Automated finite element meshing of the lumbar spine: Verification and validation with 18 specimen-specific models

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.

Validation and Estimation of Obesity-Induced Intervertebral Disc Degeneration through Subject-Specific Finite Element Modelling of Functional Spinal Units

(1) Background: Intervertebral disc degeneration has been linked to obesity; its potential mechanical effects on the intervertebral disc remain unknown. This study aimed to develop and validate a patient-specific model of L3-L4 vertebrae and then use the model to estimate the impact of increasing body weight on disc degeneration. (2) Methods: A three-dimensional model of the functional spinal unit of L3-L4 vertebrae and its components were developed and validated. Validation was achieved by comparing the range of motions (RoM) and intradiscal pressures with the previous literature. Subsequently, the validated model was loaded according to the body mass index and estimated stress, deformation, and RoM to assess disc degeneration. (3) Results: During validation, L3-L4 RoM and intradiscal pressures: flexion 5.17° and 1.04 MPa, extension 1.54° and 0.22 MPa, lateral bending 3.36° and 0.54 MPa, axial rotation 1.14° and 0.52 MPa, respectively. When investigating the impact of weight on disc degeneration, escalating from normal weight to obesity reveals an increased RoM, by 3.44% during flexion, 22.7% during extension, 29.71% during lateral bending, and 33.2% during axial rotation, respectively. Also, stress and disc deformation elevated with increasing weight across all RoM. (4) Conclusions: The predicted mechanical responses of the developed model closely matched the validation dataset. The validated model predicts disc degeneration under increased weight and could lay the foundation for future recommendations aimed at identifying predictors of lower back pain due to disc degeneration.

Biomechanical Evaluation of 2 Endoscopic Spine Surgery Methods for Treating Lumbar Disc Herniation: A Finite Element Study

OBJECTIVE

This study aimed to evaluate the effects of 2 endoscopic spine surgeries on the biomechanical properties of normal and osteoporotic spines.

METHODS

Based on computed tomography images of a healthy adult volunteer, 6 finite element models were created. After validating the normal intact model, a concentrated force of 400 N and a moment of 7.5 Nm were exerted on the upper surface of L3 to simulate 6 physiological activities of the spine. Five types of indices were used to assess the biomechanical properties of the 6 models, range of motion (ROM), maximum displacement value, intervertebral disc stress, maximum stress value, and articular protrusion stress, and by combining them with finite element stress cloud.

RESULTS

In normal and osteoporotic spines, there was no meaningful change in ROM or disc stress in the 2 surgical models for the 6 motion states. Model N1 (osteoporotic percutaneous transforaminal endoscopic discectomy model) showed a decrease in maximum displacement value of 20.28% in right lateral bending. Model M2 (unilateral biportal endoscopic model) increased maximum displacement values of 16.88% and 17.82% during left and right lateral bending, respectively. The maximum stress value of L4-5 increased by 11.72% for model M2 during left rotation. In addition, using the same surgical approach, ROM, maximum displacement values, disc stress, and maximum stress values were more significant in the osteoporotic model than in the normal model.

CONCLUSION

In both normal and osteoporotic spines, both surgical approaches were less disruptive to the physiologic structure of the spine. Furthermore, using the same endoscopic spine surgery, normal spine biomechanical properties are superior to osteoporotic spines.

Impact of osteoporosis and Cement-Augmented fusion on adjacent spinal levels Post-Fusion Surgery: Patient-Specific finite element analysis

Cement-augmentation is a technique commonly used during posterior lumbar instrumented fusion (PLIF) to reinforce compromised osteoporotic vertebral bone, minimize the risk of loosening screws, enhance stability, and improve overall surgical outcomes. In this study, we introduce a novel segmented vertebral body regional modeling approach to investigate the effects of osteoporosis and cement-augmented lumbar fusion on disc biomechanics at spinal levels adjacent to the fused vertebrae. Using our previously validated personalized-poroelastic-osteoligamentous FE model of the spine, fusion was simulated at L4-L5, and the biomechanics of adjacent levels were studied for 30 patients (non-osteoporotic patients (N = 15), osteoporotic patients (N = 15)). PLIF models, with and without cement-augmentation, were developed and compared after an 8 h-rest period (200 N), following a 16 h-cyclic compressive loading of 500-1000 N (40 and 20 min, respectively). Movement in different directions (flexion/ extension/ lateral bending/ axial rotation) was simulated using 10Nm moment before and after cyclic loading. The material mapping algorithm was validated by comparing the results of voxel-based and parametric models. The FE cement-augmented models, subject to daily activity loading, demonstrated significant differences in disc height loss and fluid loss as compared to non-cemented models. The calculated axial stress and fiber strain values were also significantly higher for these models. This work demonstrates that although osteoporosis does not significantly alter the time-dependent characteristics of adjacent IVDs post-surgery, cement-augmentation increases the risk of adjacent segment disease (ASD) incidence. A holistic understanding of the trade-offs and long-term complex interplay between structural reinforcement modalities, including cement augmentation, and altered biomechanics warrants further investigation.

