Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal

Actualmente, para corregir patologías septales a menudo se requiere de injertos cartilaginosos, pero los métodos actuales de obtención de injertos presentan limitaciones en la calidad y cantidad de los mismos. En respuesta la ingeniería tisular ha diseñado neocartílagos prometedores (Lavernia et al....

Full description

Autores:
Buitrago Gonzalez, Milton Julian
Tipo de recurso:
https://purl.org/coar/resource_type/c_7a1f
Fecha de publicación:
2025
Institución:
Universidad El Bosque
Repositorio:
Repositorio U. El Bosque
Idioma:
spa
OAI Identifier:
oai:repositorio.unbosque.edu.co:20.500.12495/14569
Acceso en línea:
https://hdl.handle.net/20.500.12495/14569
https://repositorio.unbosque.edu.co
Palabra clave:
Ingeniería tisular
Biomateriales
Modelado matemático
610.28
Tissue engineering
Biomaterials
Mathematical modeling
Rights
License
Attribution-NonCommercial-ShareAlike 4.0 International
id UNBOSQUE2_0d39077df4c5c7162c60be252f11a6b7
oai_identifier_str oai:repositorio.unbosque.edu.co:20.500.12495/14569
network_acronym_str UNBOSQUE2
network_name_str Repositorio U. El Bosque
repository_id_str
dc.title.none.fl_str_mv Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
dc.title.translated.none.fl_str_mv Design of a mathematical model for predicting interactions between a hyaluronic acid-chitosan scaffold and nasal septum chondrocytes
title Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
spellingShingle Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
Ingeniería tisular
Biomateriales
Modelado matemático
610.28
Tissue engineering
Biomaterials
Mathematical modeling
title_short Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
title_full Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
title_fullStr Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
title_full_unstemmed Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
title_sort Diseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasal
dc.creator.fl_str_mv Buitrago Gonzalez, Milton Julian
dc.contributor.advisor.none.fl_str_mv Ibla Gordillo, José Francisco
dc.contributor.author.none.fl_str_mv Buitrago Gonzalez, Milton Julian
dc.subject.none.fl_str_mv Ingeniería tisular
Biomateriales
Modelado matemático
topic Ingeniería tisular
Biomateriales
Modelado matemático
610.28
Tissue engineering
Biomaterials
Mathematical modeling
dc.subject.ddc.none.fl_str_mv 610.28
dc.subject.keywords.none.fl_str_mv Tissue engineering
Biomaterials
Mathematical modeling
description Actualmente, para corregir patologías septales a menudo se requiere de injertos cartilaginosos, pero los métodos actuales de obtención de injertos presentan limitaciones en la calidad y cantidad de los mismos. En respuesta la ingeniería tisular ha diseñado neocartílagos prometedores (Lavernia et al., 2019) basados en el uso de condrocitos y andamios (Li et al., 2019), destacando la combinación ácido hialurónico-quitosano (HA/CS), por sus propiedades fisicoquímicas complementarias y su capacidad para favorecer la adhesión celular (Hu et al., 2021), sin embargo, para que el biomaterial cumpla con su propósito se deben establecer criterios de diseño de ingeniería a partir de las propiedades del tejido nativo (S. Zhang et al., 2019). En este contexto, el presente proyecto se centra en el diseño de un modelo matemático de la fuerza de interacción entre condrocitos y un andamio de HA/CS, a través del establecimiento de las variables críticas de este sistema, como el estado semisólido del material o la fuerza de adhesión, e integrando modelos fisicoquímicos a estas variables, como el criterio de von Mises a la fuerza biomecánica que influye en el sistema, además se realizaron una serie de simulaciones numérica en MATLAB que permiten representar gráficamente la respuesta de los modelos preliminares, los resultados del análisis de sensibilidad global que identifican los parámetros más influyentes en la respuesta del modelo, como la tasa de adhesión, además de los resultados de un análisis Monte Carlo que demostró la sensibilidad del modelo, al presentar en aproximadamente el 50% de las simulaciones respuestas en un rango de 1,5 μN y 1,55 μN, demostrando la precisión del modelo.
publishDate 2025
dc.date.accessioned.none.fl_str_mv 2025-06-06T14:15:01Z
dc.date.available.none.fl_str_mv 2025-06-06T14:15:01Z
dc.date.issued.none.fl_str_mv 2025-05
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_7a1f
dc.type.local.spa.fl_str_mv Tesis/Trabajo de grado - Monografía - Pregrado
dc.type.coar.none.fl_str_mv https://purl.org/coar/resource_type/c_7a1f
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/bachelorThesis
dc.type.coarversion.none.fl_str_mv https://purl.org/coar/version/c_970fb48d4fbd8a85
format https://purl.org/coar/resource_type/c_7a1f
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12495/14569
dc.identifier.instname.spa.fl_str_mv instname:Universidad El Bosque
dc.identifier.reponame.spa.fl_str_mv reponame:Repositorio Institucional Universidad El Bosque
dc.identifier.repourl.none.fl_str_mv https://repositorio.unbosque.edu.co
url https://hdl.handle.net/20.500.12495/14569
https://repositorio.unbosque.edu.co
identifier_str_mv instname:Universidad El Bosque
reponame:Repositorio Institucional Universidad El Bosque
dc.language.iso.fl_str_mv spa
language spa
dc.relation.references.none.fl_str_mv Afshar, A., Gultekinoglu, M., & Edirisinghe, M. (2023). Binary polymer systems for biomedical applications. International Materials Reviews, 68(2), 184–224. https://doi.org/10.1080/09506608.2022.2069451
Ardatov, O., Aleksiuk, V., Maknickas, A., Stonkus, R., Uzieliene, I., Vaiciuleviciute, R., Pachaleva, J., Kvederas, G., & Bernotiene, E. (2023). Modeling the Impact of Meniscal Tears on von Mises Stress of Knee Cartilage Tissue. Bioengineering 2023, Vol. 10, Page 314, 10(3), 314. https://doi.org/10.3390/BIOENGINEERING10030314
Bandeiras, C., & Completo, A. (2017). A mathematical model of tissue-engineered cartilage development under cyclic compressive loading. Biomechanics and Modeling in Mechanobiology, 16(2), 651–666. https://doi.org/10.1007/s10237-016-0843-9
Bell, G. (1978). Models for the Specific Adhesion of Cells to Cells. Science.
