Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus
Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic an...
- 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:10614/11407
- Acceso en línea:
- http://hdl.handle.net/10614/11407
- Palabra clave:
- Mecánica
Disco intervertebral
Biomecánica - Modelos matemáticos
Intervertebral disk
Mechanics
Biomechanics - Mathematical models
- Rights
- openAccess
- License
- Derechos Reservados - Universidad Autónoma de Occidente
| id |
REPOUAO2_73b0b4b945578a2fb876e790361f308d |
|---|---|
| oai_identifier_str |
oai:red.uao.edu.co:10614/11407 |
| network_acronym_str |
REPOUAO2 |
| network_name_str |
RED: Repositorio Educativo Digital UAO |
| repository_id_str |
|
| dc.title.eng.fl_str_mv |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| title |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| spellingShingle |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus Mecánica Disco intervertebral Biomecánica - Modelos matemáticos Intervertebral disk Mechanics Biomechanics - Mathematical models |
| title_short |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| title_full |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| title_fullStr |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| title_full_unstemmed |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| title_sort |
Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus |
| dc.creator.fl_str_mv |
Jaramillo Suárez, Héctor Enrique |
| dc.contributor.author.none.fl_str_mv |
Jaramillo Suárez, Héctor Enrique |
| dc.subject.armarc.spa.fl_str_mv |
Mecánica Disco intervertebral Biomecánica - Modelos matemáticos |
| topic |
Mecánica Disco intervertebral Biomecánica - Modelos matemáticos Intervertebral disk Mechanics Biomechanics - Mathematical models |
| dc.subject.armarc.eng.fl_str_mv |
Intervertebral disk Mechanics Biomechanics - Mathematical models |
| description |
Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region |
| publishDate |
2018 |
| dc.date.issued.none.fl_str_mv |
2018-11-07 |
| dc.date.accessioned.none.fl_str_mv |
2019-11-06T14:36:37Z |
| dc.date.available.none.fl_str_mv |
2019-11-06T14:36:37Z |
| dc.type.spa.fl_str_mv |
Artículo de revista |
| dc.type.coar.fl_str_mv |
http://purl.org/coar/resource_type/c_2df8fbb1 |
| dc.type.coarversion.fl_str_mv |
http://purl.org/coar/version/c_970fb48d4fbd8a85 |
| dc.type.coar.eng.fl_str_mv |
http://purl.org/coar/resource_type/c_6501 |
| dc.type.content.eng.fl_str_mv |
Text |
| dc.type.driver.eng.fl_str_mv |
info:eu-repo/semantics/article |
| dc.type.redcol.eng.fl_str_mv |
http://purl.org/redcol/resource_type/ARTREF |
| dc.type.version.eng.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
| format |
http://purl.org/coar/resource_type/c_6501 |
| status_str |
publishedVersion |
| dc.identifier.issn.spa.fl_str_mv |
1024-123X |
| dc.identifier.uri.none.fl_str_mv |
http://hdl.handle.net/10614/11407 |
| dc.identifier.doi.spa.fl_str_mv |
10.1155/2018/1570142 |
| identifier_str_mv |
1024-123X 10.1155/2018/1570142 |
| url |
http://hdl.handle.net/10614/11407 |
| dc.language.iso.eng.fl_str_mv |
eng |
| language |
eng |
| dc.relation.cites.eng.fl_str_mv |
Jaramillo, H. E. (2018). Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus. Mathematical Problems in Engineering, vol. 2018. 10. Article ID 1570142. https://doi.org/10.1155/2018/15701422018 |
| dc.relation.ispartofjournal.eng.fl_str_mv |
Mathematical Problems in Engineering |
| dc.relation.references.none.fl_str_mv |
