Modelación de andamios porosos basados en las estructuras triplemente periódicas P y G
Palabras clave:
Andamios porosos híbridos, superficies minimales triplemente periódicas, Mathematica, regresión multilineal.
Resumen
En este trabajo se estudia la modelación de estructuras híbridas de andamios porosos para regeneración de tejido óseo basadas en las superficies minimales triplemente periódicas Giroide (G) y primitiva de Schwarz (P). El diseño de las probetas prismáticas híbridas, con dimensiones según la norma ASTM D695_15, se logra a partir de las ecuaciones que definen a cada estructura utilizando la función de enlace sigmoidea con valor k=0.5 mediante el software CAS Wolfram Mathematica v11.2. Los aspectos relacionados con el uso de Mathematica como herramienta para el diseño de las probetas son discutidos en detalle. Las constantes de la ecuación de cada estructura son utilizadas como variables en un diseño factorial 32 para estudiar su efecto en la porosidad y tamaño de poros. A partir de regresión multilineal se obtienen las ecuaciones que relacionan los factores con las variables dependientes y se discuten los modelos obtenidos. Se concluye que el modelo bilineal es adecuado para la descripción de las variables de respuesta lo que justifica la elección del diseño experimental utilizado.
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Ahmadi, S. M., Yavari, S. A., Wauthle, R., Pouran, B., Schrooten, J., Weinans, H., & Zadpoor, A. A. (2015). Additively Manufactured Open-Cell Porous Biomaterials Made from Six Different Space-Filling Unit Cells: The Mechanical and Morphological Properties. Materials, 8, 1871-1896. doi:10.3390/ma8041871
Amirkhani, S., Bagheri, R., & Zehtab Yazdi, A. (2012). Effect of pore geometry and loading direction on deformation mechanism of rapid prototyped scaffolds. Acta Materialia, 60(6), 2778-2789. doi:https://doi.org/10.1016/j.actamat.2012.01.044
Anderson, D., Davis, H., Nitsche, J., & Scriven, L. (1990). Periodic surfaces of prescribed mean curvature. In Physics of amphiphilic layers (pp. 130-130): Springer.
Anderson, T. W., & Darling, D. A. (1952). Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics (2), 193-212, 120.
Bidan, C. M., Wang, F. M., & Dunlop, J. W. C. (2013). A three-dimensional model for tissue deposition on complex surfaces. Computer methods in biomechanics and biomedical engineering, 16(10), 1056-1070. doi:10.1080/10255842.2013.774384
Blanquer, S. B., Werner, M., Hannula, M., Sharifi, S., Lajoinie, G. P., Eglin, D., Grijpma, D. W. (2017). Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds. BioFa, 9(2), 025001.
Bobbert, F., Lietaert, K., Eftekhari, A. A., Pouran, B., Ahmadi, S., Weinans, H., & Zadpoor, A. (2017). Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties. Acta Biomaterialia, 53, 572-584.
Corder, G. W., & Foreman, D. I. (2009). Chapter 2. Testing data for normality. In Nonparametric statistics for non-statisticians: a step-by-step approach. United States: John Wiley & Sons, Inc.
Cuan-Urquizo, E., Barocio, E., Tejada-Ortigoza, V., Pipes, R. B., Rodriguez, C. A., & Roman-Flores, A. (2019). Characterization of the mechanical properties of FFF structures and materials: A review on the experimental, computational and theoretical approaches. Materials, 12(6), 895.
Cuan-Urquizo, E., Yang, S., & Bhaskar, A. (2015). Mechanical characterisation of additively manufactured material having lattice microstructure. Paper presented at the IOP Conf. Series: Materials Science and Engineering.
D´Agostino, R. B., & Stephens, M. A. (Eds.). (1986). Goodness-of-fit techniques. United States: Marcel Dekker, Inc.
