A simple model for the function of proteoglycans and collagen in the response to compression of the intervertebral disc.

The nucleus pulposus of the intervertebral disc exerts a pressure which enables it to support axial compression when contained by the annulus fibrosus. The disc was modelled as a thick-walled cylindrical pressure vessel in which the nucleus was contained radially by the annulus. As a result, the stress in the annulus had radial (compressive) as well as tangential (tensile) components. The radial stress at a given point in the annulus was considered to be balanced by the internal pressure which is expected to arise from the attraction of water by proteoglycans. There was a reasonable agreement between the calculated radial stress distribution and published results on the distribution of water within the annulus. As the internal pressure is expected to be isotropic, the annulus was expected to contribute to the axial resistance to compression of the disc; this contribution would be equal, in magnitude, to the radial stress. Predictions of the pressure distribution within the annulus were similar to published experimental measurements made in the radial and axial directions. The tangential stress within the annulus was considered to arise from the restoring stress in its strained collagen fibrils.     

Statistical factorial analysis on the poroelastic material properties sensitivity of the lumbar intervertebral disc under compression,flexion and axial rotation

A statistical factorial analysis approach was conducted on a poroelastic finite element model of a lumbar intervertebral disc to analyse the influence of six material parameters (permeabilities of annulus, nucleus, trabecular vertebral bone, cartilage endplate and Young's moduli of annulus and nucleus) on the displacement, fluid pore pressure and velocity fields. Three different loading modes were investigated: compression, flexion and axial rotation. Parameters were varied considering low and high levels in agreement with values found in the literature for both healthy and degenerated lumbar discs. Results indicated that annulus stiffness and cartilage endplate permeability have a strong effect on the overall fluid- and solid-phase responses in all loading conditions studied. Nucleus stiffness showed its main relevance in compression while annulus permeability influenced mainly the annular pressure field. This study confirms the permeability's central role in biphasic modelling and highlights for the lumbar disc which experiments of material property characterization should be performed. Moreover, such sensitivity study gives important guidelines in poroelastic material modelling and finite element disc validation.     

Numerical analysis of the influence of nucleus pulposus removal on the biomechanical behavior of a lumbar motion segment

Nucleus replacement was deemed to have therapeutic potential for patients with intervertebral disc herniation. However, whether a patient would benefit from nucleus replacement is technically unclear. This study aimed to investigate the influence of nucleus pulposus (NP) removal on the biomechanical behavior of a lumbar motion segment and to further explore a computational method of biomechanical characteristics of NP removal, which can evaluate the mechanical stability of pulposus replacement. We, respectively, reconstructed three types of models for a mildly herniated disc and three types of models for a severely herniated disc based on a L4–L5 segment finite element model with computed tomography image data from a healthy adult. First, the NP was removed from the herniated disc models, and the biomechanical behavior of NP removal was simulated. Second, the NP cavities were filled with an experimental material (Poisson's ratio = 0.3; elastic modulus = 3 MPa), and the biomechanical behavior of pulposus replacement was simulated. The simulations were carried out under the five loadings of axial compression, flexion, lateral bending, extension, and axial rotation. The changes of the four biomechanical characteristics, i.e. the rotation degree, the maximum stress in the annulus fibrosus (AF), joint facet contact forces, and the maximum disc deformation, were computed for all models. Experimental results showed that the rotation range, the maximum AF stress, and joint facet contact forces increased, and the maximum disc deformation decreased after NP removal, while they changed in the opposite way after the nucleus cavities were filled with the experimental material.     

Biomechanical comparison of the effects of anterior,posterior and transforaminal lumbar interbody fusion on vibration characteristics of the human lumbar spine

Previous studies have compared the effects of different interbody fusion approaches on biomechanical responses of the lumbar spine to static loadings. However, very few have dealt with the whole body vibration (WBV) condition that is typically present in vehicles. This study was designed to determine the biomechanical differences among anterior, posterior and transforaminal lumbar interbody fusion (ALIF, PLIF and TLIF) under vertical WBV. A previously developed and validated finite element (FE) model of the intact L1–sacrum human lumbar spine was modified to simulate ALIF, PLIF and TLIF with bilateral pedicle screw fixation at L4–L5. Comparative studies on dynamic responses to the axial cyclic loading in these developed models were conducted. The results showed that at the fused L4–L5 level, dynamic responses of the von-Mises stress in L4 inferior and L5 superior endplates for the ALIF, PLIF and TLIF models were increased compared with the intact model. The endplate stresses in the TLIF model were lower than in the ALIF and PLIF models, but the TLIF generated greater stresses in the screws and rods compared with the ALIF and PLIF. At other levels, a decrease in dynamic responses of the disc bulge, annulus stress and intradiscal pressure was observed in all the fusion models compared with the intact one, but there was no obvious difference in these dynamic responses among the ALIF, PLIF and TLIF models. These findings might be useful in understanding vibration characteristics of the whole lumbar spine after different types of fusion surgery.     