[1] R. N. Natarajan, J. R.Williams, and G. B. J. Andersson, “Recent advances in analytical modeling of lumbar disc degeneration,” The Spine Journal, vol. 29, no. 23, pp. 2733–2741, 2004. [2] J.-L. Wang, M. Parnianpour, A. Shirazi-Adl, and A. E. Engin, “Viscoelastic finite-element analysis of a lumbar motion segment in combined compression and sagittal flexion: Effect of loading rate,”The Spine Journal, vol. 25, no. 3, pp. 310–318, 2000. [3] R. K. Wilcox, T.O. Boerger, D. J.Allen et al., “Adynamic study of thoracolumbar burst fractures,”The Journal of Bone and Joint Surgery—American Volume, vol. 85, no. 11, pp. 2184–2189, 2003. [4] R. K.Wilcox, D. J. Allen, R. M. Hall, D. Limb, D. C. Barton, and R. A. Dickson, “A dynamic investigation of the burst fracture process using a combined experimental and finite element approach,” European Spine Journal, vol. 13, no. 6, pp. 481–488, 2004. [5] P.Tropiano, L.Thollon, P. J. Arnoux et al., “Using a finite element model to evaluate human injuries application to the HUMOS model in whiplash situation,” The Spine Journal, vol. 29, no. 16, pp. 1709–1716, 2004. [6] C. E. Tschirhart, A. Nagpurkar, and C. M. Whyne, “Effects of tumor location, shape and surface serration on burst fracture risk in themetastatic spine,” Journal of Biomechanics, vol. 37, no. 5, pp. 653–660, 2004. [7] T. Belytschko and R. F. Kulak, “A finite-element method for a solid enclosing an inviscid, incompressible fluid,” Journal of Applied Mechanics, vol. 40, no. 2, pp. 609-610, 1973. [8] S. A. Shirazi-Adl, S. C. Shrivastava, and A. M. Ahmed, “Stress analysis of the lumbar disc-body unit in compression. A threedimensional nonlinear finite element study,” The Spine Journal, vol. 9, no. 2, pp. 120–134, 1984. [9] V. K. Goel, B. T. Monroe, L. G. Gilbertson, and P. Brinckmann, “Interlaminar shear stresses and laminae separation in a disc: Finite element analysis of the l3-l4 motion segment subjected to axial compressive loads,” The Spine Journal, vol. 20, no. 6, pp. 689–698, 1995. [10] H. Schmidt, F. Heuer, U. Simon et al., “Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus,” Clinical Biomechanics, vol. 21, no. 4, pp. 337–344, 2006. [11] F. Ezquerro, F. G. Vacas, S. Postigo, M. Prado, and A. Sim´on, “Calibration of the finite elementmodel of a lumbar functional spinal unit using an optimization technique based on differential evolution,” Medical Engineering & Physics, vol. 33, no. 1, pp. 89–95, 2011. [12] Y. Guan, N. Yoganandan, J. Zhang et al., “Validation of a clinical finite element model of the human lumbosacral spine,” Medical & Biological Engineering & Computing, vol. 44, no. 8, pp. 633–641, 2006. [13] W. M. Park, K. Kim, and Y. H. Kim, “Effects of degenerated intervertebral discs on intersegmental rotations, intradiscal pressures, and facet joint forces of the whole lumbar spine,” Computers in Biology andMedicine, vol. 43, no. 9, pp. 1234–1240, 2013. [14] A.-P. Zhang, H.-M. Wang, S.-L. Xu, and R.-Q. Chen, “Experimental study on the photoelasticity of lumbosacral joint model and finite element,” Chinese Journal of Clinical Rehabilitation, vol. 8, no. 29, pp. 6367–6369, 2004. [15] H. Schmidt, F. Galbusera, A. Rohlmann, T. Zander, and H.-J. Wilke, “Effect of multilevel lumbar disc arthroplasty on spine kinematics and facet joint loads in flexion and extension: A finite element analysis,” European Spine Journal, vol. 21, no. 5, pp. S663–S674, 2012. [16] H. Schmidt, A. Kettler, F. Heuer, U. Simon, L. Claes, and H.-J. Wilke, “Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading,” The Spine Journal, vol. 32, no. 7, pp. 748–755, 2007. [17] T. Liu, K. Khalaf, S. Naserkhaki, andM. El-Rich, “Load-sharing in the lumbosacral spine in neutral standing & flexed postures – A combined finite element and inverse static study,” Journal of Biomechanics, vol. 70, pp. 43–50, 2018. [18] W. Fan and L.-X.Guo, “Finite element investigation of the effect of nucleus removal on vibration characteristics of the lumbar spine under a compressive follower preload,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 78, pp. 342–351, 2018. [19] E. Charriere, F. Sirey, and P. K. Zysset, “Afinite elementmodel of the L5-S1 functional spinal unit: Development and comparison with biomechanical tests in vitro,” ComputerMethods in Biomechanics and Biomedical Engineering, vol. 6, no. 4, pp. 249–261, 2003. [20] C. M. Puttlitz, V. K. Goel, V. C. Traynelis, and C. R. Clark, “A finite element investigation of upper cervical instrumentation,” The Spine