Three-dimensional geometrical and mechanical modelling of the lumbar spine

Finite Element Analysis of Stress Distribution and Range of Motion in Discogenic Back Pain

OBJECTIVE

Precise knowledge regarding the mechanical stress applied to the intervertebral disc following each individual spine motion enables physicians and patients to understand how people with discogenic back pain should be guided in their exercises and which spine motions to specifically avoid. We created an intervertebral disc degeneration model and conducted a finite element (FE) analysis of loaded stresses following each spinal posture or motion.

METHODS

A 3-dimensional FE model of intervertebral disc degeneration at L4-5 was constructed. The intervertebral disc degeneration model was created according to the modified Dallas discogram scale. The von Mises stress and range of motion (ROM) regarding the intervertebral discs and the endplates were analyzed.

RESULTS

We observed that mechanical stresses loaded onto the intervertebral discs were similar during flexion, extension, and lateral bending, which were greater than those occurring during torsion. Based on the comparison among the grades divided by the modified Dallas discogram scale, the mechanical stress during extension was greater in grades 3-5 than it was during the others. During extension, the mechanical stress loaded onto the intervertebral disc and endplate was greatest in the posterior portion. Mechanical stresses loaded onto the intervertebral disc were greater in grades 3-5 compared to those in grades 0-2.

CONCLUSION

Our findings suggest that it might be beneficial for patients experiencing discogenic back pain to maintain a neutral posture in their lumbar spine when engaging in daily activities and exercises, especially those suffering from significant intravertebral disc degeneration.

Assessment of a fully-parametric thoraco-lumbar spine model generator with articulated ribcage

The present paper describes a novel user-friendly fully-parametric thoraco-lumbar spine CAD model generator including the ribcage, based on 22 independent parameters (1 posterior vertebral body height per vertebra + 4 sagittal alignment parameters, namely pelvic incidence, sacral slope, L1-L5 lumbar lordosis, and T1-T12 thoracic kyphosis). Reliable third-order polynomial regression equations were implemented in Solidworks to analytically calculate 56 morphological dependent parameters and to automatically generate the spine CAD model based on primitive geometrical features. A standard spine CAD model, representing the case-study of an average healthy adult, was then created and positively assessed in terms of spinal anatomy, ribcage morphology, and sagittal profile. The immediate translation from CAD to FEM for relevant biomechanical analyses was successfully demonstrated, first, importing the CAD model into Abaqus, and then, iteratively calibrating the constitutive parameters of one lumbar and three thoracic FSUs, with particular interest on the hyperelastic material properties of the IVD, and the spinal and costo-vertebral ligaments. The credibility of the resulting lumbo-sacral and thoracic spine FEM with/without ribcage were assessed and validated throughout comparison with extensive in vitro and in vivo data both in terms of kinematics (range of motion) and dynamics (intradiscal pressure) either collected under pure bending moments and complex loading conditions (bending moments + axial compressive force).

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.

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.

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.

Biomechanical Effects of a Cross Connector in Sacral Fractures - A Finite Element Analysis

Background: Spinopelvic fractures and approaches of operative stabilization have been a source of controversial discussion. Biomechanical data support the benefit of a spinopelvic stabilization and minimally invasive procedures help to reduce the dissatisfying complication rate. The role of a cross connector within spinopelvic devices remains inconclusive. We aimed to analyze the effect of a cross connector in a finite element model (FE model). Study Design: A FE model of the L1-L5 spine segment with pelvis and a spinopelvic stabilization was reconstructed from patient-specific CT images. The biomechanical relevance of a cross connector in a Denis zone I (AO: 61-B2) sacrum fracture was assessed in the FE model by applying bending and twisting forces with and without a cross connector. Biomechanical outcomes from the numerical model were investigated also considering uncertainties in material properties and levels of osseointegration. Results: The designed FE model showed comparable values in range-of-motion (ROM) and stresses with reference to the literature. The superiority of the spinopelvic stabilization (L5/Os ilium) ± cross connector compared to a non-operative procedure was confirmed in all analyzed loading conditions by reduced ROM and principal stresses in the disk L5/S1, vertebral body L5 and the fracture area. By considering the combination of all loading cases, the presence of a cross connector reduced the maximum stresses in the fracture area of around 10%. This difference has been statistically validated (p < 0.0001). Conclusion: The implementation of a spinopelvic stabilization (L5/Os ilium) in sacrum fractures sustained the fracture and led to enhanced biomechanical properties compared to a non-reductive procedure. While the additional cross connector did not alter the resulting ROM in L4/L5 or L5/sacrum, the reduction of the maximum stresses in the fracture area was significant.