Farah, S., Anderson, D. G., & Langer, R. (2016). Physical and mechanical properties of PLA, and their functions in widespread applications — A comprehensive review. Advanced Drug Delivery Reviews, 107, 367-392. doi:https://doi.org/10.1016/j.addr.2016.06.012
Gandy, P. J. F., Bardhan, S., Mackay, A. L., & Klinowski, J. (2001). Nodal surface approximations to the P,G,D and I-WP triply periodic minimal surfaces. Chemical Physics Letters, 336(3), 187-195. doi:https://doi.org/10.1016/S0009-2614(00)01418-4
Giannitelli, S. M., Accoto, D., Trombetta, M., & Rainer, A. (2014). Current trends in the design of scaffolds for computer-aided tissue engineering. Acta Biomaterialia, 10(2), 580-594. doi:https://doi.org/10.1016/j.actbio.2013.10.024
González, C. G., Liste, A. V., & Felpeto, A. B. (2013a). Apéndice I. Tablas Estadísticas: Tabla de Durbin-Watson. In Tratamiento de datos con R, STATISTICA y SPSS (pp. 875). España: Editorial Díaz de Santos.
González, C. G., Liste, A. V., & Felpeto, A. B. (2013b). Capítulo XI. Regresiones. In Tratamiento de datos con R, STATISTICA y SPSS (pp. 460). España: Editorial Díaz de Santos.
Han, L., & Che, S. (2018). An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self-Assembled Systems. Advanced Materials, 30(17), 1705708. doi:10.1002/adma.201705708
Hollister, S. J. (2005). Porous scaffold design for tissue engineering. Nature Materials, 4(7), 518-524. doi:10.1038/nmat1421
Jung, Y., & Torquato, S. (2005). Fluid permeabilities of triply periodic minimal surfaces. Physical Review E, 72(5), 056319.
Kanczler, J. M., Wells, J. A., Gibbs, D. M. R., Marshall, K. M., Tang, D. K. O., & Oreffo, R. O. C. (2020). Bone tissue engineering and bone regeneration. In R. Lanza, R. Langer, J. P. Vacanti, & A. Atala (Eds.), Principles of Tissue Engineering (5th ed.). United States of America: Elsevier Inc.
Knychala, J., Bouropoulos, N., Catt, C., Katsamenis, O., Please, C., & Sengers, B. (2013). Pore geometry regulates early stage human bone marrow cell tissue formation and organisation. Annals of Biomedical Engineering, 41(5), 917-930.
Lee, J. S., Cha, H. D., Shim, J. H., Jung, J. W., Kim, J. Y., & Cho, D. W. (2012). Effect of pore architecture and stacking direction on mechanical properties of solid freeform fabrication‐based scaffold for bone tissue engineering. Journal of Biomedical Materials Research Part A, 100(7), 1846-1853.
Malinauskas, M., Skliutas, E., Jonušauskas, L., Mizeras, D., Šešok, A., & Piskarskas, A. (2015). Tailoring bulk mechanical properties of 3D printed objects of polylactic acid varying internal micro-architecture (Vol. 9505), SPIE.
Maskery, I., Sturm, L., Aremu, A. O., Panesar, A., Williams, C. B., Tuck, C. J., . . . Hague, R. J. M. (2017). Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer. doi:10.1016/j.polymer.2017.11.049.
Meeks III, W. H. (1990). The theory of triply periodic minimal surfaces. Indiana University Mathematics Journal, 877-936.
