Influence of geometrical factors on the behavior of lumbar spine segments: a finite element analysis

Morphology and Composition of Lumbar Intervertebral Discs: Comparative Analyses of Manual Measurement and Computer-Assisted Algorithms

BACKGROUND

The morphology and internal composition, particularly the nucleus-to-cross sectional area (NP-to-CSA) ratio of the lumbar intervertebral discs (IVDs), is important information for finite element models (FEMs) of spinal loadings and biomechanical behaviors, and, yet, this has not been well investigated and reported.

METHODS

Anonymized MRI scans were retrieved from a previously established database, including a total of 400 lumbar IVDs from 123 subjects (58 F and 65 M). Measurements were conducted manually by a spine surgeon and using two computer-assisted segmentation algorithms, i.e., fuzzy C-means (FCM) and region growing (RG). The respective results were compared. The influence of gender and spinal level was also investigated.

RESULTS

Ratios derived from manual measurements and the two computer-assisted algorithms (FCM and RG) were 46%, 39%, and 38%, respectively. Ratios derived manually were significantly larger.

CONCLUSIONS

Computer-assisted methods provide reliable outcomes that are traditionally difficult for the manual measurement of internal composition. FEMs should consider the variability of NP-to-CSA ratios when studying the biomechanical behavior of the spine.

Subject-Specific Geometry of FE Lumbar Spine Models for the Replication of Fracture Locations Using Dynamic Drop Tests

For traumatic lumbar spine injuries, the mechanisms and influence of anthropometrical variation are not yet fully understood under dynamic loading. Our objective was to evaluate whether geometrically subject-specific explicit finite element (FE) lumbar spine models based on state-of-the-art clinical CT data combined with general material properties from the literature could replicate the experimental responses and the fracture locations via a dynamic drop tower-test setup. The experimental CT datasets from a dynamic drop tower-test setup were used to create anatomical details of four lumbar spine models (T12 to L5). The soft tissues from THUMS v4.1 were integrated by morphing. Each model was simulated with the corresponding loading and boundary conditions from the dynamic lumbar spine tests that produced differing injuries and injury locations. The simulations resulted in force, moment, and kinematic responses that effectively matched the experimental data. The pressure distribution within the models was used to compare the fracture occurrence and location. The spinal levels that sustained vertebral body fracture in the experiment showed higher simulation pressure values in the anterior elements than those in the levels that did not fracture in the reference experiments. Similarly, the spinal levels that sustained posterior element fracture in the experiments showed higher simulation pressure values in the vertebral posterior structures compared to those in the levels that did not sustain fracture. Our study showed that the incorporation of the spinal geometry and orientation could be used to replicate the fracture type and location under dynamic loading. Our results provided an understanding of the lumbar injury mechanisms and knowledge on the load thresholds that could be used for injury prediction with explicit FE lumbar spine models.

The influence of geometry on intervertebral disc stiffness

Geometry plays an important role in intervertebral disc (IVD) mechanics. Previous computational studies have found a link between IVD geometry and stiffness. However, few experimental studies have investigated this link, possibly due to difficulties in non-destructively quantifying internal geometric features. Recent advances in ultra-high resolution MRI provides the opportunity to visualise IVD features in unprecedented detail. This study aimed to quantify 3D human IVD geometries using 9.4 T MRIs and to investigate correlations between geometric variations and IVD stiffness. Thirty human lumbar motion segments (fourteen non-degenerate and sixteen degenerate) were scanned using a 9.4 T MRI and geometric parameters were measured. A 1kN compressive load was applied to each motion segment and stiffness was calculated. Degeneration caused a reduction (p < 0.05) in IVD height, a decreased nucleus-annulus area ratio, and a 1.6 ± 3.0 mm inward collapse of the inner annulus. The IVD height, anteroposterior (AP) width, lateral width, cross-sectional area, nucleus-annulus boundary curvature, and nucleus-annulus area ratio had a significant (p < 0.05) influence on IVD stiffness. Linear relationships (p < 0.05, r > 0.47) were observed between these geometric features and IVD compressive stiffness and a multivariate regression model was generated to enable stiffness to be predicted from features observable on clinical imaging (stiffness, N/mm = 6062 - (61.2 × AP width, mm) - (169.2 × IVD height, mm)). This study advances our understanding of disc structure-function relationships and how these change with degeneration, which can be used to both generate and validate more realistic computational models.

