Computational model of bone remodeling using discrete structures
Libro de tesis, algunas figuras en color, mayoría en blanco y negro.
- Autores:
-
Quexada Rodríguez, Diego Alfredo
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/79884
- Palabra clave:
- 610 - Medicina y salud
Simulación por computador
Simulation Computer
Modelado en medicina
Moulage in medicine
Bone remodelling
bone architecture
discrete modelling
trabecular bone
Remodelamiento óseo
Arquitectura ósea
Modelamiento discreto
Hueso trabecular
- Rights
- openAccess
- License
- Atribución-SinDerivadas 4.0 Internacional
| id |
UNACIONAL2_15c69b339189f97d6438b3df4d46c927 |
|---|---|
| oai_identifier_str |
oai:repositorio.unal.edu.co:unal/79884 |
| network_acronym_str |
UNACIONAL2 |
| network_name_str |
Universidad Nacional de Colombia |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Computational model of bone remodeling using discrete structures |
| dc.title.translated.spa.fl_str_mv |
Modelo computacional de remodelamiento óseo mediante estructuras discretas |
| title |
Computational model of bone remodeling using discrete structures |
| spellingShingle |
Computational model of bone remodeling using discrete structures 610 - Medicina y salud Simulación por computador Simulation Computer Modelado en medicina Moulage in medicine Bone remodelling bone architecture discrete modelling trabecular bone Remodelamiento óseo Arquitectura ósea Modelamiento discreto Hueso trabecular |
| title_short |
Computational model of bone remodeling using discrete structures |
| title_full |
Computational model of bone remodeling using discrete structures |
| title_fullStr |
Computational model of bone remodeling using discrete structures |
| title_full_unstemmed |
Computational model of bone remodeling using discrete structures |
| title_sort |
Computational model of bone remodeling using discrete structures |
| dc.creator.fl_str_mv |
Quexada Rodríguez, Diego Alfredo |
| dc.contributor.advisor.none.fl_str_mv |
Garzón Alvarado, Diego Alexander Márquez, Kalenia María |
| dc.contributor.author.none.fl_str_mv |
Quexada Rodríguez, Diego Alfredo |
| dc.contributor.researchgroup.spa.fl_str_mv |
GNUM - Grupo de Modelado y Métodos Numericos en Ingeniería |
| dc.subject.ddc.spa.fl_str_mv |
610 - Medicina y salud |
| topic |
610 - Medicina y salud Simulación por computador Simulation Computer Modelado en medicina Moulage in medicine Bone remodelling bone architecture discrete modelling trabecular bone Remodelamiento óseo Arquitectura ósea Modelamiento discreto Hueso trabecular |
| dc.subject.decs.none.fl_str_mv |
Simulación por computador Simulation Computer |
| dc.subject.lemb.none.fl_str_mv |
Modelado en medicina Moulage in medicine |
| dc.subject.proposal.eng.fl_str_mv |
Bone remodelling bone architecture discrete modelling trabecular bone |
| dc.subject.proposal.spa.fl_str_mv |
Remodelamiento óseo Arquitectura ósea Modelamiento discreto Hueso trabecular |
| description |
Libro de tesis, algunas figuras en color, mayoría en blanco y negro. |
| publishDate |
2021 |
| dc.date.accessioned.none.fl_str_mv |
2021-08-03T17:05:07Z |
| dc.date.available.none.fl_str_mv |
2021-08-03T17:05:07Z |
| dc.date.issued.none.fl_str_mv |
2021-06-22 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
| dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
| dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
| dc.type.content.spa.fl_str_mv |
Text |
| dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
| status_str |
acceptedVersion |
| dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/79884 |
| dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
| url |
https://repositorio.unal.edu.co/handle/unal/79884 https://repositorio.unal.edu.co/ |
| identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
| dc.language.iso.spa.fl_str_mv |
eng |
| language |
eng |
| dc.relation.references.spa.fl_str_mv |
Abboud, Fraser Harrold;Rami. 2018. “Biomechanics of the Foot and Ankle.” Orthopaedic Knowledge Update: Foot and Ankle 5, 3–12. Andreassen, Erik, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, and Ole Sigmund. 2011. “Efficient Topology Optimization in MATLAB Using 88 Lines of Code.” Structural and Multidisciplinary Optimization 43 (1): 1–16. https://doi.org/10.1007/s00158-010-0594-7. Annicchiarico, W., G. Martinez, and M. Cerrolaza. 2007. “Boundary Elements and β-Spline Surface Modeling for Medical Applications.” Applied Mathematical Modelling 31 (2): 194–208. https://doi.org/10.1016/j.apm.2005.08.021. Bahia, M. T., M. B. Hecke, E. G.F. Mercuri, and M. M. Pinheiro. 2020. “A Bone Remodeling Model Governed by Cellular Micromechanics and Physiologically Based Pharmacokinetics.” Journal of the Mechanical Behavior of Biomedical Materials 104: 103657. https://doi.org/10.1016/j.jmbbm.2020.103657. Beaupre, G S, and T E Orr. 1990. “An Approach for Time-Dependent Bone Modeling and Remodeling—Application: A Preliminary Remodeling Simulation - Beaupré - 2005 - Journal of Orthopaedic Research - Wiley Online Library.” Journal of Orthopaedic …, 662–70. http://onlinelibrary.wiley.com/doi/10.1002/jor.1100080507/abstract%5Cnpapers2://publication/uuid/9D5C378F-EDD8-4736-B052-510B4EFC85B9. Belinha, J., R. M. Natal Jorge, and L. M.J.S. Dinis. 2012. “Bone Tissue Remodelling Analysis Considering a Radial Point Interpolator Meshless Method.” Engineering Analysis with Boundary Elements 36 (11): 1660–70. https://doi.org/10.1016/j.enganabound.2012.05.009. Bhate, Dhruv, Clint A. Penick, Lara A. Ferry, and Christine Lee. 2019. “Classification and Selection of Cellular Materials in Mechanical Design: Engineering and Biomimetic Approaches.” Designs 3 (1): 1–31. https://doi.org/10.3390/designs3010019. Braun, Jan-matthias, Poramate Manoonpong, and Xiaofeng Xiong. n.d. BIOLOGY-INSPIRED ENGINEERING AND ENGINEERING-INSPIRED BIOLOGY. https://doi.org/10.3389/978-2-88966-340-8. Buenzli, P. R., P. Pivonka, and D. W. Smith. 2011. “Spatio-Temporal Structure of Cell Distribution in Cortical Bone Multicellular Units: A Mathematical Model.” Bone 48 (4): 918–26. https://doi.org/10.1016/j.bone.2010.12.009. Bullock, Whitney A., Frederick M. Pavalko, and Alexander G. Robling. 2019. “Osteocytes and Mechanical Loading: The Wnt Connection.” Orthodontics and Craniofacial Research 22 (S1): 175–79. https://doi.org/10.1111/ocr.12282. Cerrolaza, M., F. Nieto, and Y. González. 