Multiaxial validation of a finite element model of the intervertebral disc with multigenerational fibers to establish residual strain.

Finite element models of the intervertebral disc are used to address research questions that cannot be tested through typical experimentation. A disc model requires complex geometry and tissue properties to be accurately defined to mimic the physiological disc. The physiological disc possesses residual strain in the annulus fibrosus (AF) due to osmotic swelling and due to inherently pre-strained fibers. We developed a disc model with residual contributions due to swelling-only, and a multigeneration model with residual contributions due to both swelling and AF fiber pre-strain and validated it against organ-scale uniaxial, quasi-static and multiaxial, dynamic mechanical tests. In addition, we demonstrated the models' ability to mimic the opening angle observed following radial incision of bovine discs. Both models were validated against organ-scale experimental data. While the swelling only model responses were within the experimental 95% confidence interval, the multigeneration model offered outcomes closer to the experimental mean and had a bovine model opening angle within one SD of the experimental mean. The better outcomes for the multigeneration model, which allowed for the inclusion of inherently pre-strained fibers in AF, is likely due to its uniform fiber contribution throughout the AF. We conclude that the residual contribution of pre-strained fibers in the AF should be included to best simulate the physiological disc and its behaviors.

Off-axis response due to mechanical coupling across all six degrees of freedom in the human disc.

The kinematics of the intervertebral disc are defined by six degrees of freedom (DOF): three translations (Tz: axial compression, Tx: lateral shear, and Ty: anterior-posterior shear) and three rotations (Rz: torsion, Rx: flexion-extension, and Ry: lateral bending). There is some evidence that the six DOFs are mechanically coupled, such that loading in one DOF affects the mechanics of the other five "off-axis" DOFs, however, most studies have not controlled and/or measured all six DOFs simultaneously. Additionally, the relationships between disc geometry and disc mechanics are important for evaluation of data from different sized donor and patient discs. The objectives of this study were to quantify the mechanical behavior of the intervertebral disc in all six degrees of freedom (DOFs), measure the coupling between the applied motion in each DOF with the resulting off-axis motions, and test the hypothesis that disc geometry influences these mechanical behaviors. All off-axis displacements and rotations were significantly correlated with the applied DOF and were of similar magnitude as physiologically relevant motion, confirming that off-axis coupling is an important mechanical response. Interestingly, there were pairs of DOFs that were especially strongly coupled: lateral shear (Tx) and lateral bending (Ry), anterior-posterior shear (Ty) and flexion-extension (Rx), and compression (Tz) and torsion (Rz). Large off-axis shears may contribute to injury risk in bending and flexion. In addition, the disc responded to shear (Tx, Ty) and rotational loading (Rx, Ry, and Rz) by increasing in disc height in order to maintain the applied compressive load. Quantifying these mechanical behaviors across all six DOF are critical for designing and testing disc therapies, such as implants and tissue engineered constructs, and also for validating finite element models.

MRI quantification of human spine cartilage endplate geometry: Comparison with age, degeneration, level, and disc geometry.

Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3-1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1410-1417, 2016.

Human cartilage endplate permeability varies with degeneration and intervertebral disc site.

Despite the critical functions the human cartilage endplate (CEP) plays in the intervertebral disc, little is known about its structural and mechanical properties and their changes with degeneration. Quantifying these changes with degeneration is important for understanding how the CEP contributes to the function and pathology of the disc. Therefore the objectives of this study were to quantify the effect of disc degeneration on human CEP mechanical properties, determine the influence of superior and inferior disc site on mechanics and composition, and simulate the role of collagen fibers in CEP and disc mechanics using a validated finite element model. Confined compression data and biochemical composition data were used in a biphasic-swelling model to calculate compressive extrafibrillar elastic and permeability properties. Tensile properties were obtained by applying published tensile test data to an ellipsoidal fiber distribution. Results showed that with degeneration CEP permeability decreased 50-60% suggesting that transport is inhibited in the degenerate disc. CEP fibers are organized parallel to the vertebrae and nucleus pulposus and may contribute to large shear strains (0.1-0.2) and delamination failure of the CEP commonly seen in herniated disc tissue. Fiber-reinforcement also reduces CEP axial strains thereby enhancing fluid flux by a factor of 1.8. Collectively, these results suggest that the structure and mechanics of the CEP may play critical roles in the solute transport and disc mechanics.

Microstructural heterogeneity directs micromechanics and mechanobiology in native and engineered fibrocartilage.

Treatment strategies to address pathologies of fibrocartilaginous tissue are in part limited by an incomplete understanding of structure-function relationships in these load-bearing tissues. There is therefore a pressing need to develop micro-engineered tissue platforms that can recreate the highly inhomogeneous tissue microstructures that are known to influence mechanotransductive processes in normal and diseased tissue. Here, we report the quantification of proteoglycan-rich microdomains in developing, ageing and diseased fibrocartilaginous tissues, and the impact of these microdomains on endogenous cell responses to physiologic deformation within a native-tissue context. We also developed a method to generate heterogeneous tissue-engineered constructs (hetTECs) with non-fibrous proteoglycan-rich microdomains engineered into the fibrous structure, and show that these hetTECs match the microstructural, micromechanical and mechanobiological benchmarks of native tissue. Our tissue-engineered platform should facilitate the study of the mechanobiology of developing, homeostatic, degenerating and regenerating fibrous tissues.

Novel human intervertebral disc strain template to quantify regional three-dimensional strains in a population and compare to internal strains predicted by a finite element model.

Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4-L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81-99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1264-1273, 2016.

Elastic, permeability and swelling properties of human intervertebral disc tissues: A benchmark for tissue engineering.

The aim of functional tissue engineering is to repair and replace tissues that have a biomechanical function, i.e., connective orthopaedic tissues. To do this, it is necessary to have accurate benchmarks for the elastic, permeability, and swelling (i.e., biphasic-swelling) properties of native tissues. However, in the case of the intervertebral disc, the biphasic-swelling properties of individual tissues reported in the literature exhibit great variation and even span several orders of magnitude. This variation is probably caused by differences in the testing protocols and the constitutive models used to analyze the data. Therefore, the objective of this study was to measure the human lumbar disc annulus fibrosus (AF), nucleus pulposus (NP), and cartilaginous endplates (CEP) biphasic-swelling properties using a consistent experimental protocol and analyses. The testing protocol was composed of a swelling period followed by multiple confined compression ramps. To analyze the confined compression data, the tissues were modeled using a biphasic-swelling model, which augments the standard biphasic model through the addition of a deformation-dependent osmotic pressure term. This model allows considering the swelling deformations and the contribution of osmotic pressure in the analysis of the experimental data. The swelling stretch was not different between the disc regions (AF: 1.28±0.16; NP: 1.73±0.74; CEP: 1.29±0.26), with a total average of 1.42. The aggregate modulus (Ha) of the extra-fibrillar matrix was higher in the CEP (390kPa) compared to the NP (100kPa) or AF (30kPa). The permeability was very different across tissue regions, with the AF permeability (64 E(-16)m(4)/Ns) higher than the NP and CEP (~5.5 E(-16)m(4)/Ns). Additionally, a normalized time-constant (3000s) for the stress relaxation was similar for all the disc tissues. The properties measured in this study are important as benchmarks for tissue engineering and for modeling the disc's mechanical behavior and transport.