How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis
The annulus fibrosus has substantial variations in its geometrical properties (among individuals and between levels), and plays an important role in the biomechanics of the spine. Few works have studied the influence of the geometrical properties including annulus area, anterior / posterior disc hei...
- Autores:
-
Jaramillo Suárez, Héctor Enrique
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2018
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/11405
- Acceso en línea:
- http://hdl.handle.net/10614/11405
- Palabra clave:
- Análisis matemático
Mathematical analysis
Matrices estocásticas
Stochastic matrices
Stochastic analysis
Finite element analysis
Annulus fibrosus
Spine
Intervertebral disc
- Rights
- restrictedAccess
- License
- Derechos Reservados - Universidad Autónoma de Occidente
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| dc.title.eng.fl_str_mv |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| title |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| spellingShingle |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis Análisis matemático Mathematical analysis Matrices estocásticas Stochastic matrices Stochastic analysis Finite element analysis Annulus fibrosus Spine Intervertebral disc |
| title_short |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| title_full |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| title_fullStr |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| title_full_unstemmed |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| title_sort |
How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis |
| dc.creator.fl_str_mv |
Jaramillo Suárez, Héctor Enrique |
| dc.contributor.author.none.fl_str_mv |
Jaramillo Suárez, Héctor Enrique |
| dc.subject.lemb.spa.fl_str_mv |
Análisis matemático |
| topic |
Análisis matemático Mathematical analysis Matrices estocásticas Stochastic matrices Stochastic analysis Finite element analysis Annulus fibrosus Spine Intervertebral disc |
| dc.subject.lemb.eng.fl_str_mv |
Mathematical analysis |
| dc.subject.armarc.spa.fl_str_mv |
Matrices estocásticas |
| dc.subject.armarc.eng.fl_str_mv |
Stochastic matrices |
| dc.subject.proposal.eng.fl_str_mv |
Stochastic analysis Finite element analysis Annulus fibrosus Spine Intervertebral disc |
| description |
The annulus fibrosus has substantial variations in its geometrical properties (among individuals and between levels), and plays an important role in the biomechanics of the spine. Few works have studied the influence of the geometrical properties including annulus area, anterior / posterior disc height, and over the range of motion, but in general these properties have not been reported in the finite element models. This paper presents a probabilistic finite element analyses (Abaqus 6.14.2) intended to assess the effects of the average disc height (hp) and the area (A) of the annulus fibrosus on the biomechanics of the lumbar spine. The annulus model was loaded under flexion, extension, lateral bending, and axial rotation and analyzed for different combinations of hp and A in order to obtain their effects over the range of motion. A set of 50 combinations of hp (mean = 18.1 mm, SD = 3.5 mm) and A (mean = 49.8%, SD = 4.6%) were determined randomly according to a normal distribution. A Yeoh energy function was used for the matrix and an exponential function for the fibers. The range of motion was more sensitive to hp than to A. With regard to the range of motion the segment was more sensitive in the following order: flexion, axial rotation, extension, and lateral bending. An increase of the hp produces an increase of the range of motion, but this decreases when A increases. Comparing the range of motion with the experimental data, on average, 56.0% and 73.0% of the total of data were within the experimental range for the L4–L5 and L5–S1 segments, respectively. Further, an analytic equation was derived to obtain the range of motion as a function of the hp and A. This equation can be used to calibrate a finite element model of the spine segment, and also to understand the influence of each geometrical parameter on the range of motion. |
| publishDate |
2018 |
| dc.date.issued.none.fl_str_mv |
2018-10-11 |
| dc.date.accessioned.none.fl_str_mv |
2019-11-06T14:35:50Z |
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2019-11-06T14:35:50Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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Text |
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1464-4207 |
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http://hdl.handle.net/10614/11405 |