Ligamentous tethering and intradiscal pressure affecting the mechanical environment of scoliotic spines

Despite several theories have been proposed to explain the progression of Adolescent Idiopathic Scoliosis (AIS), there is no consensus on the mechanical factors that control the spinal deformities. Prominent biomechanical notions focus on the geometrical asymmetry and differential growth, however, the correlation between these phenomena remains unclear. We postulate that intradiscal pressure and its connection with the supporting ligamentous structures are the reasons behind the asymmetric growth in AIS. To investigate this hypothesis, a numerical 3D patient-specific model of a scoliotic spine is constructed to carry upper body weight. Four analyses are performed: control simulation with no ligaments followed by 3 simulations, in each, a different and stiffer set of ligaments is employed. The analyses showed that intradiscal pressure is relatively high in the spine's higher-deformity region. Moreover, the stiffness effect of the ligamentous tethering correlated directly to intradiscal pressure; the stiffer the ligaments, the higher the intradiscal pressure. Due to geometrical asymmetry, the pressure is eccentric toward the concave region of deformed vertebral units. As a result, the deformed annulus fibrosus generated uplifts in the convex side of deformed vertebral units. The eccentric pressure and the uplift are opposite in location and direction creating an imbalanced mechanical environment for the spine during growth.

Development, calibration and validation of a comprehensive customizable lumbar spine FE model for simulating fusion constructs

Instrumentation alters the biomechanics of the spine, and therefore prediction of all output quantities that have critical influence post-surgically is significant for engineering models to aid in clinical predictions. Geometrical morphological finite element models can bring down the development time and cost of custom intact and instrumented models and thus aids in the better inference of biomechanics of surgical instrumentation on patient-specific diseased spine segments. A comprehensive hexahedral morphological lumbosacral finite element model is developed in this work to predict the range of motions, disc pressures, and facet contact forces of the intact and instrumented spine. Facet contact forces are needed to predict the impact of fusion surgeries on adjacent facet contacts in bending, axial rotation, and extension motions. Extensive validation in major physiological loading regimes of the pure moment, pure compression, and combined loading is undertaken. In vitro, experimental corridor results from six different studies reported in the literature are compared and the generated model had statistically significant comparable values with these studies. Flexion, extension and bending moment rotation curves of all segments of the developed model were favourable and within two separately established experimental corridor windows as well as recent simulation results. Axial torque moment rotation curves were comparable to in vitro results for four out of five lumbar functional units. The facet contact force results also agreed with in vitro experimental results. The current model is also computationally efficient with respect to contemporary models since it uses significantly smaller number of elements without losing the accuracy in terms of response prediction. This model can further be used for predicting the impact of different instrumentation techniques on the lumbar vertebral column.

Recent Advances in Coupled MBS and FEM Models of the Spine—A Review

How back pain is related to intervertebral disc degeneration, spinal loading or sports-related overuse remains an unanswered question of biomechanics. Coupled MBS and FEM simulations can provide a holistic view of the spine by considering both the overall kinematics and kinetics of the spine and the inner stress distribution of flexible components. We reviewed studies that included MBS and FEM co-simulations of the spine. Thereby, we classified the studies into unidirectional and bidirectional co-simulation, according to their data exchange methods. Several studies have demonstrated that using unidirectional co-simulation models provides useful insights into spinal biomechanics, although synchronizing the two distinct models remains a key challenge, often requiring extensive manual intervention. The use of a bidirectional co-simulation features an iterative, automated process with a constant data exchange between integrated subsystems. It reduces manual corrections of vertebra positions or reaction forces and enables detailed modeling of dynamic load cases. Bidirectional co-simulations are thus a promising new research approach for improved spine modeling, as a main challenge in spinal biomechanics is the nonlinear deformation of the intervertebral discs. Future studies will likely include the automated implementation of patient-specific bidirectional co-simulation models using hyper- or poroelastic intervertebral disc FEM models and muscle forces examined by an optimization algorithm in MBS. Applications range from clinical diagnosis to biomechanical analysis of overload situations in sports and injury prediction.

