0
Research Papers

A Computational Model to Describe the Regional Interlamellar Shear of the Annulus Fibrosus

[+] Author and Article Information
Kevin M. Labus

School of Biomedical Engineering,
Colorado State University,
Fort Collins, CO 80523-1374

Sang Kuy Han

Fischell Department of Bioengineering,
University of Maryland,
College Park, MD 20742

Adam H. Hsieh

Fischell Department of Bioengineering,
University of Maryland,
College Park, MD 20742;
Department of Orthopaedics,
School of Medicine,
University of Maryland,
Baltimore, MD 21201

Christian M. Puttlitz

Associate Professor
Orthopaedic Research Center,
Department of Mechanical Engineering,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523-1374
e-mail: puttlitz@engr.colostate.edu

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received October 16, 2013; final manuscript received February 3, 2014; accepted manuscript posted March 6, 2014; published online April 10, 2014. Assoc. Editor: James C. Iatridis.

J Biomech Eng 136(5), 051009 (Apr 10, 2014) (7 pages) Paper No: BIO-13-1493; doi: 10.1115/1.4027061 History: Received October 16, 2013; Revised February 03, 2014; Accepted March 06, 2014

Interlamellar shear may play an important role in the homeostasis and degeneration of the intervertebral disk. Accurately modeling the shear behavior of the interlamellar compartment would enhance the study of its mechanobiology. In this study, physical experiments were utilized to describe interlamellar shear and define a constitutive model, which was implemented into a finite element analysis. Ovine annulus fibrosus (AF) specimens from three locations within the intervertebral disk (lateral, outer anterior, and inner anterior) were subjected to in vitro mechanical shear testing. The local shear stress–stretch relationship was described for the lamellae and across the interlamellar layer of the AF. A hyperelastic constitutive model was defined for interlamellar and lamellar materials at each location tested. The constitutive models were incorporated into a finite element model of a block of AF, which modeled the interlamellar and lamellar layers using a continuum description. The global shear behavior of the AF was compared between the finite element model and physical experiments. The shear moduli at the initial and final regions of the stress–strain curve were greater within the lamellae than across the interlamellar layer. The difference between interlamellar and lamellar shear was greater at the outer anterior AF than at the inner anterior region. The finite element model was shown to accurately predict the global shear behavior or the AF. Future studies incorporating finite element analysis of the interlamellar compartment may be useful for predicting its physiological mechanical behavior to inform the study of its mechanobiology.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Parker, S. L., Xu, R., McGirt, M. J., Witham, T. F., Long, D. M., and BydonA., 2010, “Long-Term Back Pain After a Single-Level Discectomy for Radiculopathy: Incidence and Health Care Cost Analysis,” J. Neurosurg. Spine, 12(2), pp. 178–182. [CrossRef] [PubMed]
Sherman, J., Cauthen, J., Schoenberg, D., Burns, M., Reaven, N. L., and Griffith, S. L., 2010, “Economic Impact of Improving Outcomes of Lumbar Discectomy,” Spine J., 10(2), pp. 108–116. [CrossRef] [PubMed]
Iatridis, J. C., Nicoll, S. B., Michalek, A. J., Walter, B. A., and Gupta, M. S., 2013, “Role of Biomechanics in Intervertebral Disc Degeneration and Regenerative Therapies: What Needs Repairing in the Disc and What Are Promising Biomaterials for Its Repair?” Spine J., 13(3), pp. 243–262. [CrossRef] [PubMed]
Driscoll, T. P., Nakasone, R. H., Szczesny, S. E., Elliott, D. M., and Mauck, R. L., 2013, “Biaxial Mechanics and Inter-Lamellar Shearing of Stem-Cell Seeded Electrospun Angle-Ply Laminates for Annulus Fibrosus Tissue Engineering,” J. Orthop. Res., 31, pp. 864–870. [CrossRef] [PubMed]
Bowles, R. D., Williams, R. M., Zipfel, W. R., and Bonassar, L. J., 2010, “Self-Assembly of Aligned Tissue-Engineered Annulus Fibrosus and Intervertebral Disc Composite via Collagen Gel Contraction,” Tissue Eng. A, 16(4), pp. 1339–1348. [CrossRef]
Yu, J., Tirlapur, U., Fairbank, J., Handford, P., Roberts, S., Winlove, C. P., Cui, Z., and Urban, J., 2007, “Microfibrils, Elasin Fibres and Collagen Fibres in the Human Intervertebral Disc and Bovine Tail Disc,” J. Anat., 210(4), pp. 460–471. [CrossRef] [PubMed]
Melrose, J., Smaith, 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. [CrossRef] [PubMed]
Bruehlmann, S. B., Rattner, J. B., Matyas, J. R., and Duncan. N. A., 2002, “Regional Variations in the Cellular Matrix of the Annulus Fibrosus of the Intervertebral Disc,” J. Anat., 201(2), pp. 159–171. [CrossRef] [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, pp. 317–330. [CrossRef] [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. [CrossRef] [PubMed]
Nerurkar, N. L., Baker, B. M., Sen, S., Wible, E. E., Elliott, D. M., and Mauck, R. L., 2009, “Nanofibrous Biologic Laminates Replicate the Form and Function of the Annulus Fibrosus,” Nat. Mater., 8, pp. 986–992. [CrossRef] [PubMed]
Nerurkar, N. L., Mauck, R. L., and Elliott, D. M., 2011, “Modeling Interlamellar Interactions in Angle-Ply Biologic Laminates for Annulus Fibrosus Tissue Engineering,” Biomech. Model. Mechanobiol., 10, pp. 973–984. [CrossRef] [PubMed]