Numerical analysis of the mechanical behaviour of intact and implanted lumbar functional spinal units: Effects of loading and boundary conditions

The objective of this study was to develop an improved finite element (FE) model of a lumbar functional spinal unit (FSU) and to subsequently analyse the deviations in load transfer owing to implantation. The effects of loading and boundary conditions on load transfer in intact and implanted FSUs and its relationship with the potential risk of vertebral fracture were investigated. The FE models of L1-L5 and L3-L4 FSUs, intact and implanted, were developed using patient-specific CT-scan dataset and segmentation of cortical and cancellous bone regions. The effect of submodelling technique, as compared to artificial boundary conditions, on the elastic behaviour of lumbar spine was examined. Applied forces and moments, corresponding to physiologic movements, were used as loading conditions. Results indicated that the loading and boundary conditions considerably affect stress-strain distributions within a FSU. This study, based on an improved FE model of a vertebra, highlights the importance of using the submodelling technique to adequately evaluate the mechanical behaviour of a FSU. In the intact FSU, strains of 200-400 µε were observed in the cancellous bone of vertebral body and pedicles. High equivalent stresses of 10-25 MPa and 1-5 MPa were generated around the pars interarticularis for cortical and cancellous regions, respectively. Implantation caused reductions of 85%-92% in the range of motion for all movements. Insertion of the intervertebral cage resulted in major deviations in load transfer across a FSU for all movements. The cancellous bone around cage experienced pronounced increase in stresses of 10-15 MPa, which indicated potential risk of failure initiation in the vertebra.

Restoring lumbar lordosis: a systematic review of controlled trials utilizing Chiropractic Bio Physics® (CBP®) non-surgical approach to increasing lumbar lordosis in the treatment of low back disorders

[Purpose] To systematically review controlled trial evidence for the use of lumbar extension traction by Chiropractic BioPhysics^® methods for the purpose of increasing lumbar lordosis in those with hypolordosis and low back disorders. [Methods] Literature searches were performed in Pubmed, PEDro, CINAHL, Cochrane, and ICL databases. Search terms included iterations related to the lumbar spine, low back pain and extension traction rehabilitation. [Results] Four articles detailing 2 randomized and 1 non-randomized trial were located. Trials demonstrated increases in radiographic measured lordosis of 7–11°, over 10–12 weeks, after 30–36 treatment sessions. Randomized trials demonstrated traction treated groups mostly maintained lordosis correction, pain relief, and disability after 6-months follow-up. The non-randomized trial showed lordosis and pain intensity were maintained with periodic maintenance care for 1.5 years. Importantly, control/comparison groups had no increase in lumbar lordosis. Randomized trials showed comparison groups receiving physiotherapy-less the traction, had temporary pain reduction during treatment that regressed towards baseline levels as early as 3-months after treatment. [Conclusion] Limited but good quality evidence substantiates that the use of extension traction methods in rehabilitation programs definitively increases lumbar hypolordosis. Preliminarily, these studies indicate these methods provide longer-term relief to patients with low back disorders versus conventional rehabilitation approaches tested.

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.

Effects of Low Bone Mineral Status on Biomechanical Characteristics in Idiopathic Scoliotic Spinal Deformity

BACKGROUND

Low bone mass in patients with adolescent idiopathic scoliosis has been well reported. Poor bone quality was regarded as a new and unique prognostic factor in aggravating curve progression. However, the potential biomechanical correlation between them remains unclear.

METHODS

Three-dimensional finite element models of idiopathic scoliotic spine with different bone mineral status were created for axial loading simulation. An axial load of 3 different body weights was applied on different bone mineral mass models. The mechanical responses of the vertebral cortical and cancellous bone, facet joints, end plate, and intervertebral disc were analyzed.

RESULTS

Accompanied with the low bone mineral status, thoracic scoliosis produced asymmetric and higher stress in the cortical bone, lumbar facet joints, and end plate at the concave side of the thoracic structure curve. Stress increased in the disc at the apex of the scoliosis, whereas it mildly decreased in the L4-5 and L5-S1 disc. Body weight gain increased the stress in scoliotic spine structures in all bone mineral statues.

CONCLUSIONS

Biomechanical simulations indicated that low bone mineral mass might aggravate curve progression and induce more serious lumbar compensatory scoliosis in patients with adolescent idiopathic scoliosis. Weight gain was also a risk factor for curve progression.

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Limiting interpedicular screw displacement increases shear forces in screws: A finite element study

BACKGROUND CONTEXT

Screw loosening has been reported for non-fusion devices. Forces on pedicle screws could be related to kinematic parameters as the interpedicular displacement (ID), which consists of the displacement between superior and inferior screw heads from full extension to full flexion.

PURPOSE

To investigate the relationship between ID and screw loosening for different designs of posterior implants using a finite element model.

