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

Role of intra-lamellar collagen and hyaluronan nanostructures in annulus fibrosus on lumbar spine biomechanics: insights from molecular mechanics-finite element-based multiscale analyses

Annulus fibrosus' (AF) ability to transmit multi-directional spinal motion is contributed by a combination of chemical interactions among biomolecular constituents-collagen type I (COL-I), collagen type II (COL-II), and proteoglycans (aggrecan and hyaluronan)-and mechanical interactions at multiple length scales. However, the mechanistic role of such interactions on spinal motion is unclear. The present work employs a molecular mechanics-finite element (FE) multiscale approach to investigate the mechanistic role of molecular-scale collagen and hyaluronan nanostructures in AF, on spinal motion. For this, an FE model of the lumbar segment is developed wherein a multiscale model of AF collagen fiber, developed from COL-I, COL-II, and hyaluronan using the molecular dynamics-cohesive finite element multiscale method, is incorporated. Analyses show AF collagen fibers primarily contribute to axial rotation (AR) motion, owing to angle-ply orientation. Maximum fiber strain values of 2.45% in AR, observed at the outer annulus, are 25% lower than the reported values. This indicates native collagen fibers are softer, attributed to the softer non-fibrillar matrix and higher interfibrillar sliding. Additionally, elastic zone stiffness of 8.61 Nm/° is observed to be 20% higher than the reported range, suggesting native AF lamellae exhibit lower stiffness, resulting from inter-collagen fiber bundle sliding. The presented study has further implications towards the hierarchy-driven designing of AF-substitute materials.

Effect of meniscus modelling assumptions in a static tibiofemoral finite element model: importance of geometry over material

Finite element studies of the tibiofemoral joint have increased use in research, with attention often placed on the material models. Few studies assess the effect of meniscus modelling assumptions in image-based models on contact mechanics outcomes. This work aimed to assess the effect of modelling assumptions of the meniscus on knee contact mechanics and meniscus kinematics. A sensitivity analysis was performed using three specimen-specific tibiofemoral models and one generic knee model. The assumptions in representing the meniscus attachment on the tibia (shape of the roots and position of the attachment), the material properties of the meniscus, the shape of the meniscus and the alignment of the joint were evaluated, creating 40 model instances. The values of material parameters for the meniscus and the position of the root attachment had a small influence on the total contact area but not on the meniscus displacement or the force balance between condyles. Using 3D shapes to represent the roots instead of springs had a large influence in meniscus displacement but not in knee contact area. Changes in meniscus shape and in knee alignment had a significantly larger influence on all outcomes of interest, with differences two to six times larger than those due to material properties. The sensitivity study demonstrated the importance of meniscus shape and knee alignment on meniscus kinematics and knee contact mechanics, both being more important than the material properties or the position of the roots. It also showed that differences between knees were large, suggesting that clinical interpretations of modelling studies using single geometries should be avoided.

Analyzing isolated degeneration of lumbar facet joints: implications for degenerative instability and lumbar biomechanics using finite element analysis

The facet joint contributes to lumbar spine stability as it supports the weight of body along with the intervertebral discs. However, most studies on the causes of degenerative lumbar diseases focus on the intervertebral discs and often overlook the facet joints. This study aimed to investigate the impact of facet joint degeneration on the degenerative changes and diseases of the lumbar spine. A finite element model of the lumbar spine (L1-S1) was fabricated and validated to study the biomechanical characteristics of the facet joints. To simulate degeneration of the facet joint, the model was divided into four grades based on the number of degenerative segments (L4-L5 or L4-S1) and the contact condition between the facet joint surfaces. Finite element analysis was performed on four spine motions: flexion, extension, lateral bending, and axial torsion, by applying a pure moment to the upper surface of L1. Important parameters that could be used to confirm the effect of facet joint degeneration on the lumbar spine were calculated, including the range of motion (ROM) of the lumbar segments, maximum von Mises stress on the intervertebral discs, and reaction force at the facet joint. Facet joint degeneration affected the biomechanical characteristics of the lumbar spine depending on the movements of the spine. When analyzed by dividing it into degenerative onset and onset-adjacent segments, lumbar ROM and the maximum von Mises stress of the intervertebral discs decreased as the degree of degeneration increased in the degenerative onset segments. The reaction force at the facet joint decreased with flexion and increased with lateral bending and axial torsion. In contrast, lumbar ROM of the onset-adjacent segments remained almost unchanged despite severe degeneration of the facet joint, and the maximum von Mises stress of the intervertebral discs increased with flexion and extension but decreased with lateral bending and axial torsion. Additionally, the facet joint reaction force increased with extension, lateral bending, and axial rotation. This analysis, which combined the ROM of the lumbar segment, maximum von Mises stress on the intervertebral disc, and facet joint reaction force, confirmed the biomechanical changes in the lumbar spine due to the degeneration of isolated facet joints under the load of spinal motion. In the degenerative onset segment, spinal instability decreased, whereas in the onset-adjacent segment, a greater load was applied than in the intact state. When conducting biomechanical studies on the lumbar spine, considering facet joint degeneration is important since it can lead to degenerative spinal diseases, including adjacent segment diseases.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