Fagan, M. J., Julian, S., and Mohsen, A. M., “Finite Element Analysis in Spine Research,” J. Eng. Med., 216(5), pp. 281–298. [CrossRef]
Galbusera, F., Wilke, H. J., Brayda-Bruno, M., Costa, F., and Fornari, M., 2013, “Influence of Sagittal Balance on Spinal Lumbar Loads: A Numerical Approach,” Clin. Biomech., 28(4), pp. 370–377. [CrossRef]
Webster, D., Wirth, A., van Lenthe, G. H., and Muller, R., 2012, “Experimental and Finite Element Analysis of the Mouse Caudal Vertebrae Loading Model: Prediction of Cortical and Trabecular Bone Aadaptation,” Biomech. Model. Mechanobiol., 11, pp. 221–230. [CrossRef] [PubMed]
Tchako, A., and Sadegh, A., 2009, “A Cervical Spine Model to Predict Injury Scenarios and Clinical Instability,” Sports Biomech., 8(1), pp. 78–95. [CrossRef] [PubMed]
Woldtvedt, D. J., Womack, W., Gadomski, B. C., Schuldt, D., and Puttlitz, C. M., 2011, “Finite Element Lumbar Spine Facet Contact Parameter Predictions are Affected by the Cartilage Thickness Distribution and Initial Joint Gap Size,” ASME J. Biomech. Eng., 133(6), p. 061009. [CrossRef]
Ayturk, U. M., Gadomski, B., Schuldt, D., Patel, V., and Puttlitz, C. M., 2012, “Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach,” ASME J. Biomech. Eng., 134(10), p. 101003. [CrossRef]
Wagner, D. R., and Lotz, J. C., 2004, “Theoretical Model and Experimental Results for the Nonlinear Elastic Behavior of Human Annulus Fibrosus,” J. Orthop. Res., 22, pp. 901–909. [CrossRef] [PubMed]
Guerin, H. L., and Elliott, D. M., 2007, “Quantifying the Contributions of Structure to Annulus Fibrosus Mechanical Function Using a Nonlinear, Anisotropic, Hyperelastic Model,” J. Orthop. Res., 25, pp. 508–516. [CrossRef] [PubMed]
Wu, H.-C. and Yao, R.-F., 1976, “Mechanical Behavior of the Human Annulus Fibrosus,” J. Biomech., 9, pp. 1–7.
Costi, J. J., Stokes, I. A., Gardner-Morse, M., Laible, J. P., Scoffone, H. M., and Iatridis, J. C., 2007, “Direct Measurement of Intervertebral Disc Maximum Shear Strain in Six Degrees of Freedom: Motions That Place Disc Tissue at Risk of Injury,” J. Biomech., 40, pp. 2457–2466. [CrossRef] [PubMed]
Iatridis, J. C., Kumar, S., Foster, R. J., Weidenbaum, M., and Mow, V. C., 1999, “Shear Mechanical Properties of Human Lumbar Annulus Fibrosus,” J. Orthop. Res., 17, pp. 732–737. [CrossRef] [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, pp. 97–102. [CrossRef] [PubMed]
Spencer, A. J. M., 1984, Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer-Verlag, New York, NY.
Michalek, A. J., Buckley, M. R., Bonassar, L. J., Cohen, I., and Iatridis, J. C., 2009, “Measurement of Local Strains in Intervertebral Disc Annulus Fibrosus Tissue Under Dynamic Shear: Contributions of Matrix Fiber Orientation and Elastin Content,” J. Biomech., 42, pp. 2279–2285. [CrossRef] [PubMed]
Han, W. M., Nernurkar, 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. [CrossRef] [PubMed]
Romgens, A. M., Donkelaar, C. C., and Ito, K., 2013, “Contribution of Collagen Fibers to the Compressive Stiffness of Cartilaginous Tissues,” Biomech. Model. Mechanobiol, 12(6), pp. 1221–1231.
Iatridis, J. C., MacLean, J. J., O'Brien, M., and Stokes, I. A. F., 2007, “Measurement of Proteoglycan and Water Content Distribution in Human Lumbar Intervertebral Discs,” Spine, 32(14), pp. 1493–1497. [CrossRef] [PubMed]
Lyons, G., Eisenstein, S. M., and Sweet, M. B. E., 1981, “Biochemical Changes in Intervertebral Disc Degeneration,” Biochim. Biophys. Acta, 673, pp. 443–453. [CrossRef] [PubMed]
Reid, J. E., Meakin, J. R., Robins, S. P., Skakle, J. M. S., and Hukins, D. W. L., 2002, “Sheep Lumbar Intervertebral Discs as Models for Human Discs,” Clin. Biomech., 17, pp. 312–314. [CrossRef]
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, pp. 337–344. [CrossRef]
Lyons, A. S., Sherman, B. P., PuttlitzC. M., Patel, V.V., Abjornson, C., Turner, A. S., Seim, H. B., Burger, E. L., and Lindley, E. M., 2011, “Failure of Resorbable Plates and Screws in an Ovine Model of Anterior Cervical Discectomy and Fusion,” Spine J., 11, pp. 876–883. [CrossRef] [PubMed]
Huntington, C. F., Murrell, W. D., Betz, R. R., Cole, B. A., Clements, D. H., and Balsara, R. K., 1998, “Comparison of Thoracoscopic and Open Thoracic Discectomy in a Live Ovine Model for Anterior Spinal Fusion,” Spine, 23(15), pp. 1699–1702. [CrossRef] [PubMed]
Kandziora, F., Pflugmacher, R., Schafer, J., Born, C., Duda, G., Haas, N. P., and Mittlmeier, T., 2001, “Biomechanical Comparison of Cervical Spine Interbody Fusion Cages,” Spine, 26(17), pp. 1850–1857. [CrossRef] [PubMed]
Wilke, H. J., KettlerA., Wenger, K. H., and Claes, L. E., 1997, “Anatomy of the Sheep Spine and Its Comparison to the Human Spine,” Anat. Rec., 247, pp. 542–555. [CrossRef] [PubMed]
Wilke, H. J., Kettler, A., and Claes, L. E., 1997, “Are Sheep Spines a Valid Biomechanical Model for Human Spines?,” Spine, 22(20), pp. 2365–2374. [CrossRef] [PubMed]
BruehlmannS. B., Matyas, J. R., and Duncan, N. A., 2004, “ISSLS Prize Winner: Collagen Fibril Sliding Governs Cell Mechanics in the Anulus Fibrosus,” Spine, 29(23), pp. 2612–2620. [CrossRef] [PubMed]
Gilbert, H. T. J., Hoyland, J. A., Freemont, A. J., and Millward-Sadler, S. J., 2011, “The Involvement of Interleukin-1 and Interleukin-4 in the Response of Human Annulus Fibrosus Cells to Cyclic Tensile Strain: An Altered Mechanotransduction Pathway With Degeneration,” Arthritis Res. Ther., 13(R8), pp. 1–13. [CrossRef]

