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Effect of Sharpey's Fibers on the Stress Distribution in the Anulus Fibrosus of an Intervertebral Disc Subjected to Compression

Sébastien Demers(1*), Abdel-Hakim Bouzid(2), Sylvie Nadeau(3)

(1) Mechanical engineering department at Cégep de St-Jérôme, Canada
(2) École de Technologie Supérieure, Canada
(3) Occupational safety research group at École de technologie supérieure, Canada
(*) Corresponding author



Theoretical analyses of stress and strain in intervertebral discs have received little attention in the scientific literature, in favor of experimental and finite element studies. Constitutive modeling using the finite element method is effective and powerful. However, only few model variables can be verified by experimental measurements which may result in insufficient model validation. Triangulation of methodologies reinforces model reliability, and could be achieved by developing an analytical approach. This study examines the potential of thin-shell theory and beam on elastic foundation theory for simulation of the anulus fibrosus multi-shell structure and the endplate anchorage of lamellae via Sharpeys fibers. The model is based on a simplified axisymmetric disc subjected to axial compression and takes into account large deformations of the disc. The performance of the model was compared to that of a simplified finite element model. The two models responded similarly, and the results demonstrate that beam on elastic foundation theory is applicable to simulate Sharpey’s fiber effects and should be considered for use in the analytical study of intervertebral discs. Future research should focus on realistic representation of the complex changes in lamellar geometry due to large deformation, and on inclusion of material anisotropy and hyperelasticity, asymmetric geometry and complex loadings.
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Anulus Fibrosus; Sharpey’s Fibers; Stress Analysis; Lamellae; Bulge; Modeling

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M. A. Adams and P. J. Roughley, "What is intervertebral disc degeneration, and what causes it?," Spine, vol. 31, pp. 2151-2161, 2006.

R. Gunzburg, W. C. Hutton, G. Crane, and R. D. Fraser, "Role of the capsulo-ligamentous structures in rotation and combined flexion-rotation of the lumbar spine," Journal of Spinal Disorders, vol. 5, pp. 1-7, 1992.

R. Roaf, "A study of the mechanics of spinal injuries," The Journal of Bone and Joint Surgery, vol. 42, pp. 810-823, 1960.

A. Nachemson, "Lumbar intradiscal pressure. Experimental studies on post-mortem material," Acta Orthop. Scand., vol. Supplementum 43, pp. 1-104, 1960.

F. Marchand and A. M. Ahmed, "Investigation of the laminate structure of lumbar disc anulus fibrosus," Spine, vol. 15, pp. 402-410, 1990.

G. A. Holzapfel, C. A. J. Schulze-Bauer, G. Feigl, and P. Regitnig, "Single lamellar mechanics of the human lumbar anulus fibrosus," Biomech Model Mechanobiol, vol. 3, pp. 125-140, 2005.

L. J. Smith and N. L. Fazzalari, "The elastic fibre network of the human lumbar anulus fibrosus: architecture, mechanical function and potential role in the progression of intervertebral disc degeneration," European spine journal, vol. 18, pp. 439-448, 2009.

J. M. Spivak and P. J. Connolly, Orthopaedic knowledge update: spine 3. Rosemont, IL: American Academy of Orthopaedic Surgeons, 2006.

N. Karajan, "Multiphasic intervertebral disc mechanics: theory and application," Arc Comput Methods Eng, vol. 19, pp. 261-339, 2012.

D. W. L. Hukins, "A simple model for the function of proteoclycans and collagen in the response to compression of the intervertebral disc," Proceedings: Biological sciences. Royal Society, vol. 249, pp. 281-285, 1992.

H. Schmidt, F. Heuer, J. Drumm, Z. Klezl, a. L. Claes, and H.-J. Wilke, "Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment," Clinical Biomechanics, vol. 22, pp. 377-384, 2007.

F. Ezquerro, F. G. i. Vacas, S. Postigo, M. Prado, and A. Sim'on, "Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution," Medical Engineering & Physics, vol. 33, pp. 89-95, 2011.

Z. Guo, X. Shi, X. Peng, and F. Caner, "Fibre–matrix interaction in the human annulus fibrosus," Journal of the Biomechanical Behavior of Biomedical Materials, vol. 5, pp. 193-205, 2012.

M. Viceconti, "Extracting clinically relevant data from finite element simulations," Clinical Biomechanics, vol. 20, pp. 451-454, 2005.

D. S. Hickey and D. W. Hukins, "Relation between the structure of the annulus fibrosus and the function and failure of the intervertebral disc," Spine (Philadelphia Pa 1976), vol. 5, pp. 106-116, 1980.

D. Prud'Homme, "Mécanisme de la hernie discale: modélisation non-linéaire," École de technologie supérieure, Montréal, 2008.

K. B. Broberg and H. O. von Essen, "Modeling of intervertebral discs," Spine, vol. 5, pp. 155-167, 1980.

K. B. Broberg, "On the mechanical behaviour of intervertebral discs," Spine, vol. 8, pp. 151-165, 1983.

J. A. Klein, D. S. Hickey, and D. W. Hukins, "Radial bulging of the annulus fibrosus during compression of the intervertebral disc," J Biomech, vol. 16, pp. 211-217, 1983.

D. S. McNally and R. G. C. Arridge, "An analytical model of intervertebral disc mechanics," J. Biomechanics, vol. 28, pp. 53-68, 1995.

J. C. Iatridis and I. ap Gwynn, "Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus," Journal of Biomechanics, vol. 37, pp. 1165-1175, 2004.