2018. “Computation of the Dynamic Compression Effects in Spine Discs Using Integral Methods.” Journal of Mechanics in Medicine and Biology 18 (5): 1–16. https://doi.org/10.1142/S0219519417501032. Cesar, R., R. S. Boffa, L. T. Fachine, T. P. Leivas, A. M.H. Silva, C. A.M. Pereira, R. B.M. Reiff, and J. M.D.A. Rollo. 2013. “Evaluation of Trabecular Microarchitecture of Normal Osteoporotic and Osteopenic Human Vertebrae.” Procedia Engineering 59: 6–15. https://doi.org/10.1016/j.proeng.2013.05.087. Cha, Yong Han, Jun Il Yoo, Seok Young Hwang, Kap Jung Kim, Ha Yong Kim, Won Sik Choy, and Sun Chul Hwang. 2019. “Biomechanical Evaluation of Internal Fixation of Pauwels Type III Femoral Neck Fractures: A Systematic Review of Various Fixation Methods.” CiOS Clinics in Orthopedic Surgery 11 (1): 1–14. https://doi.org/10.4055/cios.2019.11.1.1. Chen, Wenjiong, Xiaonan Zheng, and Shutian Liu. 2018. “Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing.” Materials 11 (11). https://doi.org/10.3390/ma11112073. “Computer-Assisted Femoral Augmentation for Osteoporotic Hip Fracture Prevention.” 2013. Corte, Alessandro Della, Ivan Giorgio, and Daria Scerrato. 2020. “A Review of Recent Developments in Mathematical Modeling of Bone Remodeling.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 234 (3): 273–81. https://doi.org/10.1177/0954411919857599. Cowin, SC, and JJ Telega,. 2003. Bone Mechanics Handbook, 2nd Edition. -. Applied Mechanics Reviews. Vol. 56. https://doi.org/10.1115/1.1579463. Cowin, S. C. 1986. “Wolff’s Law of Trabecular Architecture at Remodeling Equilibrium.” Journal of Biomechanical Engineering 108 (1): 83–88. https://doi.org/10.1115/1.3138584. Daxner, Thomas. 2010. “Finite Element Modeling of Cellular Materials. In: Altenbach H., Öchsner A. (Eds) Cellular and Porous Materials in Structures and Processes. CISM International Centre for Mechanical Sciences, Vol 521. Springer, Vienna. Https://Doi.Org/10.1007/978-3-7091-0.” In , 634. Eriksen, E. F., H. J.G. Gundersen, F. Melsen, and L. Mosekilde. 1984. “Reconstruction of the Formative Site in Iliac Trabecular Bone in 20 Normal Individuals Employing a Kinetic Model for Matrix and Mineral Apposition.” Metabolic Bone Disease and Related Research 5 (5): 243–52. https://doi.org/10.1016/0221-8747(84)90066-3. Feng, Xu, and Jay M. McDonald. 2011. “Disorders of Bone Remodeling.” Annual Review of Pathology: Mechanisms of Disease 6 (1): 121–45. https://doi.org/10.1146/annurev-pathol-011110-130203. Fonseca-vel, Aldemar. 2009. “Implementaci ´ on Del Modelo de Remodelaci ´ on ´ Osea de Komarova Para El Estudio de La Sensibilidad Del Proceso de Remodelamiento ´ Oseo Ante Cambios En Factores Locales,” 107–32. Gabriel García-Acosta, Fahir D. Castañeda, Diego A. Garzón-Alvarado, Kalenia Márquez-Flórez, Diego A. Quexada-Rodriguez, Armando Salgado, Marco A. Velasco. 2020. “Design for the Additive Manufacturing of Structural Elements with Cellular Materials Using Voronoi Diagrams and Delaunay Triangulations: Biological and Structural Applications.” Unpublished Manuscript, 33. Ganghoffer, Jean François, and Ibrahim Goda. 2018. “Prediction of Size Effects in Bone Brittle and Plastic Collapse.” Multiscale Biomechanics, 345–88. https://doi.org/10.1016/B978-1-78548-208-3.50008-3. Garzón-Alvarado, D. A., and D. Linero. 2012a. “Comparative Analysis of Numerical Integration Schemes of Density Equation for a Computational Model of Bone Remodelling.” Computer Methods in Biomechanics and Biomedical Engineering 15 (11): 1189–96. https://doi.org/10.1080/10255842.2011.585972. ———. 2012b. “Comparative Analysis of Numerical Integration Schemes of Density Equation for a Computational Model of Bone Remodelling.” Computer Methods in Biomechanics and Biomedical Engineering 15 (11): 1189–96. https://doi.org/10.1080/10255842.2011.585972. Gasser, Jürg Andreas, and Michaela Kneissel. 2017. Bone Toxicology. Bone Toxicology. https://doi.org/10.1007/978-3-319-56192-9. Geris, L., J. Vander Sloten, and H. Van Oosterwyck. 2010. “Connecting Biology and Mechanics in Fracture Healing: An Integrated Mathematical Modeling Framework for the Study of Nonunions.” Biomechanics and Modeling in Mechanobiology 9 (6): 713–24. https://doi.org/10.1007/s10237-010-0208-8. González, Y., M. Cerrolaza, and C. González. 2009. “Poroelastic Analysis of Bone Tissue Differentiation by Using the Boundary Element Method.” Engineering Analysis with Boundary Elements 33 (5): 731–40. https://doi.org/10.1016/j.enganabound.2008.09.008. Guevara, J. M., M. A. Moncayo, J. J. Vaca-González, M. L. Gutiérrez, L. A. Barrera, and D. A. Garzón-Alvarado. 2015. “Growth Plate Stress Distribution Implications during Bone Development: A Simple Framework Computational Approach.” Computer Methods and Programs in Biomedicine 118 (1): 59–68. https://doi.org/10.1016/j.cmpb.2014.10.007. Hambli, Ridha. 2014. “Connecting Mechanics and Bone Cell Activities in the Bone Remodeling Process: An Integrated Finite Element Modeling.” Frontiers in Bioengineering and Biotechnology 2 (APR): 1–12. https://doi.org/10.3389/fbioe.2014.00006. Hambli, Ridha, Mohamed Hafedh Boughattas, Jean Luc Daniel, and Azeddine Kourta. 2016. “Prediction of Denosumab Effects on Bone Remodeling: A Combined Pharmacokinetics and Finite Element Modeling.” Journal of the Mechanical Behavior of Biomedical Materials 60 (January 2016): 492–504. https://doi.org/10.1016/j.jmbbm.2016.03.010. Hopkins, R. B., N. Burke, C. Von Keyserlingk, W. D. Leslie, S. N. Morin, J. D. Adachi, A. Papaioannou, et al. 2016. “The Current Economic Burden of Illness of Osteoporosis in Canada.” Osteoporosis International 27 (10): 3023–32. https://doi.org/10.1007/s00198-016-3631-6. Jerez, S., and B. Chen. 2015. “Stability Analysis of a Komarova Type Model for the Interactions of Osteoblast and Osteoclast Cells during Bone Remodeling.” Mathematical Biosciences 264 (1): 29–37. https://doi.org/10.1016/j.mbs.2015.03.003. Kenkre, J. S., and J. H.D. Bassett. 2018. The Bone Remodelling Cycle. Annals of Clinical Biochemistry. Vol. 55. https://doi.org/10.1177/0004563218759371. Key, Radiolology. 2020. “Bone Mineral Density and Quantitative Imaging.” 12 de Junio. 2020. https://radiologykey.com/bone-mineral-density-and-quantitative-imaging/. KOCH, JOHN C. 1993. “THE LAWS OF BONE ARCHITECTURE.” From the Department of Anatomy, Johns Hopkins Medical School, Baltimore, Md. 2 (6): 444–54. Komarova, Svetlana V., Robert J. Smith, S. Jeffrey Dixon, Stephen M. Sims, and Lindi M. Wahl. 2003. “Mathematical Model Predicts a Critical Role for Osteoclast Autocrine Regulation in the Control of Bone Remodeling.” Bone 33 (2): 206–15. https://doi.org/10.1016/S8756-3282(03)00157-1. Kumar, Natarajan Chennimalai, Iwona Jasiuk, and Jonathan Dantzig. 