Figures

Grahic Jump Location
Fig. 3

Finite element model of AF block, with simple shear loading conditions matching experiments. Element dimension was 180 μm in the axial (out of plane) direction.

Grahic Jump Location
Fig. 2

Specimen image demonstrating the AF's distinct layers. Lamellar and L + IL shear were defined by marker triads within a lamellae and across the interlamellar space, respectively.

Grahic Jump Location
Fig. 1

(a) Rectangular AF specimen blocks were isolated from three locations of the disk. (b) Schematic demonstrating the simple shear experiment with fiducial marker placements (black dots). (c) Digital image of the overall experimental apparatus that utilized a microscope to track marker displacements. (d) Close-up view of the shear experimental apparatus.

Grahic Jump Location
Fig. 4

Characteristic L + IL and lamellar experimental stress–strain curves from a single specimen (outer anterior) demonstrating the constitutive model's fit to the experimental data.

Grahic Jump Location
Fig. 5

Shear moduli at the initial (a) and final (b) regions of the stress–strain curve for the three AF locations. Data represent mean with standard deviation error bars. Similar letters indicate statistical relationships: (A) p = 0.01; (B) p = 0.63; (C) p = 0.034; (D) p < 0.01; (E) p = 0.018; (F) p < 0.01; (G) p < 0.01; (H) p = 0.015; (I) p = 0.15; (J) p < 0.01; (K) p < 0.01; (L) p = 0.041; (M) p < 0.01; and (N) p < 0.01.

Grahic Jump Location
Fig. 6

Comparison of global stress–strain relationship between the model prediction and experimental data. (a) Outer anterior, (b) inner anterior, and (c) lateral.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In