Caballero, P. (2012). Análisis computacional del comportamiento mecánico de cartílago articular basado en un modelo viscoelástico. https://repositorio.unal.edu.co/handle/unal/10010
Chang, R., & Goldsby, K. A. (2013). Química (11th ed.).
Chen, X., Jiang, C., Wang, T., Zhu, T., Li, X., & Huang, J. (2022). Hyaluronic acid-based biphasic scaffold with layer-specific induction capacity for osteochondral defect regeneration. Materials & Design, 216, 110550. https://doi.org/10.1016/J.MATDES.2022.110550
Chew, L., & Sebag, J. (2025). Vitreous. In Adler’s Physiology of the Eye.
Chiesa, C. M., Aiastui, A., González, I., Hernáez, R., Rodiño, C., Delgado, A., Garces, J. P., Paredes, J., Aldazabal, J., Altuna, X., & Izeta, A. (2021). Three-Dimensional Bioprinting Scaffolding for Nasal Cartilage Defects: A Systematic Review. Tissue Engineering and Regenerative Medicine, 18(3), 343–353. https://doi.org/10.1007/S13770-021-00331-6/TABLES/3
Comblain, F., Rocasalbas, G., Gauthier, S., & Henrotin, Y. (2017). Chitosan: A promising polymer for cartilage repair and viscosupplementation. Bio-Medical Materials and Engineering, 28(s1), S209–S215. https://doi.org/10.3233/BME-171643/ASSET/IMAGES/LARGE/10.3233_BME-171643-FIG1.JPEG
Deng, R. H., Qiu, B., & Zhou, P. H. (2018). Chitosan/hyaluronic acid/plasmid-DNA nanoparticles encoding interleukin-1 receptor antagonist attenuate inflammation in synoviocytes induced by interleukin-1 beta. Journal of Materials Science: Materials in Medicine, 29(10), 1–10. https://doi.org/10.1007/S10856-018-6160-3/FIGURES/6
Dicker, K. T., Gurski, L. A., Pradhan-Bhatt, S., Witt, R. L., Farach-Carson, M. C., & Jia, X. (2014). Hyaluronan: A simple polysaccharide with diverse biological functions. Acta Biomaterialia, 10(4), 1558–1570. https://doi.org/10.1016/J.ACTBIO.2013.12.019
Faust, H. J., Guo, Q., & Elisseeff, J. H. (2018). Cartilage Tissue Engineering. In Principles of Regenerative Medicine (pp. 937–952). Elsevier. https://doi.org/10.1016/B978-0-12-809880-6.00053-9
Gao, Y., Liu, S., Huang, J., Guo, W., Chen, J., Zhang, L., Zhao, B., Peng, J., Wang, A., Wang, Y., Xu, W., Lu, S., Yuan, M., & Guo, Q. (2014). The ECM-cell interaction of cartilage extracellular matrix on chondrocytes. BioMed Research International, 2014. https://doi.org/10.1155/2014/648459
García, L. (2017). Generación de sustituto biomimético de cartílago artificial con matriz extracelular de fibrina-agarosa y condrocitos humanos para su utilización en ingenieria tisular maxilofacial. Universidad de Granada.
Gelfert, A. (2017). The Ontology of Models. In Springer Handbook of Model-Based Science (pp. 5–23). Springer. https://doi.org/10.1007/978-3-319-30526-4_1
Gomez, J. (2011). Vista de Un singular desfile de modelos. http://polipapers.upv.es/index.php/MSEL/article/view/3052/3107
Grabska-Zielińska, S., Sosik, A., Małkowska, A., Olewnik-Kruszkowska, E., Steinbrink, K., Kleszczyński, K., & Kaczmarek-Szczepańska, B. (2021). The Characterization of Scaffolds Based on Dialdehyde Chitosan/Hyaluronic Acid. Materials, 14(17), 4993. https://doi.org/10.3390/MA14174993
Hall, A. C. (2019). The Role of Chondrocyte Morphology and Volume in Controlling Phenotype—Implications for Osteoarthritis, Cartilage Repair, and Cartilage Engineering. Current Rheumatology Reports, 21(8), 1–13. https://doi.org/10.1007/S11926-019-0837-6/FIGURES/1
Hu, M., Yang, J., & Xu, J. (2021). Structural and biological investigation of chitosan/hyaluronic acid with silanized-hydroxypropyl methylcellulose as an injectable reinforced interpenetrating network hydrogel for cartilage tissue engineering. Drug Delivery, 28(1), 607–619. https://doi.org/10.1080/10717544.2021.1895906
Ingalls, B. P. (2015). Mathematical modeling in systems biology : an introduction. MIT Press Journals, 408. https://books.google.com.co/books?id=OYr6AQAAQBAJ&printsec=frontcover&source=gbs_atb&redir_esc=y#v=onepage&q&f=false
Israelachvili, J. (2011). Intermolecular and Surface Forces (3rd ed.).
Joseph, S., Rouissi, T., & Brar, S. K. (2020). Fungal chitosan: prospects and challenges. In Handbook of Chitin and Chitosan: Volume 1: Preparation and Properties (Vol. 1, pp. 419–452). Elsevier. https://doi.org/10.1016/B978-0-12-817970-3.00014-6
Keppie, S. J., Mansfield, J. C., Tang, X., Philp, C. J., Graham, H. K., Önnerfjord, P., Wall, A., Mclean, C., Winlove, C. P., Sherratt, M. J., Pavlovskaya, G. E., & Vincent, T. L. (2021). Matrix-Bound Growth Factors are Released upon Cartilage Compression by an Aggrecan-Dependent Sodium Flux that is Lost in Osteoarthritis. Function, 2(5), 37–2021. https://doi.org/10.1093/FUNCTION/ZQAB037
Kim, T. K., & Jeong, J. Y. (2020). Deviated nose: Physiological and pathological changes of the nasal cavity. Archives of Plastic Surgery, 47(6), 505–515. https://doi.org/10.5999/APS.2020.01781/ID/JR_37/BIB
Knudson, W., Ishizuka, S., Terabe, K., Askew, E. B., & Knudson, C. B. (2019). The pericellular hyaluronan of articular chondrocytes. Matrix Biology, 78–79, 32–46. https://doi.org/10.1016/J.MATBIO.2018.02.005
Kulkarni, V. S., & Shaw, C. (2016). Rheological Studies. In Essential Chemistry for Formulators of Semisolid and Liquid Dosages (pp. 145–182). Academic Press. https://doi.org/10.1016/B978-0-12-801024-2.00009-1
Kumari, S., & Kishor, R. (2020). Chitin and chitosan: origin, properties, and applications. In Handbook of Chitin and Chitosan: Volume 1: Preparation and Properties (Vol. 1, pp. 1–33). Elsevier. https://doi.org/10.1016/B978-0-12-817970-3.00001-8
Lamana, A., Rodríguez, A., Millán, M. M., & Castañeda Sanz, S. (2020). Bases de biología celular y molecular en cirugía ortopédica y traumatología. In Ciencia básica de aplicación en cirugía ortopédica y traumatología.