Stepwise reduction of functional spinal structures increase disc bulge and surface strains

Previous studies postulated that an axial compression of lumbar intervertebral discs causes a complex strain pattern on the annulus. This pattern is not fully understood, since most studies measured only the uniaxial ultimate tensile strain of the annulus. The aim of this study was to investigate surface strains and their relation to disc bulging. This work was extended to study some defects that are relevant for the intermediate process of finite element modeling. Six specimens (L2-3) with a median age of 51 years were utilized for this in vitro study. Specimens were loaded with pure moments (2.5-7.5Nm) in the principal directions. The anatomy was subsequently reduced in three steps: (1) ligamentous and bony posterior structures, (2) anterior and posterior ligaments and (3) nucleus. Measured were ranges of motion, three-dimensional disc bulging and surface strains of the outer annulus. Lateral bending showed the largest axial strains (9.7%) for intact specimens, which increased to 15.1% after the removal of posterior structures. Disc bulging was largest in flexion with 1.56mm, which increased to 2.06mm after step (1). Defect (2) caused that flexion yielded the largest axial strains with 22.6% and 2.17mm of bulging. We could also determine a constriction effect of these ligaments. Nucleotomy did not essentially increase anterior disc bulging in flexion, but inward disc bulging increased by 0.55mm, in extension. Due to the increase in the complexity of finite element models, it is difficult to obtain data from the literature for validation purposes. This study presents new data, which assist in the development of such models.     

Effect of collagen fibre orientation on intervertebral disc torsion mechanics

The intervertebral disc is a complex fibro-cartilaginous material, consisting of a pressurized nucleus pulposus surrounded by the annulus fibrosus, which has an angle-ply structure. Disc injury and degeneration are noted by significant changes in tissue structure and function, which significantly alters stress distribution and disc joint stiffness. Differences in fibre orientation are thought to contribute to changes in disc torsion mechanics. Therefore, the objective of this study was to evaluate the effect of collagen fibre orientation on internal disc mechanics under compression combined with axial rotation. We developed and validated a finite element model (FEM) to delineate changes in disc mechanics due to fibre orientation from differences in material properties. FEM simulations were performed with fibres oriented at \(\pm 30^{\circ }\) throughout the disc (uniform by region and fibre layer). The initial model was validated by published experimental results for two load conditions, including \(0.48\,\hbox {MPa}\) axial compression and \(10\,\hbox {Nm}\) axial rotation. Once validated, fibre orientation was rotated by \(4^{\circ }\) or \(8^{\circ }\) towards the horizontal plane, resulting in a decrease in disc joint torsional stiffness. Furthermore, we observed that axial rotation caused a sinusoidal change in disc height and radial bulge, which may be beneficial for nutrient transport. In conclusion, including anatomically relevant fibre angles in disc joint FEMs is important for understanding stress distribution throughout the disc and will be important for understanding potential causes for disc injury. Future models will include regional differences in fibre orientation to better represent the fibre architecture of the native disc.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Measurement of surface deformation of soft tissue

A method is described for measuring the surface shape and deformations of soft tissue in three dimensions. The method uses close range stereophotogrammetry to record the three-dimensional locations of miniature optical targets applied to the tissue surface. This has been applied to study of human lumbar intervertebral disc. Measurements of the strain along surface annular fibers have been made under varying loads. In this case the maximum expected errors are about 0.15 mm, which corresponds to a strain of less than 1%. Preliminary findings have differed from predictions made in published mathematical models for the disc in that they show very little strain of the annulus in compression loading, but confirm axial torsional loading as liable to produce mechanical disruption of the disc annulus.     