2011. “Dissipation Energy as a Stimulus for Cortical Bone Adaptation.” Journal of Mechanics of Materials and Structures 6 (1–4): 303–19. https://doi.org/10.2140/jomms.2011.6.303. Lemaire, Vincent, Frank L. Tobin, Larry D. Greller, Carolyn R. Cho, and Larry J. Suva. 2004. “Modeling the Interactions between Osteoblast and Osteoclast Activities in Bone Remodeling.” Journal of Theoretical Biology 229 (3): 293–309. https://doi.org/10.1016/j.jtbi.2004.03.023. Lenthe, G. Harry van, and Ralph Müller. 2006. “Prediction of Failure Load Using Micro-Finite Element Analysis Models: Toward in Vivo Strength Assessment.” Drug Discovery Today: Technologies 3 (2): 221–29. https://doi.org/10.1016/j.ddtec.2006.06.001. Li, Jianying, Haiyan Li, Li Shi, Alex S.L. Fok, Cemal Ucer, Hugh Devlin, Keith Horner, and Nick Silikas. 2007. “A Mathematical Model for Simulating the Bone Remodeling Process under Mechanical Stimulus.” Dental Materials 23 (9): 1073–78. https://doi.org/10.1016/j.dental.2006.10.004. Li, Xiaofeng, Yazhou Zhang, Heeseog Kang, Wenzhong Liu, Peng Liu, Jianghong Zhang, Stephen E. Harris, and Dianqing Wu. 2005. “Sclerostin Binds to LRP5/6 and Antagonizes Canonical Wnt Signaling.” Journal of Biological Chemistry 280 (20): 19883–87. https://doi.org/10.1074/jbc.M413274200. Luxner, Mathias H., Alexander Woesz, Juergen Stampfl, Peter Fratzl, and Heinz E. Pettermann. 2009. “A Finite Element Study on the Effects of Disorder in Cellular Structures.” Acta Biomaterialia 5 (1): 381–90. https://doi.org/10.1016/j.actbio.2008.07.025. Makris, Panagiotis A., Christopher G. Provatidis, and Demetrios A. Rellakis. 2006. “Discrete Variable Optimization of Frames Using a Strain Energy Criterion.” Structural and Multidisciplinary Optimization 31 (5): 410–17. https://doi.org/10.1007/s00158-005-0588-z. Marco, Miguel, Eugenio Giner, José Ramón Caeiro-Rey, M. Henar Miguélez, and Ricardo Larraínzar-Garijo. 2019. “Numerical Modelling of Hip Fracture Patterns in Human Femur.” Computer Methods and Programs in Biomedicine 173: 67–75. https://doi.org/10.1016/j.cmpb.2019.03.010. Martín, Raúl Álvarez San, and José Antonio Velutini Kochen. 2011. “Anatomía de La Cabeza Femoral Humana: Consideraciones En Ortopedia, Parte II. Biomecánica y Morfología Microscópica.” International Journal of Morphology 29 (2): 371–76. Martínez, G., and M. Cerrolaza. 2006. “A Bone Adaptation Integrated Approach Using BEM.” Engineering Analysis with Boundary Elements 30 (2): 107–15. https://doi.org/10.1016/j.enganabound.2005.08.010. Maxwell, Clerk. n.d. “Prof . Maxwell on Reciprocal Figures XLV . On Reciprocal Figures and Diagrams of Forces . JBy J . CLERK MAXWELL , F . R . S ., Professor of Natural Philosophy in King ’ s College , London ~ . and Diagrams of Forces . On Reciprocal Plane Figures . Definiti” xxv: 250–61. Metcalf, Louis M., Enrico Dall’Ara, Margaret A. Paggiosi, John R. Rochester, Nicolas Vilayphiou, Graham J. Kemp, and Eugene V. McCloskey. 2018. “Validation of Calcaneus Trabecular Microstructure Measurements by HR-PQCT.” Bone 106: 69–77. https://doi.org/10.1016/j.bone.2017.09.013. Meyer, G. H. 1867. “‘Die Architektur Der Spongiosa,’ Archiv Fur Anatomie, Physiologie Und Wissenschaftliche Medizin, Reichert Und DuBois-Reymonds Archiv.” Nackenhorst, Udo. 1997. “Numerical Simulation of Stress Stimulated Bone Remodeling.” Technische Mechanik 17 (1): 31–40. http://www.uni-magdeburg.de/ifme/zeitschrift_tm/1997_Heft1/Nackenhorst.pdf. Niu, Tianhua, and Clifford J. Rosen. 2005. “The Insulin-like Growth Factor-I Gene and Osteoporosis: A Critical Appraisal.” Gene 361 (1–2): 38–56. https://doi.org/10.1016/j.gene.2005.07.016. Okaji, Masayo, Hideaki Sakai, Eiko Sakai, Mitsue Shibata, Fumio Hashimoto, Yasuhiro Kobayashi, Noriaki Yoshida, Kuniaki Okamoto, Kenji Yamamoto, and Yuzo Kato. 2003. “The Regulation of Bone Resorption in Tooth Formation and Eruption Processes in Mouse Alveolar Crest Devoid of Cathepsin K.” Journal Pharmacological Sciences 91 (4): 285–94. https://doi.org/10.1254/jphs.91.285. Owen, Robert, and Gwendolen C. Reilly. 2018. “In Vitro Models of Bone Remodelling and Associated Disorders.” Frontiers in Bioengineering and Biotechnology 6 (OCT): 1–22. https://doi.org/10.3389/fbioe.2018.00134. Parfitt, A. M. 1994. “Osteonal and Hemi‐osteonal Remodeling: The Spatial and Temporal Framework for Signal Traffic in Adult Human Bone.” Journal of Cellular Biochemistry 55 (3): 273–86. https://doi.org/10.1002/jcb.240550303. Peng, Matthew Jian Qiao, Hong Wen Xu, Hai Yan Chen, Ze Lin, Xin Xu Li, Chu Long Shen, Yong Qiang Lau, Er Xing He, and Yue Ming Guo. 2020. “Biomechanical Analysis for Five Fixation Techniques of Pauwels-III Fracture by Finite Element Modeling.” Computer Methods and Programs in Biomedicine 193: 105491. https://doi.org/10.1016/j.cmpb.2020.105491. Peyroteo, M. M.A., J. Belinha, S. Vinga, L. M.J.S. Dinis, and R. M. Natal Jorge. 2019. “Mechanical Bone Remodelling: Comparative Study of Distinct Numerical Approaches.” Engineering Analysis with Boundary Elements 100 (January 2018): 125–39. https://doi.org/10.1016/j.enganabound.2018.01.011. Pivonka, Peter, Jan Zimak, David W. Smith, Bruce S. Gardiner, Colin R. Dunstan, Natalie A. Sims, T. John Martin, and Gregory R. Mundy. 2008. “Model Structure and Control of Bone Remodeling: A Theoretical Study.” Bone 43 (2): 249–63. https://doi.org/10.1016/j.bone.2008.03.025. Raggatt, Liza J., and Nicola C. Partridge. 2010. “Cellular and Molecular Mechanisms of Bone Remodeling.” Journal of Biological Chemistry 285 (33): 25103–8. https://doi.org/10.1074/jbc.R109.041087. Rapisarda, Alessio Ciro, Alessandro Della Corte, Rafał Drobnicki, Fabio Di Cosmo, and Luigi Rosa. 2019. “A Model for Bone Mechanics and Remodeling Including Cell Populations Dynamics.” Zeitschrift Fur Angewandte Mathematik Und Physik 70 (1): 1–17. https://doi.org/10.1007/s00033-018-1055-1. Ruff1. Ruffoni, D. & Van Lenthe, G. H. 3.10 Finite element analysis in bone research: A computational method relating structure to mechanical function. Comprehensive Biomaterials II vol. 3 (Elsevier Ltd., 2017).oni, D., and G. H. Van Lenthe. 2017. 3.10 Finite Element Analysis in Bone Research: A Computational Method Relating Structure to Mechanical Function. Comprehensive Biomaterials II. Vol. 3. Elsevier Ltd. https://doi.org/10.1016/B978-0-12-803581-8.09798-8. Schaedler, Tobias A., and William B. Carter. 