A systematic comparison between FEBio and PolyFEM for biomechanical systems

BACKGROUND AND OBJECTIVES

Finite element simulations are widely employed as a non-invasive and cost-effective approach for predicting outcomes in biomechanical simulations. However, traditional finite element software, primarily designed for engineering materials, often encountered limitations in contact detection and enforcement, leading to simulation failure when dealing with complex biomechanical configurations. Currently, a lot of model tuning is required to get physically accurate finite element simulations without failures. This adds significant human interaction to each iteration of a biomechanical model. This study addressed these issues by introducing PolyFEM, a novel finite element solver that guarantees inversion- and intersection-free solutions with completely automatic collision detection. The objective of this research is to validate PolyFEM's capabilities by comparing its results with those obtained from a well-established finite element solver, FEBio.

METHODS

To achieve this goal, five comparison scenarios were formulated to assess and validate PolyFEM's performance. The simulations were reproduced using both PolyFEM and FEBio, and the final results were compared. The five comparison scenarios included: (1) reproducing simulations from the FEBio test suite, consisting of static, dynamic, and contact-driven simulations; (2) replicating simulations from the verification paper published alongside the original release of FEBio; (3) a biomechanically based contact problem; (4) creating a custom simulation involving high-energy collisions between soft materials to highlight the difference in collision methods between the two solvers; and (5) performing biomechanical simulations of biting and quasi-stance.

RESULTS

We found that PolyFEM was capable of replicating all simulations previously conducted in FEBio. Particularly noteworthy is PolyFEM's superiority in high-energy contact simulations, where FEBio fell short, unable to complete over half of the simulations in Scenario 4. Although some of the simulations required significantly more simulation time in PolyFEM compared to FEBio, it is important to highlight that PolyFEM achieved these results without the need for any additional model tuning or contact declaration.

DISCUSSION

Despite being in the early stages of development, PolyFEM currently provides verified solutions for hyperelastic materials that are consistent with FEBio, both in previously published workflows and novel finite element scenarios. PolyFEM exhibited the ability to tackle challenging biomechanical problems where other solvers fell short, thus offering the potential to enhance the accuracy and realism of future finite element analyses.

Annulus Calibration Increases the Computational Accuracy of the Lumbar Finite Element Model

STUDY DESIGN

Mechanical simulations.

OBJECTIVE

Inadequate calibration of annuli negatively affects the computational accuracy of finite element (FE) models. Specifically, the definition of annulus average radius (AR) does not have uniformity standards. Differences between the elastic moduli in the different layers and parts of the annulus were not fully calibrated when a linear elastic material is used to define its material properties. This study aims to optimize the computational accuracy of the FE model by calibrating the annulus.

METHODS

We calibrated the annulus AR and elastic modulus in our anterior-constructed lumbar model by eliminating the difference between the computed range of motion and that measured by in vitro studies under a flexion-extension loading condition. Multi-indicator validation was performed by comparing the computed indicators with those measured in in vitro studies. The computation time required for the different models has also been recorded to evaluate the computational efficiency.

RESULTS

The difference between computed and measured ROMs was less than 1% when the annulus AR and elastic modulus were calibrated. In the model validation process, all the indicators computed by the calibrated FE model were within ±1 standard deviation of the average values obtained from in vitro studies. The maximum difference between the computed and measured values was less than 10% under nearly all loading conditions. There is no apparent variation tendency for the computational time associated with different models.

CONCLUSION

The FE model with calibrated annulus AR and regional elastic modulus has higher computational accuracy and can be used in subsequent mechanical studies.