Inter-Specimen Analysis of Diverse Finite Element Models of the Lumbar Spine

Over the past few decades, there has been a growing popularity in utilizing finite element analysis to study the spine. However, most current studies tend to use one specimen for their models. This research aimed to validate multiple finite element models by comparing them with data from in vivo experiments and other existing finite element studies. Additionally, this study sought to analyze the data based on the gender and age of the specimens. For this study, eight lumbar spine (L2-L5) finite element models were developed. These models were then subjected to finite element analysis to simulate the six fundamental motions. CT scans were obtained from a total of eight individuals, four males and four females, ranging in age from forty-four (44) to seventy-three (73) years old. The CT scans were preprocessed and used to construct finite element models that accurately emulated the motions of flexion, extension, lateral bending, and axial rotation. Preloads and moments were applied to the models to replicate physiological loading conditions. This study focused on analyzing various parameters such as vertebral rotation, facet forces, and intradiscal pressure in all loading directions. The obtained data were then compared with the results of other finite element analyses and in vivo experimental measurements found in the existing literature to ensure their validity. This study successfully validated the intervertebral rotation, intradiscal pressure, and facet force results by comparing them with previous research findings. Notably, this study concluded that gender did not have a significant impact on the results. However, the results did highlight the importance of age as a critical variable when modeling the lumbar spine.

Development and validation of lumbar spine finite element model

The functional biomechanics of the lumbar spine have been better understood by finite element method (FEM) simulations. However, there are still areas where the behavior of soft tissues can be better modeled or described in a different way. The purpose of this research is to develop and validate a lumbar spine section intended for biomechanical research. A FE model of the 50th percentile adult male (AM) Total Human Model for Safety (THUMS) v6.1 was used to implement the modifications. The main modifications were to apply orthotropic material properties and nonlinear stress-strain behavior for ligaments, hyperelastic material properties for annulus fibrosus and nucleus pulposus, and the specific content of collagenous fibers in the annulus fibrosus ground substance. Additionally, a separation of the nucleus pulposus from surrounding bones and tissues was implemented. The FE model was subjected to different loading modes, in which intervertebral rotations and disc pressures were calculated. Loading modes contained different forces and moments acting on the lumbar section: axial forces (compression and tension), shear forces, pure moments, and combined loading modes of axial forces and pure moments. The obtained ranges of motion from the modified numerical model agreed with experimental data for all loading modes. Moreover, intradiscal pressure validation for the modified model presented a good agreement with the data available from the literature. This study demonstrated the modifications of the THUMS v6.1 model and validated the obtained numerical results with existing literature in the sub-injurious range. By applying the proposed changes, it is possible to better model the behavior of the human lumbar section under various loads and moments.

Computational lumbar spine models: A literature review

BACKGROUND

Computational spine models of various types have been employed to understand spine function, assess the risk that different activities pose to the spine, and evaluate techniques to prevent injury. The areas in which these models are applied has expanded greatly, potentially beyond the appropriate scope of each, given their capabilities. A comprehensive understanding of the components of these models provides insight into their current capabilities and limitations.

METHODS

The objective of this review was to provide a critical assessment of the different characteristics of model elements employed across the spectrum of lumbar spine modeling and in newer combined methodologies to help better evaluate existing studies and delineate areas for future research and refinement.

FINDINGS

A total of 155 studies met selection criteria and were included in this review. Most current studies use either highly detailed Finite Element models or simpler Musculoskeletal models driven with in vivo data. Many models feature significant geometric or loading simplifications that limit their realism and validity. Frequently, studies only create a single model and thus can't account for the impact of subject variability. The lack of model representation for certain subject cohorts leaves significant gaps in spine knowledge. Combining features from both types of modeling could result in more accurate and predictive models.

INTERPRETATION

Development of integrated models combining elements from different model types in a framework that enables the evaluation of larger populations of subjects could address existing voids and enable more realistic representation of the biomechanics of the lumbar spine.

Finite Element Analysis of a Bionate Ring-Shaped Customized Lumbar Disc Nucleus Prosthesis

Study design: Biomechanical study of a nucleus replacement with a finite element model. Objective: To validate a Bionate 80A ring-shaped nucleus replacement. Methods: The ANSYS lumbar spine model made from lumbar spine X-rays and magnetic resonance images obtained from cadaveric spine specimens were used. All materials were assumed homogeneous, isotropic, and linearly elastic. We studied three options: intact spine, nucleotomy, and nucleus implant. Two loading conditions were evaluated at L₃-L₄, L₄-L₅, and L₅-S₁ discs: a 1000 N axial compression load and this load after the addition of 8 Nm flexion moment in the sagittal plane plus 8 Nm axial rotation torque. Results: Maximum nucleus implant axial compression stresses in the range of 16–34 MPa and tensile stress in the range of 5–16 MPa, below Bionate 80A resistance were obtained. Therefore, there is little risk of permanent implant deformation or severe damage under normal loading conditions. Nucleotomy increased segment mobility, zygapophyseal joint and end plate pressures, and annulus stresses and strains. All these parameters were restored satisfactorily by nucleus replacement but never reached the intact status. In addition, annulus stresses and strains were lower with the nucleus implant than in the intact spine under axial compression and higher under complex loading conditions. Conclusions: Under normal loading conditions, there is a negligible risk of nucleus replacement, permanent deformation or severe damage. Nucleotomy increased segmental mobility, zygapophyseal joint pressures, and annulus stresses and strains. Nucleus replacement restored segmental mobility and zygapophyseal joint pressures close to the intact spine. End plate pressures were similar for the intact and nucleus implant conditions under both loading modes. Manufacturing customized nucleus implants is considered feasible, as satisfactory biomechanical performance is confirmed.