Journal, vol. 26, no. 22, pp. 2449–2455, 2001. [21] U. M. Ayturk, B. Gadomski, D. Schuldt, V. Patel, and C. M. Puttlitz, “Modeling degenerative disk disease in the lumbar spine: A combined experimental, constitutive, and computational approach,” Journal of Biomechanical Engineering, vol. 134, no. 10, Article ID 101003, 2012. [22] U. M. Ayturk and C. M. Puttlitz, “Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 14, no. 8, pp. 695–705, 2011. [23] U. M. Ayturk, J. J. Garcia, and C. M. Puttlitz, “The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine,” Journal of Biomechanical Engineering, vol. 132, no. 6, 2010. [24] G. Marini and S. J. Ferguson, “Modelling the influence of heterogeneous annulusmaterial property distribution on intervertebral disk mechanics,” Annals of Biomedical Engineering, vol. 42, no. 8, pp. 1760–1772, 2014. [25] M. Sharabi, K. Wade, and R. Haj-Ali, “Chapter 7 – the mechanical role of collagen fibers in the intervertebral disc,” in Biomechanics of the Spine, F. Galbusera and H.-J.Wilke, Eds., vol. 7, pp. 105–123, 2018. [26] M. Mengoni, K. Vasiljeva, A. C. Jones, S. M. Tarsuslugil, and R. K.Wilcox, “Subject-specificmulti-validation of a finite element model of ovine cervical functional spinal units,” Journal of Biomechanics, vol. 49, no. 2, pp. 259–266, 2016. [27] H. E. Jaramillo, L. G´omez, and J. J. Garc´ıa, “A finite element model of the L4-L5-S1 human spine segment including the heterogeneity and anisotropy of the discs,” Acta of Bioengineering and Biomechanics, vol. 17, no. 2, pp. 15–24, 2015. [28] G. J. M. Meijer, J. Homminga, E. E. G. Hekman, A. G. Veldhuizen, and G. J. Verkerke, “The effect of three-dimensional geometrical changes during adolescent growth on the biomechanics of a spinal motion segment,” Journal of Biomechanics, vol. 43, no. 8, pp. 1590–1597, 2010. [29] J. Huyghe, R. Roos, R. Petterson et al., “Characterisation of intervertebral disc tissue and its substitutes,” Journal of Biomechanics, vol. 39, pp. S27–S28, 2006. [30] D. G. T. Strange, S. T. Fisher, P. C. Boughton, T. J. Kishen, and A. D. Diwan, “Restoration of compressive loading properties of lumbar discs with a nucleus implant-a finite element analysis study,” The Spine Journal, vol. 10, no. 7, pp. 602–609, 2010. [31] N. Bogduk, Clinical Anatomy of the Lumbar Spine & Sacrum, 1995, http://www.lavoisier.fr/livre/notice.asp?id=OKKW2RAORR6OWX [Accessed: 14-Aug-2012]. [32] S. H. Reynolds, The Vertebrate Skeleton, Create Space Independent Publishing Platform, 2013. [33] N. Newell, J. P. Little, A. Christou, M. A. Adams, C. J. Adam, and S. D.Masouros, “Biomechanics of the human intervertebral disc: A review of testing techniques and results,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 69, pp. 420–434, 2017. [34] J. J. Cassidy, A. Hiltner, and E. Baer, “Hierarchical structure of the intervertebral disc,” Connective Tissue Research, vol. 23, no. 1, pp. 75–88, 1989. [35] R. Eberlein, G. A. Holzapfel, and C. A. J. Schulze-Bauer, “An anisotropic model for annulus tissue and enhanced finite element analyses of intact lumbar disc bodies,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 4, no. 3, pp. 209–229, 2001. [36] H. E. Jaramillo, C. M. Puttlitz, K. McGilvray, and J. J. Garc´ıa, “Characterization of the L4-L5-S1 motion segment using the stepwise reduction method,” Journal of Biomechanics, vol. 49, no. 7, pp. 1248–1254, 2016. [37] M. Dreischarf, T. Zander, A. Shirazi-Adl et al., “Comparison of eight published static finite elementmodels of the intact lumbar spine: Predictive power of models improves when combined together,” Journal of Biomechanics, vol. 47, no. 8, pp. 1757–1766, 2014. [38] D. H.Cortes andD.M. Elliott, “Extra-fibrillarmatrixmechanics of annulus fibrosus in tension and compression,” Biomechanics andModeling inMechanobiology, vol. 11, no. 6, pp. 781–790, 2012. [39] D. H. Cortes, W. M. Han, L. J. Smith, and D. M. Elliott, “Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent,” Journal of Orthopaedic Research, vol. 31, no. 11, pp. 1725–1732, 2013. [40] N. T. Jacobs, D. H. Cortes, J. M. Peloquin, E. J. Vresilovic, and D. M. Elliott, “Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent,” Journal of Biomechanics, vol. 47, no. 11, pp. 2540–2546, 2014. [41] N. T. Jacobs, D. H. Cortes, E. J. Vresilovic, and D. M. Elliott, “Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising fromboundary conditions and anisotropy,” Journal of Biomechanical Engineering, vol. 135, no. 2, Article ID 021004, 2013. [42] F. Heuer, H. Schmidt, and H.