Research Papers

The Mechanical Role of the Radial Fiber Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study

[+] Author and Article Information
Mirit Sharabi, Aviad Levi-Sasson, Roza Wolfson

The Fleischman Faculty of Engineering,
School of Mechanical Engineering,
Tel Aviv University,
Tel Aviv 69978, Israel

Kelly R. Wade, Hans-Joachim Wilke

Institute of Orthopaedic
Research and Biomechanics,
University of Ulm,
Ulm 89081, Germany

Fabio Galbusera

Institute of Orthopaedic
Research and Biomechanics,
University of Ulm,
Ulm 89081, Germany;
IRCCS Galeazzi Orthopaedic Institute,
Milan 20161, Italy

Dafna Benayahu

Department of Cell and Developmental Biology,
Sackler School of Medicine,
Tel Aviv University,
Tel Aviv 69978, Israel

Rami Haj-Ali

The Fleischman Faculty of Engineering,
School of Mechanical Engineering,
Tel Aviv University,
Tel Aviv 69978, Israel
e-mail: rami98@tau.ac.il

1Corresponding author.

Manuscript received April 29, 2018; final manuscript received October 4, 2018; published online December 5, 2018. Assoc. Editor: Kyle Allen.

J Biomech Eng 141(2), 021006 (Dec 05, 2018) (11 pages) Paper No: BIO-18-1208; doi: 10.1115/1.4041769 History: Received April 29, 2018; Revised October 04, 2018

The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3–L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