Contribution of Shape Features to Intradiscal Pressure and Facets Contact Pressure in L4/L5 FSUs: An In-Silico Study

Finite element models (FEMs) of the spine commonly use a limited number of simplified geometries. Nevertheless, the geometric features of the spine are important in determining its FEM outcomes. The link between a spinal segment's shape and its biomechanical response has been studied, but the co-variances of the shape features have been omitted. We used a principal component (PCA)-based statistical shape modelling (SSM) approach to investigate the contribution of shape features to the intradiscal pressure (IDP) and the facets contact pressure (FCP) in a cohort of synthetic L4/L5 functional spinal units under axial compression. We quantified the uncertainty in the FEM results, and the contribution of individual shape modes to these results. This parameterisation approach is able to capture the variability in the correlated anatomical features in a real population and sample plausible synthetic geometries. The first shape mode ([Formula: see text]) explained 22.6% of the shape variation in the subject-specific cohort used to train the SSM, and had the largest correlation with, and contribution to IDP (17%) and FCP (11%). The largest geometric variation in ([Formula: see text]) was in the annulus-nucleus ratio.

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.

Yeditepe spine mesh: Finite element modeling and validation of a parametric CAD model of lumbar spine

Finite element analysis is a powerful tool that is often used to study the biomechanical response of the spine. The primary objective of this study was to illustrate the mechanical behavior of a previously proposed parametric CAD spine model in comparison with a segmented FSU model and the literature. In this study, two finite element models of the L4-L5 spinal level were developed from the same patient's CT scan data. The first was developed using well-known segmentation methods, whereas the second was developed from the new by using a novel parametric CAD model. Both models were subjected to the same loading and boundary conditions to perform flexion, extension, lateral bending and axial rotation motions. The segmented finite element model was observed to be in good agreement with the literature. The parametric finite element model results were also observed to be in good agreement with the segmented finite element model and with the literature except under extension.

Biomechanical tests and finite element analyses of pelvic stability using bilateral single iliac screws with different channels in lumbo-iliac fixation

Background

In lumbo-iliac fixation, the iliac screw can be placed in several locations and directions. There is no uniform standard for the placement of a single iliac screw. Biomechanical tests and finite element analyses were used to compare the effect of bilateral single iliac screws with three channels on pelvic stability to determine the best channel.

Methods

Five embalmed adult cadaver pelvic specimens were selected. An unstable Tile C1 pelvic injury model was established. Lumbo-iliac fixation for the treatment of left sacral Denis II fracture includes the following: three channels of bilateral, single iliac screws (channel A from posterior superior iliac spine (PSIS) to anterior inferior iliac spine (AIIS), channel B from 1 cm medial and 1 cm caudal of PSIS to AIIS, and channel C from 2 cm below PSIS to AIIS). Biomechanical testing was performed for stiffness evaluations. A finite element model was established to study the stress distribution of the model and the maximum von Mises stress of internal fixation.

Results

Biomechanical tests revealed that under vertical compression loading. The compressive stiffness fixed by channel B (246.15 ± 27.85 N/mm) was better than that fixed by channel A and channel C. Under torsional load, the torsional stiffness fixed by channel B (2.234 ± 0.223 N·m/°) was stronger than that fixed by channel A and channel C. However, there was no significant difference in terms of compressive and torsional stiffness between channel B and channel A (P > 0.05). Finite element analyses conformed that the maximum von Mises stress of the internal fixator fixed in channel B under the conditions of vertical, forwards bending, backwards extension, left bending, left rotating, and right bending (213.98 MPa, 338.96 MPa, 100.63 MPa, 297.06 MPa, 200.95 MPa and 284.75 MPa, respectively) was significantly lower than those fixed in channel A and channel C.

Conclusions

The construct stiffness of the channel from 1 cm medial and 1 cm caudal of PSIS to AIIS is better than that of the other two channels. This channel has the advantages of good biomechanical stability, small maximum von Mises stress of internal fixation.

Biomechanical evaluation of lumbar spondylolysis repair with various fixation options: A finite element analysis

Objective: This study was designed to compare the biomechanical properties of lumbar spondylolysis repairs using different fixation methods by using three-dimensional finite element analysis.

Methods: Five finite element models (A, B, C, D, and E) of L4-S1 vertebral body were reconstructed by CT images of a male patient (A: intact model; B: spondylolysis model; C: spondylolysis model with intrasegmental direct fixation by Buck screw; D: spondylolysis model with intersegmental indirect fixation by pedicle screw system; E: spondylolysis model with hybrid internal fixation). L5-S1 level was defined as the operative level. After the intact model was verified, six physiological motion states were simulated by applying 500 N concentrated force and 10 Nm torque on the upper surface of L4. The biomechanical properties of the three different internal fixation methods were evaluated by comparing the range of motion (ROM), maximum stress, and maximum displacement.