-J. Wilke, “Stepwise reduction of functional spinal structures increase disc bulge and Surface strains,” Journal of Biomechanics, vol. 41, no. 9, pp. 1953–1960, 2008. [43] F. Heuer, H. Schmidt, L. Claes, and H.-J. Wilke, “Stepwise reduction of functional spinal structures increase vertebral translation and intradiscal pressure,” Journal of Biomechanics, vol. 40, no. 4, pp. 795–803, 2007. [44] F. Heuer, U.Wolfram, H. Schmidt, and H.-J.Wilke, “A method to obtain surface strains of soft tissues using a laser scanning device,” Journal of Biomechanics, vol. 41, no. 11, pp. 2402–2410, 2008. [45] A. Rohlmann, S. Neller, L. Claes, G. Bergmann, and H. J. Wilke, “Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine,” The Spine Journal, vol. 26, no. 24, pp. 557–561, 2001. [46] ““Welcome to Python.org,” Python.org,” Available: https://www.python.org/. [Accessed: 16-Mar-2017]. [47] F. Heuer, H. Schmidt, Z. Klezl, L. Claes, and H.-J.Wilke, “Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle,” Journal of Biomechanics, vol. 40, no. 2, pp. 271–280, 2007. [48] J. Q. Campbell and A. J. Petrella, “Automated finite element modeling of the lumbar spine: Using a statistical shape model to generate a virtual population of models,” Journal of Biomechanics, vol. 49, no. 13, pp. 2593–2599, 2016. [49] S. Ebara, J. C. Iatridis, L. A. Setton, R. J. Foster, C.VanMow, and M.Weidenbaum, “Tensile properties of nondegenerate human lumbar anulus fibrosus,” The Spine Journal, vol. 21, no. 4, pp. 452–461, 1996. [50] Y. Fujita,N. A.Duncan, andJ. C.Lotz, “Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent,” Journal of Orthopaedic Research, vol. 15, no. 6, pp. 814–819, 1997. [51] D. L. Skaggs, M. Weidenbaum, J. C. Latridis, A. Ratcliffe, and V. C. Mow, “Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus,” The Spine Journal, vol. 19, no. 12, pp. 1310–1319, 1994. [52] T. P. Green, M. A. Adams, and P. Dolan, “Tensile properties of the annulus fibrosus,” European Spine Journal, vol. 2, no. 4, pp. 209–214, 1993. [53] G. D. O’Connell, H. L. Guerin, and D. M. Elliott, “Theoretical and uniaxial experimental evaluation of human annulus fibrosus degeneration,” Journal of Biomechanical Engineering, vol. 131, no. 11, Article ID 111007, 2009. [54] J. C. Iatridis, J. P. Laible, and M. H. Krag, “Influence of fixed charge density magnitude and distribution on the intervertebral disc: Applications of a poroelastic and chemical electric (PEACE)model,” Journal of Biomechanical Engineering, vol. 125, no. 1, pp. 12–24, 2003. [55] S. V. Beekmans, K. S. Emanuel, T. H. Smit, and D. Iannuzzi, “Stiffening of the nucleus pulposus upon axial loading of the intervertebral disc: An experimental in situ study,” JOR Spine, vol. 1, no. 1, p. e1005, 2018. |
| dc.rights.spa.fl_str_mv |
Derechos Reservados - Universidad Autónoma de Occidente |
| dc.rights.coar.fl_str_mv |
http://purl.org/coar/access_right/c_abf2 |
| dc.rights.uri.eng.fl_str_mv |
https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| dc.rights.accessrights.eng.fl_str_mv |
info:eu-repo/semantics/openAccess |
| dc.rights.creativecommons.spa.fl_str_mv |
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0) |
| rights_invalid_str_mv |
Derechos Reservados - Universidad Autónoma de Occidente https://creativecommons.org/licenses/by-nc-nd/4.0/ Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0) http://purl.org/coar/access_right/c_abf2 |
| eu_rights_str_mv |
openAccess |
| dc.format.eng.fl_str_mv |