Sensitivity of Intervertebral Disc Finite Element Models to Internal Geometric and Non-geometric Parameters

Finite element models are useful for investigating internal intervertebral disc (IVD) behaviours without using disruptive experimental techniques. Simplified geometries are commonly used to reduce computational time or because internal geometries cannot be acquired from CT scans. This study aimed to (1) investigate the effect of altered geometries both at endplates and the nucleus-anulus boundary on model response, and (2) to investigate model sensitivity to material and geometric inputs, and different modelling approaches (graduated or consistent fibre bundle angles and glued or cohesive inter-lamellar contact). Six models were developed from 9.4 T MRIs of bovine IVDs. Models had two variations of endplate geometry (a simple curved profile from the centre of the disc to the periphery, and precise geometry segmented from MRIs), and three variations of NP-AF boundary (linear, curved, and segmented). Models were subjected to axial compressive loading (to 0.86 mm at a strain rate of 0.1/s) and the effect on stiffness and strain distributions, and the sensitivity to modelling approaches was investigated. The model with the most complex geometry (segmented endplates, curved NP-AF boundary) was 3.1 times stiffer than the model with the simplest geometry (curved endplates, linear NP-AF boundary), although this difference may be exaggerated since segmenting the endplates in the complex geometry models resulted in a shorter average disc height. Peak strains were close to the endplates at locations of high curvature in the segmented endplate models which were not captured in the curved endplate models. Differences were also seen in sensitivity to material properties, graduated fibre angles, cohesive rather than glued inter-lamellar contact, and NP:AF ratios. These results show that FE modellers must take care to ensure geometries are realistic so that load is distributed and passes through IVDs accurately.

Development of a finite element biomechanical whole spine model for analyzing lumbar spine loads under caudocephalad acceleration

Background:Spine injury risk due to military conflict is an ongoing concern among defense organizations throughout the world. A better understanding of spine biomechanics could assist in developing protection devices to reduce injuries caused by caudocephalad acceleration (+Gz) in under-body blasts (UBB). Although some finite element (FE) human models have demonstrated reasonable lumbar spine biofidelity, they were either partial spine models or not validated for UBB-type loading modes at the lumbar functional spinal unit (FSU) level, thus limiting their ability to analyze UBB-associated occupant kinematics.Methods:An FE functional representation of the human spine with simplified geometry was developed to study the lumbar spine responses under +Gz loading. Fifty-seven load curves obtained from post mortem human subject experiments were used to optimize the model.Results:The model was cumulatively validated for compression, flexion, extension, and anterior-, posterior-, and lateral-shears of the lumbar spine and flexion and extension of the cervical spine. The thoracic spine was optimized for flexion and compression. The cumulative CORrelation and Analysis (CORA) rating for the lumbar spine was 0.766 and the cervical spine was 0.818; both surpassed the 0.7 objective goal. The model's element size was confirmed as converged.Conclusions:An FE functional representation of the human spine was developed for +Gz lumbar load analysis. The lumbar and cervical spines were demonstrated to be quantitatively biofidelic to the FSU level for multi-directional loading and bending typically experienced in +Gz loading, filling the capability gap in current models.

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.

FEBio finite element models of the human lumbar spine

Finite element analysis has proven to be a viable method for assessing many structure-function relationships in the human lumbar spine. Several validated models of the spine have been published, but they typically rely on commercial packages and are difficult to share between labs. The goal of this study is to present the development of the first open-access models of the human lumbar spine in FEBio. This modeling framework currently targets three deficient areas in the field of lumbar spine modeling: 1) open-access models, 2) accessibility for multiple meshing schemes, and 3) options to include advanced hyperelastic and biphasic constitutive models.

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.

On the load-sharing along the ligamentous lumbosacral spine in flexed and extended postures: Finite element study

A harmonic synergy between the load-bearing and stabilizing components of the spine is necessary to maintain its normal function. This study aimed to investigate the load-sharing along the ligamentous lumbosacral spine under sagittal loading. A 3D nonlinear detailed Finite Element (FE) model of lumbosacral spine with realistic geometry was developed and validated using wide range of numerical and experimental (in-vivo and in-vitro) data. The model was subjected to 500 N compressive Follower Load (FL) combined with 7.5 Nm flexion (FLX) or extension (EXT) moments. Load-sharing was expressed as percentage of total internal force/moment developed along the spine that each spinal component carried. These internal forces and moments were determined at the discs centres and included the applied load and the resisting forces in the ligaments and facet joints. The contribution of the facet joints and ligaments in supporting bending moments produced additional forces and moments in the discs. The intervertebral discs carried up to 81% and 68% of the total internal force in case of FL combined with FLX and EXT, respectively. The ligaments withstood up to 67% and 81% of the total internal moment in cases of FL combined with EXT and FLX, respectively. Contribution of the facet joints in resisting internal force and moment was noticeable at levels L4-S1 only particularly in case of FL combined with EXT and reached up 29% and 52% of the internal moment and force, respectively. This study demonstrated that spinal load-sharing depended on applied load and varied along the spine.