Latour, R. A. (2015). The langmuir isotherm: A commonly applied but misleading approach for the analysis of protein adsorption behavior. Journal of Biomedical Materials Research Part A, 103(3), 949–958. https://doi.org/10.1002/JBM.A.35235
Lavernia, L., Brown, W. E., Wong, B. J. F., Hu, J. C., & Athanasiou, K. A. (2019). Toward tissue-engineering of nasal cartilages. Acta Biomaterialia, 88, 42–56. https://doi.org/10.1016/J.ACTBIO.2019.02.025
Lee, J. H., Kim, D. H., Lee, H. H., & Kim, H. W. (2019). Role of nuclear mechanosensitivity in determining cellular responses to forces and biomaterials. Biomaterials, 197, 60–71. https://doi.org/10.1016/J.BIOMATERIALS.2019.01.010
Lee, W., Guilak, F., & Liedtke, W. (2017). Role of Piezo Channels in Joint Health and Injury. Current Topics in Membranes, 79, 263–273. https://doi.org/10.1016/BS.CTM.2016.10.003
Li, J., Chen, G., Xu, X., Abdou, P., Jiang, Q., Shi, D., & Gu, Z. (2019). Advances of injectable hydrogel-based scaffolds for cartilage regeneration. Regenerative Biomaterials, 6(3), 129–140. https://doi.org/10.1093/RB/RBZ022
Loeser, R. F. (2014). Integrins and chondrocyte–matrix interactions in articular cartilage. Matrix Biology, 39, 11–16. https://doi.org/10.1016/J.MATBIO.2014.08.007
Luo, Y., & Wang, Q. (2014). Recent development of chitosan-based polyelectrolyte complexes with natural polysaccharides for drug delivery. International Journal of Biological Macromolecules, 64, 353–367. https://doi.org/10.1016/J.IJBIOMAC.2013.12.017
Maestrando, M. F. (2023). Simulación numérica de las respuesta mecánicas de tejidos biológicos.
Maldonado, L., Sanabria, L., Franco, H., Drachman, R., Montenegro, A., Macías, D., Rodríguez, M., Lizcano, A., & Ibáñez, J. (2015). El modelamiento matemático en la formación del ingeniero (L. Maldonado, Ed.). Universidad Central.
Marquez, K., Arroyave, S., & Linares, J. M. (2023). From biological morphogenesis to engineering joint design: A bio-inspired algorithm. Materials & Design, 225, 111466. https://doi.org/10.1016/J.MATDES.2022.111466
Matta, C., Zhang, X., Liddell, S., Smith, J. R., & Mobasheri, A. (2015). Label-free proteomic analysis of the hydrophobic membrane protein complement in articular chondrocytes: a technique for identification of membrane biomarkers. Biomarkers, 20(8), 572–589. https://doi.org/10.3109/1354750X.2015.1130191
Meccia, B. (2018). Forward Solution Modeling: An In Vivo Theoretical Simulator of the Knee. In Insall & Scott Surgery of the Knee.
Mobasheri, A., Goldring, M. B., & Loeser, R. F. (2022). Cartílago y condrocitos. In Firestein y Kelley. Tratado de reumatología.
Mokbel, M., Hosseini, K., Aland, S., & Fischer-Friedrich, E. (2020). The Poisson Ratio of the Cellular Actin Cortex Is Frequency Dependent. Biophysical Journal, 118(8), 1968–1976. https://doi.org/10.1016/j.bpj.2020.03.002
Moreno, B., Muñoz, M., Cuellar, J., Domancic, S., Villanueva, J., Moreno, B., Muñoz, M., Cuellar, J., Domancic, S., & Villanueva, J. (2018). Revisiones Sistemáticas: definición y nociones básicas. Revista Clínica de Periodoncia, Implantología y Rehabilitación Oral, 11(3), 184–186. https://doi.org/10.4067/S0719-01072018000300184
Nasrollahzadeh, M., Sajjadi, M., Nezafat, Z., & Shafiei, N. (2021). Polysaccharide biopolymer chemistry. In Biopolymer-Based Metal Nanoparticle Chemistry for Sustainable Applications: Volume 1: Classification, Properties and Synthesis (pp. 45–105). Elsevier. https://doi.org/10.1016/B978-0-12-822108-2.00019-3
Navas, H., & Braga, D. (2011). Selection of a Stirrer Drive Configuration Using Pugh Decision Matrix. Methodology Científica, 15(3), 139–143. http://www.redalyc.org/articulo.oa?id=61420811006
Nease, C., & Sturm, L. (2023). Nasal Anatomy. Rhinoplasty: A Case-Based Approach, 7–15. https://doi.org/10.1016/B978-0-323-69775-0.00002-0
Nguyen, T. D., & Gu, Y. (2016). Investigation of Cell-Substrate Adhesion Properties of Living Chondrocyte by Measuring Adhesive Shear Force and Detachment Using AFM and Inverse FEA. Scientific Reports 2016 6:1, 6(1), 1–13. https://doi.org/10.1038/srep38059
Nguyen, T. D., Oloyede, A., & Gu, Y. (2014). Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments. Theoretical and Applied Mechanics Letters, 4(5), 054001. https://doi.org/10.1063/2.1405401
Pearce, D., Fischer, S., Huda, F., & Vahdati, A. (2020). Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering. In Tissue Engineering and Regenerative Medicine (Vol. 17, Issue 1). Korean Tissue Engineering and Regenerative Medicine Society. https://doi.org/10.1007/s13770-019-00216-9
Rahmati, M., Silva, E. A., Reseland, J. E., A. Heyward, C., & Haugen, H. J. (2020). Biological responses to physicochemical properties of biomaterial surface. In Chemical Society Reviews (Vol. 49, Issue 15, pp. 5178–5224). Royal Society of Chemistry. https://doi.org/10.1039/d0cs00103a
Renardy, M., Hult, C., Evans, S., Linderman, J. J., & Kirschner, D. E. (2019). Global sensitivity analysis of biological multiscale models. Current Opinion in Biomedical Engineering, 11, 109–116. https://doi.org/10.1016/j.cobme.2019.09.012
Rivas, C. F., Núñez, O., Longoria, F., & Gonzalez, L. (2014). Isoterma de langmuir y freundlich como modelos para la adsorción de componentes de ácido nucleico sonbre WO3. Saber, 26(1), 43–49. http://ve.scielo.org/scielo.php?script=sci_arttext&pid=S1315-01622014000100008&lng=es&nrm=iso&tlng=es
Roa, D., & Quitian, R. (2016). SITUACIÓN ACTUAL DE LA INGENIERIA DE TEJIDOS Y MEDICINA REGENERATIVA EN COLOMBIA. Universidad de ciencias aplicadas y ambientales.