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Wade, K. R. , Robertson, P. A. , and Broom, N. D. , 2011, “ A Fresh Look at the Nucleus-Endplate Region: New Evidence for Significant Structural Integration,” Eur. Spine J., 20(8), pp. 1225–1232. [PubMed]
Bogduk, N. , 2005, Clinical Anatomy of the Lumbar Spine and Sacrum, 4th ed., Elsevier, Amsterdam, The Netherlands.
Rodrigues, S. A. , Wade, K. R. , Thambyah, A. , and Broom, N. D. , 2012, “ Micromechanics of Annulus-End Plate Integration in the Intervertebral Disc,” Spine J., 12(2), pp. 143–150. [PubMed]
Marchand, F. , and Ahmed, A. M. , 1990, “ Investigation of the Laminate Structure of Lumbar Disc Anulus Fibrosus,” Spine, 15(5), pp. 402–410. [PubMed]
Holzapfel, G. A. , Schulze-Bauer, C. , Feigl, G. , and Regitnig, P. , 2005, “ Single Lamellar Mechanics of the Human Lumbar Anulus Fibrosus,” Biomech. Model. Mechanobiol., 3(3), pp. 125–140. [PubMed]
Schollum, M. L. , Robertson, P. A. , and Broom, N. D. , 2010, “ How Age Influences Unravelling Morphology of Annular Lamellae—A Study of Interfibre Cohesivity in the Lumbar Disc,” J. Anat., 216(3), pp. 310–319. [PubMed]
Schollum, M. L. , Robertson, P. A. , and Broom, N. D. , 2009, “ A Microstructural Investigation of Intervertebral Disc Lamellar Connectivity: Detailed Analysis of the Translamellar Bridges,” J. Anat., 214(6), pp. 805–816. [PubMed]
Schollum, M. L. , Robertson, P. A. , and Broom, N. D. , 2008, “ ISSLS Prize Winner: Microstructure and Mechanical Disruption of the Lumbar Disc Annulus—Part I: A Microscopic Investigation of the Translamellar Bridging Network,” Spine, 33(25), pp. 2702–2710. [PubMed]
Han, S. K. , Chen, C. W. , Wierwille, J. , Chen, Y. , and Hsieh, A. H. , 2015, “ Three Dimensional Mesoscale Analysis of Translamellar Cross‐Bridge Morphologies in the Annulus Fibrosus Using Optical Coherence Tomography,” J. Orthop. Res., 33(3), pp. 304–311. [PubMed]
Smith, L. J. , and Elliott, D. M. , 2011, “ Formation of Lamellar Cross Bridges in the Annulus Fibrosus of the Intervertebral Disc Is a Consequence of Vascular Regression,” Matrix Biol., 30(4), pp. 267–274. [PubMed]
Pezowicz, C. A. , Robertson, P. A. , and Broom, N. D. , 2006, “ The Structural Basis of Interlamellar Cohesion in the Intervertebral Disc Wall,” J. Anat., 208(3), pp. 317–330. [PubMed]
Yu, J. , Tirlapur, U. , Fairbank, J. , Handford, P. , Roberts, S. , Winlove, C. P. , Cui, Z. , and Urban, J. , 2007, “ Microfibrils, Elastin Fibres and Collagen Fibres in the Human Intervertebral Disc and Bovine Tail Disc,” J. Anat., 210(4), pp. 460–471. [PubMed]
Yu, J. , Peter, C. , Roberts, S. , and Urban, J. P. , 2002, “ Elastic Fibre Organization in the Intervertebral Discs of the Bovine Tail,” J. Anat., 201(6), pp. 465–475. [PubMed]
Melrose, J. , Smith, S. M. , Appleyard, R. C. , and Little, C. B. , 2008, “ Aggrecan, Versican and Type VI Collagen Are Components of Annular Translamellar Crossbridges in the Intervertebral Disc,” Eur. Spine J., 17(2), pp. 314–324. [PubMed]
Tavakoli, J. , Elliott, D. M. , and Costi, J. J. , 2016, “ The Structure and Mechanical Function of the Inter-Lamellar Matrix of the Annulus Fibrosus in the Disc,” J. Orthop. Res., 34(8), pp. 1307–1315. [PubMed]
Tavakoli, J. , and Costi, J. J. , 2018, “ New Insights Into the Viscoelastic and Failure Mechanical Properties of the Elastic Fiber Network of the Inter-Lamellar Matrix in the Annulus Fibrosus of the Disc,” Acta Biomater., 77, pp. 292–300.
Tavakoli, J. , Elliott, D. M. , and Costi, J. J. , 2017, “ The Ultra-Structural Organization of the Elastic Network in the Intra- and Inter-Lamellar Matrix of the Intervertebral Disc,” Acta Biomater., 58, pp. 269–277. [PubMed]
Yu, J. , Schollum, M. L. , Wade, K. R. , Broom, N. D. , and Urban, J. P. , 2015, “ ISSLS Prize Winner: A Detailed Examination of the Elastic Network Leads to a New Understanding of Annulus Fibrosus Organization,” Spine, 40, pp. 1149–1157. [PubMed]
Vernon-Roberts, B. , Fazzalari, N. L. , and Manthey, B. A. , 1997, “ Pathogenesis of Tears of the Anulus Investigated by Multiple‐Level Transaxial Analysis of the T12‐L1 Disc,” Spine, 22(22), pp. 2641–2646. [PubMed]