Results: Compared with Model B, the ROM and maximum displacement of Model C, D, and E decreased. The maximum stress on L5/S1 disc in models A, B, and C was much higher than that in Model D and E under extension and lateral bending conditions. Under axial rotation and lateral bending conditions, the maximum stress of interarticular muscle and internal fixation system in Model B and Model C was significantly higher than that in Model D and Model E. In contrast to Model D, the stress in Model E was distributed in two internal fixation systems.

Conclusion: In several mechanical comparisons, hybrid fixation had better biomechanical properties than other fixation methods. The experimental results show that hybrid fixation can stabilize the isthmus and reduce intervertebral disc stress, which making it the preferred treatment for lumbar spondylolysis.

Comparison of two internal fixation systems in lumbar spondylolysis by finite element methods

BACKGROUND AND PURPOSE

Internal fixation surgeries are currently the most effective treatments for lumbar spondylolysis, but the optimal fixation method is still on debate. This study was designed to compare the biomechanical characteristics of two fixation methods for lumbar spondylolysis, the pedicle screw-U shape rod (PSUSR) internal fixation system, and the pedicle screw-vertebral plate hook (PSVPH) internal fixation system, through three-dimensional finite element analysis, expecting to provide clinical guidance.

METHODS

Four finite element models (A, B, C, D) of L4-S1 vertebral body of a female patient were reconstructed by CT image segmentation. (A: intact model. B: spondylolysis model. C: spondylolysis model with PSUSR internal fixation. D: spondylolysis model with PSVPH internal fixation). Six physiological motion states were simulated by applying 500N concentrated force and 10Nm moment load to four models. The biomechanical advantages of the two internal fixation systems were evaluated by comparing the range of motion (ROM), maximum stress, maximum strain, and maximum displacement of the models.

RESULTS

Compared to model B, the ROM decreased by 35.7%-57.1% in model C and 39.7%-64.8% in model D. The maximum displacements of model C and D both decreased. The maximum stresses in both vertebral and the internal fixation system are greater in model C than those in model D. The maximum stress and strain reduction of L5-S1 intervertebral disc in model D was greater than that in model C. Model D restores the articular cartilage stresses to the normal levels of model A. The maximum stress and maximum displacement of the bone graft in model C are greater than those in model D.

CONCLUSIONS

The PSVPH internal fixation system has better biomechanical properties than PSUSR internal fixation system in several mechanical comparisons. Experimental results suggest that PSVPH internal fixation system can effectively treat lumbar spondylolysis while preserving segmental mobility, and can be the treatment of choice.

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

A biomechanical investigation of lumbar interbody fusion techniques

The anterior, posterior, transforaminal, and circumferential lumbar interbody fusions (ALIF, PLIF, TLIF, CLIF/360) are used to treat spondylolisthesis, trauma, and degenerative pathologies. This study aims to investigate the biomechanical effects of the lumbar interbody fusion techniques on the spine. A validated T12-sacrum lumbar spine finite-element model was used to simulate surgical fusion of L4-L5 segment using ALIF, PLIF with one and two cages, TLIF with unilateral and bilateral fixation, and CLIF/360. The models were simulated under pure-moment and combined (moment and compression) loadings to investigate the effect of different lumbar interbody fusion techniques on range of motion, forces transferred through the vertebral bodies, disc pressures, and endplate stresses. The range of motion of the lumbar spine was decreased the most for fusions with bilateral posterior instrumentations (TLIF, PLIF, and CLIF/360). The increase in forces transmitted through the vertebrae and increase in disc pressures were directly proportional to the range of motion. The discs superior to fusion were under higher pressure, which was attributed to adjacent segment degeneration in the superior discs. The increase in endplate stresses was directly proportional to the cross-sectional area and was greater in caudal endplates at the fusion level, which was attributed to cage subsidence. The response of the models was in line with overall clinical observations from the patients and can be further used for future studies, which aim to investigate the effect of geometrical and material variations in the spine. The model results will assist surgeons in making informed decisions when selecting fusion procedures based on biomechanical effects.

Development of a flexible instrumented lumbar spine finite element model and comparison with in-vitro experiments

Surgical corrections of degenerative lumbar scoliosis and sagittal malalignment are associated with significant complications, such as rod fractures and pseudarthrosis, particularly in the lumbosacral junction. Finite element studies can provide relevant insights to improve performance of spinal implants. The aim of the present study was to present the development of non-instrumented and instrumented Finite Element Models (FEMs) of the lumbopelvic spine and to compare numerical results with experimental data available in the literature. The lumbo-pelvic spine FEM was based on a CT-scan from an asymptomatic volunteer representing the 50th percentile male. In a first step a calibration of mechanical properties was performed in order to obtain a quantitative agreement between numerical results and experimental data for defect stages of spinal segments. Then, FEM results were compared in terms of range of motion and strains in rods to in-vitro experimental data from the literature for flexible non-instrumented and instrumented lumbar spines. Numerical results from the calibration process were consistent with experimental data, especially in flexion. A positive agreement was obtained between FEM and experimental results for the lumbar and sacroiliac segments. Instrumented FEMs predicted the same trends as experimental in-vitro studies. The instrumentation configuration consisting of double rods and an interbody cage at L5-S1 maximally reduced range of motion and strains in main rods and thus had the lowest risk of pseudarthrosis and rod fracture. The developed FEMs were found to be consistent with published experimental results; therefore they can be used for further post-operative complication investigations.