Shen, C. (2022). Physical and Chemical Properties of Solids. In Phillips’ Science of Dental Materials.
Taheri, S., Ghazali, H. S., Ghazali, Z. S., Bhattacharyya, A., & Noh, I. (2023). Progress in biomechanical stimuli on the cell-encapsulated hydrogels for cartilage tissue regeneration. Biomaterials Research, 27(1), 1–17. https://doi.org/10.1186/S40824-023-00358-X/FIGURES/3
Tedeschi, L. O. (2006). Assessment of the adequacy of mathematical models. Agricultural Systems, 89(2–3), 225–247. https://doi.org/10.1016/J.AGSY.2005.11.004
Tripathy, N., Perumal, E., Ahmad, R., Song, J. E., & Khang, G. (2018). Hybrid Composite Biomaterials. In Principles of Regenerative Medicine (pp. 695–714). Elsevier. https://doi.org/10.1016/B978-0-12-809880-6.00040-0
Vainieri, M. L., Wahl, D., Alini, M., van Osch, G. J. V. M., & Grad, S. (2018). Mechanically stimulated osteochondral organ culture for evaluation of biomaterials in cartilage repair studies. Acta Biomaterialia, 81, 256–266. https://doi.org/10.1016/J.ACTBIO.2018.09.058
Vincent, T. L., & Wann, A. K. T. (2019). Mechanoadaptation: articular cartilage through thick and thin. Journal of Physiology, 597(5), 1271–1281. https://doi.org/10.1113/JP275451
Wei, L., Guangdong, Z., & Yilin, C. (2024). Repair, grafting, and engineering of cartilage. In Plastic Surgery, Volume 1: Principles.
Wu, Y., Li, X., Wang, Y., Shi, Y., Wang, F., & Lin, G. (2022). Research progress on mechanical properties and wear resistance of cartilage repair hydrogel. Materials & Design, 216, 110575. https://doi.org/10.1016/J.MATDES.2022.110575
Yepes, J. J., Urrútia, G., Romero, M., & Alonso, S. (2021). Declaración PRISMA 2020: una guía actualizada para la publicación de revisiones sistemáticas. Revista Española de Cardiología, 74(9), 790–799. https://doi.org/10.1016/J.RECESP.2021.06.016
Yu, T., & Xue, P. (2022). Yield criteria. In Introduction to Engineering Plasticity (pp. 67–87). Elsevier. https://doi.org/10.1016/B978-0-323-98981-7.00004-X
Zhang, Q., Zhang, M., Meng, N., Wei, X., & Chen, W. (2024). Mechanobiology of the articular chondrocyte. In Bone Cell Biomechanics, Mechanobiology and Bone Diseases (pp. 249–287). Academic Press. https://doi.org/10.1016/B978-0-323-96123-3.00016-6
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. Journal of Biomedical Materials Research. Part B, Applied Biomaterials, 107(5), 1329–1351. https://doi.org/10.1002/JBM.B.34226
Zhang, X., Zhan, X., Cheng, H., Dong, Z., Hu, C., Liu, C., Liang, J., Chen, Y., Fan, Y., & Zhang, X. (2024). Cartilage-like protein-polysaccharide hybrid hydrogel for enhancing chondrogenic differentiation of bone marrow mesenchymal stem cells. Collagen and Leather, 6(1), 1–12. https://doi.org/10.1186/S42825-023-00146-2/FIGURES/5
dc.rights.en.fl_str_mv Attribution-NonCommercial-ShareAlike 4.0 International
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.none.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.local.spa.fl_str_mv Acceso abierto
dc.rights.accessrights.none.fl_str_mv https://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Attribution-NonCommercial-ShareAlike 4.0 International
http://creativecommons.org/licenses/by-nc-sa/4.0/
Acceso abierto
https://purl.org/coar/access_right/c_abf2
http://purl.org/coar/access_right/c_abf2
dc.format.mimetype.none.fl_str_mv application/pdf
dc.publisher.program.spa.fl_str_mv Bioingeniería
dc.publisher.grantor.spa.fl_str_mv Universidad El Bosque
dc.publisher.faculty.spa.fl_str_mv Facultad de Ingeniería
institution Universidad El Bosque
bitstream.url.fl_str_mv https://repositorio.unbosque.edu.co/bitstreams/53f064f0-fe24-403e-8d87-0682432a989d/download
https://repositorio.unbosque.edu.co/bitstreams/89f981de-560f-403d-aa02-fde3a228195b/download
https://repositorio.unbosque.edu.co/bitstreams/7a4965ad-e27e-4a82-8871-2ff77cc444b2/download
https://repositorio.unbosque.edu.co/bitstreams/0f4ae81c-69a3-48d4-83bd-3ef5f38ee781/download
https://repositorio.unbosque.edu.co/bitstreams/0f4a5432-b5db-40bc-b81c-4a1b32c18427/download
https://repositorio.unbosque.edu.co/bitstreams/91a0fe79-d1c1-44cd-b496-95e2366b87ed/download
bitstream.checksum.fl_str_mv 17cc15b951e7cc6b3728a574117320f9
2cb43e282844adf1477f43bc4f87e3e3
220d054b02bd3be07e7e758ed427a875
5643bfd9bcf29d560eeec56d584edaa9
f3fe0914f302b56e15b14957e91ac329
75044870c1465283fc486db3ff396c67
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad El Bosque
repository.mail.fl_str_mv bibliotecas@biteca.com
_version_ 1836752056664195072
