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Simulating Intervertebral Disc Mechanics Using Finite Element Method


The intervertebral disc has a complex fibrocartilaginous structure, comprised of a jel-like nucleus pulposus (NP) surrounded by the annulus fibrosus (AF) and is sandwiched between cartilaginous (CEPs) and bony endplates. Collagen fibers in AF orient in a cross-ply pattern and fiber angle to the horizontal plane decreases from 43 degree in the inner AF to 28 degree in the outer AF. NP, AF, and CEP are comprised primarily of water, proteoglycans (GAGs), and collagen fibers. A high GAG content gives these tissues an excellent capacity to absorb water resulting in an increase in tissue volume and swelling. in vivo, disc undergoes axial compression, torsion, flexion, extension, and lateral bending. Fluid flows out of the disc during the day and flows back at night exhibiting viscous effects.

Disc malfunctions including herniation and degeneration are the main contributors to low back pain. Disc herniation occurs as NP extrudes through a damaged region of the AF, compressing the spinal nerves and causing neurologic dysfunction. Painful herniations are treated with nucleotomy to remove the herniated material. Disc degeneration is noted by alterations in tissue structure and composition. These changes alter stress distributions between NP and AF, resulting in altered disc joint mechanics during loading and unloaded recovery.

Although the disc structural mechanics has been extensively studied, there are still a lot of unknowns from the literature. During my Ph.D., I studied the effects of fiber orientation, NP size and position, and nucleotomy on disc mechanics. A finite element model of the human lumbar disc based on averaged disc geometry was developed and validated. Then the validated model was modified to do parameter studies. Simulation results showed: (1) Discs with collagen fibers oriented closer to the horizontal plane experienced a decrease in AF stresses, NP pressure, and torsional stiffness. (2) NP size had a significant impact on compressive stiffness, intradiscal pressure, and principal strain. The location of NP centroid within the disc space had a significant impact on the magnitude and distribution of intradiscal pressure in flexion and extension. (3) The effects of nucleotomy on disc mechanics differed between single and more complex loading modalities.

Under single loading conditions, disc joint stiffness decreased with nucleotomy. However, more complex loading conditions resulted in an increase in bending stiffness (25 - 40%), suggesting that the disc is more resistant to bending after nucleotomy. Simulation results indicate that fiber orientation, NP size, and NP location are important factors for developing accurate computational models to study the mechanical behavior of native, injured, or degenerated discs and for creating a tissue-engineered disc. The discrepancy between single- and dual-loading conditions highlights the importance of evaluating disc joint mechanics under conditions that more closely represent in situ loading, which will be important for elucidating mechanisms for disc joint failure.

While multiple studies have reported disc tissues swelling, however, the effects of fiber network, fiber stiffness, GAG distribution, and boundary condition on disc swelling are not clear. Besides the relationships between disc tissue swelling and residual stress/strain/pressure formation are missing from the literature. To answer these questions, I developed finite element models for the intact disc joint and tissue subcomponents, including NP with AF and ex situ tissue explants (NP and CEP tissue cubes, AF rings, and rectangular AF samples based on uniaxial test specimens). Fiber orientation, fiber stiffness, and GAG content were varied to study the effects on tissue swelling and residual strain formation. Variations in GAG content and distribution replicated the healthy and degenerated discs. Simulation results showed: (1) Fiber angle, fiber architecture, and the number of lamellae in single fiber-family structures altered tissue swelling capacity, fiber deformation, and tissue rotation. (2) The kidney-bean shape played an important role in forming residual stress and strain in native AF (compressive stress and strain in the circumferential direction in the inner AF and tensile in the outer). These stretch and stress were comparable to experimental observations. GAG loss in the inner AF, as observed with degeneration, decreased circumferential direction stress by over 65%. (3) Boundary conditions created by surrounding tissues resulted in a relative decrease in swelling capacity by 40% in the NP and 25% in the AF and cartilaginous endplate forming a uniform stretch distribution in the AF. Our model predicted a decrease in equilibrium NP pressure from 0.21 MPa in a healthy disc to 0.03 MPa in the severely degenerated disc, agreeing with data in the literature. Early degeneration decreased the circumferential-direction residual deformation by over 60% and flipped the radial-direction stretch from compressive ~0.95 to tensile ~1.05, which may lead to apoptosis accelerating further degeneration. Degeneration also greatly altered AF residual stress/stretch and fiber stretch in the posterior region, which may cause disc failure. Findings from these studies demonstrate the need to include the native fiber network in computational models to accurately simulate tissue-swelling behavior and the need to replicate NP swelling capacity in engineered discs to prevent degradation of the inner AF.

Water content in nucleus pulposus (NP) and annulus fibrosus (AF) decrease greatly with aging and degeneration (over 10%) resulting in altered disc joint mechanics. Water content is also a key parameter in disc computational models to simulate swelling behavior as well as nutrition transportation. Therefore, accurately measuring disc water content is important to develop accurate patient-specific disc model and to detect disc early degeneration.

Using quantitative magnetic resonance imaging (MRI) to measure disc water content is a promising approach, as signal intensity depends on the single proton density within the tissue and the approach is non-invasive. However, MRI signal intensity is also dependent on scan-parameters, the concentration of free water molecules, and collagen fiber content and architecture. Therefore, how accurately MRI can quantify NP and AF water content is unclear. In this research, experiments were conducted to compare MR based water content measurement with traditional biochemical measurement (lyophilization). Experimental results showed that normalizing NP spin density by mass density provided an excellent agreement between MR measured water content and water content measured through lyophilization. However, normalizing spin density by mass density underestimated AF water content. This discrepancy is likely due to a higher concentration of bound water molecules in the AF, compared to the NP, where tightly bounded water molecules have too short T2 values to be detected in MR imaging.

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