Melchels, F. P. W., Bertoldi, K., Gabbrielli, R., H., V. A., Feijen, J., & Grijpma, D. W. (2010). Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials, 31(27), 6909-6916. doi:https://doi.org/10.1016/j.actbio.2010.06.012
Montazerian, H., Davoodi, E., Asadi-Eydivand, M., Kadkhodapour, J., & Solati-Hashjin, M. (2017). Porous scaffold internal architecture design based on minimal surfaces: A compromise between permeability and elastic properties. Materials & Design, 126, doi: 10.1016/j.matdes.2017.04.009
Moroni, L., de Wijn, J. R., & van Blitterswijk, C. A. (2006). 3D fiber-deposited scaffolds for tissue engineering: Influence of pores geometry and architecture on dynamic mechanical properties. Biomaterials, 27(7), 974-985. doi:https://doi.org/10.1016/j.biomaterials.2005.07.023
Naing, M. W., Chua, C. K., Leong, K. F., & Wang, Y. (2005). Fabrication of customised scaffolds using computer‐aided design and rapid prototyping techniques. Rapid Prototyping Journal, 11(4), 249-259. doi:10.1108/13552540510612938
Nikolova, M. P., & Chavali, M. S. (2019). Recent advances in biomaterials for 3D scaffolds: A review. Bioactive Materials, 4, 271-292. doi:https://doi.org/10.1016/j.bioactmat.2019.10.005
Norato, J. A., & Johnson, A. J. W. (2011). A Computational and Cellular Solids Approach to the Stiffness-Based Design of Bone Scaffolds. Journal of Biomechanical Engineering, 133, 091003-091001:8091003-8091001. doi:10.1115/1.4004994
Restrepo, S., Ocampo, S., Ramírez, J. A., Paucar, C., & García, C. (2017). Mechanical properties of ceramic structures based on Triply Periodic Minimal Surface (TPMS) processed by 3D printing. Journal of Physics: Conference Series, 935(012036). doi:10.1088/1742-6596/935/1/012036
Saito, E., Kang, H., Taboas, J. M., Diggs, A., Flanagan, C. L., & Hollister, S. J. (2010). Experimental and computational characterization of designed and fabricated 50:50 PLGA porous scaffolds for human trabecular bone applications. Journal of Materials Science: Materials in Medicine, 21(8), 2371-2383. doi:10.1007/s10856-010-4091-8
Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968). A Comparative Study of Various Tests for Normality. Journal of the American Statistical Association, 63(324), 1343-1372. doi:10.2307/2285889
Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69(347), 730-737. doi:10.2307/2286009
Wu, D., Spanou, A., Diez-Escudero, A., & Persson, C. (2019). 3D-printed PLA/HA composite structures as synthetic trabecular bone: A feasibility study using Fused Deposition Modelling. Journal of the Mechanical Behavior of Biomedical Materials, 103, doi: https://doi.org/10.1016/j.jmbbm.2019.103608
Yang, N., Quan, Z., Zhang, D., & Tian, Y. (2014). Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering. Computer-Aided Design, 56, 11-21. doi:https://doi.org/10.1016/j.cad.2014.06.006
Yang, N., & Zhou, K. (2014). Effective method for multi-scale gradient porous scaffold design and fabrication. Materials Science and Engineering: C, 43, 502-505. doi:https://doi.org/10.1016/j.msec.2014.07.052
Zadpoor, A. A. (2014). Bone tissue regeneration: the role of scaffold geometry. Biomaterials Science, 1-34.
Amirkhani, S., Bagheri, R., & Zehtab Yazdi, A. (2012). Effect of pore geometry and loading direction on deformation mechanism of rapid prototyped scaffolds. Acta Materialia, 60(6), 2778-2789. doi:https://doi.org/10.1016/j.actamat.2012.01.044
Anderson, D., Davis, H., Nitsche, J., & Scriven, L. (1990). Periodic surfaces of prescribed mean curvature. In Physics of amphiphilic layers (pp. 130-130): Springer.
Anderson, T. W., & Darling, D. A. (1952). Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics (2), 193-212, 120.
Bidan, C. M., Wang, F. M., & Dunlop, J. W. C. (2013). A three-dimensional model for tissue deposition on complex surfaces. Computer methods in biomechanics and biomedical engineering, 16(10), 1056-1070. doi:10.1080/10255842.2013.774384
Blanquer, S. B., Werner, M., Hannula, M., Sharifi, S., Lajoinie, G. P., Eglin, D., Grijpma, D. W. (2017). Surface curvature in triply-periodic minimal surface architectures as a distinct design parameter in preparing advanced tissue engineering scaffolds. BioFa, 9(2), 025001.
Bobbert, F., Lietaert, K., Eftekhari, A. A., Pouran, B., Ahmadi, S., Weinans, H., & Zadpoor, A. (2017). Additively manufactured metallic porous biomaterials based on minimal surfaces: A unique combination of topological, mechanical, and mass transport properties. Acta Biomaterialia, 53, 572-584.
Corder, G. W., & Foreman, D. I. (2009). Chapter 2. Testing data for normality. In Nonparametric statistics for non-statisticians: a step-by-step approach. United States: John Wiley & Sons, Inc.