2016. “Architected Cellular Materials.” Annual Review of Materials Research 46 (April): 187–210. https://doi.org/10.1146/annurev-matsci-070115-031624. Seeman, Ego. 2003. “The Structural and Biomechanical Basis of the Gain and Loss of Bone Strength in Women and Men.” Endocrinology and Metabolism Clinics of North America 32 (1): 25–38. https://doi.org/10.1016/S0889-8529(02)00078-6. Sozen, Tumay, Lale Ozisik, and Nursel Calik Basaran. 2017. “An Overview and Management of Osteoporosis.” European Journal of Rheumatology 4 (1): 46–56. https://doi.org/10.5152/eurjrheum.2016.048. Stein, Emily M., Barbara C. Silva, Stephanie Boutroy, Bin Zhou, Ji Wang, Julia Udesky, Chiyuan Zhang, et al. 2013. “Primary Hyperparathyroidism Is Associated with Abnormal Cortical and Trabecular Microstructure and Reduced Bone Stiffness in Postmenopausal Women.” Journal of Bone and Mineral Research 28 (5): 1029–40. https://doi.org/10.1002/jbmr.1841. Ström, O., F. Borgström, John A. Kanis, Juliet Compston, Cyrus Cooper, Eugene V. McCloskey, and Bengt Jönsson. 2011. “Osteoporosis: Burden, Health Care Provision and Opportunities in the EU.” Archives of Osteoporosis 6 (1–2): 59–155. https://doi.org/10.1007/s11657-011-0060-1. Sun, Xiaoqiang, Yunqing Kang, Jiguang Bao, Yuanyuan Zhang, Yunzhi Yang, and Xiaobo Zhou. 2013. “Modeling Vascularized Bone Regeneration within a Porous Biodegradable CaP Scaffold Loaded with Growth Factors.” Biomaterials 34 (21): 4971–81. https://doi.org/10.1016/j.biomaterials.2013.03.015. Swarthout, John T., Richard C. D’Alonzo, Nagarajan Selvamurugan, and Nicola C. Partridge. 2002. “Parathyroid Hormone-Dependent Signaling Pathways Regulating Genes in Bone Cells.” Gene 282 (1–2): 1–17. https://doi.org/10.1016/S0378-1119(01)00798-3. Valdez, S. Ivvan, Salvador Botello, Miguel A. Ochoa, José L. Marroquín, and Victor Cardoso. 2017. “Topology Optimization Benchmarks in 2D: Results for Minimum Compliance and Minimum Volume in Planar Stress Problems.” Archives of Computational Methods in Engineering 24 (4): 803–39. https://doi.org/10.1007/s11831-016-9190-3. Vanegas-Acosta, J. C., N. S. Landinez P., D. A. Garzón-Alvarado, and M. C. Casale R. 2011. “A Finite Element Method Approach for the Mechanobiological Modeling of the Osseointegration of a Dental Implant.” Computer Methods and Programs in Biomedicine 101 (3): 297–314. https://doi.org/10.1016/j.cmpb.2010.11.007. Walton, Dan, and Hadi Moztarzadeh. 2017. “Design and Development of an Additive Manufactured Component by Topology Optimisation.” Procedia CIRP 60: 205–10. https://doi.org/10.1016/j.procir.2017.03.027. Weinans, H., R. Huiskes, and H. J. Grootenboer. 1992. “The Behavior of Adaptive Bone-Remodeling Simulation Models.” Journal of Biomechanics 25 (12): 1425–41. https://doi.org/10.1016/0021-9290(92)90056-7. Wippert, Pia Maria, Michael Rector, Gisela Kuhn, and Karin Wuertz-Kozak. 2017. “Stress and Alterations in Bones: An Interdisciplinary Perspective.” Frontiers in Endocrinology 8 (MAY): 1–7. https://doi.org/10.3389/fendo.2017.00096. Wu, Jun, Weiming Wang, and Xifeng Gao. 2019. “Design and Optimization of Conforming Lattice Structures.” IEEE Transactions on Visualization and Computer Graphics, 1–1. https://doi.org/10.1109/tvcg.2019.2938946. Yamamoto, Yoko, Tatsuya Yoshizawa, Toru Fukuda, Yuko Shirode-Fukuda, Taiyong Yu, Keisuke Sekine, Takashi Sato, et al. 2013. “Vitamin D Receptor in Osteoblasts Is a Negative Regulator of Bone Mass Control.” Endocrinology 154 (3): 1008–20. https://doi.org/10.1210/en.2012-1542. |
| dc.rights.spa.fl_str_mv |
Derechos reservados al autor, 2021 |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.license.spa.fl_str_mv |
Atribución-SinDerivadas 4.0 Internacional |
| dc.rights.uri.spa.fl_str_mv |
http://creativecommons.org/licenses/by-nd/4.0/ |
| dc.rights.accessrights.spa.fl_str_mv |
info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
Atribución-SinDerivadas 4.0 Internacional Derechos reservados al autor, 2021 http://creativecommons.org/licenses/by-nd/4.0/ http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.extent.spa.fl_str_mv |
117 páginas |
| dc.format.mimetype.spa.fl_str_mv |
application/pdf |
| dc.publisher.spa.fl_str_mv |
Universidad Nacional de Colombia |
| dc.publisher.program.spa.fl_str_mv |
Bogotá - Medicina - Maestría en Ingeniería Biomédica |
| dc.publisher.department.spa.fl_str_mv |
Departamento de Imágenes diagnósticas |
| dc.publisher.faculty.spa.fl_str_mv |
Facultad de Medicina |
| dc.publisher.place.spa.fl_str_mv |
Bogotá, Colombia |
| dc.publisher.branch.spa.fl_str_mv |
Universidad Nacional de Colombia - Sede Bogotá |
| institution |
Universidad Nacional de Colombia |
| bitstream.url.fl_str_mv |
https://repositorio.unal.edu.co/bitstream/unal/79884/5/Thesis_final_repositorio.pdf https://repositorio.unal.edu.co/bitstream/unal/79884/3/license.txt https://repositorio.unal.edu.co/bitstream/unal/79884/6/license_rdf https://repositorio.unal.edu.co/bitstream/unal/79884/7/Thesis_final_repositorio.pdf.jpg |
| bitstream.checksum.fl_str_mv |
89b320659ef0826ccd496bfb9d392610 cccfe52f796b7c63423298c2d3365fc6 f7d494f61e544413a13e6ba1da2089cd a3ea6c92143c95e1f7daaae462388c25 |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
| repository.mail.fl_str_mv |
repositorio_nal@unal.edu.co |
| _version_ |
1814089640179662848 |
| spelling |
Atribución-SinDerivadas 4.0 InternacionalDerechos reservados al autor, 2021http://creativecommons.org/licenses/by-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Garzón Alvarado, Diego Alexandera780fc0a2dd14ac611c37bca9998c94bMárquez, Kalenia Maríae186134afe93556c150f523ea26ee1a6Quexada Rodríguez, Diego Alfredocdf18e00acff5ba5d4e1c870b254085cGNUM - Grupo de Modelado y Métodos Numericos en Ingeniería2021-08-03T17:05:07Z2021-08-03T17:05:07Z2021-06-22https://repositorio.unal.edu.co/handle/unal/79884Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/Libro de tesis, algunas figuras en color, mayoría en blanco y negro.ilustraciones, tablasIn-silico models applied to bone remodeling are widely used to investigate bone mechanics, bone diseases, bone-implant interactions, and also the effect of treatments in bone pathologies. This work proposes a new methodology to solve the bone remodeling problem using one-dimensional (1D) elements to discretize trabecular structures more efficiently. First a concept review on the bone remodelling process and mathematical approaches, such as homogenization for its modelling are revised along with famous previous works on this field, later, in chapter two, the discrete modelling approach is validated by comparing FE simulations with experimental results for a cellular