METHODS

An L3-sacrum previously validated spine FE model was used. Three-rod designs were considered in L4-L5 segment: a rigid screw-rod implant, a flexible one and a specific design with a sliding rod providing limited restrain in ID. In order to simulate intermediate configurations, the friction coefficient between the sliding rods and connectors were varied. The sacrum was rigidly fixed. Rotations (flexion-extension, lateral bending and axial rotation) were applied to L3, for each modeled configuration: intact, injured, injured with different implants. Model consistency was checked with existing experimental in vitro data on intact and instrumented segments. Screw loads were computed as well as ID.

RESULTS

In flexion-extension, the ID was less than 2mm for rigid (R) and flexible (F) constructs and 5.5mm for intact spine and the sliding implant (S3). Screw's shear forces were 272N, 153N, 43N respectively for R, F and S3 constructs.

CONCLUSIONS

Implants that allow ID presented lower screws loads. A compromise between the ability of the implant to withstand compressive forces, which requires longitudinal stiffness, and its ability to allow ID could be important for future implant designs in order to prevent screw loosening.

Biomechanical Effects of the Geometry of Ball-and-Socket Artificial Disc on Lumbar Spine: A Finite Element Study

STUDY DESIGN

A three-dimensional finite element model of intact lumbar spine was constructed and four surgical finite element models implanted with ball-and-socket artificial discs with four different radii of curvature were compared.

OBJECTIVE

To investigate biomechanical effects of the curvature of ball-and-socket artificial disc using finite element analysis.

SUMMARY OF BACKGROUND DATA

Total disc replacement (TDR) has been accepted as an alternative treatment because of its advantages over spinal fusion methods in degenerative disc disease. However, the influence of the curvature of artificial ball-and-socket discs has not been fully understood.

METHODS

Four surgical finite element models with different radii of curvature of ball-and-socket artificial discs were constructed.

RESULTS

The range of motion (ROM) increased with decreasing radius of curvature in extension, flexion, and lateral bending, whereas it increased with increasing radius of curvature in axial torsion. The facet contact force was minimum with the largest radius of curvature in extension, flexion, and lateral bending, whereas it was maximum with the largest radius in axial torsion. It was also affected by the disc placement, more with posterior placement than anterior placement. The stress in L4 cancellous bone increased when the radius of curvature was too large or small.

CONCLUSION

The geometry of ball-and-socket artificial disc significantly affects the ROM, facet contact force, and stress in the cancellous bone at the surgical level. The implication is that in performing TDR, the ball-and-socket design may not be ideal, as ROM and facet contact force are sensitive to the disc design, which may be exaggerated by the individual difference of anatomical geometry.

LEVEL OF EVIDENCE

N/A.

Biomechanical Comparison of Spinal Fusion Methods Using Interspinous Process Compressor and Pedicle Screw Fixation System Based on Finite Element Method

Objective

To investigate the biomechanical effects of a newly proposed Interspinous Process Compressor (IPC) and compare with pedicle screw fixation at surgical and adjacent levels of lumbar spine.

Methods

A three dimensional finite element model of intact lumbar spine was constructed and two spinal fusion models using pedicle screw fixation system and a new type of interspinous devices, IPC, were developed. The biomechanical effects such as range of motion (ROM) and facet contact force were analyzed at surgical level (L3/4) and adjacent levels (L2/3, L4/5). In addition, the stress in adjacent intervertebral discs (D2, D4) was investigated.

Results

The entire results show biomechanical parameters such as ROM, facet contact force, and stress in adjacent intervertebral discs were similar between PLIF and IPC models in all motions based on the assumption that the implants were perfectly fused with the spine.

Conclusion

The newly proposed fusion device, IPC, had similar fusion effect at surgical level, and biomechanical effects at adjacent levels were also similar with those of pedicle screw fixation system. However, for clinical applications, real fusion effect between spinous process and hooks, duration of fusion, and influence on spinous process need to be investigated through clinical study.

Computational Biomechanical Modeling of Scoliotic Spine: Challenges and Opportunities

BACKGROUND

Biomechanical computer models of the spine have important roles in the treatment and correction of scoliosis by providing predictive information for surgeons and other clinicians.

OBJECTIVES

This article reviews computational models of intact and scoliotic spine and its components; vertebra, intervertebral disc, ligament, facet joints, and muscle. Several spine models, developed using multi-body modelling and finite element modelling schemes, and their pros and cons are discussed.

CONCLUSIONS

The review reveals that scoliosis modelling is performed for 3 main applications: 1) brace simulation; 2) analysis of surgical correction technique; and 3) patient positioning before surgical instrumentation. The models provide predictive information for a priori choice of brace configurations and mechanically effective surgical correction techniques and the expected degree of correction. However, they have many shortcomings: for instance, they do not fully reproduce the active behaviour of the spine and the models' properties are not personalized.

Influence of an auxiliary facet system on intervertebral discs and adjacent facet joints

BACKGROUND CONTEXT

Facet supplementation stabilizes after facetectomy and undercutting laminectomy. It is indicated in degenerative spondylolisthesis with moderate disc degeneration and dynamic stenosis.

