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

Abstract

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.

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

“…Specimens were cut into approximately 9 mm long (circumferential) by 4 mm wide (radial) by 3 mm thick (axial) tissue blocks. Prior to testing, the cross-sectional area of the specimens was measured via digital image analysis for post hoc stress calculations [18]. Specimens were attached to two acrylic platens with cyanoacrylate on their inner and outer radial surfaces for placement into the testing apparatus (Fig.…”

“…The material properties used in a model are typically obtained via physical mechanical testing of tissue specimens. AF lamellar mechanics have been well characterized previously via biaxial tension, compression, and shear testing [18][19][20]23]. Computational models derived from these experiments have treated the AF as a homogeneous tissue with two families of fibers rather than describing the mechanics of the lamellar and interlamellar spaces individually.…”

“…Computational models derived from these experiments have treated the AF as a homogeneous tissue with two families of fibers rather than describing the mechanics of the lamellar and interlamellar spaces individually. It has been shown that this description is sufficient for modeling global AF tissue behavior under a variety of loading conditions [18][19][20], but it does not provide specific information with respect to interlamellar mechanics. There is also limited experimental data describing the relatively high displacements of adjacent lamellae under shear loading [9,24].…”

Biaxial Response of Ovine Spinal Cord Dura Mater

“…The fitted parameters in this study were associated with a high degree of variance, which necessitated the use of a nonparametric statistical measure. Previous studies investigating the mechanical behavior of biological tissue via constitutive modeling have also reported a high degree of variance in their fitted parameters (Ayturk et al, 2012;Guerin and Elliott, 2007;Vande Geest et al, 2006). However, the ability of our fitted parameters to accurately predict the dura's uniaxial behavior demonstrates the robust nature of the data and somewhat mitigates this limitation.…”

“…Thus, this anisotropic Gasser model (ANISO_G) variant of Equation 3 resulted in an eightparameter strain energy density function: (5) A visual description of the two formulations and their associated strain energy and invariant equations are provided in Figure 2. The theoretical Cauchy stress was obtained by differentiating the total strain energy density by the right-Cauchy-Green deformation tensor (C) (Ayturk et al, 2012;Holzapfel, 2000;Holzapfel and Ogden, 2009). All fitting was performed with the lsqcurvefit function in MATLAB (Version 2013a, MathWorks, Natick, MA) via minimization of the sum of squared errors in the predicted stresses.…”