Influence of single-level lumbar degenerative disc disease on the behavior of the adjacent segments—A finite element model study

The current study investigated mechanical predictors for the development of adjacent disc degeneration. A 3-D finite element model of a lumbar spine was modified to simulate two grades of degeneration at the L4–L5 disc. Degeneration was modeled by changes in geometry and material properties. All models were subjected to follower preloads of 800 N and moment loads in the three principal directions of motion using a hybrid protocol. Degeneration caused changes in the loading and motion patterns of the segments above and below the degenerated disc. At the level (L3–L4) above the degenerated disc, the motion increased due to moderate degeneration by 21% under lateral bending, 26% under axial rotation and 28% under flexion/extension. At the level (L5-S1) below the degenerated disc, motion increased only during lateral bending by 20% due to moderate degeneration. Both the L3–L4 and L5-S1 segment showed a monotonic increase in both the maximum von Mises stress and shear stress in the annulus as degeneration progressed for all loading directions, expect extension at L3–L4. The most significant increase in stress was observed at the L5-S1 level during axial rotation with nearly a ten-fold increase in the maximum shear stress and 103% increase in the maximum von Mises stress. The L5-S1 segment also showed a progressive increase in facet contact force for all loading directions with degeneration. Nucleus pressure did not increase significantly for any loading direction at either the caudal or cephalic adjacent segment. Results suggest that single-level degeneration can increase the risk for injury at the adjacent levels.     

Computational biomechanics of a lumbar motion segment in pure and combined shear loads

Anterior shear has been implicated as a risk factor in spinal injuries. A 3D nonlinear poroelastic finite element model study of a lumbar motion segment L4-L5 was performed to predict the temporal shear response under various single and combined shear loads. Effects of nucleotomy and facetectomy as well as changes in the posture and facet gap distance were analyzed as well.     

Effect of lumbar fasciae on the stability of the lower lumbar spine

The biomechanical effect of tensioning the lumbar fasciae (LF) on the stability of the spine during sagittal plane motion was analysed using a validated finite element model of the normal lumbosacral spine (L4-S1). To apply the tension in the LF along the direction of the fibres, a local coordinate was allocated using dummy rigid beam elements that originated from the spinous process. Up to 10 Nm of flexion and 7.5 Nm of extension moment was applied with and without 20 N of lateral tension in the LF. A follower load of 400 N was additionally applied along the curvature of the spine. To identify how the magnitude of LF tension related to the stability of the spine, the tensioning on the fasciae was increased up to 40 N with an interval of 10 N under 7.5 Nm of flexion/extension moment. A fascial tension of 20 N produced a 59% decrease in angular motion at 2.5 Nm of flexion moment while there was a 12.3% decrease at 10 Nm in the L5-S1 segment. Its decrement was 53 and 9.6% at 2.5 Nm and 10 Nm, respectively, in the L4-L5 segment. Anterior translation was reduced by 12.1 and 39.0% at the L4-L5 and L5-S1 segments under 10 Nm of flexion moment, respectively. The flexion stiffness shows an almost linear increment with the increase in fascial tension. The results of this study showed that the effect of the LF on the stability of the spine is significant.     

Differences in 3D vs. 2D analysis in lumbar spinal fusion simulations

Lumbar interbody fusion is currently the gold standard in treating patients with disc degeneration or segmental instability. Despite it having been used for several decades, the non-union rate remains high. A failed fusion is frequently attributed to an inadequate mechanical environment after instrumentation. Finite element (FE) models can provide insights into the mechanics of the fusion process. Previous fusion simulations using FE models showed that the geometries and material of the cage can greatly influence the fusion outcome. However, these studies used axisymmetric models which lacked realistic spinal geometries. Therefore, different modeling approaches were evaluated to understand the bone-formation process.Three FE models of the lumbar motion segment (L4–L5) were developed: 2D, Sym-3D and Nonsym-3D. The fusion process based on existing mechano-regulation algorithms using the FE simulations to evaluate the mechanical environment was then integrated into these models. In addition, the influence of different lordotic angles (5, 10 and 15°) was investigated. The volume of newly formed bone, the axial stiffness of the whole segment and bone distribution inside and surrounding the cage were evaluated.In contrast to the Nonsym-3D, the 2D and Sym-3D models predicted excessive bone formation prior to bridging (peak values with 36 and 9% higher than in equilibrium, respectively). The 3D models predicted a more uniform bone distribution compared to the 2D model.The current results demonstrate the crucial role of the realistic 3D geometry of the lumbar motion segment in predicting bone formation after lumbar spinal fusion.     

Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method

Compared to a healthy intervertebral disc, the geometry and the material properties of the involved tissues are altered in a degenerated disc. It is not completely understood how this affects the mechanical behaviour of a motion segment. In order to study the influence of disc degeneration on motion segment mechanics a three-dimensional, nonlinear finite element model of the L3/L4 functional unit was used. Different grades of disc degeneration were simulated by varying disc height and bulk modulus of the nucleus pulposus. The model was loaded with pure moments of 10Nm in the three main anatomic planes. The finite element model predicted the same trends for intersegmental rotation and intradiscal pressure as described in the literature for in vitro studies. A comparison between calculated intersegmental rotation and experimental data showed a mean difference of 1.9 degrees while the mean standard deviation was 2.5 degrees . A mildly degenerated disc increases intersegmental rotation for all loading cases. With further increasing disc degeneration intersegmental rotation is decreased. For axial rotation the decrease takes place in the final stage. Intradiscal pressure is lower while facet joint force and maximum von Mises stress in the annulus are higher in a degenerated compared to a healthy disc.     

A finite element model of the L5-S1 functional spinal unit: development and comparison with biomechanical tests in vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro. Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

A Finite Element Model of the L5-S1 Functional Spinal Unit: Development and Comparison with Biomechanical Tests In Vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro . Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

An upper bound computational model for investigation of fusion effects on adjacent segment biomechanics of the lumbar spine

Abstract

Prediction of the biomechanical effects of fusion surgery on adjacent segments is a challenge in computational biomechanics of the spine. In this study, a two-segment L3-L4-L5 computational model was developed to simulate the effects of spinal fusion on adjacent segment biomechanical responses under a follower load condition. The interaction between the degenerative segment (L4-5) and the adjacent segment (L3-4) was simulated using an equivalent follower spring. The spring stiffness was calibrated using a rigid fusion of a completely degenerated disc model at the L4-5 level, resulting in an upper bound response at the adjacent (L3-4) segment. The obtained upper bound equivalent follower spring was used to simulate the upper bound biomechanical responses of fusion of the disc with different degeneration grades. It was predicted that as the disc degeneration grade at the degenerative segment decreased, the effect on the adjacent segment responses decreased accordingly after fusion. The data indicated that the upper bound computational model can be a useful computational tool for evaluation of the interaction between segments and for investigation of the biomechanical mechanisms of adjacent segment degeneration after fusion.     

Finite element analysis of moment-rotation relationships for human cervical spine

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.     

Is the sheep a suitable model to study the mechanical alterations of disc degeneration in humans? A probabilistic finite element model study

Intervertebral disc degeneration is one major source of low back pain, which because of its complex multifactorial nature renders the treatment challenging and thus necessitates extensive research. Experimental animal models have proven valuable in improving our understanding of degenerative processes and potentially promising therapies. Currently, the sheep is the most frequently used large animal in vivo model in intervertebral disc research. However, despite its undoubted value for investigations of the complex biological and cellular aspects, to date, it is unclear whether the sheep is also suited to study the mechanical aspects of disc degeneration in humans.A parametric finite element (FE) model of the L4–5 spinal motion segment was developed. Using this model, the geometry and the material properties of both the human and the ovine spinal segment as well as different appearances of disc degeneration can be depicted. Under pure and combined loads, it was investigated whether degenerative changes to both the human and the ovine model equivalent caused the same mechanical response.Different patterns of degeneration resulted in large variations in the ranges of motion, intradiscal pressure, ligament and facet loads. In the human, but not in the ovine model, all these results differed significantly between different degrees of degeneration.This FE model study highlighted possible differences in the mechanical response to disc degeneration between human and ovine intervertebral discs and indicates the necessity of further, more detailed, investigations.     

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2–L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate?Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5°/ms.     

Geometry strongly influences the response of numerical models of the lumbar spine--a probabilistic finite element analysis

Typical FE models of the human lumbar spine consider a single, fixed geometry. Such models cannot account for potential effects of the natural variability of the spine's geometry. In this study, we performed a probabilistic uncertainty and sensitivity analysis of a fully parameterized, geometrically simplified model of the L3-L4 segment. We examined the impact of the uncertainty in all 40 geometry parameters, estimated lower and upper bounds for the required sample size and determined the most important geometry parameters. The natural variability of the spine's geometry indeed strongly affects intradiscal pressure, range of motion and facet joint contact forces. Deriving generalized statements from fixed-geometry models as well as transferring those results to different cases thus can easily lead to wrong conclusions and should only be performed with extreme caution. We recommend a sample size of ≈ 100 to obtain reasonable accurate point estimates and a sufficient overview of the remaining uncertainties. Yet, only few parameters, especially those determining the disc geometry (disc height, end-plate width and depth) and the facets' position (intra-articular space, pedicle length, facet angles), proved to be truly important. Accurate measurement and modeling of those structures should therefore be prioritized.     