spelling Ibla Gordillo, José FranciscoBuitrago Gonzalez, Milton Julian2025-06-06T14:15:01Z2025-06-06T14:15:01Z2025-05https://hdl.handle.net/20.500.12495/14569instname:Universidad El Bosquereponame:Repositorio Institucional Universidad El Bosquehttps://repositorio.unbosque.edu.coActualmente, para corregir patologías septales a menudo se requiere de injertos cartilaginosos, pero los métodos actuales de obtención de injertos presentan limitaciones en la calidad y cantidad de los mismos. En respuesta la ingeniería tisular ha diseñado neocartílagos prometedores (Lavernia et al., 2019) basados en el uso de condrocitos y andamios (Li et al., 2019), destacando la combinación ácido hialurónico-quitosano (HA/CS), por sus propiedades fisicoquímicas complementarias y su capacidad para favorecer la adhesión celular (Hu et al., 2021), sin embargo, para que el biomaterial cumpla con su propósito se deben establecer criterios de diseño de ingeniería a partir de las propiedades del tejido nativo (S. Zhang et al., 2019). En este contexto, el presente proyecto se centra en el diseño de un modelo matemático de la fuerza de interacción entre condrocitos y un andamio de HA/CS, a través del establecimiento de las variables críticas de este sistema, como el estado semisólido del material o la fuerza de adhesión, e integrando modelos fisicoquímicos a estas variables, como el criterio de von Mises a la fuerza biomecánica que influye en el sistema, además se realizaron una serie de simulaciones numérica en MATLAB que permiten representar gráficamente la respuesta de los modelos preliminares, los resultados del análisis de sensibilidad global que identifican los parámetros más influyentes en la respuesta del modelo, como la tasa de adhesión, además de los resultados de un análisis Monte Carlo que demostró la sensibilidad del modelo, al presentar en aproximadamente el 50% de las simulaciones respuestas en un rango de 1,5 μN y 1,55 μN, demostrando la precisión del modelo.BioingenieroPregradoCurrently, cartilage grafts are often required to correct septal pathologies, but current methods of obtaining grafts have limitations in terms of quality and quantity. In response, tissue engineering has designed promising neocartilages (Lavernia et al., 2019) based on the use of chondrocytes and scaffolds (Li et al., 2019), with the hyaluronic acid-chitosan (HA/CS) combination standing out for its complementary physicochemical properties and its ability to promote cell adhesion (Hu et al., 2021). However, for the biomaterial to fulfill its purpose, engineering design criteria must be established based on the properties of the native tissue (S. Zhang et al., 2019). In this context, the present project focuses on the design of a mathematical model of the interaction force between chondrocytes and an HA/CS scaffold, through the establishment of the critical variables of this system, such as the semi-solid state of the material or the adhesion force, and integrating physicochemical models into these variables, such as the von Mises criterion for the biomechanical force that influences the system. In addition, a series of numerical simulations were performed in MATLAB to graphically represent the response of the preliminary models, the results of the global sensitivity analysis that identify the most influential parameters in the model's response, such as the adhesion rate, and the results of a Monte Carlo analysis that demonstrated the sensitivity of the model, by presenting responses in a range of 1.5 μN and 1.55 μN in approximately 50% of the simulations, demonstrating the accuracy of the model.application/pdfAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/Acceso abiertohttps://purl.org/coar/access_right/c_abf2http://purl.org/coar/access_right/c_abf2Ingeniería tisularBiomaterialesModelado matemático610.28Tissue engineeringBiomaterialsMathematical modelingDiseño de un modelo matemático para la predicción de las interacciones entre un andamio de ácido hialurónico-quitosano y condrocitos del septum nasalDesign of a mathematical model for predicting interactions between a hyaluronic acid-chitosan scaffold and nasal septum chondrocytesBioingenieríaUniversidad El BosqueFacultad de IngenieríaTesis/Trabajo de grado - Monografía - Pregradohttps://purl.org/coar/resource_type/c_7a1fhttp://purl.org/coar/resource_type/c_7a1finfo:eu-repo/semantics/bachelorThesishttps://purl.org/coar/version/c_970fb48d4fbd8a85Afshar, A., Gultekinoglu, M., & Edirisinghe, M. (2023). Binary polymer systems for biomedical applications. International Materials Reviews, 68(2), 184–224. https://doi.org/10.1080/09506608.2022.2069451Ardatov, O., Aleksiuk, V., Maknickas, A., Stonkus, R., Uzieliene, I., Vaiciuleviciute, R., Pachaleva, J., Kvederas, G., & Bernotiene, E. (2023). Modeling the Impact of Meniscal Tears on von Mises Stress of Knee Cartilage Tissue. Bioengineering 2023, Vol. 10, Page 314, 10(3), 314. https://doi.org/10.3390/BIOENGINEERING10030314Bandeiras, C., & Completo, A. (2017). A mathematical model of tissue-engineered cartilage development under cyclic compressive loading. Biomechanics and Modeling in Mechanobiology, 16(2), 651–666. https://doi.org/10.1007/s10237-016-0843-9Bell, G. (1978). Models for the Specific Adhesion of Cells to Cells. Science.Caballero, P. (2012). Análisis computacional del comportamiento mecánico de cartílago articular basado en un modelo viscoelástico. https://repositorio.unal.edu.co/handle/unal/10010Chang, R., & Goldsby, K. A. (2013). Química (11th ed.).Chen, X., Jiang, C., Wang, T., Zhu, T., Li, X., & Huang, J. (2022). Hyaluronic acid-based biphasic scaffold