like material created using additive manufacturing and following a tessellation algorithm, and later, applying an optimization scheme based on maximum stiffness for a given porosity. In chapter three, an Euler integration scheme for a bone remodelling problem is coupled with the momentum equations to obtain the evolution of material density at each step. For the simulations, the equations were solved by using the finite element method and a direct formulation, and two benchmark tests were solved varying mesh parameters in two dimensions, an additional three-dimensional benchmark was addressed with the same methodology. Proximal femur and calcaneus bone were selected as study cases given the vast research available on the topology of these bones, and compared with the anatomical features of trabecular bone reported in the literature, the study cases were examined mainly in two dimensions, but the main trabecular groups for the femur were also obtained in three dimensions. The presented methodology has proven to be efficient in optimizing topologies of lattice structures; It can predict the trend in formation patterns of the main trabecular groups from two different cancellous bones (femur and calcaneus) using domains set up by discrete elements as a starting point. Preliminary results confirm that the proposed approach is suitable and useful in bone remodeling problems in 2D and 3D leading to a considerable computational cost reduction. Characteristics similar to those encountered in topological optimization algorithms were identified in the benchmark tests as well, showing the viability of the proposed approach in other applications such as bio-inspired design. Finally, in the last part of this work, the discrete approach developed in chapter two and three is coupled with two classic bone remodelling models, forming a new model that takes into account a variety of biological parameters such as paracrine and autocrine regulators and is able to predict different periodical responses in the bone remodelling process within a 2D domain with mechanical field variables. (Text taken from source)Los modelos in-silico aplicados a la remodelación ósea son ampliamente utilizados para investigar la mecánica del hueso, las enfermedades óseas, las interacciones hueso-implante y también el efecto de los tratamientos en las patologías óseas. Este trabajo propone una nueva metodología para resolver el problema de la remodelación ósea utilizando elementos unidimensionales (1D) para discretizar las estructuras trabeculares de forma más eficiente. En primer lugar se revisa una revisión conceptual sobre el proceso de remodelación ósea y las aproximaciones matemáticas, como el método de homogeneización para su modelización, junto con famosos trabajos previos en este campo, posteriormente, en el capítulo dos, se valida la modelación discreta comparando las simulaciones de FE (elementos finitos) con los resultados experimentales para un material similar al celular creado mediante fabricación aditiva y siguiendo un algoritmo de teselación, y posteriormente, aplicando un esquema de optimización basado en la máxima rigidez para una determinada porosidad. En el capítulo tres, se acopla un esquema de integración de Euler para un problema de remodelación ósea con las ecuaciones de momento para obtener la evolución de la densidad del material en cada paso de tiempo. Para las simulaciones, las ecuaciones se resolvieron utilizando el método de los elementos finitos y una formulación directa, y se resolvieron dos pruebas de referencia variando los parámetros de la malla en dos dimensiones, adicionalmente, se abordó una prueba de referencia tridimensional adicional con la misma metodología. Se seleccionaron el fémur proximal y el hueso calcáneo como casos de estudio, dada la amplia investigación disponible sobre la topología de estos huesos, y se compararon con las características anatómicas del hueso trabecular reportadas en la literatura, los casos de estudio se examinaron principalmente en dos dimensiones, pero los principales grupos trabeculares para el fémur también se obtuvieron en tres dimensiones. La metodología presentada ha demostrado ser eficaz en la optimización de las topologías de estructuras reticulares; puede predecir la tendencia de los patrones de formación de los principales grupos trabeculares de dos huesos esponjosos diferentes (fémur y calcáneo) utilizando dominios establecidos por elementos discretos como punto de partida. Los resultados preliminares confirmaron que el enfoque propuesto es adecuado y útil en problemas de remodelación ósea en 2D y 3D, lo que conlleva una considerable reducción del coste computacional. En las pruebas de referencia también se identificaron características similares a las encontradas en los algoritmos de optimización topológica, lo que demuestra la viabilidad del enfoque propuesto en otras aplicaciones como el diseño bioinspirado. Finalmente, en la última parte de este trabajo, el enfoque discreto desarrollado en los capítulos dos y tres se acopla con dos modelos clásicos de remodelación ósea, formando un nuevo modelo que tiene en cuenta una variedad de parámetros biológicos como los reguladores paracrinos y autocrinos, y es capaz de predecir diferentes respuestas periódicas en el proceso de remodelación ósea dentro de un dominio 2D con variables de campo mecánico. (Texto tomado de la fuente)MaestríaMagíster en Ingeniería BiomédicaMecánica computacional117 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Medicina - Maestría en Ingeniería BiomédicaDepartamento de Imágenes diagnósticasFacultad de MedicinaBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá610 - Medicina y saludSimulación por computadorSimulation ComputerModelado en medicinaMoulage in medicineBone remodellingbone architecturediscrete modellingtrabecular boneRemodelamiento óseoArquitectura óseaModelamiento discretoHueso trabecularComputational model of bone remodeling using discrete structuresModelo computacional de remodelamiento óseo mediante estructuras discretasTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAbboud, Fraser Harrold;Rami. 2018. “Biomechanics of the Foot and Ankle.” Orthopaedic Knowledge Update: Foot and Ankle 5, 3–12.Andreassen, Erik, Anders Clausen, Mattias Schevenels, Boyan S. Lazarov, and Ole Sigmund. 2011. “Efficient Topology Optimization in MATLAB Using 88 Lines of Code.” Structural and Multidisciplinary Optimization 43 (1): 1–16. https://doi.org/10.1007/s00158-010-0594-7.Annicchiarico, W., G. Martinez, and M. Cerrolaza. 