Schmidt, H. , Galbusera, F. , Rohlmann, A. , Zander, T. , and Wilke, H.-J. , 2012, “ Effect of Multilevel Lumbar Disc Arthroplasty on Spine Kinematics and Facet Joint Loads in Flexion and Extension: A Finite Element Analysis,” Eur. Spine J., 21(S5), pp. 663–674.
Schmidt, H. , Kettler, A. , Rohlmann, A. , Claes, L. , and Wilke, H.-J. , 2007, “ The Risk of Disc Prolapses With Complex Loading in Different Degrees of Disc Degeneration—A Finite Element Analysis,” Clin. Biomech., 22(9), pp. 988–998.
Schmidt, H. , Heuer, F. , Simon, U. , Kettler, A. , Rohlmann, A. , Claes, L. , and Wilke, H.-J. , 2006, “ Application of a New Calibration Method for a Three-Dimensional Finite Element Model of a Human Lumbar Annulus Fibrosus,” Clin. Biomech., 21(4), pp. 337–344.
Dreischarf, M. , Zander, T. , Shirazi-Adl, A. , Puttlitz, C. , Adam, C. , Chen, C. , 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. , and Schmidt, H. , 2014, “ Comparison of Eight Published Static Finite Element Models of the Intact Lumbar Spine: Predictive Power of Models Improves When Combined Together,” J. Biomech., 47(8), pp. 1757–1766. [PubMed]
Moramarco, V. , del Palomar, A. P. , Pappalettere, C. , and Doblaré, M. , 2010, “ An Accurate Validation of a Computational Model of a Human Lumbosacral Segment,” J. Biomech., 43(2), pp. 334–342. [PubMed]
Niemeyer, F. , Wilke, H.-J. , and Schmidt, H. , 2012, “ Geometry Strongly Influences the Response of Numerical Models of the Lumbar Spine—A Probabilistic Finite Element Analysis,” J. Biomech., 45(8), pp. 1414–1423. [PubMed]
Peng, X. , Guo, Z. , and Moran, B. , 2006, “ An Anisotropic Hyperelastic Constitutive Model With Fiber-Matrix Shear Interaction for the Human Annulus Fibrosus,” ASME J. Appl. Mech., 73(5), pp. 815–824.
Caner, F. C. , Guo, Z. , Moran, B. , Bažant, Z. P. , and Carol, I. , 2007, “ Hyperelastic Anisotropic Microplane Constitutive Model for Annulus Fibrosus,” ASME J. Biomech. Eng., 129(5), pp. 632–641.
Hollingsworth, N. T. , and Wagner, D. R. , 2011, “ Modeling Shear Behavior of the Annulus Fibrosus,” J. Mech. Behav. Biomed. Mater., 4(7), pp. 1103–1114. [PubMed]
Reutlinger, C. , Bürki, A. , Brandejsky, V. , Ebert, L. , and Büchler, P. , 2014, “ Specimen Specific Parameter Identification of Ovine Lumbar Intervertebral Discs: On the Influence of Fibre–Matrix and Fibre–Fibre Shear Interactions,” J. Mech. Behav. Biomed. Mater., 30, pp. 279–289. [PubMed]
Eberlein, R. , Holzapfel, G. A. , and Schulze-Bauer, C. A. , 2001, “ An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies,” Comput. Methods Biomech. Biomed. Eng., 4, pp. 209–229.
Shirazi-Adl, S. A. , Shrivastava, S. C. , and Ahmed, A. M. , 1984, “ Stress Analysis of the Lumbar Disc-Body Unit in Compression. A Three-Dimensional Nonlinear Finite Element Study,” Spine, 9(2), p. 120. [PubMed]
Goel, V. , Monroe, B. , Gilbertson, L. , and Brinckmann, P. , 1995, “ Interlaminar Shear Stresses and Laminae Separation in a Disc: Finite Element Analysis of the L3-L4 Motion Segment Subjected to Axial Compressive Loads,” Spine, 20(6), pp. 689–698. [PubMed]
Mengoni, M. , Luxmoore, B. J. , Wijayathunga, V. N. , Jones, A. C. , Broom, N. D. , and Wilcox, R. K. , 2015, “ Derivation of Inter-Lamellar Behaviour of the Intervertebral Disc Annulus,” J. Mech. Behav. Biomed. Mater., 48, pp. 164–172. [PubMed]
Labus, K. M. , Han, S. K. , Hsieh, A. H. , and Puttlitz, C. M. , 2014, “ A Computational Model to Describe the Regional Interlamellar Shear of the Annulus Fibrosus,” ASME J. Biomech. Eng., 136(5), p. 051009.
Luxmoore, B. , Wijayathunga, V. , Rehman, S. , Wade, K. , Rodrigues, S. , Broom, N. , and Wilcox, R. K. , 2012, “ Investigating the Mechanical Role of Cross-Bridging in the Annulus Fibrosus Using Finite Element Analysis,” 58th Annual Meeting of Orthopaedic Research Society, San Francisco, CA, p. 2164.
Luxmoore, B. J. , 2013, Computational Simulation of the Intervertebral Disc, The University of Leeds, Leeds, UK.
