Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis
A probabilistic finite element (FE) analysis of the L4-L5 and L5-S1 human annulus fibrosus (AF) was conducted to obtain a better understanding of the biomechanics of the AF and to quantify its influence on the range of motion (ROM) of the L4-L5 and L5-S1 segments. Methods: The FE models were compose...
- Autores:
-
Jaramillo Suárez, Héctor Enrique
García Álvarez, José Jaime
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2017
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
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- oai:red.uao.edu.co:10614/11216
- Acceso en línea:
- http://hdl.handle.net/10614/11216
- Palabra clave:
- Biomecánica
Método de elementos finitos
Biomechanics
Finite element analysis
Hyperelastic
Range of motion
Intervertebral discs
Probabilistic analysis
Sensitivity factor
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- openAccess
- License
- Derechos Reservados - Universidad Autónoma de Occidente
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Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| title |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| spellingShingle |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis Biomecánica Método de elementos finitos Biomechanics Finite element analysis Hyperelastic Range of motion Intervertebral discs Probabilistic analysis Sensitivity factor |
| title_short |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| title_full |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| title_fullStr |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| title_full_unstemmed |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| title_sort |
Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis |
| dc.creator.fl_str_mv |
Jaramillo Suárez, Héctor Enrique García Álvarez, José Jaime |
| dc.contributor.author.none.fl_str_mv |
Jaramillo Suárez, Héctor Enrique García Álvarez, José Jaime |
| dc.subject.armarc.spa.fl_str_mv |
Biomecánica Método de elementos finitos |
| topic |
Biomecánica Método de elementos finitos Biomechanics Finite element analysis Hyperelastic Range of motion Intervertebral discs Probabilistic analysis Sensitivity factor |
| dc.subject.armarc.eng.fl_str_mv |
Biomechanics |
| dc.subject.proposal.eng.fl_str_mv |
Finite element analysis Hyperelastic Range of motion Intervertebral discs Probabilistic analysis Sensitivity factor |
| description |
A probabilistic finite element (FE) analysis of the L4-L5 and L5-S1 human annulus fibrosus (AF) was conducted to obtain a better understanding of the biomechanics of the AF and to quantify its influence on the range of motion (ROM) of the L4-L5 and L5-S1 segments. Methods: The FE models were composed of the AF and the upper and lower endplates. The AF was represented as a continuous material composed of a hyperelastic isotropic Yeoh matrix reinforced with two families of fibers described with an exponential energy function. The caudal endplate was fully restricted and 8 Nm pure moment was applied to the cranial endplate in flexion, extension, lateral flexion and axial rotation. The mechanical constants were determined randomly based on a normal distribution and average values reported. Results: Results of the 576 models show that the ROM was more sensitive to the initial stiffness of the fibers rather than to the stiffening coefficient represented in the exponential function. The ROM was more sensitive to the input variables in extension, flexion, axial rotation and lateral bending. The analysis showed an increased probability for the L5-S1 ROM to be higher in flexion, extension and axial rotation, and smaller in lateral flexion, with respect to the L4-L5 ROM. Conclusions: An equation was proposed to obtain the ROM as a function of the elastic constants of the fibers and it may be used to facilitate the calibration process of the human spine segments and to understand the influence of each elastic constant on the ROM |
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2017 |
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2017 |
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2019-10-16T13:32:04Z |
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2019-10-16T13:32:04Z |