application/pdf |
| dc.format.extent.spa.fl_str_mv |
10 páginas |
| dc.coverage.spatial.none.fl_str_mv |
Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí |
| dc.publisher.eng.fl_str_mv |
Hindawi |
| institution |
Universidad Autónoma de Occidente |
| bitstream.url.fl_str_mv |
https://red.uao.edu.co/bitstreams/266116b7-e3f9-4433-a8ff-856a13c8c307/download https://red.uao.edu.co/bitstreams/4bdb60b1-9599-4416-8390-38f64ff55fa2/download https://red.uao.edu.co/bitstreams/d703b5d2-f496-4d8b-ad1c-70766246a94e/download https://red.uao.edu.co/bitstreams/c927963c-ce71-4cd5-844c-4eb21ffbd9ed/download https://red.uao.edu.co/bitstreams/92223744-8448-417a-a49b-b5c29ebbbb25/download |
| bitstream.checksum.fl_str_mv |
4460e5956bc1d1639be9ae6146a50347 20b5ba22b1117f71589c7318baa2c560 e75f3babc50601ea5985ab27e1620051 703819db79c4e034384ea72db0df3402 84b1d2ba5c0a90e3ababbecf2914487f |
| bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 MD5 |
| repository.name.fl_str_mv |
Repositorio Digital Universidad Autonoma de Occidente |
| repository.mail.fl_str_mv |
repositorio@uao.edu.co |
| _version_ |
1814260089482117120 |
| spelling |
Jaramillo Suárez, Héctor Enriquevirtual::2723-1Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-06T14:36:37Z2019-11-06T14:36:37Z2018-11-071024-123Xhttp://hdl.handle.net/10614/1140710.1155/2018/1570142Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed of the nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25° on the outer boundary to 46° on the inner boundary, measuring it with respect to the transverse plane. The mechanical constants were taken from the reported literature. The range of motion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear regionapplication/pdf10 páginasengHindawiDerechos 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_abf2Evaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosusArtículo 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_970fb48d4fbd8a85MecánicaDisco intervertebralBiomecánica - Modelos matemáticosIntervertebral diskMechanicsBiomechanics - Mathematical modelsJaramillo, H. E. (2018). Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus. Mathematical Problems in Engineering, vol. 2018. 10. Article ID 1570142. https://doi.org/10.1155/2018/15701422018Mathematical Problems in Engineering[1] R. N. Natarajan, J. R.Williams, and G. B. J. Andersson, “Recent advances in analytical modeling of lumbar disc degeneration,” The Spine Journal, vol. 29, no. 23, pp. 2733–2741, 2004.[2] J.-L. Wang, M. Parnianpour, A. Shirazi-Adl, and A. E. Engin, “Viscoelastic finite-element analysis of a lumbar motion segment in combined compression and sagittal flexion: Effect of loading rate,”The Spine Journal, vol. 25, no. 3, pp. 310–318, 2000.[3] R. K. Wilcox, T.O. Boerger, D. J.Allen et al., “Adynamic study of thoracolumbar burst fractures,”The Journal of Bone and Joint Surgery—American Volume, vol. 85, no. 11, pp. 2184–2189, 2003.[4] R. K.Wilcox, D. J. Allen, R. M. Hall, D. Limb, D. C. Barton, and R. A. Dickson, “A dynamic investigation of the burst fracture process using a combined experimental and finite element approach,” European Spine Journal, vol. 13, no. 6, pp. 481–488, 2004.[5] P.Tropiano, L.Thollon, P. J. Arnoux et al., “Using a finite element model to evaluate human injuries application to the HUMOS model in whiplash situation,” The Spine Journal, vol. 29, no. 16, pp. 1709–1716, 2004.[6] C. E. Tschirhart, A. Nagpurkar, and C. M. Whyne, “Effects of tumor location, shape and surface serration on burst fracture risk in themetastatic spine,” Journal of Biomechanics, vol. 37, no. 5, pp. 653–660, 2004.[7] T. Belytschko and R. F. Kulak, “A finite-element method for a solid enclosing an inviscid, incompressible fluid,” Journal of Applied Mechanics, vol. 40, no. 2, pp. 609-610, 1973.[8] S. A. Shirazi-Adl, S. C. Shrivastava, and A. M. Ahmed, “Stress analysis of the lumbar disc-body unit in compression. A threedimensional nonlinear finite element study,” The Spine Journal, vol. 9, no. 2, pp. 120–134, 1984.