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.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4-L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion-extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion-extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

The effect of degenerative morphological changes of the intervertebral disc on the lumbar spine biomechanics: a poroelastic finite element investigation

Intervertebral disc degeneration involves changes in the spinal anatomical structures. The mechanical relevance of the following changes was investigated: disc height, endplate sclerosis, disc water content, permeability and depressurisation. A poroelastic nonlinear finite element model of the L4–L5 human spine segments was employed. Loads represented a daily cycle (500 N compression combined with flexion–extension motion for 16 h followed by 200 N compression for 8 h). In non-degenerative conditions, the model predicted a diurnal axial displacement of 1.32 mm and a peak intradiscal pressure of 0.47 MPa. Axial displacement, facet force and range of motion in flexion–extension are decreased by decreasing disc height. By decreasing the initial water content, axial displacement, facet force and fluid loss were all reduced. Endplate sclerosis did not have a significant influence on the calculated results. Depressurisation determined an increase of the disc effective stress, possibly inducing failure. Degenerative instability was not calculated in any simulations.     

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 finite element study of a lumbar motion segment subjected to pure sagittal plane moments

A nonlinear finite element program has been developed and applied to the analysis of a three-dimensional model of the lumbar L2-3 motion segment subjected to sagittal plane moments. The analysis accounts for both material and geometric nonlinearities and is based on the Updated Lagrangian approach. The disc nucleus has been considered as an incompressible inviscid fluid and the annulus as a composite of collagenous fibres embedded in a matrix of ground substance. Articulation at the facet joints has been treated as a general moving contact problem and the spinal ligaments have been modelled as a collection of nonlinear axial elements. Effects of the loss of intradiscal pressure in flexion and of facetectomy in extension have been analyzed. Comparison of the predicted gross response characteristics with available measurements indicates satisfactory agreement. In flexion relatively large intradiscal pressures are generated, while in extension negative pressures (i.e. suction) of low magnitude are predicted. The stress distribution results indicate that the load transfer path through the posterior elements of the joint in flexion is different from that in extension. In flexion the ligaments are the means of load transfer, while in extension the load is transmitted through the pedicles, laminae and articular processes. In flexion, the inner annulus fibres at the posterolateral location are subject to maximum tensile strain. It is suggested that large flexion moment in combination with other loads is a likely cause of disc prolapse commonly found at this location of the annulus.     

Sensitivity of lumbar spine response to follower load and flexion moment: finite element study

The follower load (FL) combined with moments is commonly used to approximate flexed/extended posture of the lumbar spine in absence of muscles in biomechanical studies. There is a lack of consensus as to what magnitudes simulate better the physiological conditions. Considering the in-vivo measured values of the intradiscal pressure (IDP), intervertebral rotations (IVRs) and the disc loads, sensitivity of these spinal responses to different FL and flexion moment magnitudes was investigated using a 3D nonlinear finite element (FE) model of ligamentous lumbosacral spine. Optimal magnitudes of FL and moment that minimize deviation of the model predictions from in-vivo data were determined. Results revealed that the spinal parameters i.e. the IVRs, disc moment, and the increase in disc force and moment from neutral to flexed posture were more sensitive to moment magnitude than FL magnitude in case of flexion. The disc force and IDP were more sensitive to the FL magnitude than moment magnitude. The optimal ranges of FL and flexion moment magnitudes were 900–1100 N and 9.9–11.2 Nm, respectively. The FL magnitude had reverse effect on the IDP and disc force. Thus, magnitude for FL or flexion that minimizes the deviation of all the spinal parameters together from the in-vivo data can vary. To obtain reasonable compromise between the IDP and disc force, our findings recommend that FL of low magnitude must be combined with flexion moment of high intensity and vice versa.     