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Artículo de revista |
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Jaramillo, H. E., & Garcia, J. J. (2017). Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis. Acta of bioengineering and biomechanics, 19(4) |
| dc.identifier.issn.spa.fl_str_mv |
1509409X |
| dc.identifier.uri.spa.fl_str_mv |
http://hdl.handle.net/10614/11216 |
| identifier_str_mv |
Jaramillo, H. E., & Garcia, J. J. (2017). Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis. Acta of bioengineering and biomechanics, 19(4) 1509409X |
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http://hdl.handle.net/10614/11216 |
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eng |
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eng |
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12 |
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4 |
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3 |
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19 |
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Acta of Bioengineering and Biomechanics |
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[1] AYTURK U.M., GARCIA J.J., PUTTLITZ C.M., The Micromechanical Role of the Annulus Fibrosus Components Under Physiological Loading of the Lumbar Spine, J. Biomech Eng., 2010, 132, 061007–061007. [2] CEGOÑINO J., MORAMARCO V., CALVO-ECHENIQUE A., PAPPALETTERE C., PÉREZ DEL PALOMAR A., A Constitutive Model for the Annulus of Human Intervertebral Disc: Implications for Developing a Degeneration Model and Its Influence on Lumbar Spine Functioning, J. of Appl. Mathematics, 2014, e658719. [3] CORTES D.H., ELLIOTT D.M., Extra-fibrillar matrix mechanics of annulus fibrosus in tension and compression, Biomech. Model Mechanobiol., 2012, 11, 781–790. [4] CORTES D.H., HAN W.M., SMITH L.J., ELLIOTT D.M., Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent, J. of Orthop. Res., 2013, 1725–1732. [5] DIAZ C.A., GARCÍA J.J. PUTTLITZ C., Influence of vertebra stiffness in the finite element analysis of the intervertebral disc, ASME, Fajarado, Puerto Rico, USA, 2012, 2. [6] DREISCHARF M., ZANDER T., SHIRAZI-ADL A., PUTTLITZ C.M., ADAM C.J., CHEN C.S., GOEL V.K., KIAPOUR A., KIM Y.H., LABUS K.M., LITTLE J.P., PARK W.M., WANG Y.H., WILKE H.J., ROHLMANN A., SCHMIDT H., Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together, J. of Biomech., 2014, 47, 1757–1766. [7] FAGAN M.J., JULIAN S., SIDDALL D.J., MOHSEN A.M., Patient--specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc – a material sensitivity study, Proceedings of the Institution of Mechanical Engineers, Part H: J. of Engineering in Medicine, 2002, 216, 299–314. [8] FUJITA Y., DUNCAN N.A., LOTZ J.C., Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent, J. of Orthop. Res., 1997, 15, 814–819. [9] GREEN T.P., ADAMS M.A., DOLAN P., Tensile properties of the annulus fibrosus, Eur. Spine J., 1993, 2, 209–214. [10] GUAN Y., YOGANANDAN N., ZHANG J., PINTAR F.A., CUSICK J.F., WOLFLA C.E., MAIMAN D.J., Validation of a clinical finite element model of the human lumbosacral spine, Med. Bio. Eng. Comput., 2006, 44, 633–641. [11] GUO L.-X., Finite Element Model of Spine Lumbosacral Joint and its Validation, Chinese J. of Biom. Eng., 2006, 25, 426–429. [12] JARAMILLO H.E., GARCÍA J.J., GÓMEZ L., A finite element model of the L4-L5-S1 human spine segment including the heterogeneity and anisotropy of the discs, Acta Bioeng. Biomech., 2015, 17. [13] JARAMILLO H.E., PUTTLITZ C.M., MCGILVRAY K., GARCÍA J.J., Characterization of the L4-L5-S1 motion segment using the stepwise reduction method, J. Biomech., 2016, 49, 1248–1254. [14] LAZ P.J., BROWNE M., A review of probabilistic analysis in orthopaedic biomechanics, Proceedings of the Institution of Mechanical Engineers, Part H: J. of Eng. in Medicine, 2010, 224, 927–943. [15] MADSEN H.O., KRENK S., LIND N.C., Methods of Estructural Safety, Dover Publications Inc., United States of America, 1986. [16] MALANDRINO A., PLANELL J.A., LACROIX D., Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation, J. of Biomech., 2009, 42, 2780–2788. [17] MORAMARCO V., PÉREZ DEL PALOMAR A., PAPPALETTERE C., DOBLARÉ M., An accurate validation of a computational model of a human lumbosacral segment, J. of Biomech., 2010, 43, 334–342. [18] NIEMEYER F., WILKE H.