[9] V. K. Goel, B. T. Monroe, L. G. Gilbertson, and P. Brinckmann, “Interlaminar shear stresses and laminae separation in a disc: Finite element analysis of the l3-l4 motion segment subjected to axial compressive loads,” The Spine Journal, vol. 20, no. 6, pp. 689–698, 1995.[10] H. Schmidt, F. Heuer, U. Simon et al., “Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus,” Clinical Biomechanics, vol. 21, no. 4, pp. 337–344, 2006.[11] F. Ezquerro, F. G. Vacas, S. Postigo, M. Prado, and A. Sim´on, “Calibration of the finite elementmodel of a lumbar functional spinal unit using an optimization technique based on differential evolution,” Medical Engineering & Physics, vol. 33, no. 1, pp. 89–95, 2011.[12] Y. Guan, N. Yoganandan, J. Zhang et al., “Validation of a clinical finite element model of the human lumbosacral spine,” Medical & Biological Engineering & Computing, vol. 44, no. 8, pp. 633–641, 2006.[13] W. M. Park, K. Kim, and Y. H. Kim, “Effects of degenerated intervertebral discs on intersegmental rotations, intradiscal pressures, and facet joint forces of the whole lumbar spine,” Computers in Biology andMedicine, vol. 43, no. 9, pp. 1234–1240, 2013.[14] A.-P. Zhang, H.-M. Wang, S.-L. Xu, and R.-Q. Chen, “Experimental study on the photoelasticity of lumbosacral joint model and finite element,” Chinese Journal of Clinical Rehabilitation, vol. 8, no. 29, pp. 6367–6369, 2004.[15] H. Schmidt, F. Galbusera, A. Rohlmann, T. Zander, and H.-J. Wilke, “Effect of multilevel lumbar disc arthroplasty on spine kinematics and facet joint loads in flexion and extension: A finite element analysis,” European Spine Journal, vol. 21, no. 5, pp. S663–S674, 2012.[16] H. Schmidt, A. Kettler, F. Heuer, U. Simon, L. Claes, and H.-J. Wilke, “Intradiscal pressure, shear strain, and fiber strain in the intervertebral disc under combined loading,” The Spine Journal, vol. 32, no. 7, pp. 748–755, 2007.[17] T. Liu, K. Khalaf, S. Naserkhaki, andM. El-Rich, “Load-sharing in the lumbosacral spine in neutral standing & flexed postures – A combined finite element and inverse static study,” Journal of Biomechanics, vol. 70, pp. 43–50, 2018.[18] W. Fan and L.-X.Guo, “Finite element investigation of the effect of nucleus removal on vibration characteristics of the lumbar spine under a compressive follower preload,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 78, pp. 342–351, 2018.[19] E. Charriere, F. Sirey, and P. K. Zysset, “Afinite elementmodel of the L5-S1 functional spinal unit: Development and comparison with biomechanical tests in vitro,” ComputerMethods in Biomechanics and Biomedical Engineering, vol. 6, no. 4, pp. 249–261, 2003.[20] C. M. Puttlitz, V. K. Goel, V. C. Traynelis, and C. R. Clark, “A finite element investigation of upper cervical instrumentation,” The Spine Journal, vol. 26, no. 22, pp. 2449–2455, 2001.[21] U. M. Ayturk, B. Gadomski, D. Schuldt, V. Patel, and C. M. Puttlitz, “Modeling degenerative disk disease in the lumbar spine: A combined experimental, constitutive, and computational approach,” Journal of Biomechanical Engineering, vol. 134, no. 10, Article ID 101003, 2012.[22] U. M. Ayturk and C. M. Puttlitz, “Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 14, no. 8, pp. 695–705, 2011.[23] U. M. Ayturk, J. J. Garcia, and C. M. Puttlitz, “The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine,” Journal of Biomechanical Engineering, vol. 132, no. 6, 2010.[24] G. Marini and S. J. Ferguson, “Modelling the influence of heterogeneous annulusmaterial property distribution on intervertebral disk mechanics,” Annals of Biomedical Engineering, vol. 42, no. 8, pp. 1760–1772, 2014.[25] M. Sharabi, K. Wade, and R. Haj-Ali, “Chapter 7 – the mechanical role of collagen fibers in the intervertebral disc,” in Biomechanics of the Spine, F. Galbusera and H.-J.Wilke, Eds., vol. 7, pp. 105–123, 2018.