Relevant Anatomic and Morphological Measurements of the Rat Spine: Considerations for Rodent Models of Human Spine Trauma

STUDY DESIGN

Basic science study measuring anatomical features of the cervical and lumbar spine in rat with normalized comparison with the human.

OBJECTIVE

The goal of this study is to comprehensively compare the rat and human cervical and lumbar spines to investigate whether the rat is an appropriate model for spine biomechanics investigations.

SUMMARY OF BACKGROUND DATA

Animal models have been used for a long time to investigate the effects of trauma, degenerative changes, and mechanical loading on the structure and function of the spine. Comparative studies have reported some mechanical properties and/or anatomical dimensions of the spine to be similar between various species. However, those studies are largely limited to the lumbar spine, and a comprehensive comparison of the rat and human spines is lacking.

METHODS

Spines were harvested from male Holtzman rats (n = 5) and were scanned using micro- computed tomography and digitally rendered in 3 dimensions to quantify the spinal bony anatomy, including the lateral width and anteroposterior depth of the vertebra, vertebral body, and spinal canal, as well as the vertebral body and intervertebral disc heights. Normalized measurements of the vertebra, vertebral body, and spinal canal of the rat were computed and compared with corresponding measurements from the literature for the human in the cervical and lumbar spinal regions.

RESULTS

The vertebral dimensions of the rat spine vary more between spinal levels than in humans. Rat vertebrae are more slender than human vertebrae, but the width-to-depth axial aspect ratios are very similar in both species in both the cervical and lumbar regions, especially for the spinal canal.

CONCLUSION

The similar spinal morphology in the axial plane between rats and humans supports using the rat spine as an appropriate surrogate for modeling axial and shear loading of the human spine.

Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together

Finite element (FE) model studies have made important contributions to our understanding of functional biomechanics of the lumbar spine. However, if a model is used to answer clinical and biomechanical questions over a certain population, their inherently large inter-subject variability has to be considered. Current FE model studies, however, generally account only for a single distinct spinal geometry with one set of material properties. This raises questions concerning their predictive power, their range of results and on their agreement with in vitro and in vivo values. Eight well-established FE models of the lumbar spine (L1-5) of different research centers around the globe were subjected to pure and combined loading modes and compared to in vitro and in vivo measurements for intervertebral rotations, disc pressures and facet joint forces. Under pure moment loading, the predicted L1-5 rotations of almost all models fell within the reported in vitro ranges, and their median values differed on average by only 2° for flexion-extension, 1° for lateral bending and 5° for axial rotation. Predicted median facet joint forces and disc pressures were also in good agreement with published median in vitro values. However, the ranges of predictions were larger and exceeded those reported in vitro, especially for the facet joint forces. For all combined loading modes, except for flexion, predicted median segmental intervertebral rotations and disc pressures were in good agreement with measured in vivo values. In light of high inter-subject variability, the generalization of results of a single model to a population remains a concern. This study demonstrated that the pooled median of individual model results, similar to a probabilistic approach, can be used as an improved predictive tool in order to estimate the response of the lumbar spine.

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. This paper aims to review and discuss some salient findings of reported finite element simulations of lumbar intervertebral discs with special focus on their relevance and implications in disc functional biomechanics. Towards this goal, the earlier investigations are presented, discussed and summarized separately in three distinct groups of elastic, multi-phasic transient and transport model studies. The disc overall response as well as the relative role of its constituents are markedly influenced by loading rate, magnitude, combinations/preloads and posture. The nucleus fluid content and pressurizing capacity affect the disc compliance, annulus strains and failure sites/modes. Biodynamics of the disc is affected by not only the excitation characteristics but also preloads, existing mass and nucleus condition. The role of fluid pressurization and collagen fiber stiffening diminish with time during diurnal loading. The endplates permeability influences the time-dependent response of the disc in both loaded and unloaded recovery phases. The transport of solutes is substantially influenced by the disc size, tissue diffusivity and endplates permeability.

An improved level set method for vertebra CT image segmentation

Background

Clinical diagnosis and therapy for the lumbar disc herniation requires accurate vertebra segmentation. The complex anatomical structure and the degenerative deformations of the vertebrae makes its segmentation challenging.

Methods

An improved level set method, namely edge- and region-based level set method (ERBLS), is proposed for vertebra CT images segmentation. By considering the gradient information and local region characteristics of images, the proposed model can efficiently segment images with intensity inhomogeneity and blurry or discontinuous boundaries. To reduce the dependency on manual initialization in many active contour models and for an automatic segmentation, a simple initialization method for the level set function is built, which utilizes the Otsu threshold. In addition, the need of the costly re-initialization procedure is completely eliminated.