Mengoni, M. , Wijayathunga, V. N. , Jones, A. C. , and Wilcox, R. K. , 2013, “ Structural Modelling of the Annulus Fibrosus-an Anisotropic Hyperelastic Model Approach at the Lamellar Level,” Third International Conference on Mathematical and Computational Biomedical Engineering (CMBE), Hong Kong, China, Dec. 16–18. https://www.researchgate.net/publication/260122074_Structural_modelling_of_the_annulus_fibrosus_-_an_anisotropic_hyperelastic_model_approach_at_the_lamellar_level
Yusupov, R. , 2011, Nonlinear Finite Element Analysis for Normal and Pathological Mechanical Behavior of the Lumbar Spine, Tel Aviv University, Tel-Aviv, Israel.
Platzer, W. , 2009, Color Atlas of Human Anatomy: Locomotor System, 6th ed., Theime, New York.
Schünke, M. , Schulte, E. , and Schumacher, U. , 2006, General Anatomy and Musculoskeletal System (THIEME Atlas of Anatomy), 1st ed., Thieme Medical Pblishers, New York, pp. 100–142.
White, A. A. , and Panjabi, M. M. , 1990, Clinical Biomechanics of the Spine, Lippincott, Philadelphia, PA.
Clemente, C. D. , 1997, Anatomy: A Regional Atlas of the Human Body, 4th ed., Williams & Wilkins, Baltimore, MA, p. 132.
Jaumard, N. V. , Welch, W. C. , and Winkelstein, B. A. , 2011, “ Spinal Facet Joint Biomechanics and Mechanotransduction in Normal, Injury and Degenerative Conditions,” ASME J. Biomech. Eng., 133(7), p. 071010.
Goto, K. , Tajima, N. , Chosa, E. , Totoribe, K. , Kuroki, H. , Arizumi, Y. , and Arai, T. , 2002, “ Mechanical Analysis of the Lumbar Vertebrae in a Three-Dimensional Finite Element Method Model in Which Intradiscal Pressure in the Nucleus Pulposus Was Used to Establish the Model,” J. Orthop. Sci., 7(2), pp. 243–246. [PubMed]
Humzah, M. , and Soames, R. , 1988, “ Human Intervertebral Disc: Structure and Function,” Anat. Rec., 220(4), pp. 337–356. [PubMed]
Wade, K. R. , Robertson, P. A. , and Broom, N. D. , 2012, “ On the Extent and Nature of Nucleus-Annulus Integration,” Spine, 37(21), pp. 1826–1833. [PubMed]
Taylor, T. , Ghosh, P. , and Bushell, G. , 1981, “ The Contribution of the Intervertebral Disc to the Scoliotic Deformity,” Clin. Orthop. Relat. Res., 156, pp. 79–90.
Tsuji, H. , Hirano, N. , Ohshima, H. , Ishihara, H. , Terahata, N. , and Motoe, T. , 1993, “ Structural Variation of the Anterior and Posterior Anulus Fibrosus in the Development of Human Lumbar Intervertebral Disc—A Risk Factor for Intervertebral Disc Rupture,” Spine, 18(2), pp. 204–210. [PubMed]
Baek, G. H. , Carlin, G. J. , Vogrin, T. M. , Woo, S. L. , and Harner, C. D. , 1998, “ Quantitative Analysis of Collagen Fibrils of Human Cruciate and Meniscofemoral Ligaments,” Clin. Orthop. Relat. Res., 357, pp. 205–211.
Han, W. M. , Nerurkar, N. L. , Smith, L. J. , Jacobs, N. T. , Mauck, R. L. , and Elliott, D. M. , 2012, “ Multi-Scale Structural and Tensile Mechanical Response of Annulus Fibrosus to Osmotic Loading,” Ann. Biomed. Eng., 40(7), pp. 1610–1621. [PubMed]
Sharabi, M. , Wade, K. R. , Galbusera, F. , Rasche, V. , Haj-Ali, R. , and Wilke, H.-J. , 2018, “ Three-Dimensional Microstructural Reconstruction of the Ovine Intervertebral Disc Using Ultra-High Field MRI,” Spine J. (in press).
Lu, Y. M. , Hutton, W. C. , and Gharpuray, V. M. , 1996, “ Do Bending, Twisting, and Diurnal Fluid Changes in the Disc Affect the Propensity to Prolapse? A Viscoelastic Finite Element Model,” Spine, 21(22), pp. 2570–2579. [PubMed]
Goel, V. K. , Kong, W. , Han, J. S. , Weinstein, J. N. , and Gilbertson, L. G. , 1993, “ A Combined Finite Element and Optimization Investigation of Lumbar Spine Mechanics With and Without Muscles,” Spine, 18(11), p. 1531. [PubMed]
Totoribe, K. , Tajima, N. , and Chosa, E. , 1999, “ A Biomechanical Study of Posterolateral Lumbar Fusion Using a Three-Dimensional Nonlinear Finite Element Method,” J. Orthop. Sci., 4(2), pp. 115–126. [PubMed]
Wu, H.-C. , and Yao, R.-F. , 1976, “ Mechanical Behavior of the Human Annulus Fibrosus,” J. Biomech., 9(1), pp. 1–7. [PubMed]
Shirazi-Adl, A. , Ahmed, A. , and Shrivastava, S. , 1986, “ A Finite Element Study of a Lumbar Motion Segment Subjected to Pure Sagittal Plane Moments,” J. Biomech., 19(4), pp. 331–350. [PubMed]
Chen, C.-S. , Cheng, C.-K. , Liu, C.-L. , and Lo, W.-H. , 2001, “ Stress Analysis of the Disc Adjacent to Interbody Fusion in Lumbar Spine,” Med. Eng. Phys., 23(7), pp. 485–493.