Automatic generation of subject-specific finite element models of the spine from magnetic resonance images

The generation of subject-specific finite element models of the spine is generally a time-consuming process based on computed tomography (CT) images, where scanning exposes subjects to harmful radiation. In this study, a method is presented for the automatic generation of spine finite element models using images from a single magnetic resonance (MR) sequence. The thoracic and lumbar spine of eight adult volunteers was imaged using a 3D multi-echo-gradient-echo sagittal MR sequence. A deep-learning method was used to generate synthetic CT images from the MR images. A pre-trained deep-learning network was used for the automatic segmentation of vertebrae from the synthetic CT images. Another deep-learning network was trained for the automatic segmentation of intervertebral discs from the MR images. The automatic segmentations were validated against manual segmentations for two subjects, one with scoliosis, and another with a spine implant. A template mesh of the spine was registered to the segmentations in three steps using a Bayesian coherent point drift algorithm. First, rigid registration was applied on the complete spine. Second, non-rigid registration was used for the individual discs and vertebrae. Third, the complete spine was non-rigidly registered to the individually registered discs and vertebrae. Comparison of the automatic and manual segmentations led to dice-scores of 0.93-0.96 for all vertebrae and discs. The lowest dice-score was in the disc at the height of the implant where artifacts led to under-segmentation. The mean distance between the morphed meshes and the segmentations was below 1 mm. In conclusion, the presented method can be used to automatically generate accurate subject-specific spine models.

A comparison of intervertebral ligament properties utilized in a thoracic spine functional unit through kinematic evaluation

Ligament properties in the literature are variable, yet scarce, but needed to calibrate computational models for spine clinical research applications. A comparison of ligament stiffness properties and their effect on the kinematic behavior of a thoracic functional spinal unit (FSU) is examined in this paper. Six unique ligament property sets were utilized within a volumetric T7-T8 finite element (FE) model developed using computer-aided design (CAD) spinal geometry. A 7.5 Nm moment was applied along three anatomical planes both with and without costovertebral (CV) joints present. Range of Motion (RoM) was assessed for each property set and compared to published experimental data. Intact and serial ligament removal procedures were implemented in accordance with experimental protocol. The variance in both kinematic behavior and comparability with experimental data among property sets emphasizes the role nonlinear characterization plays in determining proper kinematic behavior in spinal FE models. Additionally, a decrease in RoM variation among property sets was exhibited when the model setup incorporated the CV joint. With proper assessment of the source and size of each ligament, the material properties considered here could be expanded and justified for implementation into thoracic spine clinical studies.

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.

Biomechanical effect of endplate defects on the intermediate vertebral bone in consecutive two-level anterior cervical discectomy and fusion: a finite element analysis

BACKGROUND

Intermediate vertebral collapse is a newly discovered complication of consecutive two-level anterior cervical discectomy and fusion (ACDF). There have been no analytical studies related to the effects of endplate defects on the biomechanics of the intermediate vertebral bone after ACDF. This study aimed to compare the effects of endplate defects on the intermediate vertebral bone biomechanics in the zero-profile (ZP) and cage-and-plate (CP) methods of consecutive 2-level ACDF and to determine whether collapse of the intermediate vertebra is more likely to occur using ZP.

METHODS

A three-dimensional finite element (FE) model of the intact cervical spine (C2-T1) was constructed and validated. The intact FE model was then modified to build ACDF models and imitate the situation of endplate injury, establishing two groups of models (ZP, IM-ZP and CP, IM-ZP). We simulated cervical motion, such as flexion, extension, lateral bending and axial rotation, and compared the range of motion (ROM), upper and lower endplate stress, fusion fixation device stress, C5 vertebral body stress, intervertebral disc internal pressure (intradiscal pressure, or IDP) and the ROM of adjacent segments in the models.

RESULTS

There was no significant difference between the IM-CP model and the CP model in the ROM of the surgical segment, upper and lower endplate stress, fusion fixation device stress, C5 vertebral body stress, IDP, or ROM of the adjacent segments. Compared with the CP model, the endplate stress of the ZP model is significantly higher in the flexion, extension, lateral bending and axial rotation conditions. Compared with the ZP model, endplate stress, screw stress, C5 vertebral stress and IDP in IM-ZP were significantly increased under flexion, extension, lateral bending and axial rotation conditions.

CONCLUSIONS

Compared to consecutive 2-level ACDF using CP, collapse of the intermediate vertebra is more likely to occur using ZP due to its mechanical characteristics. Intraoperative endplate defects of the anterior lower margin of the middle vertebra are a risk factor leading to collapse of the middle vertebra after consecutive 2-level ACDF using ZP.

Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

In spine research, two possibilities to generate models exist: generic (population-based) models representing the average human and subject-specific representations of individuals. Despite the increasing interest in subject specificity, individualisation of spine models remains challenging. Neuro-musculoskeletal (NMS) models enable the analysis and prediction of dynamic motions by incorporating active muscles attaching to bones that are connected using articulating joints under the assumption of rigid body dynamics. In this study, we used forward-dynamic simulations to compare a generic NMS multibody model of the thoracolumbar spine including fully articulated vertebrae, detailed musculature, passive ligaments and linear intervertebral disc (IVD) models with an individualised model to assess the contribution of individual biological structures. Individualisation was achieved by integrating skeletal geometry from computed tomography and custom-selected muscle and ligament paths. Both models underwent a gravitational settling process and a forward flexion-to-extension movement. The model-specific load distribution in an equilibrated upright position and local stiffness in the L4/5 functional spinal unit (FSU) is compared. Load sharing between occurring internal forces generated by individual biological structures and their contribution to the FSU stiffness was computed. The main finding of our simulations is an apparent shift in load sharing with individualisation from an equally distributed element contribution of IVD, ligaments and muscles in the generic spine model to a predominant muscle contribution in the individualised model depending on the analysed spine level.

Development of a Computational Model of the Mechanical Behavior of the L4-L5 Lumbar Spine: Application to Disc Degeneration

Degenerative changes in the lumbar spine significantly reduce the quality of life of people. In order to fully understand the biomechanics of the affected spine, it is crucial to consider the biomechanical alterations caused by degeneration of the intervertebral disc (IVD). Therefore, this study is aimed at the development of a discrete element model of the mechanical behavior of the L4-L5 spinal motion segment, which covers all the degeneration grades from healthy IVD to its severe degeneration, and numerical study of the influence of the IVD degeneration on stress state and biomechanics of the spine. In order to analyze the effects of IVD degeneration on spine biomechanics, we simulated physiological loading conditions using compressive forces. The results of modeling showed that at the initial stages of degenerative changes, an increase in the amplitude and area of maximum compressive stresses in the disc is observed. At the late stages of disc degradation, a decrease in the value of intradiscal pressure and a shift in the maximum compressive stresses in the dorsal direction is observed. Such an influence of the degradation of the geometric and mechanical parameters of the tissues of the disc leads to the effect of bulging, which in turn leads to the formation of an intervertebral hernia.

Biochemical and biomechanical characterization of the cervical, thoracic, and lumbar facet joint cartilage in the Yucatan minipig

Facet joint arthrosis causes pain in approximately 7 % of the U.S. population, but current treatments are palliative. The objective of this study was to elucidate structure-function relationships and aid in the development of future treatments for the facet joint. This study characterized the articular surfaces of cervical, thoracic, and lumbar facet cartilage from skeletally mature (18-24 mo) Yucatan minipigs. The minipig was selected as the animal model because it is recognized by the U.S. Food and Drug Administration (FDA) and the American Society for Testing and Materials (ASTM) as a translationally relevant model for spine-related indications. It was found that the thoracic facets had a ∼2 times higher aspect ratio than lumbar and cervical facets. Lumbar facets had 6.9-9.6 times higher % depth than the cervical and thoracic facets. Aggregate modulus values ranged from 135 to 262 kPa, much lower than reported aggregate modulus in the human knee (reported to be 530-701 kPa). The tensile Young's modulus values ranged from 6.7 to 20.3 MPa, with the lumbar superior facet being 304 % and 286 % higher than the cervical inferior and thoracic superior facets, respectively. Moreover, 3D reconstructions of entire vertebral segments were generated. The results of this study imply that structure-function relationships in the facet cartilage are different from other joint cartilages because biochemical properties are analogous to other articular cartilage sources whereas mechanical properties are not. By providing functional properties and a 3D database of minipig facet geometries, this work may supply design criteria for future facet tissue engineering efforts.

Comparison of In Vivo Intradiscal Pressure between Sitting and Standing in Human Lumbar Spine: A Systematic Review and Meta-Analysis

BACKGROUND

Non-specific low back pain (LBP) is highly prevalent today. Disc degeneration could be one of the causes of non-specific LBP, and increased intradiscal pressure (IDP) can potentially induce disc degeneration. The differences in vivo IDP in sitting and standing postures have been studied, but inconsistent results have been reported. The primary objective of this systematic review is to compare the differences in vivo IDP between sitting and standing postures. The secondary objective of this review is to compare effect size estimates between (1) dated and more recent studies and (2) healthy and degenerated intervertebral discs.