A comparison of Cartesian-only vs. Cartesian-spherical hybrid coordinates for statistical shape modeling in the lumbar spine

OBJECTIVE

The purpose of this study was to compare two methods for quantifying differences in geometric shapes of human lumbar vertebra using statistical shape modeling (SSM).

METHODS

A novel 3D implementation of a previously published 2D, nonlinear SSM was implemented and compared to a commonly used, Cartesian method of SSM. The nonlinear method, or Hybrid SSM, and Cartesian SSM were applied to lumbar vertebra shapes from a cohort of 18 full lumbar triangle meshes derived from CT scans. The comparison included traditional metrics for cumulative variance, generality, and specificity and results from application-based biomechanics using finite element simulation.

RESULTS

The Hybrid SSM has less compactness - likely due to the increased number of mathematical constraints in the SSM formulation. Similar results were found between methods for specificity and generality. Compared to the previously validated, manually-segmented FE model, both SSM methods produced similar and agreeable results.

CONCLUSION

Visual, statistical, and biomechanical findings did not convincingly support the superiority of the Hybrid SSM over the simpler Cartesian SSM.

SIGNIFICANCE

This work suggests that, of the two methods compared, the Cartesian SSM is adequate to capture the variations in shape of the posterior spinal structures for biomechanical modeling applications.

Investigation of physiological stress shielding within lumbar spinal tissue as a contributor to unilateral low back pain: A finite element study

INTRODUCTION

The pathomechanism of low back pain (LBP) remains unknown. Unilateral LBP patients have demonstrated ipsilateral morphological and material property changes within the lumbar soft tissues, potentially leading to asymmetric tissue loading. Through the comparison of healthy and unilateral LBP validated finite element models (FEMs), this study investigates potential stress shielding consequential of spinal tissue property augmentation.

METHODS

Two FEMs of the musculoskeletal system - one demonstrating healthy and unilateral LBP conditions - were developed undergoing 30-degree flexion. FEMs included the vertebrae, intervertebral discs, and soft tissues from L1-S1. Material properties selected for the soft tissues were retrieved from published literature. To reflect unilateral LBP, the paraspinal morphology was atrophied, while the tissue moduli were increased. The symptomatic thoracolumbar fascia (TLF) was uniformly increased. Validation of the models preceded testing.

RESULTS

Model validation in spinal flexion was accomplished through comparison to literature. Compared to the healthy model, the unilateral LBP multifidus (MF), longissimus thoracis (LT), and TLF exhibited average tension changes of +7.9, -5.1, and +9.3%, respectively. Likewise, the symptomatic MF, LT, and TLF exhibited tension changes of +19.0, -10.4, and +16.1% respectively, whereas the asymptomatic MF, LT, and TLF exhibited -4.0, -2.0, and +0.4% changes in tension, respectively.

CONCLUSION

Relative to the healthy tissues, the symptomatic LBP soft tissues demonstrated a 19.5 kPa increase in stress, with 99.8% of this increase distributed towards the TLF, suggesting a load allocation bias within the symptomatic unilateral LBP tissues. Consequentially, symptomatic paraspinal muscles may be unable to withstand loading, leading to stress shielding.

Finite element analysis of EBM manufactured bespoke implants: A probabilistic study

This study analyses three additively manufactured canine implants designed for angular limb deformity correction procedure through probabilistic numerical analysis. These implants have produced excellent results in-vivo and are operational to-date. Therefore, this study uses finite element analysis in conjunction with statistical analysis in order to further validate these implants from a numerical perspective. Due to uncertainties associated with boundary conditions for a bespoke implant geometry, the analyses in this study were conducted on a range of input values. An interrogation of these parameters through sensitivity analysis enabled in identifying the vital inputs. These inputs were then employed to conduct robustness analysis in order to determine the mean value of stress on which these implants ideally operate. These mean values were then compared with the associated safety and failure limit to obtain the probability of reaching these limits through different reliability techniques. A low probability of failure computed from numerical analysis in combination with the continued performance of these implants, suggests a successful integration of the methodology in the design phase of bespoke implants.

