Zimmermann, E. A., & Ritchie, R. O. (2015). Bone as a Structural Material. Advanced Healthcare Materials, 4(9), 1287–1304.

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