PURPOSE

To determine the influence of an auxiliary facet system (AFS) on the instrumented disc, adjacent levels' discs, and facet joints and to compare it with fusion.

STUDY DESIGN

Finite element study.

METHODS

L3-L4, L4-L5, and L5-S1 were studied using a validated finite element model with prescribed displacements for an intact spine, lesion by facetectomy and undercutting laminectomy, AFS, and fusion at L4-L5. The distribution of segmental range of motion (ROM) and applied moments, von Mises stress at the annulus, and facet joint contact forces were calculated with rotations in all planes. Institutional support for implant evaluation and modeling was received by Clariance.

RESULTS

In flexion-extension and lateral bending, fusion decreased L4-L5 ROM and increased adjacent levels' ROM. Range of motion was similarly distributed with intact lesion and AFS. In axial rotation, L4-L5 ROM represented 33% with intact, 55% after lesion, 25% with AFS, and 21% with fusion. Fusion increased annulus stress at adjacent levels in flexion-extension and lateral bending, but decreased stress at L4-L5 compared with AFS. In axial rotation, von Mises stress was similar with fusion and AFS. Facet loading increased in extension and lateral bending with fusion. It was comparable for fusion and AFS in axial rotation.

CONCLUSIONS

This study suggests that the AFS stabilizes L4-L5 in axial rotation after facetectomy and undercutting laminectomy as fusion does. This is because of the cross-link that generates an increased annulus stress in axial rotation at adjacent levels. With imposed displacements, without in vivo compensation of the hips, the solicitation at adjacent levels' discs and facet joints is higher with fusion compared with AFS. Fusion decreases intradiscal stress at the instrumented level.

Posteriorly directed shear loads and disc degeneration affect the torsional stiffness of spinal motion segments: a biomechanical modeling study

STUDY DESIGN

Finite element study.

OBJECTIVE

To analyze the effects of posterior shear loads, disc degeneration, and the combination of both on spinal torsion stiffness.

SUMMARY OF BACKGROUND DATA

Scoliosis is a 3-dimensional deformity of the spine that presents itself mainly in adolescent girls and elderly patients. Our concept of its etiopathogenesis is that an excess of posteriorly directed shear loads, relative to the body's intrinsic stabilizing mechanisms, induces a torsional instability of the spine, making it vulnerable to scoliosis. Our hypothesis for the elderly spine is that disc degeneration compromises the stabilizing mechanisms.

METHODS

In an adult lumbar motion segment model, the disc properties were varied to simulate different aspects of disc degeneration. These models were then loaded with a pure torsion moment in combination with either a shear load in posterior direction, no shear, or a shear load in anterior direction.

RESULTS

Posteriorly directed shear loads reduced torsion stiffness, anteriorly directed shear loads increased torsion stiffness. These effects were mainly caused by a later (respectively earlier) onset of facet joint contact. Disc degeneration cases with a decreased disc height that leads to slackness of the annular fibers and ligaments caused a significantly decreased torsional stiffness. The combination of this stage with posterior shear loading reduced the torsion stiffness to less than half the stiffness of a healthy disc without shear loads. The end stage of disc degeneration increased torsion stiffness again.

CONCLUSION

The combination of a decreased disc height, that leads to slack annular fibers and ligaments, and posterior shear loads very significantly affects torsional stiffness: reduced to less than half the stiffness of a healthy disc without shear loads. Disc degeneration, thus, indeed compromises the stabilizing mechanisms of the elderly spine. A combination with posteriorly directed shear loads could then make it vulnerable to scoliosis.

LEVEL OF EVIDENCE

N/A.

Three-dimensional static modeling of the lumbar spine

This paper presents three-dimensional static modeling of the human lumbar spine to be used in the formation of anatomically-correct movement patterns for a fully cable-actuated robotic lumbar spine which can mimic in vivo human lumbar spine movements to provide better hands-on training for medical students. The mathematical model incorporates five lumbar vertebrae between the first lumbar vertebra and the sacrum, with dimensions of an average adult human spine. The vertebrae are connected to each other by elastic elements, torsional springs and a spherical joint located at the inferoposterior corner in the mid-sagittal plane of the vertebral body. Elastic elements represent the ligaments that surround the facet joints and the torsional springs represent the collective effect of intervertebral disc which plays a major role in balancing torsional load during upper body motion and the remaining ligaments that support the spinal column. The elastic elements and torsional springs are considered to be nonlinear. The nonlinear stiffness constants for six motion types were solved using a multiobjective optimization technique. The quantitative comparison between the angles of rotations predicted by the proposed model and in the experimental data confirmed that the model yields angles of rotation close to the experimental data. The main contribution is that the new model can be used for all motions while the experimental data was only obtained at discrete measurement points.