QCT-FE modeling of the proximal tibia: Effect of mapping strategy on convergence time and model accuracy

Quantitative computed tomography (QCT) based finite element (FE) modeling, referred to as QCT-FE, has seen rapid growth and application for modeling bone mechanics. With this approach, varying bone material properties are set via experimentally-derived density-modulus equations. One challenge though associated with QCT-FE is to identify the appropriate mapping strategy for assigning elastic moduli to elements. The goal of this study was to evaluate different QCT-FE mapping strategies to identify the optimum approach with fastest convergence rate and highest accuracy. Four proximal tibial medial compartments were imaged using QCT and experimentally tested to characterize proximal tibial subchondral bone stiffness at four surface points, resulting in a total of 16 indentation measures. Three material mapping methods were analyzed: (1) constant-E where an average elastic modulus was assigned to each element; (2) node-based where the material properties were first mapped on nodes then interpolated to Gaussian integration points; and (3) element-based in which the material properties were directly assigned to Gaussian integration points. Different element sizes were assessed with edge-lengths ranging from 0.9 to 3 mm. Results indicated that all converged models showed similar coefficient-of-determination (R²) and normalized root-mean-square errors (RMSE%). Though, the constant-E and node-based methods converged with the element edge-length of 1.5 mm (prediction error of 4.8% and 2.5%, respectively) whereas the element-based method converged with a larger element having an edge-length 2.5 mm (error = 4.9%). In conclusion, the element-based method, with a larger element size, resulted in similar predictive accuracy, faster convergence and shorter run-times relative to the constant-E and node-based approaches. As such, we recommend the element-based method for future subject-specific QCT-FE modeling.

Biomechanical modelling of the facet joints: a review of methods and validation processes in finite element analysis

There is an increased interest in studying the biomechanics of the facet joints. For in silico studies, it is therefore important to understand the level of reliability of models for outputs of interest related to the facet joints. In this work, a systematic review of finite element models of multi-level spinal section with facet joints output of interest was performed. The review focused on the methodology used to model the facet joints and its associated validation. From the 110 papers analysed, 18 presented some validation of the facet joints outputs. Validation was done by comparing outputs to literature data, either computational or experimental values; with the major drawback that, when comparing to computational values, the baseline data was rarely validated. Analysis of the modelling methodology showed that there seems to be a compromise made between accuracy of the geometry and nonlinearity of the cartilage behaviour in compression. Most models either used a soft contact representation of the cartilage layer at the joint or included a cartilage layer which was linear elastic. Most concerning, soft contact models usually did not contain much information on the pressure-overclosure law. This review shows that to increase the reliability of in silico model of the spine for facet joints outputs, more needs to be done regarding the description of the methods used to model the facet joints, and the validation for specific outputs of interest needs to be more thorough, with recommendation to systematically share input and output data of validation studies.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.

Development and validation of osteoligamentous lumbar spine under complex loading conditions: A step towards patient-specific modeling

Finite-element models are used to investigate the biomechanics of normal, diseased and surgically fused spines. Generally, nominal spine geometries are used to understand the biomechanics, which has created a need for a technique that develops patient-specific lumbar spine geometries. In the current study, a lumbar spine (T12-Sacrum) was developed using a technique that facilitates geometrical morphing, which assists in incorporating patient-specific morphologies into the model. The model evaluations can be used to propose a biomechanically suitable lumbar spine fusion procedure for patients. This study focuses on the validation of the base model under pure-moment, pure-compression and combined-compression-and-moment loadings. Experimental data from the literature were used to validate the response of the model. The L1-L2, L2-L3, L3-L4, L4-L5 and L5-sacrum segments demonstrated a range of motion of 4.5, 4.0, 5.4, 5.0 and 8.9° in flexion; 3.0, 2.5, 3.6, 3.1 and 5.2° in extension; 6.2, 5.8, 6.4, 5.0 and 6.1° in right and left lateral bending; and 2.9, 3.0, 2.9, 1.9 and 2.5° in right and left axial rotation, all under 10 Nm pure-moment loading. The L1-L2, L2-L3, L3-L4, L4-L5 and L5-sacrum discs demonstrated compressions of 1.1, 1.4, 1.6, 1.4 and 0.9 mm under 1200 N follower- or pure-compression loading. With the combined loading of 280 N follower and 7.5 Nm moment, the L1-L5 model demonstrated 11.7, 7.2, 18.3 and 10.4 degrees of range of motion in flexion, extension, bending and rotation, respectively. The model results were in good agreement with corridors from six different experimental studies and can be used for future clinical studies.