2007. “Boundary Elements and β-Spline Surface Modeling for Medical Applications.” Applied Mathematical Modelling 31 (2): 194–208. https://doi.org/10.1016/j.apm.2005.08.021.Bahia, M. T., M. B. Hecke, E. G.F. Mercuri, and M. M. Pinheiro. 2020. “A Bone Remodeling Model Governed by Cellular Micromechanics and Physiologically Based Pharmacokinetics.” Journal of the Mechanical Behavior of Biomedical Materials 104: 103657. https://doi.org/10.1016/j.jmbbm.2020.103657.Beaupre, G S, and T E Orr. 1990. “An Approach for Time-Dependent Bone Modeling and Remodeling—Application: A Preliminary Remodeling Simulation - Beaupré - 2005 - Journal of Orthopaedic Research - Wiley Online Library.” Journal of Orthopaedic …, 662–70. http://onlinelibrary.wiley.com/doi/10.1002/jor.1100080507/abstract%5Cnpapers2://publication/uuid/9D5C378F-EDD8-4736-B052-510B4EFC85B9.Belinha, J., R. M. Natal Jorge, and L. M.J.S. Dinis. 2012. “Bone Tissue Remodelling Analysis Considering a Radial Point Interpolator Meshless Method.” Engineering Analysis with Boundary Elements 36 (11): 1660–70. https://doi.org/10.1016/j.enganabound.2012.05.009.Bhate, Dhruv, Clint A. Penick, Lara A. Ferry, and Christine Lee. 2019. “Classification and Selection of Cellular Materials in Mechanical Design: Engineering and Biomimetic Approaches.” Designs 3 (1): 1–31. https://doi.org/10.3390/designs3010019.Braun, Jan-matthias, Poramate Manoonpong, and Xiaofeng Xiong. n.d. BIOLOGY-INSPIRED ENGINEERING AND ENGINEERING-INSPIRED BIOLOGY. https://doi.org/10.3389/978-2-88966-340-8.Buenzli, P. R., P. Pivonka, and D. W. Smith. 2011. “Spatio-Temporal Structure of Cell Distribution in Cortical Bone Multicellular Units: A Mathematical Model.” Bone 48 (4): 918–26. https://doi.org/10.1016/j.bone.2010.12.009.Bullock, Whitney A., Frederick M. Pavalko, and Alexander G. Robling. 2019. “Osteocytes and Mechanical Loading: The Wnt Connection.” Orthodontics and Craniofacial Research 22 (S1): 175–79. https://doi.org/10.1111/ocr.12282.Cerrolaza, M., F. Nieto, and Y. González. 2018. “Computation of the Dynamic Compression Effects in Spine Discs Using Integral Methods.” Journal of Mechanics in Medicine and Biology 18 (5): 1–16. https://doi.org/10.1142/S0219519417501032.Cesar, R., R. S. Boffa, L. T. Fachine, T. P. Leivas, A. M.H. Silva, C. A.M. Pereira, R. B.M. Reiff, and J. M.D.A. Rollo. 2013. “Evaluation of Trabecular Microarchitecture of Normal Osteoporotic and Osteopenic Human Vertebrae.” Procedia Engineering 59: 6–15. https://doi.org/10.1016/j.proeng.2013.05.087.Cha, Yong Han, Jun Il Yoo, Seok Young Hwang, Kap Jung Kim, Ha Yong Kim, Won Sik Choy, and Sun Chul Hwang. 2019. “Biomechanical Evaluation of Internal Fixation of Pauwels Type III Femoral Neck Fractures: A Systematic Review of Various Fixation Methods.” CiOS Clinics in Orthopedic Surgery 11 (1): 1–14. https://doi.org/10.4055/cios.2019.11.1.1.Chen, Wenjiong, Xiaonan Zheng, and Shutian Liu. 2018. “Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing.” Materials 11 (11). https://doi.org/10.3390/ma11112073.“Computer-Assisted Femoral Augmentation for Osteoporotic Hip Fracture Prevention.” 2013.Corte, Alessandro Della, Ivan Giorgio, and Daria Scerrato. 2020. “A Review of Recent Developments in Mathematical Modeling of Bone Remodeling.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 234 (3): 273–81. https://doi.org/10.1177/0954411919857599.Cowin, SC, and JJ Telega,. 2003. Bone Mechanics Handbook, 2nd Edition. -. Applied Mechanics Reviews. Vol. 56. https://doi.org/10.1115/1.1579463.Cowin, S. C. 1986. “Wolff’s Law of Trabecular Architecture at Remodeling Equilibrium.” Journal of Biomechanical Engineering 108 (1): 83–88. https://doi.org/10.1115/1.3138584.Daxner, Thomas. 2010. “Finite Element Modeling of Cellular Materials. In: Altenbach H., Öchsner A. (Eds) Cellular and Porous Materials in Structures and Processes. CISM International Centre for Mechanical Sciences, Vol 521. Springer, Vienna. Https://Doi.Org/10.1007/978-3-7091-0.” In , 634.Eriksen, E. F., H. J.G. Gundersen, F. Melsen, and L. Mosekilde. 1984. “Reconstruction of the Formative Site in Iliac Trabecular Bone in 20 Normal Individuals Employing a Kinetic Model for Matrix and Mineral Apposition.” Metabolic Bone Disease and Related Research 5 (5): 243–52. https://doi.org/10.1016/0221-8747(84)90066-3.Feng, Xu, and Jay M. McDonald. 2011. “Disorders of Bone Remodeling.” Annual Review of Pathology: Mechanisms of Disease 6 (1): 121–45. https://doi.org/10.1146/annurev-pathol-011110-130203.Fonseca-vel, Aldemar. 2009. “Implementaci ´ on Del Modelo de Remodelaci ´ on ´ Osea de Komarova Para El Estudio de La Sensibilidad Del Proceso de Remodelamiento ´ Oseo Ante Cambios En Factores Locales,” 107–32.Gabriel García-Acosta, Fahir D. Castañeda, Diego A. Garzón-Alvarado, Kalenia Márquez-Flórez, Diego A. Quexada-Rodriguez, Armando Salgado, Marco A. Velasco. 2020. “Design for the Additive Manufacturing of Structural Elements with Cellular Materials Using Voronoi Diagrams and Delaunay Triangulations: Biological and Structural Applications.” Unpublished Manuscript, 33.Ganghoffer, Jean François, and Ibrahim Goda. 2018. “Prediction of Size Effects in Bone Brittle and Plastic Collapse.” Multiscale Biomechanics, 345–88. https://doi.org/10.1016/B978-1-78548-208-3.50008-3.Garzón-Alvarado, D. A., and D. Linero. 2012a. “Comparative Analysis of Numerical Integration Schemes of Density Equation for a Computational Model of Bone Remodelling.” Computer Methods in Biomechanics and Biomedical Engineering 15 (11): 1189–96. https://doi.org/10.1080/10255842.2011.585972.———. 2012b. “Comparative Analysis of Numerical Integration Schemes of Density Equation for a Computational Model of Bone Remodelling.” Computer Methods in Biomechanics and Biomedical Engineering 15 (11): 1189–96. https://doi.org/10.1080/10255842.2011.585972.Gasser, Jürg Andreas, and Michaela Kneissel. 2017. Bone Toxicology. Bone Toxicology. https://doi.org/10.1007/978-3-319-56192-9.Geris, L., J. Vander Sloten, and H. Van Oosterwyck. 2010. “Connecting Biology and Mechanics in Fracture Healing: An Integrated Mathematical Modeling Framework for the Study of Nonunions.” Biomechanics and Modeling in Mechanobiology 9 (6): 713–24. https://doi.org/10.1007/s10237-010-0208-8.González, Y., M. Cerrolaza, and C. González. 2009. “Poroelastic Analysis of Bone Tissue Differentiation by Using the Boundary Element Method.” Engineering Analysis with Boundary Elements 33 (5): 731–40. https://doi.org/10.1016/j.enganabound.2008.09.008.Guevara, J. M., M. A. Moncayo, J. J. Vaca-González, M. L. Gutiérrez, L. A. Barrera, and D. A. Garzón-Alvarado. 