Results

Experimental results on both synthetic and real images demonstrated that the proposed ERBLS model is very robust and efficient. Compared with the well-known local binary fitting (LBF) model, our method is much more computationally efficient and much less sensitive to the initial contour. The proposed method has also applied to 56 patient data sets and produced very promising results.

Conclusions

An improved level set method suitable for vertebra CT images segmentation is proposed. It has the flexibility of segmenting the vertebra CT images with blurry or discontinuous edges, internal inhomogeneity and no need of re-initialization.

Influence of interpersonal geometrical variation on spinal motion segment stiffness: implications for patient-specific modeling

STUDY DESIGN

A validated finite element model of an L3-L4 motion segment is used to analyze the effects of interpersonal differences in geometry on spinal stiffness.

OBJECTIVE

The objective of this study is to determine which of the interpersonal variations of the geometry of the spine have a large effect on spinal stiffness. This will improve patient-specific modeling.

SUMMARY OF BACKGROUND DATA

The parameters that define the geometry of a motion segment are vertebral height, disc height, endplate width, endplate depth, spinous process length, transverse process width, nucleus size, lordosis angle, facet area, facet orientation, and the cross-sectional areas of the ligaments. All these parameters differ between patients. The influence of each parameter on spinal stiffness is largely unknown and such knowledge would greatly help in patient-specific modeling of the spine.

METHODS

The range of interpersonal variation of each of the geometric parameters was set at mean±2SD (covering 95% of the population). Subsequently, we determined the effect of each of these ranges on the bending stiffness in flexion, extension, axial rotation, and lateral bending.

RESULTS

Disc height had the largest influence; a maximal disc height reduced the spinal stiffness to 75-86% of the mean motion segment stiffness, and a minimal disc height increased the spinal stiffness to 154-226% of the mean motion segment stiffness. Lordosis angle, transversal and longitudinal facet angle, endplate depth, and area of the capsular ligament also had a substantial influence (>5%) on the stiffness, but considerable less than the influence of the disc height. Ligament areas, nucleus size, spinous process length, and length of processes are of negligible effect (<2%) on the stiffness.

CONCLUSION

The disc height should be accurately determined in patients to estimate the spinal stiffness. Ligament areas, nucleus size, spinous process length, and transverse process width do not need patient-specific modeling.

A new look at the geometry of the lumbar spine

STUDY DESIGN

A retrospective cohort study of the relationship between the structures that form the lumbar spine in humans.

OBJECTIVE

To investigate the relationship between the segmental wedging of the vertebral bodies and that of the intervertebral discs, and between the overall lordosis angle and each of the 5 lumbar segments.

SUMMARY OF BACKGROUND DATA

Little attention has been paid to the internal relationship between the structures that form the lumbar spine. Understanding these relationships is instrumental to our ability to restore and rehabilitate the lordotic curvature.

METHODS

Lateral radiographs of 101 adult lumbar spines were examined in patients at spinal clinics. The patients had no history of spinal surgery and no radiographic abnormality. The radiologic parameters are the lordosis angle (LA), the body wedge angle (B), the total segmental angle (S), and the intervertebral disc angle (D). Measurements B, S, and D were taken for each of the 5 lumbar segments. Measurements B and D were used to calculate ΣB, the sum of the B, and ΣD, the sum of the D.

RESULTS

The LA correlates with the sum of the vertebral body angles and with the sum of the intervertebral disc angles. Vertebral body wedging is negatively correlated with intervertebral disc wedging. The middle 3 lumbar segments are moderately-to-poorly correlated, among themselves and with the LA, while the upper and lower lumbar segments are poorly correlated with the LA and not correlated with any lumbar segment.

CONCLUSION

Three parts of the lumbar lordosis were identified: the upper part, formed by the first lumbar segment; the middle part, formed by the middle 3 segments; and the lower part, formed by the fifth lumbar segment. The statistical study shows an inverse relationship between vertebral body and intervertebral disc wedging.

Prediction equations for human thoracic and lumbar vertebral morphometry

Statistical correlations between anatomical dimensions of human vertebral structures have indicated a potential for the prediction of vertebral morphometry, which could be applied to the creation of simplified geometrical models of the spine excluding the need for preliminary processing of medical images. The aim of this study was to perform linear and nonlinear regressions with published anatomical data to generate prediction equations for 20 vertebral parameters of the human thoracic and lumbar spine as a function of only one given parameter that was measured by X-ray. Each parameter was considered individually as a potential predictor variable in terms of its correlation with all of the other parameters, together with the readiness with which lateral X-rays could be obtained. Based on this, the parameter vertebral body height posterior was chosen and the statistical analyses described here are related to this parameter. Our linear, exponential and logarithmic regressions provided significant predictions of anterior vertebral structures. However, third-order polynomial prediction equations allowed an improvement on these predictions (P-values < 0.001), e.g. endplates and spinal canal (R(2), 0.970-0.995) as well as pedicle heights and the spinous process (R(2), 0.811-0.882), in addition to a reasonable prediction of the posterior vertebral structures, which have shown a low or no correlation in previous studies, e.g. pedicle inclination and transverse process (R(2), 0.514-0.693) (anova). Comparisons of the theoretical predictions with two other sets of experimental data indicated that the predictions generally agree well with the experimental data. A time-efficient approach for obtaining anatomical data for the description of human thoracic and lumbar geometry was provided by this method, which requires the measurement of only one parameter per vertebra (vertebral body height posterior) from a lateral X-ray and the set of developed prediction equations. Vertebral models based on this type of parameterized geometry could be used in biomechanical studies that require geometry variation, such as in spinal deformations, including scoliosis.