-J., SCHMIDT H., Geometry strongly influences the response of numerical models of the lumbar spine – A probabilistic finite element analysis, J. of Biomech., 2012, 45, 1414–1423. [19] O’CONNELL G.D., GUERIN H.L., ELLIOTT D.M., Theoretical and Uniaxial Experimental Evaluation of Human Annulus Fibrosus Degeneration, J. Biomech. Eng., 2009, 131, 111007. [20] PRENDERGAST P., Finite element models in tissue mechanics and orthopaedic implant design, Clinical Biomechanics, 1997, 12, 343–366. [21] RAO A.A., DUMAS G.A., Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study, J. of Biomed. Eng., 1991, 13, 139–151. [22] ROHLMANN A., MANN A., ZANDER T., BERGMANN G., Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study, Eur. Spine J., 2009, 18, 89–97. [23] SCHMIDT H., HEUER F., SIMON U., KETTLER A., ROHLMANN A., CLAES L., WILKE H.-J., Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus, Clin. Biomech., 2006, 21, 337–344. [24] SHIN D.S., LEE K., KIM D., Biomechanical study of lumbar spine with dynamic stabilization device using finite element method, Computer-Aided Design., 2007, 39, 559–567. [25] SPILKER R.L., Mechanical behavior of a simple model of an intervertebral disk under compressive loading, J. of Biomech., 1980, 13, 895–901. [26] SPILKER R.L., DAUGIRDA D.M., SCHULTZ A.B., Mechanical response of a simple finite element model of the intervertebral disc under complex loading, J. of Biomech., 1984, 17, 103–112. [27] SPILKER R.L., JAKOBS D.M., SCHULTZ A.B., Material constants for a finite element model of the intervertebral disk with a fiber composite annulus, J. of Biomech. Eng., 1986, 108, 1–11. [28] THACKER B., NICOLELLA D., Probabilistic Finite Element Analysis of the Human Lower Cervical Spine, Abaqus., 2013, 1, 1–12. [29] THACKER B., WU Y.-T., NICOLELLA D., ANDERSON R., THACKER B., NICOLELLA D., ANDERSON R., Probabilistic injury analysis of the cervical spine, American Institute of Aeronautics and Astronautics, 1997. [30] ŁODYGOWSKI T., KĄKOL W., WIERSZYCKI M., Three-dimensional nonlinear finite element model of lumbar intervertebral disc, Acta Bioeng. Biomech., 2005, 7, 29–37. [31] YOGANANDAN N., MYKLEBUST J.B., RAY G., PINTAR F., SANCES A. Jr., A non-linear finite element model of a spinal segment, Mathematical Modelling, 1987, 8, 617–622. [32] ŻAK M., PEZOWICZ C., Spinal sections and regional variations in the mechanical properties of the annulus fibrosus subjected to tensile loading, Acta Bioeng. Biomech., 2013, 15, 51–59. [33] ZHU D., GU G., WU W., GONG H., ZHU W., JIANG T., CAO Z., Micro-structure and mechanical properties of annulus fibrous of the L4-5 and L5-S1 intervertebral discs, Clinical Biomech., 2008, 23, Suppl. 1, S74–S82. |
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Jaramillo Suárez, Héctor Enriquevirtual::2383-1García Álvarez, José Jaime56b4754cf01bc1970626b07be8e549b9Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-10-16T13:32:04Z2019-10-16T13:32:04Z2017Jaramillo, H. E., & Garcia, J. J. (2017). Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis. Acta of bioengineering and biomechanics, 19(4)1509409Xhttp://hdl.handle.net/10614/11216A probabilistic finite element (FE) analysis of the L4-L5 and L5-S1 human annulus fibrosus (AF) was conducted to obtain a better understanding of the biomechanics of the AF and to quantify its influence on the range of motion (ROM) of the L4-L5 and L5-S1 segments. Methods: The FE models were composed of the AF and the upper and lower endplates. The AF was represented as a continuous material composed of a hyperelastic isotropic Yeoh matrix reinforced with two families of fibers described with an exponential energy function. The caudal endplate was fully restricted and 8 Nm pure moment was applied to the cranial endplate in flexion, extension, lateral flexion and axial rotation. The mechanical constants were determined randomly based on a normal distribution and average values reported. Results: Results of the 576 models show that the ROM was more sensitive to the initial stiffness of the fibers rather than to the stiffening coefficient represented in