2015. “Growth Plate Stress Distribution Implications during Bone Development: A Simple Framework Computational Approach.” Computer Methods and Programs in Biomedicine 118 (1): 59–68. https://doi.org/10.1016/j.cmpb.2014.10.007.Hambli, Ridha. 2014. “Connecting Mechanics and Bone Cell Activities in the Bone Remodeling Process: An Integrated Finite Element Modeling.” Frontiers in Bioengineering and Biotechnology 2 (APR): 1–12. https://doi.org/10.3389/fbioe.2014.00006.Hambli, Ridha, Mohamed Hafedh Boughattas, Jean Luc Daniel, and Azeddine Kourta. 2016. “Prediction of Denosumab Effects on Bone Remodeling: A Combined Pharmacokinetics and Finite Element Modeling.” Journal of the Mechanical Behavior of Biomedical Materials 60 (January 2016): 492–504. https://doi.org/10.1016/j.jmbbm.2016.03.010.Hopkins, R. B., N. Burke, C. Von Keyserlingk, W. D. Leslie, S. N. Morin, J. D. Adachi, A. Papaioannou, et al. 2016. “The Current Economic Burden of Illness of Osteoporosis in Canada.” Osteoporosis International 27 (10): 3023–32. https://doi.org/10.1007/s00198-016-3631-6.Jerez, S., and B. Chen. 2015. “Stability Analysis of a Komarova Type Model for the Interactions of Osteoblast and Osteoclast Cells during Bone Remodeling.” Mathematical Biosciences 264 (1): 29–37. https://doi.org/10.1016/j.mbs.2015.03.003.Kenkre, J. S., and J. H.D. Bassett. 2018. The Bone Remodelling Cycle. Annals of Clinical Biochemistry. Vol. 55. https://doi.org/10.1177/0004563218759371.Key, Radiolology. 2020. “Bone Mineral Density and Quantitative Imaging.” 12 de Junio. 2020. https://radiologykey.com/bone-mineral-density-and-quantitative-imaging/.KOCH, JOHN C. 1993. “THE LAWS OF BONE ARCHITECTURE.” From the Department of Anatomy, Johns Hopkins Medical School, Baltimore, Md. 2 (6): 444–54.Komarova, Svetlana V., Robert J. Smith, S. Jeffrey Dixon, Stephen M. Sims, and Lindi M. Wahl. 2003. “Mathematical Model Predicts a Critical Role for Osteoclast Autocrine Regulation in the Control of Bone Remodeling.” Bone 33 (2): 206–15. https://doi.org/10.1016/S8756-3282(03)00157-1.Kumar, Natarajan Chennimalai, Iwona Jasiuk, and Jonathan Dantzig. 2011. “Dissipation Energy as a Stimulus for Cortical Bone Adaptation.” Journal of Mechanics of Materials and Structures 6 (1–4): 303–19. https://doi.org/10.2140/jomms.2011.6.303.Lemaire, Vincent, Frank L. Tobin, Larry D. Greller, Carolyn R. Cho, and Larry J. Suva. 2004. “Modeling the Interactions between Osteoblast and Osteoclast Activities in Bone Remodeling.” Journal of Theoretical Biology 229 (3): 293–309. https://doi.org/10.1016/j.jtbi.2004.03.023.Lenthe, G. Harry van, and Ralph Müller. 2006. “Prediction of Failure Load Using Micro-Finite Element Analysis Models: Toward in Vivo Strength Assessment.” Drug Discovery Today: Technologies 3 (2): 221–29. https://doi.org/10.1016/j.ddtec.2006.06.001.Li, Jianying, Haiyan Li, Li Shi, Alex S.L. Fok, Cemal Ucer, Hugh Devlin, Keith Horner, and Nick Silikas. 2007. “A Mathematical Model for Simulating the Bone Remodeling Process under Mechanical Stimulus.” Dental Materials 23 (9): 1073–78. https://doi.org/10.1016/j.dental.2006.10.004.Li, Xiaofeng, Yazhou Zhang, Heeseog Kang, Wenzhong Liu, Peng Liu, Jianghong Zhang, Stephen E. Harris, and Dianqing Wu. 2005. “Sclerostin Binds to LRP5/6 and Antagonizes Canonical Wnt Signaling.” Journal of Biological Chemistry 280 (20): 19883–87. https://doi.org/10.1074/jbc.M413274200.Luxner, Mathias H., Alexander Woesz, Juergen Stampfl, Peter Fratzl, and Heinz E. Pettermann. 2009. “A Finite Element Study on the Effects of Disorder in Cellular Structures.” Acta Biomaterialia 5 (1): 381–90. https://doi.org/10.1016/j.actbio.2008.07.025.Makris, Panagiotis A., Christopher G. Provatidis, and Demetrios A. Rellakis. 2006. “Discrete Variable Optimization of Frames Using a Strain Energy Criterion.” Structural and Multidisciplinary Optimization 31 (5): 410–17. https://doi.org/10.1007/s00158-005-0588-z.Marco, Miguel, Eugenio Giner, José Ramón Caeiro-Rey, M. Henar Miguélez, and Ricardo Larraínzar-Garijo. 2019. “Numerical Modelling of Hip Fracture Patterns in Human Femur.” Computer Methods and Programs in Biomedicine 173: 67–75. https://doi.org/10.1016/j.cmpb.2019.03.010.Martín, Raúl Álvarez San, and José Antonio Velutini Kochen. 2011. “Anatomía de La Cabeza Femoral Humana: Consideraciones En Ortopedia, Parte II. Biomecánica y Morfología Microscópica.” International Journal of Morphology 29 (2): 371–76.Martínez, G., and M. Cerrolaza. 2006. “A Bone Adaptation Integrated Approach Using BEM.” Engineering Analysis with Boundary Elements 30 (2): 107–15. https://doi.org/10.1016/j.enganabound.2005.08.010.Maxwell, Clerk. n.d. “Prof . Maxwell on Reciprocal Figures XLV . On Reciprocal Figures and Diagrams of Forces . JBy J . CLERK MAXWELL , F . R . S ., Professor of Natural Philosophy in King ’ s College , London ~ . and Diagrams of Forces . On Reciprocal Plane Figures . Definiti” xxv: 250–61.Metcalf, Louis M., Enrico Dall’Ara, Margaret A. Paggiosi, John R. Rochester, Nicolas Vilayphiou, Graham J. Kemp, and Eugene V. McCloskey. 2018. “Validation of Calcaneus Trabecular Microstructure Measurements by HR-PQCT.” Bone 106: 69–77. https://doi.org/10.1016/j.bone.2017.09.013.Meyer, G. H. 1867. “‘Die Architektur Der Spongiosa,’ Archiv Fur Anatomie, Physiologie Und Wissenschaftliche Medizin, Reichert Und DuBois-Reymonds Archiv.” Nackenhorst, Udo. 1997. “Numerical Simulation of Stress Stimulated Bone Remodeling.” Technische Mechanik 17 (1): 31–40. http://www.uni-magdeburg.de/ifme/zeitschrift_tm/1997_Heft1/Nackenhorst.pdf.Niu, Tianhua, and Clifford J. Rosen. 2005. “The Insulin-like Growth Factor-I Gene and Osteoporosis: A Critical Appraisal.” Gene 361 (1–2): 38–56. https://doi.org/10.1016/j.gene.2005.07.016.Okaji, Masayo, Hideaki Sakai, Eiko Sakai, Mitsue Shibata, Fumio Hashimoto, Yasuhiro Kobayashi, Noriaki Yoshida, Kuniaki Okamoto, Kenji Yamamoto, and Yuzo Kato. 2003. “The Regulation of Bone Resorption in Tooth Formation and Eruption Processes in Mouse Alveolar Crest Devoid of Cathepsin K.” Journal Pharmacological Sciences 91 (4): 285–94. https://doi.org/10.1254/jphs.91.285.Owen, Robert, and Gwendolen C. Reilly. 