Response analysis of the lumbar spine during regular daily activities—A finite element analysis

A non-linear poroelastic finite element model of the lumbar spine was developed to investigate spinal response during daily dynamic physiological activities. Swelling was simulated by imposing a boundary pore pressure of 0.25 MPa at all external surfaces. Partial saturation of the disc was introduced to circumvent the negative pressures otherwise computed upon unloading. The loading conditions represented a pre-conditioning full day followed by another day of loading: 8 h rest under a constant compressive load of 350 N, followed by 16 h loading phase under constant or cyclic compressive load varying in between 1000 and 1600 N. In addition, the effect of one or two short resting periods in the latter loading phase was studied.The model yielded fairly good agreement with in-vivo and in-vitro measurements. Taking the partial saturation of the disc into account, no negative pore pressures were generated during unloading and recovery phase. Recovery phase was faster than the loading period with equilibrium reached in only ～3 h. With time and during the day, the axial displacement, fluid loss, axial stress and disc radial strain increased whereas the pore pressure and disc collagen fiber strains decreased. The fluid pressurization and collagen fiber stiffening were noticeable early in the morning, which gave way to greater compression stresses and radial strains in the annulus bulk as time went by. The rest periods dampened foregoing differences between the early morning and late in the afternoon periods. The forgoing diurnal variations have profound effects on lumbar spine biomechanics and risk of injury.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1-L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades?

Finite element analysis is a powerful tool routinely used to study complex biological systems. For the last four decades, the lumbar intervertebral disc has been the focus of many such investigations. To understand the disc functional biomechanics, a precise knowledge of the disc mechanical, structural and biochemical environments at the microscopic and macroscopic levels is essential. In response to this need, finite element model studies have proven themselves as reliable and robust tools when combined with in vitro and in vivo measurements.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

A combined numerical and experimental technique for estimation of the forces and moments in the lumbar intervertebral disc

Evaluation of the loads on lumbar intervertebral discs (IVD) is critically important since it is closely related to spine biomechanics, pathology and prosthesis design. Non-invasive estimation of the loads in the discs remains a challenge. In this study, we proposed a new technique to estimate in vivo loads in the IVD using a subject-specific finite element (FE) model of the disc and the kinematics of the disc endplates as input boundary conditions. The technique was validated by comparing the forces and moments in the discs calculated from the FE analyses to the in vitro experiment measurements of three corresponding lumbar discs. The results showed that the forces and moments could be estimated within an average error of 20%. Therefore, this technique can be a promising tool for non-invasive estimation of the loads in the discs and may be extended to be used on living subjects.     

Impact of material and morphological parameters on the mechanical response of the lumbar spine – A finite element sensitivity study

Finite element models are frequently used to study lumbar spinal biomechanics. Deterministic models are used to reflect a certain configuration, including the means of geometrical and material properties, while probabilistic models account for the inherent variability in the population. Because model parameters are generally uncertain, their predictive power is frequently questioned. In the present study, we determined the sensitivities of spinal forces and motions to material parameters of intervertebral discs, vertebrae, and ligaments and to lumbar morphology. We performed 1200 model simulations using a generic model of the human lumbar spine loaded under pure moments. Coefficients of determination and of variation were determined for all parameter and response combinations. Material properties of the vertebrae displayed the least impact on results, whereas those of the discs and morphology impacted most. The most affected results were the axial compression forces in the vertebral body and in several ligaments during flexion and the facet-joint forces during extension. Intervertebral rotations were considerably affected only when several parameters were varied simultaneously. Results can be used to decide which model parameters require careful consideration in deterministic models and which parameters might be omitted in probabilistic studies. Findings allow quantitative estimation of a model׳s precision.     

Effects of the ablation of the nucleus pulposus on the vibrational behavior of the lumbosacral hinge

This study was designed to investigate the respective damping properties of the annulus fibrosus and nucleus pulposus of the intervertebral disc during propagation of vibration waves through the osteoligamento-muscular axis of the spine. The study was conducted on a 8-10 kg deeply anesthetized baboon. In the first surgical phase five accelerometers were implanted in the first sacral vertebra and on the anterior side of the four lower lumbar vertebrae. The bioinstrumented animal was placed in a restraining chair and exposed to narrow-bandwidth (0-100 Hz) 0.16 G RMS random vibration. Once data was recorded, the nuclei pulposi of the studied discs were removed by suction, the surrounding annuli remaining intact. The still deeply anesthetized animal was again exposed to the same 0-100 Hz, 0.16 G RMS vibration. Results were analyzed and their reproducibility was tested on three animals.     