Development of a novel geometrically-parametric patient-specific finite element model to investigate the effects of the lumbar lordosis angle on fusion surgery

The success of lumbar interbody fusion, the key surgical procedure for treating different pathologies of the lumbar spine, is highly dependent on determining the patient-specific lumbar lordosis (LL) and restoring sagittal balance. This study aimed to (1) develop a personalized finite element (FE) model that automatically updates spinal geometry for different patients; and (2) apply this technique to study the influence of LL on post-fusion spinal biomechanics. Using an X-Ray image-based algorithm, the geometry of the lumbar spine (L1-S1) was updated using independent parameters. Ten subject-specific nonlinear osteoligamentous FE models were developed based on pre-operative images of fusion surgery candidate patients. Post-operative FE models of the same patients were consequently created. Comparison of the obtained results from FE models with pre- and post-operation functional images demonstrated the potential value of this technique in clinical applications. A parametric study of the effect of LL was conducted for cases with zero LL angle, positive LL angles (+6° and +12°) and negative LL angles (-3° and -6°) on fused level (L4-L5), resulting in a total of 50 fusion simulation models. The average range of motion, intradiscal pressure, and fiber strain at adjacent levels were significantly higher with decreased LL during different directions except axial rotation. This study demonstrates that the LL alters both the intersegmental motion and load-sharing in fusion, which may influence the initiation and rate of adjacent level degeneration. This personalized FE platform provides a practical, clinically applicable approach for the analyses of the biomechanical changes associated with lumbar spine fusion.

Predicting bone strength from CT data: Clinical applications

In this review we summarise over 15 years of research and development around the prediction of whole bones strength from Computed Tomography data, with particular reference to the prediction of the risk of hip fracture in osteoporotic patients. We briefly discuss the theoretical background, and then provide a summary of the laboratory and clinical validation of these modelling technologies. We then discuss the three current clinical applications: in clinical research, in clinical trials, and in clinical practice. On average the strength predicted with finite element models (QCT-FE) based on computed tomography is 7% more accurate that that predicted with areal bone mineral density from Dual X-ray Absorptiometry (DXA-aBMD), the current standard of care, both in term of laboratory validation on cadaver bones and in terms of stratification accuracy on clinical cohorts of fractured and non-fractured women. This improved accuracy makes QCT-FE superior to DXA-aBMD in clinical research and in clinical trials, where the its use can cut in half the number of patients to be enrolled to get the same statistical power. For routine clinical use to decide who to treat with antiresorptive drugs, QCT-FE is more accurate but less cost-effective than DXA-aBMD, at least when the decision is on first line treatment like bisphosphonates. But the ability to predict skeletal strength from medical imaging is now opening a number of other applications, for example in paediatrics and oncology.

Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine

Low back pain is a major cause of disability and requires the development of new devices to treat pathologies and improve prognosis following surgery. Understanding the effects of new devices on the biomechanics of the spine is crucial in the development of new effective and functional devices. The aim of this study was to develop a preliminary parametric, scalable and anatomically accurate finite-element model of the lumbar spine allowing for the evaluation of the performance of spinal devices. The principal anatomical surfaces of the lumbar spine were first identified, and then accurately fitted from a previous model supplied by S14 Implants (Bordeaux, France). Finally, the reconstructed model was defined according to 17 parameters which are used to scale the model according to patient dimensions. The developed model, available as a toolbox named the lumbar model generator, enables generating a population of models using subject-specific dimensions obtained from data scans or averaged dimensions evaluated from the correlation analysis. This toolbox allows patient-specific assessment, taking into account individual morphological variation. The models have applications in the design process of new devices, evaluating the biomechanics of the spine and helping clinicians when deciding on treatment strategies.

Simplifying the human lumbar spine (L3/L4) material in order to create an elemental structure for the future modeling

The human lumbar spine incorporates the best joints in nature due to its optimal static and dynamic behavior against the internal and external loads. Developing an elemental structure based on this joint requires simplification in terms of the materials employed by keeping the mechanical and anatomical behaviors of the human lumbar spine. In the present study, the finite element (FE) of two motion segments of the human lumbar spine (L3/L4) was developed based on the CT scan data as the base for vertebrae geometry, verified geometry properties for another part of two motion segments, and combination of materials and loads obtained from the validated resources. Then, simplification occurred in four continuous steps such as omitting the annual fibers of annual matrix, representing the material of the annual matrix to the nucleus, demonstrating the material of annual matrix to the endplates too, and omitting the trabecular part of vertebrae. The present study aimed to propose the method for developing the basic structure of the human lumbar spine by simplifying its materials in the above-mentioned steps, analyzing the biomechanical effects of these four steps in terms of their internal and external responses, and validating the data obtained from the FE method. The validated simplified way introduced in this study can be used for future research by making implants, prosthesis, and modeling based on the human lumbar spine in other fields such as industrial design, building structures, or joints, which results in making the model easier, cheaper, and more effective.