2018. “In Vitro Models of Bone Remodelling and Associated Disorders.” Frontiers in Bioengineering and Biotechnology 6 (OCT): 1–22. https://doi.org/10.3389/fbioe.2018.00134.Parfitt, A. M. 1994. “Osteonal and Hemi‐osteonal Remodeling: The Spatial and Temporal Framework for Signal Traffic in Adult Human Bone.” Journal of Cellular Biochemistry 55 (3): 273–86. https://doi.org/10.1002/jcb.240550303.Peng, Matthew Jian Qiao, Hong Wen Xu, Hai Yan Chen, Ze Lin, Xin Xu Li, Chu Long Shen, Yong Qiang Lau, Er Xing He, and Yue Ming Guo. 2020. “Biomechanical Analysis for Five Fixation Techniques of Pauwels-III Fracture by Finite Element Modeling.” Computer Methods and Programs in Biomedicine 193: 105491. https://doi.org/10.1016/j.cmpb.2020.105491.Peyroteo, M. M.A., J. Belinha, S. Vinga, L. M.J.S. Dinis, and R. M. Natal Jorge. 2019. “Mechanical Bone Remodelling: Comparative Study of Distinct Numerical Approaches.” Engineering Analysis with Boundary Elements 100 (January 2018): 125–39. https://doi.org/10.1016/j.enganabound.2018.01.011.Pivonka, Peter, Jan Zimak, David W. Smith, Bruce S. Gardiner, Colin R. Dunstan, Natalie A. Sims, T. John Martin, and Gregory R. Mundy. 2008. “Model Structure and Control of Bone Remodeling: A Theoretical Study.” Bone 43 (2): 249–63. https://doi.org/10.1016/j.bone.2008.03.025. Raggatt, Liza J., and Nicola C. Partridge. 2010. “Cellular and Molecular Mechanisms of Bone Remodeling.” Journal of Biological Chemistry 285 (33): 25103–8. https://doi.org/10.1074/jbc.R109.041087.Rapisarda, Alessio Ciro, Alessandro Della Corte, Rafał Drobnicki, Fabio Di Cosmo, and Luigi Rosa. 2019. “A Model for Bone Mechanics and Remodeling Including Cell Populations Dynamics.” Zeitschrift Fur Angewandte Mathematik Und Physik 70 (1): 1–17. https://doi.org/10.1007/s00033-018-1055-1.Ruff1. Ruffoni, D. & Van Lenthe, G. H. 3.10 Finite element analysis in bone research: A computational method relating structure to mechanical function. Comprehensive Biomaterials II vol. 3 (Elsevier Ltd., 2017).oni, D., and G. H. Van Lenthe. 2017. 3.10 Finite Element Analysis in Bone Research: A Computational Method Relating Structure to Mechanical Function. Comprehensive Biomaterials II. Vol. 3. Elsevier Ltd. https://doi.org/10.1016/B978-0-12-803581-8.09798-8.Schaedler, Tobias A., and William B. Carter. 2016. “Architected Cellular Materials.” Annual Review of Materials Research 46 (April): 187–210. https://doi.org/10.1146/annurev-matsci-070115-031624.Seeman, Ego. 2003. “The Structural and Biomechanical Basis of the Gain and Loss of Bone Strength in Women and Men.” Endocrinology and Metabolism Clinics of North America 32 (1): 25–38. https://doi.org/10.1016/S0889-8529(02)00078-6.Sozen, Tumay, Lale Ozisik, and Nursel Calik Basaran. 2017. “An Overview and Management of Osteoporosis.” European Journal of Rheumatology 4 (1): 46–56. https://doi.org/10.5152/eurjrheum.2016.048.Stein, Emily M., Barbara C. Silva, Stephanie Boutroy, Bin Zhou, Ji Wang, Julia Udesky, Chiyuan Zhang, et al. 2013. “Primary Hyperparathyroidism Is Associated with Abnormal Cortical and Trabecular Microstructure and Reduced Bone Stiffness in Postmenopausal Women.” Journal of Bone and Mineral Research 28 (5): 1029–40. https://doi.org/10.1002/jbmr.1841.Ström, O., F. Borgström, John A. Kanis, Juliet Compston, Cyrus Cooper, Eugene V. McCloskey, and Bengt Jönsson. 2011. “Osteoporosis: Burden, Health Care Provision and Opportunities in the EU.” Archives of Osteoporosis 6 (1–2): 59–155. https://doi.org/10.1007/s11657-011-0060-1.Sun, Xiaoqiang, Yunqing Kang, Jiguang Bao, Yuanyuan Zhang, Yunzhi Yang, and Xiaobo Zhou. 2013. “Modeling Vascularized Bone Regeneration within a Porous Biodegradable CaP Scaffold Loaded with Growth Factors.” Biomaterials 34 (21): 4971–81. https://doi.org/10.1016/j.biomaterials.2013.03.015.Swarthout, John T., Richard C. D’Alonzo, Nagarajan Selvamurugan, and Nicola C. Partridge. 2002. “Parathyroid Hormone-Dependent Signaling Pathways Regulating Genes in Bone Cells.” Gene 282 (1–2): 1–17. https://doi.org/10.1016/S0378-1119(01)00798-3.Valdez, S. Ivvan, Salvador Botello, Miguel A. Ochoa, José L. Marroquín, and Victor Cardoso. 2017. “Topology Optimization Benchmarks in 2D: Results for Minimum Compliance and Minimum Volume in Planar Stress Problems.” Archives of Computational Methods in Engineering 24 (4): 803–39. https://doi.org/10.1007/s11831-016-9190-3.Vanegas-Acosta, J. C., N. S. Landinez P., D. A. Garzón-Alvarado, and M. C. Casale R. 2011. “A Finite Element Method Approach for the Mechanobiological Modeling of the Osseointegration of a Dental Implant.” Computer Methods and Programs in Biomedicine 101 (3): 297–314. https://doi.org/10.1016/j.cmpb.2010.11.007.Walton, Dan, and Hadi Moztarzadeh. 2017. “Design and Development of an Additive Manufactured Component by Topology Optimisation.” Procedia CIRP 60: 205–10. https://doi.org/10.1016/j.procir.2017.03.027.Weinans, H., R. Huiskes, and H. J. Grootenboer. 1992. “The Behavior of Adaptive Bone-Remodeling Simulation Models.” Journal of Biomechanics 25 (12): 1425–41. https://doi.org/10.1016/0021-9290(92)90056-7.Wippert, Pia Maria, Michael Rector, Gisela Kuhn, and Karin Wuertz-Kozak. 2017. “Stress and Alterations in Bones: An Interdisciplinary Perspective.” Frontiers in Endocrinology 8 (MAY): 1–7. https://doi.org/10.3389/fendo.2017.00096.Wu, Jun, Weiming Wang, and Xifeng Gao. 2019. “Design and Optimization of Conforming Lattice Structures.” IEEE Transactions on Visualization and Computer Graphics, 1–1. https://doi.org/10.1109/tvcg.2019.2938946.Yamamoto, Yoko, Tatsuya Yoshizawa, Toru Fukuda, Yuko Shirode-Fukuda, Taiyong Yu, Keisuke Sekine, Takashi Sato, et al. 2013. “Vitamin D Receptor in Osteoblasts Is a Negative Regulator of Bone Mass Control.” Endocrinology 154 (3): 1008–20. https://doi.org/10.1210/en.2012-1542.GeneralORIGINALThesis_final_repositorio.pdfThesis_final_repositorio.pdfTesis de Maestría en Ingeniería Biomédicaapplication/pdf3854989https://repositorio.unal.edu.co/bitstream/unal/79884/5/Thesis_final_repositorio.pdf89b320659ef0826ccd496bfb9d392610MD55LICENSElicense.txtlicense.txttext/plain; charset=utf-83964https://repositorio.unal.edu.co/bitstream/unal/79884/3/license.txtcccfe52f796b7c63423298c2d3365fc6MD53CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8799https://repositorio.unal.edu.co/bitstream/unal/79884/6/license_rdff7d494f61e544413a13e6ba1da2089cdMD56THUMBNAILThesis_final_repositorio.pdf.jpgThesis_final_repositorio.pdf.jpgGenerated Thumbnailimage/jpeg4407https://repositorio.unal.edu.co/bitstream/unal/79884/7/Thesis_final_repositorio.pdf.jpga3ea6c92143c95e1f7daaae462388c25MD57unal/79884oai:repositorio.unal.edu.co:unal/798842024-07-25 23:14:15.398Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.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 |