Research Papers

Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach

[+] Author and Article Information
Ugur M. Ayturk

 Department of Orthopaedic Surgery, Boston Children’s Hospital and Harvard Medical School, Boston, MA 02115

Benjamin Gadomski, Dieter Schuldt

 Orthopaedic Bioengineering Research Laboratory, Department of Mechanical Engineering and School of Biomedical Engineering, Colorado State University, Fort Collins, CO 80523

Vikas Patel

 The Spine Center, Department of Orthopaedics, University of Colorado Denver, Denver, CO 80045

Christian M. Puttlitz1

 Orthopaedic Bioengineering Research Laboratory, Department of Mechanical Engineering and School of Biomedical Engineering, Colorado State University, 1374 Campus Delivery, Fort Collins, CO 80523puttlitz@engr.colostate.edu


Corresponding author.

J Biomech Eng 134(10), 101003 (Oct 01, 2012) (11 pages) doi:10.1115/1.4007632 History: Received April 30, 2012; Revised September 06, 2012; Posted September 25, 2012; Published October 01, 2012; Online October 01, 2012

Using a continuum approach for modeling the constitutive mechanical behavior of the intervertebral disk’s annulus fibrosus holds the potential for facilitating the correlation of morphology and biomechanics of this clinically important tissue. Implementation of a continuum representation of the disk’s tissues into computational models would yield a particularly valuable tool for investigating the effects of degenerative disease. However, to date, relevant efforts in the literature towards this goal have been limited due to the lack of a computationally tractable and implementable constitutive function. In order to address this, annular specimens harvested from a total of 15 healthy and degenerated intervertebral disks were tested under planar biaxial tension. Predictions of a strain energy function, which was previously shown to be unconditionally convex, were fit to the experimental data, and the optimized coefficients were used to modify a previously validated finite element model of the L4/L5 functional spinal unit. Optimization of material coefficients based on experimental results indicated increases in the micro-level orientation dispersion of the collagen fibers and the mechanical nonlinearity of these fibers due to degeneration. On the other hand, the finite element model predicted a progressive increase in the stress generation in annulus fibrosus due to stepwise degeneration of initially the nucleus and then the entire disk. Range of motion was predicted to initially increase with the degeneration of the nucleus and then decrease with the degeneration of the annulus in all rotational loading directions, except for axial rotation. Overall, degeneration was observed to specifically impact the functional effectiveness of the collagen fiber network of the annulus, leading to changes in the biomechanical behavior at both the tissue level and the motion-segment level.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Sagittal magnetic resonance images of representative healthy (Grade I, left) and degenerated (Grade III, right) intervertebral disks

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Figure 2

(Top) Schematic of the specimen dissection orientations for the uniaxial (radial) and biaxial (axial-circumferential) tension experiments. (Middle) Representative samples tested under biaxial (left) and uniaxial (right) tension. (Bottom) Diagonal cross-section of a representative specimen under the microscope (bottom-left), the associated gray-scale image (bottom-middle), and the isolated view used for thickness quantification (bottom-right).

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Figure 3

Experimental measurements and model predictions for two representative samples under uniaxial loading in the radial direction

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Figure 4

Model predictions and experimental stress measurements for a particular healthy sample in 1:0, 0:1, 1:1, and 2:1 (axial:circumferential) loading conditions

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Figure 5

Model predictions and experimental stress measurements for a particular degenerated sample in 1:0, 0:1, 1:1, and 2:1 (axial:circumferential) loading conditions

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Figure 6

Fiber and matrix contributions to the total SED generated under the four tested biaxial loading configurations. Model predictions for both healthy and degenerated conditions are based on the mean optimized coefficients. All values are reported in KPa.

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Figure 7

The range of motion predictions under pure-moment loading for all modeled scenarios: (top) extension (– moment) and flexion (+ moment); (bottom, left) unilateral lateral bending; and (bottom, right) uniaxial rotation

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Figure 8

Nodal intradiskal von Mises stress predictions (middle row) and strain energy density percentage due to the matrix component (bottom row) in the annulus in the anteroposterior direction under extension (left) and flexion (middle) and in the medial-lateral direction under lateral bending (right). The white arrows indicate the positions of the nodes in the annulus corresponding to the horizontal axes of the charts below.

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Figure 9

The percentage contribution of the matrix component to the average SED predictions in the annulus fibrosus



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