Determination of the translational and rotational stiffnesses of an L4-L5 functional spinal unit using a specimen-specific finite element model

The knowledge of spinal kinematics is of paramount importance for many aspects of clinical application (i.e. diagnosis, treatment and surgical intervention) and for the development of new spinal implants. The aim of this study was to determine the translational and rotational stiffnesses of a functional spinal unit (FSU) L4-L5 using a specimen-specific finite element model. The results are needed as input data for three-dimensional (3D) multi-body musculoskeletal models in order to simulate vertebral motions and loading in the lumbar spine during daily activities. Within the modelling process, a technique to partition the constitutive members and to calibrate their mechanical properties for the complex model is presented. The material and geometrical non-linearities originating from the disc, the ligaments and the load transfer through the zygapophysial joints were considered. The FSU was subjected to pure moments and forces in the three anatomical planes. For each of the loading scenarios, with and without vertical and follower preload, the presented technique provides results in fair agreement with the literature. The novel representation of the nonlinear behaviour of the translational and rotational stiffness of the disc as a function of the displacement can be used directly as input data for multi-body models.

Prediction of the vertebral strength using a finite element model derived from low-dose biplanar imaging: benefits of subject-specific material properties

STUDY DESIGN

A finite element analysis on osteoporotic vertebrae.

OBJECTIVE

This study aims to validate subject-specific finite element models (FEMs) derived from a low-dose imaging system (EOS, Biospace Med, France) for the prediction of vertebral strength. The vertebrae are submitted to an eccentric compression force leading to compression and anterior bending.

SUMMARY OF BACKGROUND DATA

Given the aging population, osteoporosis and vertebral fractures are a major public health issue. A low bone mineral density (BMD) does not always explain incident fractures, and multifactorial analyses are required. In this context, FEMs based on quantitative computed tomography (QCT) have been proposed to predict vertebral strength in vitro or quantify effects of treatments. However, the clinical use of such a model for the in vivo follow-up of the whole spine is limited by the high-radiation dose induced by QCT and the lying position, which does not allow postural assessment with the same modality.

METHODS

Fourteen vertebrae were modeled using a parametric meshing method. The mesh was subject-specific using geometric parameters computed on the 3-dimensional (3D) reconstructions obtained from the EOS biplanar radiographs. The contribution of cortical bone was taken into account by modeling a cortico-cancellous shell whose properties were derived from experimental data. The effect of subject-specific bone Young's moduli derived from EOS vertebral areal BMD was quantified. The 3D position of the point-of-load application and the 3D orientation of the force was faithfully reproduced in the model to compare the predicted strength and experimental strength under the same loading conditions.

RESULTS

The relative error of prediction decreased from 43% to 16% (2.5 times) when subject-specific mechanical properties, derived from EOS areal BMD, were implemented in the FEM compared with averaged material properties. The resulting subject-specific FEMs predicted vertebral strength with a level of significance close to the QCT-based models (r adjusted = 0.79, root mean square error = 367 N).

CONCLUSION

This work underlines the potential of low-dose biplanar x-ray devices to make subject-specific FEMs for prediction of vertebral strength.

ASSESSMENT OF THE BIOMECHANICAL COMPATIBILITY OF AN INTERSPINOUS IMPLANT FOR "DYNAMIC STABILIZATION" THROUGH THE FINITE ELEMENT METHOD

The paper addresses the biomechanical compatibility of an interspinous implant used for "dynamic stabilization" of a diseased intervertebral disc. A comparison between the behaviour of a titanium alloy ( Ti 6 Al 4 V ) implant and that of a superelastic alloy ( Ni - Ti ) implant has been carried out.

The assessment of the biomechanical compatibility was achieved by means of the finite element method, in which suitably implemented constitutive laws for the materials have been used. The L4–L5 lumbar system in healthy state has been assumed as target for a biomechanically compatible implant. The L4–L5 system with the interspinous implant subjected to compressive force and bending moments has been simulated. A strength analysis for the bearing bone tissue in the posterior processes was also carried out.

The results have shown that both implants were able to decrease the force on the apophyseal joints; however, the titanium-based implant exhibited a low biomechanical compatibility under extension-flexion in the sagittal plane; whereas the Ni - Ti exhibited a higher compatibility.

PREDICTION OF BIOMECHANICAL CHARACTERISTICS OF INTACT AND INJURED LOWER THORACIC SPINE SEGMENT UNDER DIFFERENT LOADS

In this study, the biomechanical roles of disc nucleus and ligaments of human lower thoracic spine (T10–T12) under different loads were investigated using finite element (FE) method. The T10–T12 FE model was developed and validated against the published results. The FE model was then modified accordingly to simulate the injured conditions of nucleus, ligaments and facets and loaded under different configurations to analyze the segmental gross responses and the stress distribution around the annulus circumference. The high first-principal stress of annulus at the posterolateral region has an important role on the disc annulus's tear and a flexion moment causes a high first-principal stress at posterolateral region, despite of the existence of ligaments. The study also shows that decompression in intervertebral discs can reduce the dilatation of annulus tears by 18% around the posterolateral regions of disc annulus. The disc nucleus and the posterior ligaments have important roles in resisting compression and flexion loads, respectively. The investigations in this paper not only supplement experimental research but are also helpful in the understandings of biomechanics of lower thoracic spine.