Cuan-Urquizo, E., Barocio, E., Tejada-Ortigoza, V., Pipes, R. B., Rodriguez, C. A., & Roman-Flores, A. (2019). Characterization of the mechanical properties of FFF structures and materials: A review on the experimental, computational and theoretical approaches. Materials, 12(6), 895.
Cuan-Urquizo, E., Yang, S., & Bhaskar, A. (2015). Mechanical characterisation of additively manufactured material having lattice microstructure. Paper presented at the IOP Conf. Series: Materials Science and Engineering.
D´Agostino, R. B., & Stephens, M. A. (Eds.). (1986). Goodness-of-fit techniques. United States: Marcel Dekker, Inc.
Farah, S., Anderson, D. G., & Langer, R. (2016). Physical and mechanical properties of PLA, and their functions in widespread applications — A comprehensive review. Advanced Drug Delivery Reviews, 107, 367-392. doi:https://doi.org/10.1016/j.addr.2016.06.012
Gandy, P. J. F., Bardhan, S., Mackay, A. L., & Klinowski, J. (2001). Nodal surface approximations to the P,G,D and I-WP triply periodic minimal surfaces. Chemical Physics Letters, 336(3), 187-195. doi:https://doi.org/10.1016/S0009-2614(00)01418-4
Giannitelli, S. M., Accoto, D., Trombetta, M., & Rainer, A. (2014). Current trends in the design of scaffolds for computer-aided tissue engineering. Acta Biomaterialia, 10(2), 580-594. doi:https://doi.org/10.1016/j.actbio.2013.10.024
González, C. G., Liste, A. V., & Felpeto, A. B. (2013a). Apéndice I. Tablas Estadísticas: Tabla de Durbin-Watson. In Tratamiento de datos con R, STATISTICA y SPSS (pp. 875). España: Editorial Díaz de Santos.
González, C. G., Liste, A. V., & Felpeto, A. B. (2013b). Capítulo XI. Regresiones. In Tratamiento de datos con R, STATISTICA y SPSS (pp. 460). España: Editorial Díaz de Santos.
Han, L., & Che, S. (2018). An Overview of Materials with Triply Periodic Minimal Surfaces and Related Geometry: From Biological Structures to Self-Assembled Systems. Advanced Materials, 30(17), 1705708. doi:10.1002/adma.201705708
Hollister, S. J. (2005). Porous scaffold design for tissue engineering. Nature Materials, 4(7), 518-524. doi:10.1038/nmat1421
Jung, Y., & Torquato, S. (2005). Fluid permeabilities of triply periodic minimal surfaces. Physical Review E, 72(5), 056319.
Kanczler, J. M., Wells, J. A., Gibbs, D. M. R., Marshall, K. M., Tang, D. K. O., & Oreffo, R. O. C. (2020). Bone tissue engineering and bone regeneration. In R. Lanza, R. Langer, J. P. Vacanti, & A. Atala (Eds.), Principles of Tissue Engineering (5th ed.). United States of America: Elsevier Inc.
Knychala, J., Bouropoulos, N., Catt, C., Katsamenis, O., Please, C., & Sengers, B. (2013). Pore geometry regulates early stage human bone marrow cell tissue formation and organisation. Annals of Biomedical Engineering, 41(5), 917-930.
Lee, J. S., Cha, H. D., Shim, J. H., Jung, J. W., Kim, J. Y., & Cho, D. W. (2012). Effect of pore architecture and stacking direction on mechanical properties of solid freeform fabrication‐based scaffold for bone tissue engineering. Journal of Biomedical Materials Research Part A, 100(7), 1846-1853.
Malinauskas, M., Skliutas, E., Jonušauskas, L., Mizeras, D., Šešok, A., & Piskarskas, A. (2015). Tailoring bulk mechanical properties of 3D printed objects of polylactic acid varying internal micro-architecture (Vol. 9505), SPIE.
Maskery, I., Sturm, L., Aremu, A. O., Panesar, A., Williams, C. B., Tuck, C. J., . . . Hague, R. J. M. (2017). Insights into the mechanical properties of several triply periodic minimal surface lattice structures made by polymer additive manufacturing. Polymer. doi:10.1016/j.polymer.2017.11.049.
Meeks III, W. H. (1990). The theory of triply periodic minimal surfaces. Indiana University Mathematics Journal, 877-936.