Biomechanical analysis of lumbar interbody fusion cages with various lordotic angles: a finite element study

Inappropriate lordotic angle of lumbar fusion cage could be associated with cage damage or subsidence. The biomechanical influence of cage lordotic angle on lumbar spine has not been fully investigated. Four surgical finite element models were constructed by inserting cages with various lordotic angles at L3-L4 disc space. The four motion modes were simulated. The range of motion (ROM) decreased with increased lordotic angle of cage in flexion, extension, and rotation, whereas it was not substantially changed in bending. The maximum stress in cage decreased with increased lordotic angle of cage in all motion modes. The maximum stress in endplate at surgical level increased with increased lordotic angle of cage in flexion and rotation, whereas it was not substantially changed in extension and bending. The facet joint force (FJF) was much smaller than that for the intact conditions in extension, bending, and rotation, while it was not substantially changed in flexion. In conclusion, the ROM, stresses in the cage and endplate at surgical level are sensitive to the lordotic angle of cage. The increased cage lordotic angle may provide better stability and reduce the risk of cage damage, whereas it may increase the risk of subsidence in flexion and rotation.     

Modeling the biomechanics of the mandible: a three-dimensional finite element study.

Three-dimensional finite element models of a partially edentulated human mandible were generated to calculate the mechanical response to simulated isometric biting and mastication loads. The level of mesh refinement was established via a convergence test and showed that a model with over 30,000 degrees of freedom was required to obtain analysis accuracy. The functional loading cases included muscle loading based on an algorithm that assigns muscle forces in accordance with muscle cross-sectional area, while maintaining static equilibrium. Results were found for isometric application of unilateral and bilateral bite and mastication loading, and two different sets of displacement boundary conditions were imposed at the condyles. The mechanical response is shown in terms of displacements, principal strains, and a new measure called the 'mechanical intensity scalar'. For each load case studied, there was substantial bending in the molar region of the corpus and high tensile strains in the anterior portion of the ramus.     

Pedicle screw-based posterior dynamic stabilisation of the lumbar spine: in vitro cadaver investigation and a finite element study

Pedicle screw-based dynamic constructs either benefit from a dynamic (flexible) interconnecting rod or a dynamic (hinged) screw. Both types of systems have been reported in the literature. However, reports where the dynamic system is composed of two dynamic components, i.e. a dynamic (hinged) screw and a dynamic rod, are sparse. In this study, the biomechanical characteristics of a novel pedicle screw-based dynamic stabilisation system were investigated and compared with equivalent rigid and semi-rigid systems using in vitro testing and finite element modelling analysis. All stabilisation systems restored stability after decompression. A significant decrease in the range of motion was observed for the rigid system in all loadings. In the semi-rigid construct the range of motion was significantly less than the intact in extension, lateral bending and axial rotation loadings. There were no significant differences in motion between the intact spine and the spine treated with the dynamic system (P>0.05). The peak stress in screws was decreased when the stabilisation construct was equipped with dynamic rod and/or dynamic screws.     

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.     

Effect of screw position on load transfer in lumbar pedicle screws: a non-idealized finite element analysis

Angled screw insertion has been advocated to enhance fixation strength during posterior spine fixation. Stresses on a pedicle screw and surrounding vertebral bone with different screw angles were studied by finite element analysis during simulated multidirectional loading. Correlations between screw-specific vertebral geometric parameters and stresses were studied. Angulations in both the sagittal and axial planes affected stresses on the cortical and cancellous bones and the screw. Pedicle screws pointing laterally (vs. straight or medially) in the axial plane during superior screw angulation may be advantageous in terms of reducing the risk of both screw loosening and screw breakage.     