Porcine models in spinal research: calibration and comparative finite element analysis of various configurations during flexion-extension

This study was conducted to develop and calibrate a detailed 3-dimensional finite element model of the porcine lumbar spine and to compare this model with various configurations in flexion and extension. Computed tomography scans obtained from the L4-L5 lumbar segment of a Landrace x Large White pig were used to generate a solid volume. The various passive components were characterized by using a step-by-step calibration procedure in which the material properties of the anatomic structures were modified to match the corresponding in vitro data set-points retrieved from the literature. The range of motion of the totally assembled intact model was assessed under a 10-Nm flexion-extension moment and compared with data from a bilateral complete and hemifacetectomy configuration. In addition, the results from our porcine model were compared with published data regarding range of motion in a human finite element model in order to predict the configuration of the porcine model that most closely represented the human spine. Both the intact and hemifacetectomy configurations of the porcine model were comparable to the human spine. However, qualitative analysis of the instantaneous axis of rotation revealed a dissimilarity between the intact porcine model and human spine behavior, indicating the hemifacetectomy configuration of the porcine model as the most appropriate for spinal instrumentation studies. The present 3-dimensional finite element porcine model offers an additional tool to improve understanding of the biomechanics of the porcine spine and to decrease the expense of spinal research.     

Nonlinear gross response analysis of a lumbar motion segment in combined sagittal loadings

A 3-D nonlinear mathematical model is used to analyze the mechanical response of a lumbar L2-3 motion segment including the posterior elements when subjected to combined sagittal plane loads. The loadings consist of axial compression force, anterior and posterior shear forces, and flexion and extension moments. The facet articulation is modelled as a general moving contact problem and the ligaments as a collection of uniaxial elements. The disk nucleus is considered as an inviscid fluid and the annulus as a composite of collagenous fibers embedded in a matrix of ground substance. The presence of axial compression force reduces the segmental stiffness in flexion whereas a reverse trend is predicted in extension. In the presence of axial compression with and without sagittal shear force, flexion considerably increases the intradiscal pressure while extension reduces it. In other words, under an identical compression force, disk pressure is predicted to be noticeably larger in flexion than in extension. The segmental mechanical response in extension loadings is markedly influenced by the changes in the relative geometry of the articular surfaces at the lower regions. Finally, the deformation of the bony structures plays a significant role in the segmental mechanics under relatively large loads.     

Novel Pedicle Screw and Plate System Provides Superior Stability in Unilateral Fixation for Minimally Invasive Transforaminal Lumbar Interbody Fusion: An In Vitro Biomechanical Study

Purpose

This study aims to compare the biomechanical properties of the novel pedicle screw and plate system with the traditional rod system in asymmetrical posterior stabilization for minimally invasive transforaminal lumbar interbody fusion (MI-TLIF). We compared the immediate stabilizing effects of fusion segment and the strain distribution on the vertebral body.

Methods

Seven fresh calf lumbar spines (L3-L6) were tested. Flexion/extension, lateral bending, and axial rotation were induced by pure moments of ± 5.0 Nm and the range of motion (ROM) was recorded. Strain gauges were instrumented at L4 and L5 vertebral body to record the strain distribution under flexion and lateral bending (LB). After intact kinematic analysis, a right sided TLIF was performed at L4-L5. Then each specimen was tested for the following constructs: unilateral pedicle screw and rod (UR); unilateral pedicle screw and plate (UP); UR and transfacet pedicle screw (TFS); UP and TFS; UP and UR.

Results

All instrumented constructs significantly reduced ROM in all motion compared with the intact specimen, except the UR construct in axial rotation. Unilateral fixation (UR or UP) reduced ROM less compared with the bilateral fixation (UP/UR+TFS, UP+UR). The plate system resulted in more reduction in ROM compared with the rod system, especially in axial rotation. UP construct provided more stability in axial rotation compared with UR construct. The strain distribution on the left and right side of L4 vertebral body was significantly different from UR and UR+TFS construct under flexion motion. The strain distribution on L4 vertebral body was significantly influenced by different fixation constructs.

Conclusions

The novel plate could provide sufficient segmental stability in axial rotation. The UR construct exhibits weak stability and asymmetrical strain distribution in fusion segment, while the UP construct is a good alternative choice for unilateral posterior fixation of MI-TLIF.     