Melchels, F. P. W., Bertoldi, K., Gabbrielli, R., H., V. A., Feijen, J., & Grijpma, D. W. (2010). Mathematically defined tissue engineering scaffold architectures prepared by stereolithography. Biomaterials, 31(27), 6909-6916. doi:https://doi.org/10.1016/j.actbio.2010.06.012
Montazerian, H., Davoodi, E., Asadi-Eydivand, M., Kadkhodapour, J., & Solati-Hashjin, M. (2017). Porous scaffold internal architecture design based on minimal surfaces: A compromise between permeability and elastic properties. Materials & Design, 126, doi: 10.1016/j.matdes.2017.04.009
Moroni, L., de Wijn, J. R., & van Blitterswijk, C. A. (2006). 3D fiber-deposited scaffolds for tissue engineering: Influence of pores geometry and architecture on dynamic mechanical properties. Biomaterials, 27(7), 974-985. doi:https://doi.org/10.1016/j.biomaterials.2005.07.023
Naing, M. W., Chua, C. K., Leong, K. F., & Wang, Y. (2005). Fabrication of customised scaffolds using computer‐aided design and rapid prototyping techniques. Rapid Prototyping Journal, 11(4), 249-259. doi:10.1108/13552540510612938
Nikolova, M. P., & Chavali, M. S. (2019). Recent advances in biomaterials for 3D scaffolds: A review. Bioactive Materials, 4, 271-292. doi:https://doi.org/10.1016/j.bioactmat.2019.10.005
Norato, J. A., & Johnson, A. J. W. (2011). A Computational and Cellular Solids Approach to the Stiffness-Based Design of Bone Scaffolds. Journal of Biomechanical Engineering, 133, 091003-091001:8091003-8091001. doi:10.1115/1.4004994
Restrepo, S., Ocampo, S., Ramírez, J. A., Paucar, C., & García, C. (2017). Mechanical properties of ceramic structures based on Triply Periodic Minimal Surface (TPMS) processed by 3D printing. Journal of Physics: Conference Series, 935(012036). doi:10.1088/1742-6596/935/1/012036
Saito, E., Kang, H., Taboas, J. M., Diggs, A., Flanagan, C. L., & Hollister, S. J. (2010). Experimental and computational characterization of designed and fabricated 50:50 PLGA porous scaffolds for human trabecular bone applications. Journal of Materials Science: Materials in Medicine, 21(8), 2371-2383. doi:10.1007/s10856-010-4091-8
Shapiro, S. S., Wilk, M. B., & Chen, H. J. (1968). A Comparative Study of Various Tests for Normality. Journal of the American Statistical Association, 63(324), 1343-1372. doi:10.2307/2285889
Stephens, M. A. (1974). EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association, 69(347), 730-737. doi:10.2307/2286009
Wu, D., Spanou, A., Diez-Escudero, A., & Persson, C. (2019). 3D-printed PLA/HA composite structures as synthetic trabecular bone: A feasibility study using Fused Deposition Modelling. Journal of the Mechanical Behavior of Biomedical Materials, 103, doi: https://doi.org/10.1016/j.jmbbm.2019.103608
Yang, N., Quan, Z., Zhang, D., & Tian, Y. (2014). Multi-morphology transition hybridization CAD design of minimal surface porous structures for use in tissue engineering. Computer-Aided Design, 56, 11-21. doi:https://doi.org/10.1016/j.cad.2014.06.006
Yang, N., & Zhou, K. (2014). Effective method for multi-scale gradient porous scaffold design and fabrication. Materials Science and Engineering: C, 43, 502-505. doi:https://doi.org/10.1016/j.msec.2014.07.052
Zadpoor, A. A. (2014). Bone tissue regeneration: the role of scaffold geometry. Biomaterials Science, 1-34.
Publicado
2021-11-23
Cómo citar
González González, A., Rivas Santana, M., Quiza Sardiñas, R., Paz Estévez, E. A., & Pla Pérez, A. (2021). Modelación de andamios porosos basados en las estructuras triplemente periódicas P y G. Orange Journal, 3(5), 30-41. https://doi.org/10.46502/issn.2710-995X/2021.5.04
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