Parametric and subject-specific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns

Morphometrical and postural features of the cervical spine are supposed to significantly influence its biomechanical behaviour. However, the effects of these geometrical parameters are quite difficult to evaluate. An original numerical method is proposed in order to automatically generate parametric and subject-specific meshes of the lower cervical spine. Sixteen finite element models have been built from cadaver specimens using low dose biplanar X-rays. All the generated meshes fulfilled the quality criteria. A preliminary evaluation was performed on the C5-C6 functional units using a database of previous experimental tests. The principal and coupled motions were simulated. The responses of the numerical models were within the experimental standard deviation corridors in most cases. Rotation-moment relationships were then compared to assess the influence of geometry on the mechanical response. Geometry was found to play a significant role in the motion patterns.

Can compressive stress be measured experimentally within the annulus fibrosus of degenerated intervertebral discs?

The aims were to assess the ability of a pressure transducer to measure compressive stress within the annulus fibrosus of degenerated intervertebral discs. Measurements could help to explain the mechanisms of disc failure and low back pain.

The methods used were as follows. Thirteen full-depth cores of annulus, 7 mm in diameter, were removed from the middle and outer annuli of two severely degenerated human discs and constrained within a metal cylinder. Then static compressive forces were applied by a planeended metal indenter of diameter 6.8 mm, while a strain-gauged pressure transducer, side mounted in a needle of diameter 0.9 mm and calibrated in saline, was pulled through the issue. The transducer output was converted into stress, and the average measured stress was compared with the nominal applied stress. Measurements were repeated at up to 21 load levels, with the transducer oriented vertically and horizontally.

The results showed that the measured and applied stress were linearly related (average r2=0.98) with a mean gradient (calibration factor) of 0.98 (vertical stress) and 0.92 (horizontal stress). Gradients ranged between 1.28 and 0.73. Damaged transducers grossly under-recorded ‘stress’ even though their output remained proportional to applied load.

It was concluded that pressure transducers can measure compressive stress inside a degenerated human annulus. The tissue is sufficiently deformable to allow efficient coupling of stress between the matrix and transducer membrane. Damage to the transducer can give misleading results.

How does the geometry affect the internal biomechanics of a lumbar spine bi-segment finite element model? Consequences on the validation process

Numerical modelling can provide a thorough understanding of the mechanical influence on the spinal tissues and may offer explanations to mechanically linked pathologies. Such objective might be achieved only if the models are carefully validated. Sensitivity study must be performed in order to evaluate the influence of the approximations inherent to modelling. In this study, a new geometrically accurate L3-L5 lumbar spine bi-segmental finite-element model was acquired by modifying a previously existing model. The effect of changes in bone geometry, ligament fibres distribution, nucleus position and disc height was investigated in flexion and extension by comparison of the results obtained from the model before and after the geometrical update. Additional calculations were performed in axial rotation and lateral bending in order to compare the computed ranges of motion (ROM) with experimental results. It was found that the geometrical parameters affected the stress distribution and strain energy in the zygapophysial joints, the ligaments, and the intervertebral disc, changing qualitatively and quantitatively their relative role in resisting the imposed loads. The predicted ROM were generally in good agreement with the experimental results, independently of the geometrical changes. Hence, although the model update affected its internal biomechanics, no conclusions could be drawn from the experimental data about the validation of a particular geometry. Hence the validation of the lumbar spine model should be based on the relative role of its structural components and not only on its global mobility.

Effect of bilateral facetectomy of thoracolumbar spine T11–L1 on spinal stability

Spinal stenosis can be found in any part of the spine, though it is most commonly located on the lumbar and cervical areas. It has been documented in the literature that bilateral facetectomy in a lumbar motion segment to increase the space induces an increase in flexibility at the level at which the surgery was performed. However, the result of bilateral facetectomy on the stability of the thoracolumbar spine has not been studied. A nonlinear three-dimensional finite element (FE) model of thoracolumbar T11-L1 was built to explore the influence of bilateral facetectomy. The FE model of T11-L1 was validated against published experimental results under various physiological loadings. The FE model with bilateral facetectomy was evaluated under flexion, extension, lateral bending and axial rotation to determine alterations in kinematics. Results show that bilateral facetectomy causes increase in motion, considerable increase in axial rotation and least increase in lateral bending. Removal of facets did not result in significant change in the sagittal motion in flexion and extension.