[26] M. Mengoni, K. Vasiljeva, A. C. Jones, S. M. Tarsuslugil, and R. K.Wilcox, “Subject-specificmulti-validation of a finite element model of ovine cervical functional spinal units,” Journal of Biomechanics, vol. 49, no. 2, pp. 259–266, 2016.[27] H. E. Jaramillo, L. G´omez, and J. J. Garc´ıa, “A finite element model of the L4-L5-S1 human spine segment including the heterogeneity and anisotropy of the discs,” Acta of Bioengineering and Biomechanics, vol. 17, no. 2, pp. 15–24, 2015.[28] G. J. M. Meijer, J. Homminga, E. E. G. Hekman, A. G. Veldhuizen, and G. J. Verkerke, “The effect of three-dimensional geometrical changes during adolescent growth on the biomechanics of a spinal motion segment,” Journal of Biomechanics, vol. 43, no. 8, pp. 1590–1597, 2010.[29] J. Huyghe, R. Roos, R. Petterson et al., “Characterisation of intervertebral disc tissue and its substitutes,” Journal of Biomechanics, vol. 39, pp. S27–S28, 2006.[30] D. G. T. Strange, S. T. Fisher, P. C. Boughton, T. J. Kishen, and A. D. Diwan, “Restoration of compressive loading properties of lumbar discs with a nucleus implant-a finite element analysis study,” The Spine Journal, vol. 10, no. 7, pp. 602–609, 2010.[31] N. Bogduk, Clinical Anatomy of the Lumbar Spine & Sacrum, 1995, http://www.lavoisier.fr/livre/notice.asp?id=OKKW2RAORR6OWX [Accessed: 14-Aug-2012].[32] S. H. Reynolds, The Vertebrate Skeleton, Create Space Independent Publishing Platform, 2013.[33] N. Newell, J. P. Little, A. Christou, M. A. Adams, C. J. Adam, and S. D.Masouros, “Biomechanics of the human intervertebral disc: A review of testing techniques and results,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 69, pp. 420–434, 2017.[34] J. J. Cassidy, A. Hiltner, and E. Baer, “Hierarchical structure of the intervertebral disc,” Connective Tissue Research, vol. 23, no. 1, pp. 75–88, 1989.[35] R. Eberlein, G. A. Holzapfel, and C. A. J. Schulze-Bauer, “An anisotropic model for annulus tissue and enhanced finite element analyses of intact lumbar disc bodies,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 4, no. 3, pp. 209–229, 2001.[36] H. E. Jaramillo, C. M. Puttlitz, K. McGilvray, and J. J. Garc´ıa, “Characterization of the L4-L5-S1 motion segment using the stepwise reduction method,” Journal of Biomechanics, vol. 49, no. 7, pp. 1248–1254, 2016.[37] M. Dreischarf, T. Zander, A. Shirazi-Adl et al., “Comparison of eight published static finite elementmodels of the intact lumbar spine: Predictive power of models improves when combined together,” Journal of Biomechanics, vol. 47, no. 8, pp. 1757–1766, 2014.[38] D. H.Cortes andD.M. Elliott, “Extra-fibrillarmatrixmechanics of annulus fibrosus in tension and compression,” Biomechanics andModeling inMechanobiology, vol. 11, no. 6, pp. 781–790, 2012.[39] D. H. Cortes, W. M. Han, L. J. Smith, and D. M. Elliott, “Mechanical properties of the extra-fibrillar matrix of human annulus fibrosus are location and age dependent,” Journal of Orthopaedic Research, vol. 31, no. 11, pp. 1725–1732, 2013.[40] N. T. Jacobs, D. H. Cortes, J. M. Peloquin, E. J. Vresilovic, and D. M. Elliott, “Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear, anisotropic, and time-dependent,” Journal of Biomechanics, vol. 47, no. 11, pp. 2540–2546, 2014.[41] N. T. Jacobs, D. H. Cortes, E. J. Vresilovic, and D. M. Elliott, “Biaxial tension of fibrous tissue: using finite element methods to address experimental challenges arising fromboundary conditions and anisotropy,” Journal of Biomechanical Engineering, vol. 135, no. 2, Article ID 021004, 2013.[42] F. Heuer, H. Schmidt, and H.-J. Wilke, “Stepwise reduction of functional spinal structures increase disc bulge and Surface strains,” Journal of Biomechanics, vol. 41, no. 9, pp. 1953–1960, 2008.[43] F. Heuer, H. Schmidt, L. Claes, and H.-J. Wilke, “Stepwise reduction of functional spinal structures increase vertebral translation and intradiscal pressure,” Journal of Biomechanics, vol. 40, no. 4, pp. 795–803, 2007.[44] F. Heuer, U.Wolfram, H. Schmidt, and H.-J.Wilke, “A method to obtain surface strains of soft tissues using a laser scanning device,” Journal of Biomechanics, vol. 41, no. 11, pp. 2402–2410, 2008.