Collagen fibre orientation in the annulus fibrosus of intervertebral disc during bending and torsion measured by x-ray diffraction

X-ray diffraction has been used to measure the orientation of the collagen fibres in the ventral annulus fibrosus of intact L1/2 rabbit intervertebral disc during in vitro bending and torsion. Fibres are tilted with respect to the axis of the spine. As predicted by theory, fibre tilt decreases in those regions of the annulus which are stretched by bending but increases in the slackened regions. Good agreement with the quantitative predictions of bending theory was obtained in three of the six series of experiments, the predicted trend being found in all six. Tilt direction alternates in successive lamellae of the annulus. When discs were subjected to both clockwise and anticlockwise torsion of 5°, the two families of titled fibres reoriented in the expected directions.     

Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle

Many investigators have performed studies on specific defect situations or determined the contribution on isolated structures. Investigating the contribution of functional structures requires obtaining the kinematic response directly on spinal segments. The purpose of this study was to quantify the function of anatomical components on lumbar segments for different loading magnitudes. Eight spinal segments (L4-5) with a median age of 52 years (ranging from 38 to 59 years) and a low degree of disc degeneration were utilized for the in vitro testing. Specimens were mounted in a custom-built spine tester and loaded with pure moments (1-10 N m) to move within three anatomical planes at a loading rate of 1.0 degrees /s. Anatomy was successively reduced by: ligaments, facet capsules, joints and nucleus. Data were evaluated for range of motion, neutral zone and lordosis angle. Transection of posterior ligaments predominantly increased specimen flexion for all bending moments applied. Supraspinous ligament also indicated to resist in extension slightly, whereas the facet capsules did not. Facet joints contributed to axial rotation, but not in lateral bending. The anterior longitudinal ligament was found to slightly resist in axial rotation, but strongly in extension. Nucleotomy caused largest increase of all movements. The unloaded posture of the specimens changed after ligament dissection, indicating ligament pretension. The region of lumbar spine is interesting for finite element (FE) simulation due to the high evidence of disc degeneration and injuries. This study may help to understand the function of specific anatomical structures and assists in FE model calibration. We suggest to start a calibration procedure for such models with the smallest functional structure (annulus) and to cumulatively add further structures.     

An accurate finite element model of the cervical spine under quasi-static loading

Cervical disc injury due to impact has been observed in clinical and biomechanical investigations; however, there is a lack of data that helps to elucidate the mechanisms of disc injury during these collisions. Therefore, it is necessary to understand the behavior of the cervical spine under different types of loading situations. A three dimensional finite element (FE) model for the multi-level cervical spine segment (C0-C7) was developed using computed tomography (CT) data and applied to study the internal stresses and strains of the intervertebral discs under quasi-static loading conditions. The intervertebral discs were treated as nonlinear, anisotropic and incompressible subjected to large deformations. The model accuracy was validated by comparing it with previously published experimental and numerical results for different movements. It was shown that the use of a fiber reinforced model to describe the behavior of the annulus of the discs would predict higher maximum shear strains than an isotropic one, being therefore important the use of complex constitutive models in order to be able to detect the appearance of injured zones, since those strains and stresses are supposed to be related with damage to soft tissues. Several movements were analyzed: flexion, extension and axial rotation, obtaining that the maximum shear stresses in the disc were higher for a flexo-extension movement.     

Analysis of large compression loads on lumbar spine in flexion and in torsion using a novel wrapping element

Axial compression on the spine could reach large values especially in lifting tasks which also involve large rotations. Experimental and numerical investigations on the spinal multi motion segments in presence of physiological compression loads cannot adequately be carried out due to the structural instability and artefact loads. To circumvent these problems, a novel wrapping cable element is used in a nonlinear finite element model of the lumbosacral spine (L1-S1) to investigate the role of moderate to large compression loads on the lumbar stiffness in flexion and axial moments/rotations. The compression loads up to 2,700 N was applied with no instability or artefact loads. The lumbar stiffness substantially increased under compression force, flexion moment, and axial torque when applied alone. The presence of compression preloads significantly stiffened the load-displacement response under flexion and axial moments/rotations. This stiffening effect was much more pronounced under larger preloads and smaller moments/rotations. Compression preloads also increased intradiscal pressure, facet contact forces, and maximum disc fibre strain at different levels. Forces in posterior ligaments were, however, diminished with compression preload. The significant increase in spinal stiffness, hence, should be considered in biomechanical studies for accurate investigation of the load partitioning, system stability, and fixation systems/disc prostheses.