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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.

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References

Figures

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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.

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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.

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Fig. 6

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

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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.

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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.

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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.

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