Biomechanical study of pediatric human cervical spine: a finite element approach

Although considerable effort has been made to understand the biomechanical behavior of the adult cervical spine, relatively little information is available on the response of the pediatric cervical spine to external forces. Since significant anatomical differences exist between the adult and pediatric cervical spines, distinct biomechanical responses are expected. The present study quantified the biomechanical responses of human pediatric spines by incorporating their unique developmental anatomical features. One-, three-, and six-year-old cervical spines were simulated using the finite element modeling technique, and their responses computed and compared with the adult spine response. The effects of pure overall structural scaling of the adult spine, local component developmental anatomy variations that occur to the actual pediatric spines, and structural scaling combined with local component anatomy variations on the responses of the pediatric spines were studied. Age- and component-related developmental anatomical features included variations in the ossification centers, cartilages, growth plates, vertebral centrum, facet joints, and annular fibers and nucleus pulposus of the intervertebral discs. The flexibility responses of the models were determined under pure compression, pure flexion, pure extension, and varying degrees of combined compression-flexion and compression-extension. The pediatric spine responses obtained with the pure overall (only geometric) scaling of the adult spine indicated that the flexibilities consistently increase in a uniform manner from six- to one-year-old spines under all loading cases. In contrast, incorporation of local anatomic changes specific to the pediatric spines of the three age groups (maintaining the same adult size) not only resulted in considerable increases in flexibilities, but the responses also varied as a function of the age of the pediatric spine and type of external loading. When the geometric scaling effects were added to these spines, the increases in flexibilities were slightly higher; however, the pattern of the responses remained the same as found in the previous approach. These results indicate that inclusion of developmental anatomical changes characteristic of the pediatric spines has more of a predominant effect on biomechanical responses than extrapolating responses of the adult spine based on pure overall geometric scaling.     

Quantitative comparison of ligament formulation and pre-strain in finite element analysis of the human lumbar spine

Data has been published that quantifies the nonlinear, anisotropic material behaviour and pre-strain behaviour of the anterior longitudinal, supraspinous (SSL), and interspinous ligaments of the human lumbar spine. Additionally, data has been published on localized material properties of the SSL. These results have been incrementally incorporated into a previously validated finite element model of the human lumbar spine. Results suggest that the effects of increased ligament model fidelity on bone strain energy were moderate and the effects on disc pressure were slight, and do not justify a change in modelling strategy for most clinical applications. There were significant effects on the ligament stresses of the ligaments that were directly modified, suggesting that these phenomena should be included in FE models where ligament stresses are the desired metric.     

Stenting-induced Vasa Vasorum compression and subsequent flow resistance: a finite element study

Biomechanics and Modeling in Mechanobiology - Vascular stenting is a common intervention for the treatment for atherosclerotic plaques. However, stenting still has a significant rate of restenosis...     

Effects of eight different ligament property datasets on biomechanics of a lumbar L4-L5 finite element model

Ligaments assist trunk muscles in balancing external moments and providing spinal stability. In absence of the personalized material properties for ligaments, finite element (FE) models use dispersed data from the literature. This study aims to investigate the relative effects of eight different ligament property datasets on FE model responses. Eight L4-L5 models distinct only in ligament properties were constructed and loaded under moment (15 N m) alone or combined with a compressive follower load (FL). Range of motions (RoM) of the disc-alone model matched well in vitro data. Ligament properties significantly affected only sagittal RoMs (∼3.0–7.1° in flexion and ∼3.8–5.8° in extension at 10 N m). Sequential removal of ligaments shifted sagittal RoMs in and out of the corresponding in vitro ranges. When moment was combined with FL, center of rotation matched in vivo data for all models (3.8 ± 0.9 mm and 4.3 ± 1.8 mm posterior to the disc center in flexion and extension, respectively). Under 15 N m sagittal moments, ligament strains were often smaller or within the in vitro range in flexion whereas some posterior ligament forces approached their failure forces in some models. Ligament forces varied substantially within the models and affected the moment-sharing and internal forces on the disc and facet joints. Intradiscal pressure (IDP) had the greatest variation between models in extension. None of the datasets yielded results in agreement with all reported measurements. Results emphasized the important role of ligaments especially under larger moments and the need for their accurate representation in search for valid spinal models.     

A finite element model technique to determine the mechanical response of a lumbar spine segment under complex loads

This study presents a CT-based finite element model of the lumbar spine taking into account all function-related boundary conditions, such as anisotropy of mechanical properties, ligaments, contact elements, mesh size, etc. Through advanced mesh generation and employment of compound elements, the developed model is capable of assessing the mechanical response of the examined spine segment for complex loading conditions, thus providing valuable insight on stress development within the model and allowing the prediction of critical loading scenarios. The model was validated through a comparison of the calculated force-induced inclination/deformation and a correlation of these data to experimental values. The mechanical response of the examined functional spine segment was evaluated, and the effect of the loading scenario determined for both vertebral bodies as well as the connecting intervertebral disc.     