[45] A. Rohlmann, S. Neller, L. Claes, G. Bergmann, and H. J. Wilke, “Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine,” The Spine Journal, vol. 26, no. 24, pp. 557–561, 2001.[46] ““Welcome to Python.org,” Python.org,” Available: https://www.python.org/. [Accessed: 16-Mar-2017].[47] F. Heuer, H. Schmidt, Z. Klezl, L. Claes, and H.-J.Wilke, “Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle,” Journal of Biomechanics, vol. 40, no. 2, pp. 271–280, 2007.[48] J. Q. Campbell and A. J. Petrella, “Automated finite element modeling of the lumbar spine: Using a statistical shape model to generate a virtual population of models,” Journal of Biomechanics, vol. 49, no. 13, pp. 2593–2599, 2016.[49] S. Ebara, J. C. Iatridis, L. A. Setton, R. J. Foster, C.VanMow, and M.Weidenbaum, “Tensile properties of nondegenerate human lumbar anulus fibrosus,” The Spine Journal, vol. 21, no. 4, pp. 452–461, 1996.[50] Y. Fujita,N. A.Duncan, andJ. C.Lotz, “Radial tensile properties of the lumbar annulus fibrosus are site and degeneration dependent,” Journal of Orthopaedic Research, vol. 15, no. 6, pp. 814–819, 1997.[51] D. L. Skaggs, M. Weidenbaum, J. C. Latridis, A. Ratcliffe, and V. C. Mow, “Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus,” The Spine Journal, vol. 19, no. 12, pp. 1310–1319, 1994.[52] T. P. Green, M. A. Adams, and P. Dolan, “Tensile properties of the annulus fibrosus,” European Spine Journal, vol. 2, no. 4, pp. 209–214, 1993.[53] G. D. O’Connell, H. L. Guerin, and D. M. Elliott, “Theoretical and uniaxial experimental evaluation of human annulus fibrosus degeneration,” Journal of Biomechanical Engineering, vol. 131, no. 11, Article ID 111007, 2009.[54] J. C. Iatridis, J. P. Laible, and M. H. Krag, “Influence of fixed charge density magnitude and distribution on the intervertebral disc: Applications of a poroelastic and chemical electric (PEACE)model,” Journal of Biomechanical Engineering, vol. 125, no. 1, pp. 12–24, 2003. [55] S. V. Beekmans, K. S. Emanuel, T. H. Smit, and D. Iannuzzi, “Stiffening of the nucleus pulposus upon axial loading of the intervertebral disc: An experimental in situ study,” JOR Spine, vol. 1, no. 1, p. e1005, 2018.Publicationada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2723-1ada2f35e-57bd-4bbb-91d3-e197573bfab8virtual::2723-1https://scholar.google.com.co/citations?user=GEzrsjQAAAAJ&hl=esvirtual::2723-10000-0002-7324-9478virtual::2723-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000144967virtual::2723-1CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://red.uao.edu.co/bitstreams/266116b7-e3f9-4433-a8ff-856a13c8c307/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81665https://red.uao.edu.co/bitstreams/4bdb60b1-9599-4416-8390-38f64ff55fa2/download20b5ba22b1117f71589c7318baa2c560MD53ORIGINALEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdfEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdfTexto archivo completo del artículo de revista, PDFapplication/pdf5440754https://red.uao.edu.co/bitstreams/d703b5d2-f496-4d8b-ad1c-70766246a94e/downloade75f3babc50601ea5985ab27e1620051MD54TEXTEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdf.txtEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdf.txtExtracted texttext/plain41652https://red.uao.edu.co/bitstreams/c927963c-ce71-4cd5-844c-4eb21ffbd9ed/download703819db79c4e034384ea72db0df3402MD55THUMBNAILEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdf.jpgEvaluation of the use of the Yeoh and Mooney-Rivlin functions as strain energy density functions for the ground substance material of the annulus fibrosus.pdf.jpgGenerated Thumbnailimage/jpeg14164https://red.uao.edu.co/bitstreams/92223744-8448-417a-a49b-b5c29ebbbb25/download84b1d2ba5c0a90e3ababbecf2914487fMD5610614/11407oai:red.uao.edu.co:10614/114072024-03-07 09:57:11.064https://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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 |