Is there any advantage of using stand-alone cages? A numerical approach

Background

Segment fusion using interbody cages supplemented with pedicle screw fixation is the most common surgery for the treatment of low back pain. However, there is still much controversy regarding the use of cages in a stand-alone fashion. The goal of this work is to numerically compare the influence that each surgery has on lumbar biomechanics.

Methods

A non-linear FE model of the whole lumbar spine was developed to compare between two types of cages (OLYS and NEOLIF) with and without supplementary fixation. The motion of the whole spine was analysed and the biomechanical environment of the adjacent segments to the operated one was studied. Moreover, the risk of subsidence of the cages was qualitatively evaluated.

Results

A great ROM reduction occurred when supplementary fixation was used. This stiffening increased the stresses at the adjacent levels. It might be hypothesised that the overloading of these segments could be related with the clinically observed adjacent disc degeneration. Meanwhile, the stand-alone cages allowed for a wider movement, and therefore, the influence of the surgery on adjacent discs was much lower. Regarding the risk of subsidence, the contact pressure magnitude was similar for both intervertebral cage designs and near the value of the maximum tolerable pressure of the endplates.

Conclusions

A minimally invasive posterior insertion of an intervertebral cage (OLYS or NEOLIF) was compared using a stand-alone design or adding supplementary fixation. The outcomes of these two techniques were compared, and although stand-alone cage may diminish the risk of disease progression to the adjacent discs, the spinal movement in this case could compromise the vertebral fusion and might present a higher risk of cage subsidence.

Electronic supplementary material

The online version of this article (10.1186/s12938-019-0684-8) contains supplementary material, which is available to authorized users.

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.

Finite Element Analysis of Long Posterior Transpedicular Instrumentation for Cervicothoracic Fractures Related to Ankylosing Spondylitis

STUDY DESIGN

Biomechanical finite element model analysis.

OBJECTIVES

Spinal fractures related to ankylosing spondylitis (AS) are often treated by long posterior stabilization. The objective of this study is to develop a finite element model (FEM) for spinal fractures related to AS and to establish a biomechanical foundation for long posterior stabilization of cervicothoracic fractures related to AS.

METHODS

An existing FEM (consisting of 2 separately developed models) including the cervical and thoracic spine were adapted to the conditions of AS (all discs fused, C0-C1 and C1-C2 mobile). A fracture at the level C6-C7 was simulated. Besides a normal spine (no AS, no fracture) and the uninstrumented fractured spine 4 different posterior transpedicular instrumentations were tested. Three loads (1.5g, 3.0g, 4.5g) were applied according to a specific load curve.

RESULTS

All posterior stabilization methods could normalize the axial stability at the fracture site as measured with gap distance. The maximum stress at the cranial instrumentation end (C3-C4) was slightly greater if every level was instrumented, than in the skipped level model. The skipped level instrumentation achieved similar rotatory stability as the long multilevel instrumentation.

CONCLUSIONS

Skipping instrumentation levels without giving up instrumentation length reduced stresses in the ossified tissue within the range of the instrumentation and did not decrease the stability in a FEM of a cervicothoracic fracture related to AS. Considering the risks associated with every additional screw placed, the skipped level instrumentation has advantages regarding patient safety.

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.

Effects of Scan Resolutions and Element Sizes on Bovine Vertebral Mechanical Parameters from Quantitative Computed Tomography-Based Finite Element Analysis

Quantitative computed tomography-based finite element analysis (QCT/FEA) has been developed to predict vertebral strength. However, QCT/FEA models may be different with scan resolutions and element sizes. The aim of this study was to explore the effects of scan resolutions and element sizes on QCT/FEA outcomes. Nine bovine vertebral bodies were scanned using the clinical CT scanner and reconstructed from datasets with the two-slice thickness, that is, 0.6 mm (PA resolution) and 1 mm (PB resolution). There were significantly linear correlations between the predicted and measured principal strains (R² > 0.7, P < 0.0001), and the predicted vertebral strength and stiffness were modestly correlated with the experimental values (R² > 0.6, P < 0.05). Two different resolutions and six different element sizes were combined in pairs, and finite element (FE) models of bovine vertebral cancellous bones in the 12 cases were obtained. It showed that the mechanical parameters of FE models with the PB resolution were similar to those with the PA resolution. The computational accuracy of FE models with the element sizes of 0.41 × 0.41 × 0.6 mm³ and 0.41 × 0.41 × 1 mm³ was higher by comparing the apparent elastic modulus and yield strength. Therefore, scan resolution and element size should be chosen optimally to improve the accuracy of QCT/FEA.

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

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