Chazal, J. , Tanguy, A. , Bourges, M. , Gaurel, G. , Escande, G. , Guillot, M. , and Vanneuville, G. , 1985, “ Biomechanical Properties of Spinal Ligaments and a Histological Study of the Supraspinal Ligament in Traction,” J. Biomech., 18(3), pp. 167–176. [PubMed]
Wu, J. , and Chen, J. , 1996, “ Clarification of the Mechanical Behaviour of Spinal Motion Segments Through a Three-Dimensional Poroelastic Mixed Finite Element Model,” Med. Eng. Phys., 18(3), pp. 215–224. [PubMed]
Panjabi, M. M. , Oxland, T. , Yamamoto, I. , and Crisco, J. , 1994, “ Mechanical Behavior of the Human Lumbar and Lumbosacral Spine as Shown by Three-Dimensional Load-Displacement Curves,” J. Bone Jt. Surg., 76(3), pp. 413–424.
Yamamoto, I. , Panjabi, M. M. , Crisco, T. , and Oxland, T. , 1989, “ Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint,” Spine, 14(11), p. 1256. [PubMed]
Guan, Y. , Yoganandan, N. , Moore, J. , Pintar, F. A. , Zhang, J. , Maiman, D. J. , and Laud, P. , 2007, “ Moment–Rotation Responses of the Human Lumbosacral Spinal Column,” J. Biomech., 40(9), pp. 1975–1980. [PubMed]
Markolf, K. L. , and Morris, J. M. , 1974, “ The Structural Components of the Intervertebral Disc,” J. Bone Jt. Surg. Am., 56(4), pp. 675–687.
Brinckmann, P. , and Grootenboer, H. , 1991, “ Change of Disc Height, Radial Disc Bulge, and Intradiscal Pressure From Discectomy An In Vivo Investigation on Human Lumbar Discs,” Spine, 16(6), pp. 641–646. [PubMed]
Vergari, C. , Mansfield, J. , Meakin, J. R. , and Winlove, P. C. , 2016, “ Lamellar and Fibre Bundle Mechanics of the Annulus Fibrosus in Bovine Intervertebral Disc,” Acta Biomater., 37, pp. 14–20. [PubMed]
Michalek, A. J. , Buckley, M. R. , Bonassar, L. J. , Cohen, I. , and Iatridis, J. C. , 2009, “ Measurement of Local Strains in Intervertebral Disc Anulus Fibrosus Tissue Under Dynamic Shear: Contributions of Matrix Fiber Orientation and Elastin Content,” J. Biomech., 42(14), pp. 2279–2285. [PubMed]
Gregory, D. E. , Veldhuis, J. H. , Horst, C. , Brodland, G. W. , and Callaghan, J. P. , 2011, “ Novel Lap Test Determines the Mechanics of Delamination Between Annular Lamellae of the Intervertebral Disc,” J. Biomech., 44(1), pp. 97–102. [PubMed]
Cassidy, J. , Hiltner, A. , and Baer, E. , 1989, “ Hierarchical Structure of the Intervertebral Disc,” Connect. Tissue Res., 23(1), pp. 75–88. [PubMed]
Yang, B. , and O'Connell, G. D. , 2017, “ Effect of Collagen Fibre Orientation on Intervertebral Disc Torsion Mechanics,” Biomech. Model. Mechanobiol., 16(6), pp. 2005–2015. [PubMed]
Eyre, D. R. , and Muir, H. , 1976, “ Types I and II Collagens in Intervertebral Disc. Interchanging Radial Distributions in Annulus Fibrosus,” Biochem. J., 157(1), pp. 267–270. [PubMed]
Sharabi, M. , Wade, K. , and Haj-Ali, R. , 2018, “ The Mechanical Role of Collagen Fibers in the Intervertebral Disc,” Biomechanics of the Spine, Elsevier, Amsterdam, The Netherlands, pp. 105–123.
Pezowicz, C. A. , Robertson, P. A. , and Broom, N. D. , 2005, “ Intralamellar Relationships Within the Collagenous Architecture of the Annulus Fibrosus Imaged in Its Fully Hydrated State,” J. Anat., 207(4), pp. 299–312. [PubMed]
Gelse, K. , Pöschl, E. , and Aigner, T. , 2003, “ Collagens—Structure, Function, and Biosynthesis,” Adv. Drug Delivery Rev., 55(12), pp. 1531–1546.
Sun, S. , and Karsdal, M. A. , 2016, Type VI Collagen. Biochemistry of Collagens, Laminins and Elastin, Elsevier, Amsterdam, The Netherlands, Chap. 6, pp. 49–55.
Venkatraman, S. , Boey, F. , and Lao, L. L. , 2008, “ Implanted Cardiovascular Polymers: Natural, Synthetic and Bio-Inspired,” Prog. Polym. Sci., 33(9), pp. 853–874.
Holzapfel, G. A. , 2001, “ Biomechanics of Soft Tissue,” The Handbook of Materials Behavior Models, Vol. 3, Elsevier, Amsterdam, The Netherlands, pp. 1049–1063.
Gracovetsky, S. , and Farfan, H. , 1986, “ The Optimum Spine,” Spine, 11(6), pp. 543–573. [PubMed]
Mueller, M. J. , and Maluf, K. S. , 2002, “ Tissue Adaptation to Physical Stress: A Proposed ‘Physical Stress Theory’ to Guide Physical Therapist Practice, Education, and Research,” Phys. Ther., 82(4), pp. 383–403. [PubMed]