the exponential function. The ROM was more sensitive to the input variables in extension, flexion, axial rotation and lateral bending. The analysis showed an increased probability for the L5-S1 ROM to be higher in flexion, extension and axial rotation, and smaller in lateral flexion, with respect to the L4-L5 ROM. Conclusions: An equation was proposed to obtain the ROM as a function of the elastic constants of the fibers and it may be used to facilitate the calibration process of the human spine segments and to understand the influence of each elastic constant on the ROMapplication/pdf10 páginasengWroclaw University of Science and Technology.Derechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2Elastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysisArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85BiomecánicaMétodo de elementos finitosBiomechanicsFinite element analysisHyperelasticRange of motionIntervertebral discsProbabilistic analysisSensitivity factor124319Acta of Bioengineering and Biomechanics[1] AYTURK U.M., GARCIA J.J., PUTTLITZ C.M., The Micromechanical Role of the Annulus Fibrosus Components Under Physiological Loading of the Lumbar Spine, J. Biomech Eng., 2010, 132, 061007–061007.[2] CEGOÑINO J., MORAMARCO V., CALVO-ECHENIQUE A., PAPPALETTERE C., PÉREZ DEL PALOMAR A., A Constitutive Model for the Annulus of Human Intervertebral Disc: Implications for Developing a Degeneration Model and Its Influence on Lumbar Spine Functioning, J. of Appl. Mathematics, 2014, e658719.[3] CORTES D.H., ELLIOTT D.M., Extra-fibrillar matrix mechanics of annulus fibrosus in tension and compression, Biomech. Model Mechanobiol., 2012, 11, 781–790.[4] CORTES D.H., HAN W.M., SMITH L.J., ELLIOTT D.M., Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent, J. of Orthop. Res., 2013, 1725–1732.[5] DIAZ C.A., GARCÍA J.J. PUTTLITZ C., Influence of vertebra stiffness in the finite element analysis of the intervertebral disc, ASME, Fajarado, Puerto Rico, USA, 2012, 2.[6] DREISCHARF M., ZANDER T., SHIRAZI-ADL A., PUTTLITZ C.M., ADAM C.J., CHEN C.S., GOEL V.K., KIAPOUR A., KIM Y.H., LABUS K.M., LITTLE J.P., PARK W.M., WANG Y.H., WILKE H.J., ROHLMANN A., SCHMIDT H., Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together, J. of Biomech., 2014, 47, 1757–1766.[7] FAGAN M.J., JULIAN S., SIDDALL D.J., MOHSEN A.M., Patient--specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc – a material sensitivity study, Proceedings of the Institution of Mechanical Engineers, Part H: J. of Engineering in Medicine, 2002, 216, 299–314.[8] FUJITA Y., DUNCAN N.A., LOTZ J.C., Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent, J. of Orthop. Res., 1997, 15, 814–819.[9] GREEN T.P., ADAMS M.A., DOLAN P., Tensile properties of the annulus fibrosus, Eur. Spine J., 1993, 2, 209–214.[10] GUAN Y., YOGANANDAN N., ZHANG J., PINTAR F.A., CUSICK J.F., WOLFLA C.E., MAIMAN D.J., Validation of a clinical finite element model of the human lumbosacral spine, Med. Bio. Eng. Comput., 2006, 44, 633–641.[11] GUO L.-X., Finite Element Model of Spine Lumbosacral Joint and its Validation, Chinese J. of Biom. Eng., 2006, 25, 426–429.[12] JARAMILLO H.E., GARCÍA J.J., GÓMEZ L., A finite element model of the L4-L5-S1 human spine segment including the heterogeneity and anisotropy of the discs, Acta Bioeng. Biomech., 2015, 17.[13] JARAMILLO H.E., PUTTLITZ C.M., MCGILVRAY K., GARCÍA J.J., Characterization of the L4-L5-S1 motion segment using the stepwise reduction method, J. Biomech., 2016, 49, 1248–1254.[14] LAZ P.J., BROWNE M., A review of probabilistic analysis in orthopaedic biomechanics, Proceedings of the Institution of Mechanical Engineers, Part H: J. of Eng. in Medicine, 2010, 224, 927–943.[15] MADSEN H.O., KRENK S., LIND N.C., Methods of Estructural Safety, Dover Publications Inc., United States of America, 1986.[16] MALANDRINO A., PLANELL J.A., LACROIX D., Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation, J. of Biomech., 2009, 42, 2780–2788.[17] MORAMARCO V., PÉREZ DEL PALOMAR A., PAPPALETTERE C., DOBLARÉ M., An accurate validation of a computational model of a human lumbosacral segment, J. of Biomech., 2010, 43, 334–342.[18] NIEMEYER F., WILKE H.