METHODS

An exhaustive search of six electronic databases for studies published before November 2021 was conducted. Articles measuring in vivo IDP in sitting and standing postures were included. Two independent researchers conducted the screening and data extraction.

RESULTS

Ten studies that met the inclusion criteria were included in the systematic review, and seven studies with nine independent groups were included in meta-analyses. The sitting posture induces a significantly higher IDP on the lumbar spine (SMD: 0.87; 95% CI = [0.33, 1.41]) than the standing posture. In studies published after 1990 and subjects with degenerated discs, there are no differences in vivo IDP between both postures.

CONCLUSIONS

Sitting causes higher loads on the lumbar spine than standing in the normal discs, but recent studies do not support this conclusion. Furthermore, the degenerated discs showed no difference in IDP in both postures.

Reproducing Morphological Features Of Intervertebral Disc Using Finite Element Modeling To Predict The Course Of Cervical Spine Dorsopathy

Study objective — To evaluate how morphological features of intervertebral disc would affect the outcomes of finite element modeling of axial load in the cervical spine, C3-C5, in order to predict the risk of occurrence and course of dorsopathies. Material and Methods — Three-dimensional models of the cervical spine vertebrae were generated from the computed tomography data of a volunteer (24 years old male without detected pathology of his neck). Intervertebral disc models were developed in two configurations. For each model, we performed a finite element investigation of the stress-strain state with the same loading conditions. The load-displacement curves were compared with the experimental data generated from the results of previously conducted in vitro experiments. Results — The maximum and mean displacement values for the isotropic model were 1.15 mm and 0.73 ± 0.45 mm, respectively. For anisotropic model, maximum and mean displacement values were 0.86 mm and 0.47 ± 0.24 mm, correspondingly. Predicted displacement values for both models matched the experimental data fairly well. Stress profiles of intervertebral discs and stress diagrams of facet joints were calculated. Conclusion — The proposed geometric and constitutive configurations of the intervertebral disc take into account specific morphological features at low computational costs, thereby facilitating the modeling of degenerative disc changes.

Finite Element Method for the Evaluation of the Human Spine: A Literature Overview

The finite element method (FEM) represents a computer simulation method, originally used in civil engineering, which dates back to the early 1940s. Applications of FEM have also been used in numerous medical areas and in orthopedic surgery. Computing technology has improved over the years and as a result, more complex problems, such as those involving the spine, can be analyzed. The spine is a complex anatomical structure that maintains the erect posture and supports considerable loads. Applications of FEM in the spine have contributed to the understanding of bone biomechanics, both in healthy and abnormal conditions, such as scoliosis, fractures (trauma), degenerative disc disease and osteoporosis. However, since FEM is only a digital simulation of the real condition, it will never exactly simulate in vivo results. In particular, when it concerns biomechanics, there are many features that are difficult to represent in a FEM. More FEM studies and spine research are required in order to examine interpersonal spine stiffness, young spine biomechanics and model accuracy. In the future, patient-specific models will be used for better patient evaluations as well as for better pre- and inter-operative planning.

Biomechanical properties of a novel nonfusion artificial vertebral body for anterior lumbar vertebra resection and internal fixation

The aim of the study was to evaluate the biomechanical properties of a novel nonfused artificial vertebral body in treating lumbar diseases and to compare with those of the fusion artificial vertebral body. An intact finite element model of the L1–L5 lumbar spine was constructed and validated. Then, the finite element models of the fusion group and nonfusion group were constructed by replacing the L3 vertebral body and adjacent intervertebral discs with prostheses. For all finite element models, an axial preload of 500 N and another 10 N m imposed on the superior surface of L1. The range of motion and stress peaks in the adjacent discs, endplates, and facet joints were compared among the three groups. The ranges of motion of the L1–2 and L4–5 discs in flexion, extension, left lateral bending, right lateral bending, left rotation and right rotation were greater in the fusion group than those in the intact group and nonfusion group. The fusion group induced the greatest stress peaks in the adjacent discs and adjacent facet joints compared to the intact group and nonfusion group. The nonfused artificial vertebral body could better retain mobility of the surgical site after implantation (3.6°–8.7°), avoid increased mobility and stress of the adjacent discs and facet joints.