Spine biomechanics

Current trends in spine research are reviewed in order to suggest future opportunities for biomechanics. Recent studies show that psychosocial factors influence back pain behaviour but are not important causes of pain itself. Severe back pain most often arises from intervertebral discs, apophyseal joints and sacroiliac joints, and physical disruption of these structures is strongly but variably linked to pain. Typical forms of structural disruption can be reproduced by severe mechanical loading in-vitro, with genetic and age-related weakening sometimes leading to injury under moderate loading. Biomechanics can be used to quantify spinal loading and movements, to analyse load distributions and injury mechanisms, and to develop therapeutic interventions. The authors suggest that techniques for quantifying spinal loading should be capable of measurement "in the field" so that they can be used in epidemiological surveys and ergonomic interventions. Great accuracy is not required for this task, because injury risk depends on tissue weakness as much as peak loading. Biomechanical tissue testing and finite-element modelling should complement each other, with experiments establishing proof of concept, and models supplying detail and optimising designs. Suggested priority areas for future research include: understanding interactions between intervertebral discs and adjacent vertebrae; developing prosthetic and tissue-engineered discs; and quantifying spinal function during rehabilitation. "Mechanobiology" has perhaps the greatest future potential, because spinal degeneration and healing are both mediated by the activity of cells which are acutely sensitive to their local mechanical environment. Precise characterisation and manipulation of this environment will be a major challenge for spine biomechanics.

Analysis of stress distribution in lumbar interbody fusion

STUDY DESIGN

A 2-dimensional axisymmetric finite element model of an intervertebral segment was used to investigate the stress patterns in the adjacent vertebrae of fused spinal segment incorporating 4 common cage designs. The same was used to study the effect of maturation of bone graft on stress distribution pattern.

OBJECTIVES

To study and compare the stress distribution patterns in a normal spinal segment and in the adjacent vertebrae of a fused spinal segment. The effect of bone graft incorporation around the mesh cage was also investigated.

SUMMARY OF BACKGROUND DATA

Lumbar fusion surgery is thought to relieve discogenic low back pain by eliminating the abnormal intersegmental movement at the level of disc degeneration. Successful spinal fusion does not guarantee symptomatic pain relief. Discogenic pain is also known to be associated with an abnormal load transmission pattern across the degenerate disc. We hypothesized that the lumbar interbody fusion results in relief of discogenic pain by normalizing the load distribution pattern.

METHODS

We used a 2-dimensional axisymmetric finite element model of an intervertebral segment to investigate the stress patterns in the vertebrae adjacent to a fused spinal segment incorporating 4 common cage designs: (1) anterior lumbar interbody fusion, (2) posterior lumbar interbody fusion rectangular, (3) posterior lumbar interbody fusion threaded, and (4) mesh cage.

RESULTS

High stress concentrations and abnormal overall stress patterns were noted for all the cage designs studied. The anterior lumbar interbody fusion cage with its larger contact area showed the least abnormal stress magnitude in comparison with the other cages. Incorporation of bone in and around the mesh cage increased the area of contact and decreased the abnormal high stresses. The spine fusion model representing final bony healing showed restoration of near physiologic stress pattern.

CONCLUSIONS

Interbody fusion cages with larger area of contact between cage and vertebral endplate produces a lower stress distribution pattern. A successful bony fusion restores near physiologic stress distribution pattern. Restoration of near normal load distribution pattern may become an important aim of surgery for discogenic low back pain.

Material Sensitivity Study on Lumbar Motion Segment (L2-L3) Under Sagittal Plane Loadings Using Probabilistic Method

OBJECTIVE

In this study, the probabilistic responses of a three-dimensional finite element L2-L3 motion segment, with and without posterior elements, tested under sagittal plane loadings, are presented. Understanding the effect of biologic uncertainties and variations on the biomechanical response provides an insight into spinal behavior under normal and degenerated conditions.

METHODS

The biologic variability of 19 spinal components (nucleus, annulus, ligament, cortical/cancellous bone, endplate, and ligaments) in the motion segment was incorporated using statistical distributions into the model. A total of 2000 runs were performed using Monte Carlo probabilistic algorithms to compute the probabilistic response.

RESULTS

This study establishes the relative importance of the spinal components in resisting the loading modes. The results show that for an intact motion segment, posterior ligaments are more dominant than intervertebral disc in resisting flexion moment. In extension, the capsular ligaments were found to be the most influential parameter. The intervertebral disc (ie, nucleus and annulus) affects the angular response of the disc body segment more than the hard tissues (ie, cortical and cancellous bone).

CONCLUSIONS

The application of the probabilistic analysis provides a new approach whereby the influences of inherent uncertainties and variations in biologic structures can be studied and the biomechanical response assessed.

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.