-J., SCHMIDT H., Geometry strongly influences the response of numerical models of the lumbar spine – A probabilistic finite element analysis, J. of Biomech., 2012, 45, 1414–1423.[19] O’CONNELL G.D., GUERIN H.L., ELLIOTT D.M., Theoretical and Uniaxial Experimental Evaluation of Human Annulus Fibrosus Degeneration, J. Biomech. Eng., 2009, 131, 111007.[20] PRENDERGAST P., Finite element models in tissue mechanics and orthopaedic implant design, Clinical Biomechanics, 1997, 12, 343–366.[21] RAO A.A., DUMAS G.A., Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study, J. of Biomed. Eng., 1991, 13, 139–151.[22] ROHLMANN A., MANN A., ZANDER T., BERGMANN G., Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study, Eur. Spine J., 2009, 18, 89–97.[23] SCHMIDT H., HEUER F., SIMON U., KETTLER A., ROHLMANN A., CLAES L., WILKE H.-J., Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus, Clin. Biomech., 2006, 21, 337–344.[24] SHIN D.S., LEE K., KIM D., Biomechanical study of lumbar spine with dynamic stabilization device using finite element method, Computer-Aided Design., 2007, 39, 559–567.[25] SPILKER R.L., Mechanical behavior of a simple model of an intervertebral disk under compressive loading, J. of Biomech., 1980, 13, 895–901.[26] SPILKER R.L., DAUGIRDA D.M., SCHULTZ A.B., Mechanical response of a simple finite element model of the intervertebral disc under complex loading, J. of Biomech., 1984, 17, 103–112.[27] SPILKER R.L., JAKOBS D.M., SCHULTZ A.B., Material constants for a finite element model of the intervertebral disk with a fiber composite annulus, J. of Biomech. Eng., 1986, 108, 1–11.[28] THACKER B., NICOLELLA D., Probabilistic Finite Element Analysis of the Human Lower Cervical Spine, Abaqus., 2013, 1, 1–12.[29] THACKER B., WU Y.-T., NICOLELLA D., ANDERSON R., THACKER B., NICOLELLA D., ANDERSON R., Probabilistic injury analysis of the cervical spine, American Institute of Aeronautics and Astronautics, 1997.[30] ŁODYGOWSKI T., KĄKOL W., WIERSZYCKI M., Three-dimensional nonlinear finite element model of lumbar intervertebral disc, Acta Bioeng. Biomech., 2005, 7, 29–37.[31] YOGANANDAN N., MYKLEBUST J.B., RAY G., PINTAR F., SANCES A. Jr., A non-linear finite element model of a spinal segment, Mathematical Modelling, 1987, 8, 617–622.[32] ŻAK M., PEZOWICZ C., Spinal sections and regional variations in the mechanical properties of the annulus fibrosus subjected to tensile loading, Acta Bioeng. Biomech., 2013, 15, 51–59.[33] ZHU D., GU G., WU W., GONG H., ZHU W., JIANG T., CAO Z., Micro-structure and mechanical properties of annulus fibrous of the L4-5 and L5-S1 intervertebral discs, Clinical Biomech., 2008, 23, Suppl. 1, S74–S82.Publicationada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2383-1ada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2383-1https://scholar.google.com.co/citations?user=GEzrsjQAAAAJ&hl=esvirtual::2383-10000-0002-7324-9478virtual::2383-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000144967virtual::2383-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/d09af323-17bb-45e1-a694-2f5942014ffc/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/fd174a16-d1f6-4e9d-8b4e-5ffd40b630aa/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdfElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf9737782https://red.uao.edu.co/bitstreams/26dd9dc7-a825-49a4-a130-d6917894d3f1/downloade8c0671d248cc9685173e904773cb428MD54TEXTElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdf.txtElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdf.txtExtracted texttext/plain28113https://red.uao.edu.co/bitstreams/9148c5a5-2abf-4540-af13-ba640f1800e1/download65c5fd0ed50e216c9ec6187c10b9d4d8MD55THUMBNAILElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdf.jpgElastic constants influence on the L4-L5-S1 annuli fibrosus behavior, a probabilistic finite element analysis.pdf.jpgGenerated Thumbnailimage/jpeg13727https://red.uao.edu.co/bitstreams/af562471-ad49-4ab4-80af-07fd62231131/downloadcdcad6e94b7ebf0c0dffb6e25fe6462aMD5610614/11216oai:red.uao.edu.co:10614/112162024-03-06 16:36:41.893https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidenteopen.accesshttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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 |