A pilot finite element study of an osteoporotic L1-vertebra compared to one with normal T-score

In this paper, two patient-specific finite element (FE) models of both an L1 vertebra with a normal T-score and a mildly wedging, osteoporotic one were created and analysed under usual action. Utilising commercial software packages for image processing and FE analysis (FEA) along with in house computer codes for a posteriori assignment of material properties, in vivo high-resolution spiral computed tomography of the entire vertebrae and FEA were combined. Using the vertebra with a normal T-score as baseline it was found that the maximum value of the von Mises stress in the osteoporotic vertebra was 60% higher but still far below bone strength, while the maximum value of von Mises strain in the same vertebra was 148% higher than that of the vertebra with normal T-score. In the vertebra with normal T-score, 17% of its volume exhibited values of von Mises strain higher than the threshold of 4500 μstrains, referenced by Homminga et al. as a threshold of fracture risk, while in the osteoporotic one this percentage was raised up to 37%. The results suggested that the osteoporotic vertebra is susceptible to fracture due to raised strains and not stresses.

Finite element modeling and modal analysis of the human spine vibration configuration

This study was designed to investigate the modal characteristics of the human spine. A 3-D finite element model of the spine T12-Pelvis segment was used to extract resonant frequencies and modal modes of the human spine. By finite element modal analysis and harmonic response analysis, several lower vibration modes in the flexion-extension, lateral bending, and vertical directions were obtained and its vibration configurations were shown in this paper. The results indicate that the lowest resonant frequency of the model is in the flexion-extension direction. The second-order resonant frequency is in the lateral bending direction and the third-order resonant frequency of the T12-Pelvis model is in the vertical direction. The results also show that lumbar spinal vertebrae conduct the rotation action during whole body vibration (WBV). The vibration configurations of the lumbar spine can explore the motion mechanism of different lumbar components under WBV and make us to understand the vibration-induced spine diseases. The findings in this study will be helpful to understand WBV-related injury of the spine in clinics and the ergonomics design and development of mechanical production to protect human spine safety.

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.

Morphometric analysis of the relationships between intervertebral disc and vertebral body heights: an anatomical and radiographic study of the human thoracic spine

The main aim of this study was to provide anatomical data on the heights of the human intervertebral discs for all levels of the thoracic spine by direct and radiographic measurements. Additionally, the heights of the neighboring vertebral bodies were measured, and the prediction of the disc heights based only on the size of the vertebral bodies was investigated. The anterior (ADH), middle (MDH) and posterior heights (PDH) of the discs were measured directly and on radiographs of 72 spine segments from 30 donors (age 57.43 ± 11.27 years). The radiographic measurement error and the reliability of the measurements were calculated. Linear and non-linear regression analyses were employed for investigation of statistical correlations between the heights of the thoracic disc and vertebrae. Radiographic measurements displayed lower repeatability and were shorter than the anatomical ones (approximately 9% for ADH and 37% for PDH). The thickness of the discs varied from 4.5 to 7.2 mm, with the MDH approximately 22.7% greater. The disc heights showed good correlations with the vertebral body heights (R(2), 0.659-0.835, P-values < 0.005; anova), allowing the generation of 10 prediction equations. New data on thoracic disc morphometry were provided in this study. The generated set of regression equations could be used to predict thoracic disc heights from radiographic measurement of the vertebral body height posterior. For the creation of parameterized models of the human thoracic discs, the use of the prediction equations could eliminate the need for direct measurement on intervertebral discs. Moreover, the error produced by radiographic measurements could be reduced at least for the PDH.

Prediction of the human thoracic and lumbar articular facet joint morphometry from radiographic images