A finite element model of the L4-L5 spinal motion segment: biomechanical compatibility of an interspinous device

The biomechanical compatibility of an interspinous device, used for the "dynamic stabilization" of a diseased spinal motion segment, was investigated. The behaviour of an implant made of titanium based alloy (Ti6Al4V) and that of an implant made of a super-elastic alloy (Ni-Ti) have been compared. The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitable constitutive laws have been adopted for the annulus fibrosus and for the metal alloys. The model was aimed at simulating the healthy, the nucleotomized and the treated L4-L5 lumbar segment, subjected to compressive force and flexion-extension as well as lateral flexion moments. The computational model has shown that both the implants were able to achieve their main design purpose, which is to diminish the forces acting on the apophyseal joints. Nevertheless, the Ni-Ti implant has shown a more physiological flexural stiffness with respect to the Ti6Al4V implant, which exhibited an excessive stiffness and permanent strains (plastic strains), even under physiological loads. The computational models presented in this paper seems to be a promising tool able to predict the effectiveness of a biomedical device and to select the materials to be used for the implant manufacturing, within an engineering approach to the clinical problem of the spinal diseases.     

Study on effect of graded facetectomy on change in lumbar motion segment torsional flexibility using three-dimensional continuum contact representation for facet joints

Facet joints provide rigidity to the lumbar motion segment and thus protect the disk, particularly against torsional injury. A surgical procedure that fully or partially removes the facet joints (facetectomy) will decrease the mechanical stiffness of the motion segment, and potentially place the disk at risk of injury. Analytical models can be used to understand the effect of facet joints on motion segment stability. Using a facet joint model that represents the contact area as contact between two surfaces rather than as point contact, it was concluded that a substantial sudden change in rotational motion, due to applied torsion moment, was observed after 75 percent of any one of the facet joints was removed. Applied torsional moment loading produced coupled extension motion in the intact motion segment. This coupled motion also experienced a large change following complete unilateral facetectomy. Clinically, the present study showed that surgical intervention in the form of unilateral or bilateral total facetectomy might require fusion to reduce the primary torsion motion.     

Is Preventative Long-Segment Surgery for Multi-Level Spondylolysis Necessary? A Finite Element Analysis Study

Objective

For multi-level spondylolysis patients, surgeons commonly choose to fix all the segments with pars interarticularis defect even those without slippage and not responsible for clinical symptoms. In this study, we tried to study the necessity of the preventative long-segment surgery for the defected segment without slippage in treatment of multi-level spondylolysis patients from a biomechanical perspective.

Method

We established a bi-level spondylolysis model with pars defects at L4 and L5 segments, and simulated posterior lumbar interbody fusion (PLIF) and pedicle screw fixation at L5-S1 level. Then we compared the biomechanical changes at L4 segment before and after surgery in neutral, flexion, extension, lateral bending and axial rotation position.

Results

The stress on L4 pars interarticularis was very similar before and after surgery, and reached the highest in axial rotation. The L3-L4 intradiscal pressure was almost the same, while L4-L5 intradiscal pressure changed a little in lateral bending (increase from 1.993 to 2.160 MPa) and axial rotation (decrease from 1.639 to 1.307 MPa) after surgery. The PLIF surgery caused a little increase of range of motion at adjacent L4-L5 and L3-L4 levels, but the change is very tiny (1 degree).

Conclusion

The PLIF surgery will not cause significant biomechanical change at adjacent segment with pars defect in multi-level spondylolysis. On the contrary, excessive long-segment surgery will damage surrounding soft tissues which are important for maintaining the stability of spine. So a preventative long-segment surgery is not necessary for multi-level spondylolysis as long as there are no soft tissue degeneration signs at adjacent level.     

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.     

Simulation of the behaviour of the L1 vertebra for different material properties and loading conditions

Three-dimensional finite element models of the thoracolumbar junction (T12–L2) and isolated L1 vertebra were developed to investigate the role of material properties and loading conditions on vertebral stresses and strains to predict fracture risk. The geometry of the vertebrae was obtained from computed tomography images. The isolated vertebra model included an L1 vertebra loaded through polymethylmethacrylate plates located at the top and bottom of the vertebra, and the segment model included T12 to L2 vertebrae and seven ligaments, fibrous intervertebral discs and facet joints. Each model was examined with both homogeneous and spatially varying bone tissue properties. Stresses and strains were compared for uniform compression and flexion. Including material heterogeneity remarkably reduced the stiffness of the isolated L1 vertebra and increased the magnitudes of the minimum principal strains and stresses in the mid-transverse section. The stress and strain distributions further changed when physiological loading was applied to the L1 vertebra. In the segment models, including heterogeneous material properties increased the magnitude of the minimum principal strain by 158% in the centre of the mid-transverse section. Overall, the inclusion of heterogeneity and physiological loading increased the magnitude of the strains up to 346% in flexion and 273% in compression.