with layer-specific induction capacity for osteochondral defect regeneration. Materials & Design, 216, 110550. https://doi.org/10.1016/J.MATDES.2022.110550Chew, L., & Sebag, J. (2025). Vitreous. In Adler’s Physiology of the Eye.Chiesa, C. M., Aiastui, A., González, I., Hernáez, R., Rodiño, C., Delgado, A., Garces, J. P., Paredes, J., Aldazabal, J., Altuna, X., & Izeta, A. (2021). Three-Dimensional Bioprinting Scaffolding for Nasal Cartilage Defects: A Systematic Review. Tissue Engineering and Regenerative Medicine, 18(3), 343–353. https://doi.org/10.1007/S13770-021-00331-6/TABLES/3Comblain, F., Rocasalbas, G., Gauthier, S., & Henrotin, Y. (2017). Chitosan: A promising polymer for cartilage repair and viscosupplementation. Bio-Medical Materials and Engineering, 28(s1), S209–S215. https://doi.org/10.3233/BME-171643/ASSET/IMAGES/LARGE/10.3233_BME-171643-FIG1.JPEGDeng, R. H., Qiu, B., & Zhou, P. H. (2018). Chitosan/hyaluronic acid/plasmid-DNA nanoparticles encoding interleukin-1 receptor antagonist attenuate inflammation in synoviocytes induced by interleukin-1 beta. Journal of Materials Science: Materials in Medicine, 29(10), 1–10. https://doi.org/10.1007/S10856-018-6160-3/FIGURES/6Dicker, K. T., Gurski, L. A., Pradhan-Bhatt, S., Witt, R. L., Farach-Carson, M. C., & Jia, X. (2014). Hyaluronan: A simple polysaccharide with diverse biological functions. Acta Biomaterialia, 10(4), 1558–1570. https://doi.org/10.1016/J.ACTBIO.2013.12.019Faust, H. J., Guo, Q., & Elisseeff, J. H. (2018). Cartilage Tissue Engineering. In Principles of Regenerative Medicine (pp. 937–952). Elsevier. https://doi.org/10.1016/B978-0-12-809880-6.00053-9Gao, Y., Liu, S., Huang, J., Guo, W., Chen, J., Zhang, L., Zhao, B., Peng, J., Wang, A., Wang, Y., Xu, W., Lu, S., Yuan, M., & Guo, Q. (2014). The ECM-cell interaction of cartilage extracellular matrix on chondrocytes. BioMed Research International, 2014. https://doi.org/10.1155/2014/648459García, L. (2017). Generación de sustituto biomimético de cartílago artificial con matriz extracelular de fibrina-agarosa y condrocitos humanos para su utilización en ingenieria tisular maxilofacial. Universidad de Granada.Gelfert, A. (2017). The Ontology of Models. In Springer Handbook of Model-Based Science (pp. 5–23). Springer. https://doi.org/10.1007/978-3-319-30526-4_1Gomez, J. (2011). Vista de Un singular desfile de modelos. http://polipapers.upv.es/index.php/MSEL/article/view/3052/3107Grabska-Zielińska, S., Sosik, A., Małkowska, A., Olewnik-Kruszkowska, E., Steinbrink, K., Kleszczyński, K., & Kaczmarek-Szczepańska, B. (2021). The Characterization of Scaffolds Based on Dialdehyde Chitosan/Hyaluronic Acid. Materials, 14(17), 4993. https://doi.org/10.3390/MA14174993Hall, A. C. (2019). The Role of Chondrocyte Morphology and Volume in Controlling Phenotype—Implications for Osteoarthritis, Cartilage Repair, and Cartilage Engineering. Current Rheumatology Reports, 21(8), 1–13. https://doi.org/10.1007/S11926-019-0837-6/FIGURES/1Hu, M., Yang, J., & Xu, J. (2021). Structural and biological investigation of chitosan/hyaluronic acid with silanized-hydroxypropyl methylcellulose as an injectable reinforced interpenetrating network hydrogel for cartilage tissue engineering. Drug Delivery, 28(1), 607–619. https://doi.org/10.1080/10717544.2021.1895906Ingalls, B. P. (2015). Mathematical modeling in systems biology : an introduction. MIT Press Journals, 408. https://books.google.com.co/books?id=OYr6AQAAQBAJ&printsec=frontcover&source=gbs_atb&redir_esc=y#v=onepage&q&f=falseIsraelachvili, J. (2011). Intermolecular and Surface Forces (3rd ed.).Joseph, S., Rouissi, T., & Brar, S. K. (2020). Fungal chitosan: prospects and challenges. In Handbook of Chitin and Chitosan: Volume 1: Preparation and Properties (Vol. 1, pp. 419–452). Elsevier. https://doi.org/10.1016/B978-0-12-817970-3.00014-6Keppie, S. J., Mansfield, J. C., Tang, X., Philp, C. J., Graham, H. K., Önnerfjord, P., Wall, A., Mclean, C., Winlove, C. P., Sherratt, M. J., Pavlovskaya, G. E., & Vincent, T. L. (2021). Matrix-Bound Growth Factors are Released upon Cartilage Compression by an Aggrecan-Dependent Sodium Flux that is Lost in Osteoarthritis. Function, 2(5), 37–2021. https://doi.org/10.1093/FUNCTION/ZQAB037Kim, T. K., & Jeong, J. Y. (2020). Deviated nose: Physiological and pathological changes of the nasal cavity. Archives of Plastic Surgery, 47(6), 505–515. https://doi.org/10.5999/APS.2020.01781/ID/JR_37/BIBKnudson, W., Ishizuka, S., Terabe, K., Askew, E. B., & Knudson, C. B. (2019). The pericellular hyaluronan of articular chondrocytes. Matrix Biology, 78–79, 32–46. https://doi.org/10.1016/J.MATBIO.2018.02.005Kulkarni, V. S., & Shaw, C. (2016). Rheological Studies. In Essential Chemistry for Formulators of Semisolid and Liquid Dosages (pp. 145–182). Academic Press. https://doi.org/10.1016/B978-0-12-801024-2.00009-1Kumari, S., & Kishor, R. (2020). Chitin and chitosan: origin, properties, and applications. In Handbook of Chitin and Chitosan: Volume 1: Preparation and Properties (Vol. 1, pp. 