Finite element analysis in spine research

Finite element analysis is a widely accepted tool used in many industries and research activities. It allows new designs to be thoroughly 'tested' before a prototype is even manufactured, components and systems which cannot readily be experimented upon to be examined, and 'diagnostic' investigations to be undertaken. Finite element models are already making an important contribution to our understanding of the spine and its components. Models are being used to reveal the biomechanical function of the spine and its behaviour when healthy, diseased or damaged. They are also providing support in the design and application of spinal instrumentation. The spine is a very complex structure, and many of the models are simplified and idealized because of the complexity and uncertainty in the geometry, material properties and boundary conditions of these problems. This type of modelling simplification is not peculiar to spinal modelling problems. Indeed, the idealization is often a strength when there is such uncertainty and variation between one individual and another, allowing cause-effect relationships to be isolated and fully explored, and the inherent variability of experimental tests to be eliminated. This paper reviews the development of finite element analysis in spinal modelling. It shows how modelling provides a wealth of information on our physiological performance, reduces our dependence on animal and cadaveric experiments and is an invaluable complement to clinical studies. It also leads to the conclusion that, as computing power and software capabilities increase, it is quite conceivable that in the future it will be possible to generate patient-specific models that could be used for patient assessment and even pre- and inter-operative planning.

Patient-specific spine models. Part 1: Finite element analysis of the lumbar intervertebral disc--a material sensitivity study

If patient-specific finite element models of the spine could be developed, they would offer enormous opportunities in the diagnosis and management of back problems. Several generic models have been developed in the past, but there has been very little detailed examination of the sensitivity of these models' characteristics to the input parameters. This relationship must be thoroughly understood if representative patient-specific models are to be realized and used with confidence. In particular, the performance of the intervertebral discs are central to any spine model and need detailed investigation first. A generic non-linear model of an intervertebral disc was developed and subjected to compressive, flexion and torsional loading regimes. The effects of both material and geometric non-linearities were investigated for the three loading schemes and the results compared with experimental data. The basic material properties of the fibres, annulus and nucleus were then varied and the effects on the stiffness, annulus bulge and annulus stresses analysed. The results showed that the non-linear geometry assumption had a significant effect on the compression characteristics, whereas the non-linear material option did not. In contrast, the material non-linearity was more important for the flexural and torsional loading schemes. Thus, the inclusion of non-linear material and geometry analysis options in finite element models of intervertebral discs is necessary to predict in vivo load-deflection characteristics accurately. When the influence of the material properties was examined in detail, it was found that the fibre properties did not have a significant effect on the compressive stiffness of the disc but did affect the flexural and torsional stiffnesses by up to +/-20 per cent. All loading modes were sensitive to the annulus properties with stiffnesses varying by up to +/-16 per cent. The model also revealed that for a particular compressive deformation or flexural or torsional rotation, the disc bulge was not sensitive to any of the material properties over the range of properties considered. The annulus stresses did differ significantly as the material properties were varied (up to 70 per cent under a compressive load and 60 per cent during disc flexion).

Can the sagittal lumbar curvature be closely approximated by an ellipse?

For the sagittal lumbar curvature, existing spinal models are based only on the anthropomorphic radiographic characteristics of one individual, or, at best, of only a few individuals. This raises questions of applicability of the modeling results to clinical situations. Because spinal coupling and loads on spinal tissues have been shown to be functions of the initial static posture, a rigorously derived neutral lumbar lordosis would be important for clinicians and spine researchers. This study presents modeling of the sagittal lumbar spine in the shape of an ellipse. Vertebral body and disc heights, derived from digitized lateral lumbar radiographs of 50 normal subjects, were used to create an ellipse along the posterior body margins from the inferior of T12 to the superior sacral base. Additional data to create an elliptical lumbar model were determined from a least-squares analysis of passing ellipses through the digitized posterior body points. This confirmed that an elliptical model closely fit the lumbar curvature with a least-squares error of 1.2 mm per digitized point. The elliptical model is approximately an 85 degrees portion of a quadrant. The semi-major and semi-minor axes, a and b, are parallel to the posterior body margin of T12 and parallel to the inferior body endplate of T12, respectively, with a semi-minor to semi-major radio of b/a=0.39. The elliptic model has a height-to-length ratio of H/L=0.963, where height is the vertical distance from inferior T12 to superior S1 and length is the arc length along George's line (along the posterior longitudinal ligament) from T12 to S1.

Finite element modeling approaches of human cervical spine facet joint capsule

The human cervical spine facet joint capsule was modeled using four nonlinear finite element approaches: slideline, contact surface, hyperelastic, and fluid models. Slideline elements and contact surface definitions were used in the first two models to simulate the synovial fluid between the articulating cartilages. Incompressible solid elements approximated the synovial fluid in the hyperelastic model. Hydrostatic fluid elements idealized the synovial fluid in the fluid model. The finite element analysis incorporated geometric, material and contact nonlinearities. All models were subjected to compression, flexion, extension, and lateral bending. The fluid model idealization better approximates the actual facet joint anatomy and its behavior than the gap assumption in the slideline and contact surface models, and the solid element simulation in the hyperelastic model.