Three-dimensional finite element analysis of the foot during standing--a material sensitivity study

Information on the internal stresses/strains in the human foot and the pressure distribution at the plantar support interface under loading is useful in enhancing knowledge on the biomechanics of the ankle-foot complex. While techniques for plantar pressure measurements are well established, direct measurement of the internal stresses/strains is difficult. A three-dimensional (3D) finite element model of the human foot and ankle was developed using the actual geometry of the foot skeleton and soft tissues, which were obtained from 3D reconstruction of MR images. Except the phalanges that were fused, the interaction among the metatarsals, cuneiforms, cuboid, navicular, talus, calcaneus, tibia and fibula were defined as contact surfaces, which allow relative articulating movement. The plantar fascia and 72 major ligaments were simulated using tension-only truss elements by connecting the corresponding attachment points on the bone surfaces. The bony and ligamentous structures were embedded in a volume of soft tissues. The encapsulated soft tissue was defined as hyperelastic, while the bony and ligamentous structures were assumed to be linearly elastic. The effects of soft tissue stiffening on the stress distribution of the plantar surface and bony structures during balanced standing were investigated. Increases of soft tissue stiffness from 2 and up to 5 times the normal values were used to approximate the pathologically stiffened tissue behaviour with increasing stages of diabetic neuropathy. The results showed that a five-fold increase in soft tissue stiffness led to about 35% and 33% increase in the peak plantar pressure at the forefoot and rearfoot regions, respectively. This corresponded to about 47% decrease in the total contact area between the plantar foot and the horizontal support surface. Peak bone stress was found at the third metatarsal in all calculated cases with a minimal increase of about 7% with soft tissue stiffening.     

Evaluation of Euler's angles with a least squares method for the study of lumbar spine motion

To analyse intervertebral movements, methods with a high level of accuracy are required. Stereoradiographic methods have been used for a number of years to describe intervertebral movements, but their major problem is to identify the same anatomical landmarks, not only on the pair of radiographs used for three-dimensional reconstruction, but also on all the pairs used to analyse the displacements. To minimize the errors due to the incorrect identification of anatomical landmarks, a least squares method to resolve the parameters of Euler's angles was validated by means of measurements made on a spine obtained from a cadaver. The accuracy of this method varied between 0.69° and 0.71° in rotation and between 0.28 mm and 0.77 mm in translation. In addition, this method significantly corrected the position of the anatomical landmarks. Euler's angles, used with a least squares estimate, can provide accurate and precise results.     

The influence of different magnitudes and methods of applying preload on fusion and disc replacement constructs in the lumbar spine: a finite element analysis

In a finite element (FE) analysis of the lumbar spine, different preload application methods that are used in biomechanical studies may yield diverging results. To investigate how the biomechanical behaviour of a spinal implant is affected by the method of applying the preload, hybrid-controlled FE analysis was used to evaluate the biomechanical behaviour of the lumbar spine under different preload application methods. The FE models of anterior lumbar interbody fusion (ALIF) and artificial disc replacement (ADR) were tested under three different loading conditions: a 150 N pressure preload (PP) and 150 and 400 N follower loads (FLs). This study analysed the resulting range of motion (ROM), facet contact force (FCF), inlay contact pressure (ICP) and stress distribution of adjacent discs. The FE results indicated that the ROM of both surgical constructs was related to the preload application method and magnitude; differences in the ROM were within 7% for the ALIF model and 32% for the ADR model. Following the application of the FL and after increasing the FL magnitude, the FCF of the ADR model gradually increased, reaching 45% at the implanted level in torsion. The maximum ICP gradually decreased by 34.1% in torsion and 28.4% in lateral bending. This study concluded that the preload magnitude and application method affect the biomechanical behaviour of the lumbar spine. For the ADR, remarkable alteration was observed while increasing the FL magnitude, particularly in the ROM, FCF and ICP. However, for the ALIF, PP and FL methods had no remarkable alteration in terms of ROM and adjacent disc stress.