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10.1177/1464420718805896 |
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1464-4207 10.1177/1464420718805896 |
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eng |
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eng |
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1992 |
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10 |
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1985 |
| dc.relation.citationvolume.none.fl_str_mv |
233 |
| dc.relation.cites.eng.fl_str_mv |
Jaramillo S, H. E. (2018). How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233(10), pp. 1985-1992 |
| dc.relation.ispartofjournal.eng.fl_str_mv |
Proceedings of the Institution of Mechanical Engineers Part L-Journal of Materials-Design and Applications |
| dc.relation.references.none.fl_str_mv |
Guan, Y, Yoganandan, N, Zhang, J, et al. Validation of a clinical finite element model of the human lumbosacral spine. Med Biol Eng Comput 2006; 44: 633–641 Moramarco, V, Pérez del Palomar, A, Pappalettere, C, et al. An accurate validation of a computational model of a human lumbosacral segment. J Biomech 2010; 43: 334–342. Weisse, B, Aiyangar, AK, Affolter, C, et al. Determination of the translational and rotational stiffnesses of an L4–L5 functional spinal unit using a specimen-specific finite element model. J Mech Behav Biomed Mater 2012; 13: 45–61. Spilker, RL . Mechanical behavior of a simple model of an intervertebral disk under compressive loading. J Biomech 1980; 13: 895–901. Spilker, RL, Daugirda, DM, Schultz, AB. Mechanical response of a simple finite element model of the intervertebral disc under complex loading. J Biomech 1984; 17: 103–112. Spilker, RL, Jakobs, DM, Schultz, AB. Material constants for a finite element model of the intervertebral disk with a fiber composite annulus. J Biomech Eng 1986; 108: 1–11 Rao, AA, Dumas, GA. Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study. J Biomed Eng 1991; 13: 139–151 Fagan, MJ, Julian, S, Siddall, DJ, et al. Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc—a material sensitivity study. Proc IMechE, Part H: J Engineering in Medicine 2002; 216: 299–314. Malandrino, A, Planell, JA, Lacroix, D. Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation. J Biomech 2009; 42: 2780–2788. Rohlmann, A, Mann, A, Zander, T, et al. Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study. Eur Spine J 2009; 18: 89–97. 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 Biomech 2012; 45: 1414–1423. Thacker, B, Nicolella, D. Probabilistic finite element analysis of the human lower cervical spine. Abaqus 2013; 1: 1–12. Madsen, HO, Krenk, S, Lind, NC. Methods of estructural safety, Mineola, NY: Dover Publications Inc., 1986. Laz, PJ, Browne, M. A review of probabilistic analysis in orthopaedic biomechanics. Proc IMechE, Part H: J Engineering in Medicine 2010; 224: 927–943. Francis, WL, Eliason, TD, Thacker, BH, et al. Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine. Comput Methods Biomech Biomed Eng 2014; 17: 905–916. Jaramillo, HE, García, JJ, 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: 15–24. Ayturk, UM, Garcia, JJ, Puttlitz, CM. The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine. J Biomech Eng 2010; 132: 061007–061007 O'Connell, GD, Guerin, HL, Elliott, DM. Theoretical and uniaxial experimental evaluation of human annulus fibrosus degeneration. J Biomech Eng 2009; 131: 111007 Schmidt, H, Heuer, F, Simon, U, et al. 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 Ayturk, UM, Puttlitz, CM. Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine. Comput Methods Biomech Biomed Eng 2011; 14: 695–705. Cortes, DH, Han, WM, Smith, LJ, et al. Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent. J Orthop Res 2013; 31: 1725–1732 Jacobs, NT, Cortes, DH, Peloquin, JM, et al. Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent. J Biomech 2014; 47: 2540–2546 Jacobs, NT, Cortes, DH, Vresilovic, EJ, et al. Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising from boundary conditions and anisotropy. J Biomech Eng 2013; 135: 21004. Thacker, B, Wu, Y-T, Nicolella, D, et al. Probabilistic injury analysis of the cervical spine, Reston, VA: American Institute of Aeronautics and Astronautics, 1997. Jaramillo, HE, Puttlitz, CM, McGilvray, K, et al. Characterization of the L4-L5-S1 motion segment using the stepwise reduction method. J Biomech 2016; 49: 1248–1254. Moramarco, V, Pérez del Palomar, A, Pappalettere, C, et al. An accurate validation of a computational model of a human lumbosacral segment. J Biomech 2010; 43: 334–342. Cegoñino, J, Moramarco, V, Calvo-Echenique, A, et al. A constitutive model for the annulus of human intervertebral disc: implications for developing a degeneration model and its influence on lumbar spine functioning. J Appl Math 2014; 2014: e658719. Guan, Y, Yoganandan, N, Zhang, J, et al. Validation of a clinical finite element model of the human lumbosacral spine. Med Biol Eng Comput 2006; 44: 633–641 Guo, L-X . Finite element model of spine lumbosacral joint and its validation. Chinese J Biomed Eng 2006; 25: 426–429. Prendergast, P . Finite element models in tissue mechanics and orthopaedic implant design. Clin Biomech 1997; 12: 343–366. Yoganandan, N, Myklebust, JB, Ray, G, et al. A. A non-linear finite element model of a spinal segment. Math Model 1987; 8: 617–622. |
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Jaramillo Suárez, Héctor Enriquevirtual::2730-1Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-06T14:35:50Z2019-11-06T14:35:50Z2018-10-111464-4207http://hdl.handle.net/10614/1140510.1177/1464420718805896The annulus fibrosus has substantial variations in its geometrical properties (among individuals and between levels), and plays an important role in the biomechanics of the spine. Few works have studied the influence of the geometrical properties including annulus area, anterior / posterior disc height, and over the range of motion, but in general these properties have not been reported in the finite element models. This paper presents a probabilistic finite element analyses (Abaqus 6.14.2) intended to assess the effects of the average disc height (hp) and the area (A) of the annulus fibrosus on the biomechanics of the lumbar spine. The annulus model was loaded under flexion, extension, lateral bending, and axial rotation and analyzed for different combinations of hp and A in order to obtain their effects over the range of motion. A set of 50 combinations of hp (mean = 18.1 mm, SD = 3.5 mm) and A (mean = 49.8%, SD = 4.6%) were determined randomly according to a normal distribution. A Yeoh energy function was used for the matrix and an exponential function for the fibers. The range of motion was more sensitive to hp than to A. With regard to the range of motion the segment was more sensitive in the following order: flexion, axial rotation, extension, and lateral bending. An increase of the hp produces an increase of the range of motion, but this decreases when A increases. Comparing the range of motion with the experimental data, on average, 56.0% and 73.0% of the total of data were within the experimental range for the L4–L5 and L5–S1 segments, respectively. Further, an analytic equation was derived to obtain the range of motion as a function of the hp and A. This equation can be used to calibrate a finite element model of the spine segment, and also to understand the influence of each geometrical parameter on the range of motion.application/pdf8 páginasengSage. Proceedings of the Institution of Mechanical EngineersDerechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/restrictedAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_16ecHow the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic 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_970fb48d4fbd8a85Análisis matemáticoMathematical analysisMatrices estocásticasStochastic matricesStochastic analysisFinite element analysisAnnulus fibrosusSpineIntervertebral disc1992101985233Jaramillo S, H. E. (2018). How the height and the area of the annulus fibrosus affect the range of motion behavior: A stochastic analysis. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233(10), pp. 1985-1992Proceedings of the Institution of Mechanical Engineers Part L-Journal of Materials-Design and ApplicationsGuan, Y, Yoganandan, N, Zhang, J, et al. Validation of a clinical finite element model of the human lumbosacral spine. Med Biol Eng Comput 2006; 44: 633–641Moramarco, V, Pérez del Palomar, A, Pappalettere, C, et al. An accurate validation of a computational model of a human lumbosacral segment. J Biomech 2010; 43: 334–342.Weisse, B, Aiyangar, AK, Affolter, C, et al. Determination of the translational and rotational stiffnesses of an L4–L5 functional spinal unit using a specimen-specific finite element model. J Mech Behav Biomed Mater 2012; 13: 45–61.Spilker, RL . Mechanical behavior of a simple model of an intervertebral disk under compressive loading. J Biomech 1980; 13: 895–901.Spilker, RL, Daugirda, DM, Schultz, AB. Mechanical response of a simple finite element model of the intervertebral disc under complex loading. J Biomech 1984; 17: 103–112.Spilker, RL, Jakobs, DM, Schultz, AB. Material constants for a finite element model of the intervertebral disk with a fiber composite annulus. J Biomech Eng 1986; 108: 1–11Rao, AA, Dumas, GA. Influence of material properties on the mechanical behaviour of the L5-S1 intervertebral disc in compression: a nonlinear finite element study. J Biomed Eng 1991; 13: 139–151Fagan, MJ, Julian, S, Siddall, DJ, et al. Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc—a material sensitivity study. Proc IMechE, Part H: J Engineering in Medicine 2002; 216: 299–314.Malandrino, A, Planell, JA, Lacroix, D. Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression, flexion and axial rotation. J Biomech 2009; 42: 2780–2788.Rohlmann, A, Mann, A, Zander, T, et al. Effect of an artificial disc on lumbar spine biomechanics: a probabilistic finite element study. Eur Spine J 2009; 18: 89–97.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 Biomech 2012; 45: 1414–1423.Thacker, B, Nicolella, D. Probabilistic finite element analysis of the human lower cervical spine. Abaqus 2013; 1: 1–12.Madsen, HO, Krenk, S, Lind, NC. Methods of estructural safety, Mineola, NY: Dover Publications Inc., 1986.Laz, PJ, Browne, M. A review of probabilistic analysis in orthopaedic biomechanics. Proc IMechE, Part H: J Engineering in Medicine 2010; 224: 927–943.Francis, WL, Eliason, TD, Thacker, BH, et al. Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine. Comput Methods Biomech Biomed Eng 2014; 17: 905–916.Jaramillo, HE, García, JJ, 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: 15–24.Ayturk, UM, Garcia, JJ, Puttlitz, CM. The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine. J Biomech Eng 2010; 132: 061007–061007O'Connell, GD, Guerin, HL, Elliott, DM. Theoretical and uniaxial experimental evaluation of human annulus fibrosus degeneration. J Biomech Eng 2009; 131: 111007Schmidt, H, Heuer, F, Simon, U, et al. Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus. Clin Biomech 2006; 21: 337–344Ayturk, UM, Puttlitz, CM. Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine. Comput Methods Biomech Biomed Eng 2011; 14: 695–705.Cortes, DH, Han, WM, Smith, LJ, et al. Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent. J Orthop Res 2013; 31: 1725–1732Jacobs, NT, Cortes, DH, Peloquin, JM, et al. Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent. J Biomech 2014; 47: 2540–2546Jacobs, NT, Cortes, DH, Vresilovic, EJ, et al. Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising from boundary conditions and anisotropy. J Biomech Eng 2013; 135: 21004.Thacker, B, Wu, Y-T, Nicolella, D, et al. Probabilistic injury analysis of the cervical spine, Reston, VA: American Institute of Aeronautics and Astronautics, 1997.Jaramillo, HE, Puttlitz, CM, McGilvray, K, et al. Characterization of the L4-L5-S1 motion segment using the stepwise reduction method. J Biomech 2016; 49: 1248–1254.Moramarco, V, Pérez del Palomar, A, Pappalettere, C, et al. An accurate validation of a computational model of a human lumbosacral segment. J Biomech 2010; 43: 334–342.Cegoñino, J, Moramarco, V, Calvo-Echenique, A, et al. A constitutive model for the annulus of human intervertebral disc: implications for developing a degeneration model and its influence on lumbar spine functioning. J Appl Math 2014; 2014: e658719.Guan, Y, Yoganandan, N, Zhang, J, et al. Validation of a clinical finite element model of the human lumbosacral spine. Med Biol Eng Comput 2006; 44: 633–641Guo, L-X . Finite element model of spine lumbosacral joint and its validation. Chinese J Biomed Eng 2006; 25: 426–429.Prendergast, P . Finite element models in tissue mechanics and orthopaedic implant design. Clin Biomech 1997; 12: 343–366.Yoganandan, N, Myklebust, JB, Ray, G, et al. A. A non-linear finite element model of a spinal segment. Math Model 1987; 8: 617–622.Publicationada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2730-1ada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2730-1https://scholar.google.com.co/citations?user=GEzrsjQAAAAJ&hl=esvirtual::2730-10000-0002-7324-9478virtual::2730-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000144967virtual::2730-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/5a2cc552-b760-4732-b6ba-b2696d881d6a/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/aa1af9b8-30bb-425b-b9bf-3d53fef7df17/download20b5ba22b1117f71589c7318baa2c560MD5310614/11405oai:red.uao.edu.co:10614/114052024-03-07 09:57:30.865https://creativecommons.org/licenses/by-nc-nd/4.0/Derechos Reservados - Universidad Autónoma de Occidentemetadata.onlyhttps://red.uao.edu.coRepositorio Digital Universidad Autonoma de Occidenterepositorio@uao.edu.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 |