1–33). Elsevier. https://doi.org/10.1016/B978-0-12-817970-3.00001-8Lamana, A., Rodríguez, A., Millán, M. M., & Castañeda Sanz, S. (2020). Bases de biología celular y molecular en cirugía ortopédica y traumatología. In Ciencia básica de aplicación en cirugía ortopédica y traumatología.Latour, R. A. (2015). The langmuir isotherm: A commonly applied but misleading approach for the analysis of protein adsorption behavior. Journal of Biomedical Materials Research Part A, 103(3), 949–958. https://doi.org/10.1002/JBM.A.35235Lavernia, L., Brown, W. E., Wong, B. J. F., Hu, J. C., & Athanasiou, K. A. (2019). Toward tissue-engineering of nasal cartilages. Acta Biomaterialia, 88, 42–56. https://doi.org/10.1016/J.ACTBIO.2019.02.025Lee, J. H., Kim, D. H., Lee, H. H., & Kim, H. W. (2019). Role of nuclear mechanosensitivity in determining cellular responses to forces and biomaterials. Biomaterials, 197, 60–71. https://doi.org/10.1016/J.BIOMATERIALS.2019.01.010Lee, W., Guilak, F., & Liedtke, W. (2017). Role of Piezo Channels in Joint Health and Injury. Current Topics in Membranes, 79, 263–273. https://doi.org/10.1016/BS.CTM.2016.10.003Li, J., Chen, G., Xu, X., Abdou, P., Jiang, Q., Shi, D., & Gu, Z. (2019). Advances of injectable hydrogel-based scaffolds for cartilage regeneration. Regenerative Biomaterials, 6(3), 129–140. https://doi.org/10.1093/RB/RBZ022Loeser, R. F. (2014). Integrins and chondrocyte–matrix interactions in articular cartilage. Matrix Biology, 39, 11–16. https://doi.org/10.1016/J.MATBIO.2014.08.007Luo, Y., & Wang, Q. (2014). Recent development of chitosan-based polyelectrolyte complexes with natural polysaccharides for drug delivery. International Journal of Biological Macromolecules, 64, 353–367. https://doi.org/10.1016/J.IJBIOMAC.2013.12.017Maestrando, M. F. (2023). Simulación numérica de las respuesta mecánicas de tejidos biológicos.Maldonado, L., Sanabria, L., Franco, H., Drachman, R., Montenegro, A., Macías, D., Rodríguez, M., Lizcano, A., & Ibáñez, J. (2015). El modelamiento matemático en la formación del ingeniero (L. Maldonado, Ed.). Universidad Central.Marquez, K., Arroyave, S., & Linares, J. M. (2023). From biological morphogenesis to engineering joint design: A bio-inspired algorithm. Materials & Design, 225, 111466. https://doi.org/10.1016/J.MATDES.2022.111466Matta, C., Zhang, X., Liddell, S., Smith, J. R., & Mobasheri, A. (2015). Label-free proteomic analysis of the hydrophobic membrane protein complement in articular chondrocytes: a technique for identification of membrane biomarkers. Biomarkers, 20(8), 572–589. https://doi.org/10.3109/1354750X.2015.1130191Meccia, B. (2018). Forward Solution Modeling: An In Vivo Theoretical Simulator of the Knee. In Insall & Scott Surgery of the Knee.Mobasheri, A., Goldring, M. B., & Loeser, R. F. (2022). Cartílago y condrocitos. In Firestein y Kelley. Tratado de reumatología.Mokbel, M., Hosseini, K., Aland, S., & Fischer-Friedrich, E. (2020). The Poisson Ratio of the Cellular Actin Cortex Is Frequency Dependent. Biophysical Journal, 118(8), 1968–1976. https://doi.org/10.1016/j.bpj.2020.03.002Moreno, B., Muñoz, M., Cuellar, J., Domancic, S., Villanueva, J., Moreno, B., Muñoz, M., Cuellar, J., Domancic, S., & Villanueva, J. (2018). Revisiones Sistemáticas: definición y nociones básicas. Revista Clínica de Periodoncia, Implantología y Rehabilitación Oral, 11(3), 184–186. https://doi.org/10.4067/S0719-01072018000300184Nasrollahzadeh, M., Sajjadi, M., Nezafat, Z., & Shafiei, N. (2021). Polysaccharide biopolymer chemistry. In Biopolymer-Based Metal Nanoparticle Chemistry for Sustainable Applications: Volume 1: Classification, Properties and Synthesis (pp. 45–105). Elsevier. https://doi.org/10.1016/B978-0-12-822108-2.00019-3Navas, H., & Braga, D. (2011). Selection of a Stirrer Drive Configuration Using Pugh Decision Matrix. Methodology Científica, 15(3), 139–143. http://www.redalyc.org/articulo.oa?id=61420811006Nease, C., & Sturm, L. (2023). Nasal Anatomy. Rhinoplasty: A Case-Based Approach, 7–15. https://doi.org/10.1016/B978-0-323-69775-0.00002-0Nguyen, T. D., & Gu, Y. (2016). Investigation of Cell-Substrate Adhesion Properties of Living Chondrocyte by Measuring Adhesive Shear Force and Detachment Using AFM and Inverse FEA. Scientific Reports 2016 6:1, 6(1), 1–13. https://doi.org/10.1038/srep38059Nguyen, T. D., Oloyede, A., & Gu, Y. (2014). Stress relaxation analysis of single chondrocytes using porohyperelastic model based on AFM experiments. Theoretical and Applied Mechanics Letters, 4(5), 054001. https://doi.org/10.1063/2.1405401Pearce, D., Fischer, S., Huda, F., & Vahdati, A. (2020). Applications of Computer Modeling and Simulation in Cartilage Tissue Engineering. In Tissue Engineering and Regenerative Medicine (Vol. 17, Issue 1). Korean Tissue Engineering and Regenerative Medicine Society. https://doi.org/10.1007/s13770-019-00216-9Rahmati, M., Silva, E. A., Reseland, J. E., A. Heyward, C., & Haugen, H. J. (2020). Biological responses to physicochemical properties of biomaterial surface. In Chemical Society Reviews (Vol. 