The articular facet joints (AFJ) play an important role in the biomechanics of the spine. Although it is well known that some AFJ dimensions (e.g. facet height/width or facet angles) play a major role in spinal deformities such as scoliosis, little is known about statistical correlations between these dimensions and the size of the vertebral bodies. Such relations could allow patient-specific prediction of AFJ morphometry from a few dimensions measurable by X-ray. This would be of clinical interest and could also provide parameters for mathematical modeling of the spine. Our purpose in this study was to generate prediction equations for 20 parameters of the human thoracic and lumbar AFJ from T1 to L4 as a function of only one given parameter, the vertebral body height posterior (VBHP). Linear and nonlinear regression analyses were performed with published anatomical data, including linear and angular dimensions of the AFJ and vertebral body heights, to find the best functions to describe the correlations between these parameters. Third-order polynomial regressions, in contrast to the linear, exponential and logarithmic regressions, provided moderate to high correlations between the AFJ parameters and vertebral body heights; e.g. facet height superior and interfacet width (R², 0.605-0.880); facet height inferior, interfacet height and sagittal/transverse angle superior (R², 0.875-0.973). Different correlations were found for facet width and transverse angle inferior in the thoracic (R², 0.703-0.930) and lumbar (R², 0.457-0.892) regions. A set of 20 prediction equations for AFJ parameters was generated (P-values < 0.005, anova). Comparison of the AFJ predictions with experimental data indicated mean percent errors <13%, with the exception of the thoracolumbar junction (T12-L1). It was possible to establish useful predictions for human thoracic and lumbar AFJ dimensions based on the size of the vertebral bodies. The generated set of equations allows the prediction of 20 AFJ parameters per vertebral level from the measurement of the parameter VBHP, which is easily performed on lateral X-rays. As the vertebral body height is unique for each person and vertebral level, the predicted AFJ parameters are also specific to an individual. This approach could be used for parameterized patient-specific modeling of the spine to explore the clinically important mechanical roles of the articular facets in pathological conditions, such as scoliosis.

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.

Mesh morphing and response surface analysis: quantifying sensitivity of vertebral mechanical behavior

Vertebrae provide essential biomechanical stability to the skeleton. In this work novel morphing techniques were used to parameterize three aspects of the geometry of a specimen-specific finite element (FE) model of a rat caudal vertebra (process size, neck size, and end-plate offset). Material properties and loading were also parameterized using standard techniques. These parameterizations were then integrated within an RSM framework and used to produce a family of FE models. The mechanical behavior of each model was characterized by predictions of stress and strain. A metamodel was fit to each of the responses to yield the relative influences of the factors and their interactions. The direction of loading, offset, and neck size had the largest influences on the levels of vertebral stress and strain. Material type was influential on the strains, but not the stress. Process size was substantially less influential. A strong interaction was identified between dorsal-ventral offset and dorsal-ventral off-axis loading. The demonstrated approach has several advantages for spinal biomechanical analysis by enabling the examination of the sensitivity of a specimen to multiple variations in shape, and of the interactions between shape, material properties, and loading.

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.

Material Property Sensitivity Analysis on Resonant Frequency Characteristics of the Human Spine

The aim of this study is to investigate the effect of material property changes in the spinal components on the resonant frequency characteristics of the human spine. Several investigations have reported the material property sensitivity of human spine under static loading conditions, but less research has been devoted to the material property sensitivity of spinal biomechanical characteristics under a vibration environment. A detailed three-dimensional finite element model of the human spine, T12– pelvis, was built and used to predict the influence of material property variation on the resonant frequencies of the human spine. The simulation results reveal that material properties of spinal components have obvious influences on the dynamic characteristics of the spine. The annulus ground substance is the dominant component affecting the vertical resonant frequencies of the spine. The percentage change of the resonant frequency relative to the basic condition was more than 20% if Young’s modulus of disc annulus is less than 1.5 MPa. The vertical resonant frequency may also decrease if Poisson’s ratio of nucleus pulposus of intervertebral disc decreases.

Evaluation of load transfer characteristics of a dynamic stabilization device on disc loading under compression

In the current study, finite element analyses were conducted to examine the biomechanical capability of a newly design dynamic stabilization system, FlexPLUS, to restore the load transmission of degenerated intervertebral L4-L5 lumbar motion segment spine under compression. Detailed three-dimensional FE models of L4-L5 motion segment and the FlexPLUS were developed. Compressive loading up to 1000N was applied to the intact L4-L5 model, the L4-L5 models with slight and moderate degenerated disc, and the implanted L4-L5 model. Further more, the load transmission characteristics of Dynesys and a rigid rod was also simulated for comparison. The resultant load-displacement curves and the load transferred through annulus under various conditions were compared. The predicted axial displacement of L4 top surface against applied compressive force of the intact L4-L5 model agreed well with experimental data. The predicted results showed that degenerated disc has significant effect on the lumbar segment load bearing capacity. Not only the stiffness of the segment was greatly increased, the uniform nature of the disc stress distribution was also altered. The FlexPLUS can effectively reduce the disc loading of degenerated model. Although the non-uniform load distribution pattern through annulus was not improved, the overall stress magnitude was greatly reduced to the level of intact model for grade II degeneration.

Finite element analysis of the spine: towards a framework of verification, validation and sensitivity analysis

A number of papers have recently emphasised the importance of verification, validation and sensitivity testing in computational studies within the field of biomechanical engineering. This review examines the methods used in the development of spinal finite element models with a view to a standardised framework of verification, validation and sensitivity analysis. The scope of this paper is restricted to models of the vertebra, the intervertebral disc and short spinal segments. In the case of single vertebral models, specimen-specific methods have been developed, which allow direct validation against experimental tests. The focus of intervertebral disc modelling has been on representing the complex material properties and further sensitivity testing is required to fully understand the relative roles of these input parameters. In order to construct complex multi-component short segment models, many geometric and material parameters are required, some of which are yet to be fully characterised. There are also major challenges in terms of short segment model validation. Throughout the review, areas of good practise are highlighted and recommendations for future development are proposed, taking a step towards more robust spinal modelling procedures, promoting acceptance from the wider biomechanics community.