S. Demers, A.-H. Bouzid, and S. Nadeau, "On the Modeling of an Intervertebral Disc Using a Novel Large Deformation Multi-Shell Approach," Journal of Biomechanical Engineering, vol. 135, pp. 051003-1-051003-8, May 2013.

M. F. Eijkelkamp, "On the development of an artificial intervertebral disc," University of Groningen, Netherlands, 2002.

E. F. Johnson, K. Chetty, I. M. Moore, A. Stewart, and W. Jones, "The distribution and arrangement of elastic fibres in the intervertebral disc of the adult human," J. anat., vol. 135, pp. 301-309, 1982.

R. C. Paietta, E. L. Burger, and V. L. Ferguson, "Mineralization and collagen orientation throughout aging at the vertebral endplate in the human lumbar spine," Journal of Structural Biology, vol. 184, pp. 310-320, 2013.

Y. S. Nosikova, J. P. Santerre, M. Grynpas, G. Gibson, and R. A. Kandel, "Characterization of the annulus fibrosus-vertebral body interface: identification of new structural features," Journal of Anatomy, vol. 221, pp. 577-589, 2012.

S. A. Rodrigues, K. R. Wade, A. Thambyah, and N. D. Broom, "Micromechanics of annulus-end plate integration in the intervertebral disc," The Spine Journal, vol. 12, pp. 143-150, 2012.

J.-F. Bonneville, M. Runge, F. Cattin, P. Potelon, and Y.-S. Tang, "Extraforaminal lumbar disc herniations: CT demonstration of Sharpey's fibers avulsion," Neuroradiology, vol. 31, pp. 71-74, 1989.

S. Timoshenko and S. Woinowsky-Krieger, Theory of plates and shells. New York: Mcgraw-Hill, 1959.

R. J. Roark, W. C. Young, and R. G. Budynas, Roark's forumulas for stress and strain. New York: McGraw-Hill, 2002.

J. J. Cassidy, A. Hiltner, and E. Baer, "Hierarchical Structure of the Intervertebral Disc," Connective Tissue Research, vol. 23, pp. 75-88, 1989.

G. D. O’Connell, E. J. Vresilovic, and D. M. Elliott, "Human Intervertebral Disc Internal Strain in Compression: The Effect of Disc Region, Loading Position, and Degeneration," Journal of Orthopaedic Research, vol. 29, pp. 547-555, 2010.

S. H. Zhou, I. D. McCarthy, A. H. McGregor, R. R. H. Coombs, and S. P. F. Hughes, "Geometrical dimensions of the lower lumbar vertebrae - analysis of data from digitised CT images," European Spine Journal, vol. 9, pp. 242-248, 2000.

J. P. Little, C. J. Adam, J. H. Evans, G. J. Pettet, and M. J. Pearcy, "Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc," Journal of Biomechanics, vol. 40, pp. 2744-2751, 2007.

D. L. Skaggs, M. Weidenbaum, J. C. Iatridis, A. Ratcliffe, and V. C. Mow, "Regional variation in tensile properties and biochemical composition of the human lumbar anulus fibrosus," Spine, vol. 19, pp. 1310-1319, 1994.

M. A. Adams, D. S. McNally, and P. Dolan, "'Stress' distributions inside intervertebral discs," The Journal of Bone and Joint Surgery, vol. 78, pp. 965-972, 1996.

A. Nachemson, "Disc pressure measurements," Spine, vol. 6, pp. 93-97, 1981.

ANSYS, "Release 14.0. Software," ed. Southpointe (Pa.): ANSYS, Inc, 2011.

D. E. Gregory, W. C. Bae, R. L. Sah, and K. Masuda, "Anular delamination strength of human lumbar intervertebral disc," Eur Spine J, vol. 21, pp. 1716-1723, 2012.

L. J. Smith and D. M. Elliott, "Formation of lamellar cross bridges in the annulusfibrosus of the intervertebral disc is a consequence of vascular regression," Matrix Biology, vol. 30, pp. 267-274, 2011.

M. L. Schollum, P. A. Robertson, and N. D. Broom, "A microstructural investigation of intervertebral disc lamellar connectivity: detailed analysis of the translamellar bridges," J. Anat., vol. 241, pp. 805-816, 2009.

Matlab, "Matlab version (R2012b)," Software. Natick (Ma.): MathWorks, 2012.

A. Zingoni, "On membrane solutions for elevated shell-of-revolution tanks of certain meridional profiles," Thin-walled structures, vol. 22, pp. 121-142, 1995.

S. e. Demers, A.-H. Bouzid, and S. Nadeau, "Stress Analysis of the Intervertebral Disc Using a Developed Multi-Shell Model," Twelfth Pan American Congress of Applied Mechanics (Proceedings of PACAM XII), pp. 1-7, January 2-6, 2012.

A. Zingoni, "Stresses and deformations in egg-shaped sludge digestors: discontinuity effects," Engineering Structures, vol. 23, pp. 1373-1382, 2001.

K. H. Wenger and J. D. Schlegel, "Annular bulge contours from an axial photogrammetric method," Clinical Biomechanics, vol. 12, pp. 438-444, 1997.

G. Marini and S. J. Ferguson, "Modelling the influence of heterogeneous annulus material property distribution on intervertebral disk mechanics," Annals of Biomechanical Engineering, vol. 42, pp. 1760-1772, 2014.

J. e. o. Noailly, J. A. Planell, and D. Lacroix, "On the collagen criss-cross angles in the annuli fibrosi of lumbar spine finite element models," Biomech Model Mechanobiol, vol. 10, pp. 203-219, 2011.


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