49, Issue 15, pp. 5178–5224). Royal Society of Chemistry. https://doi.org/10.1039/d0cs00103aRenardy, M., Hult, C., Evans, S., Linderman, J. J., & Kirschner, D. E. (2019). Global sensitivity analysis of biological multiscale models. Current Opinion in Biomedical Engineering, 11, 109–116. https://doi.org/10.1016/j.cobme.2019.09.012Rivas, C. F., Núñez, O., Longoria, F., & Gonzalez, L. (2014). Isoterma de langmuir y freundlich como modelos para la adsorción de componentes de ácido nucleico sonbre WO3. Saber, 26(1), 43–49. http://ve.scielo.org/scielo.php?script=sci_arttext&pid=S1315-01622014000100008&lng=es&nrm=iso&tlng=esRoa, D., & Quitian, R. (2016). SITUACIÓN ACTUAL DE LA INGENIERIA DE TEJIDOS Y MEDICINA REGENERATIVA EN COLOMBIA. Universidad de ciencias aplicadas y ambientales.Shen, C. (2022). Physical and Chemical Properties of Solids. In Phillips’ Science of Dental Materials.Taheri, S., Ghazali, H. S., Ghazali, Z. S., Bhattacharyya, A., & Noh, I. (2023). Progress in biomechanical stimuli on the cell-encapsulated hydrogels for cartilage tissue regeneration. Biomaterials Research, 27(1), 1–17. https://doi.org/10.1186/S40824-023-00358-X/FIGURES/3Tedeschi, L. O. (2006). Assessment of the adequacy of mathematical models. Agricultural Systems, 89(2–3), 225–247. https://doi.org/10.1016/J.AGSY.2005.11.004Tripathy, N., Perumal, E., Ahmad, R., Song, J. E., & Khang, G. (2018). Hybrid Composite Biomaterials. In Principles of Regenerative Medicine (pp. 695–714). Elsevier. https://doi.org/10.1016/B978-0-12-809880-6.00040-0Vainieri, M. L., Wahl, D., Alini, M., van Osch, G. J. V. M., & Grad, S. (2018). Mechanically stimulated osteochondral organ culture for evaluation of biomaterials in cartilage repair studies. Acta Biomaterialia, 81, 256–266. https://doi.org/10.1016/J.ACTBIO.2018.09.058Vincent, T. L., & Wann, A. K. T. (2019). Mechanoadaptation: articular cartilage through thick and thin. Journal of Physiology, 597(5), 1271–1281. https://doi.org/10.1113/JP275451Wei, L., Guangdong, Z., & Yilin, C. (2024). Repair, grafting, and engineering of cartilage. In Plastic Surgery, Volume 1: Principles.Wu, Y., Li, X., Wang, Y., Shi, Y., Wang, F., & Lin, G. (2022). Research progress on mechanical properties and wear resistance of cartilage repair hydrogel. Materials & Design, 216, 110575. https://doi.org/10.1016/J.MATDES.2022.110575Yepes, J. J., Urrútia, G., Romero, M., & Alonso, S. (2021). Declaración PRISMA 2020: una guía actualizada para la publicación de revisiones sistemáticas. Revista Española de Cardiología, 74(9), 790–799. https://doi.org/10.1016/J.RECESP.2021.06.016Yu, T., & Xue, P. (2022). Yield criteria. In Introduction to Engineering Plasticity (pp. 67–87). Elsevier. https://doi.org/10.1016/B978-0-323-98981-7.00004-XZhang, Q., Zhang, M., Meng, N., Wei, X., & Chen, W. (2024). Mechanobiology of the articular chondrocyte. In Bone Cell Biomechanics, Mechanobiology and Bone Diseases (pp. 249–287). Academic Press. https://doi.org/10.1016/B978-0-323-96123-3.00016-6Zhang, 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. Journal of Biomedical Materials Research. Part B, Applied Biomaterials, 107(5), 1329–1351. https://doi.org/10.1002/JBM.B.34226Zhang, X., Zhan, X., Cheng, H., Dong, Z., Hu, C., Liu, C., Liang, J., Chen, Y., Fan, Y., & Zhang, X. (2024). Cartilage-like protein-polysaccharide hybrid hydrogel for enhancing chondrogenic differentiation of bone marrow mesenchymal stem cells. Collagen and Leather, 6(1), 1–12. https://doi.org/10.1186/S42825-023-00146-2/FIGURES/5spaLICENSElicense.txtlicense.txttext/plain; charset=utf-82000https://repositorio.unbosque.edu.co/bitstreams/53f064f0-fe24-403e-8d87-0682432a989d/download17cc15b951e7cc6b3728a574117320f9MD51Carta de autorizacion.pdfapplication/pdf203481https://repositorio.unbosque.edu.co/bitstreams/89f981de-560f-403d-aa02-fde3a228195b/download2cb43e282844adf1477f43bc4f87e3e3MD54ORIGINALTrabajo de grado.pdfTrabajo de grado.pdfapplication/pdf2476932https://repositorio.unbosque.edu.co/bitstreams/7a4965ad-e27e-4a82-8871-2ff77cc444b2/download220d054b02bd3be07e7e758ed427a875MD52CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81160https://repositorio.unbosque.edu.co/bitstreams/0f4ae81c-69a3-48d4-83bd-3ef5f38ee781/download5643bfd9bcf29d560eeec56d584edaa9MD53TEXTTrabajo de grado.pdf.txtTrabajo de grado.pdf.txtExtracted texttext/plain102310https://repositorio.unbosque.edu.co/bitstreams/0f4a5432-b5db-40bc-b81c-4a1b32c18427/downloadf3fe0914f302b56e15b14957e91ac329MD55THUMBNAILTrabajo de grado.pdf.jpgTrabajo de grado.pdf.jpgGenerated Thumbnailimage/jpeg3271https://repositorio.unbosque.edu.co/bitstreams/91a0fe79-d1c1-44cd-b496-95e2366b87ed/download75044870c1465283fc486db3ff396c67MD5620.500.12495/14569oai:repositorio.unbosque.edu.co:20.500.12495/145692025-06-07 05:02:53.775http://creativecommons.org/licenses/by-nc-sa/4.0/Attribution-NonCommercial-ShareAlike 4.0 Internationalopen.accesshttps://repositorio.unbosque.edu.coRepositorio Institucional Universidad El Bosquebibliotecas@biteca.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