Volumic patient-specific reconstruction of muscular system based on a reduced dataset of medical images

Three-dimensional mechanical modelling of muscles is essential for various biomechanical applications and clinical evaluation, but it requires a tedious manual processing of numerous images. A muscle reconstruction method is presented based on a reduced set of images to generate an approximate parametric object from basic dimensions of muscle contours. A regular volumic mesh is constructed based on this parametric object. The approximate object and the corresponding mesh are deformed to fit the exact muscles contours yielding patient-specific geometry. Evaluation was performed by comparison of geometry to that obtained by contouring all computed tomography (CT) slices, and by quantification of the mesh quality criteria. Muscle fatty infiltration was estimated using a threshold between fat and muscle. Volumic fat index (VFI) of a muscle was computed using first all the complete CT scan slices containing the muscle (VFI(ref)) and a second time only the slices used for reconstruction (VFI(recons)). Mean volume error estimation was 2.6% and hexahedron meshes fulfilled quality criteria. VFI(recons) respect the individual variation of fat content.

An anatomical subject-specific FE-model for hip fracture load prediction

In order to reduce the socio-economic burden induced by osteoporotic hip fractures, finite element models have been evaluated as an additional diagnostic tool for fracture prediction. For a future clinical application, the challenge is to reach the best compromise between model relevance and computing time. Based on this consideration, the current study focused on the development and validation of a subject-specific FE-model using an original parameterised generic model and a specific personalization method. A total of 39 human femurs were tested to failure under a quasi-static compression in stance configuration. The corresponding FE- models were generated and for each specimen the numerical fracture load (FFEM) was compared with the experimental value (FEXP), resulting in a significant correlation (FEXP = 1.006 FFEM with r2 = 0.87 and SEE = 1220 N, p < 0.05) obtained with a reasonable computing time (30 mn). Further in vivo study should confirm the ability of this FE-model to improve the fracture risk prediction.

New interspinous implant evaluation using an in vitro biomechanical study combined with a finite-element analysis

STUDY DESIGN

A combined in vitro and finite-element analysis was completed to assess the biomechanical effect of a new interspinous implant on the lumbar spine.

OBJECTIVE

The aim was to investigate the effect of an interspinous implant on the biomechanical behavior of a vertebral segment.

METHODS

An in vitro study on L3-L5 segments from fresh human cadavers was conducted combined with a 3-dimensional finite-element analysis. Intact, injured, and instrumented states of L4-L5 were compared loaded in flexion-extension, lateral-bending, and torsion. The evaluated implant is an interspinous spacer fixed to the spine by 2 polyester braids looped around the proximal and distal spinous.

RESULTS

The effect of the implant appeared mainly in flexion-extension: experimental results showed reduced range of motion of the instrumented spine regarding the injured and intact one; and finite-element analysis indicated a decrease of disc stresses and increase of loads transmitted to the spinous processes.

CONCLUSION

In this in vitro and finite-element analysis, the role of the new interspinous implant appeared to reduce motion without suppressing it and to lower stress in the disc fibers and anulus matrix. Further in vivo investigations are necessary to draw definitive conclusions.

Application of a calibration method provides more realistic results for a finite element model of a lumbar spinal segment

BACKGROUND

An important step in finite element modeling is the process of validation to derive clinical relevant data. It can be assumed that defect states of a finite element model, which have not been validated before, may predict wrong results. The purpose of this study was to show the differences in accuracy between a calibrated and a non-calibrated finite element model of a lumbar spinal segment for different clinical defects.

METHODS

For this study, two geometrically identical finite element models were used. An in vitro experiment was designed, deriving data for the calibration. Frequently used material properties were obtained from the literature and transferred into the non-calibrated model. Both models were validated on three clinical defects: bilateral hemifacetectomy, nucleotomy and interspinous defects, whereas in vitro range of motion data served as control points. Predictability and accuracy of the calibrated and non-calibrated finite element model were evaluated and compared.

FINDINGS

Both finite element models could mimic the intact situation with a good agreement. In the defects, the calibrated model predicted motion behavior with excellent agreement, whereas the non-calibrated model diverged greatly.

INTERPRETATION

Investigating the biomechanical performance of implants and load distribution of different spinal structures by numerical analysis requires not only good agreement with the intact segment, but also with the defect states, which are initiated prior to implant insertion. Because of more realistic results the calibration method may be recommended, however, it is more time consuming.