Grahic Jump Location
Fig. 1

The geometry and fibers architecture in the L3-L4 FSU-FE model. (a) The FSU in lateral view; (b) discrete fiber networks embedded in the AF matrix in the FSU-FE model. The circumferential fiber network with decreasing FVFs from the outer to inner AF (dark to bright colors) and radial fiber network with 20 deg circumferential distribution. The IVD geometry (c) and the IVD with partial removal of the AF matrix revealing theembedded fibers with (d) and without radial fibers (20 deg circumferential distribution) (e).

Grahic Jump Location
Fig. 2

Moment-rotation results of the FSU-FE models with (case 1, Table 1) and without radial fibers in different loading modes compared with in vitro measurements of Yamamoto et al. [61], Panjabi et al. [60] and Guan et al. [62]: for flexion-extension (a), lateral bending (b), torsion (c), and load–displacement results under compression compared with Markolf and Morris, 1974 [63] (d)

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Fig. 3

The max principal stresses and strains map of the radial fibers, circumferential fibers and AF matrix in the model with radial fibers under 10 N·m (for the moments loading cases: flexion, extension, right and left bending and right and left torsion) and 1.6 mm displacement (for the compression). Matrix contours were taken in the midheight of the AF matrix.

Grahic Jump Location
Fig. 4

While the radial fibers were tensioned and the AF matrix was compressed in the loading direction (active region), the circumferential fibers and AF matrix were tensioned in the opposite direction for flexion, extension and lateral bending. The figure presents the average max principal stresses and strains in the different regions of the IVD: anterior, posterior, right and left lateral for the circumferential fibers, radial fibers, and AF matrix under a moment of 10 N·m in the loading direction (active region) versus the opposite region. The stresses and strains were calculated for the anterior and posterior regions in flexion and extension and for left and right lateral regions for the lateral bending.

Grahic Jump Location
Fig. 5

The change in stresses due to the presence of radial fibers in different cross section and circumferential distributions at different loading modes. (a) Relative decrease in volume-average max principal stress on the circumferential fibers. (b) Relative decrease in average max. principal stress on the AF matrix.

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Fig. 6

The effect of the radial fibers presence, under different loading modes at 5 deg (case 3, Table 1), on (a) the decrease in averaged annulus height together with matrix sideways expansion and (b) the decrease in annulus matrix expansion (radial distance)




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