Estimation of muscle forces in the lumbar spine during upper-body inclination

Analysis of stress and stabilization in adolescent with osteoporotic idiopathic scoliosis: finite element method

Objective: To explore the effect of osteoporosis on the stress, stability, and lumbar intervertebral disc of AIS lumbar vertebrae by finite element method. Better understand the biomechanical characteristics of osteoporotic scoliosis.Methods: Based on the CT images of normal lumbar vertebrae and lumbar vertebrae with AIS, the finite element models were established to simulate the estimated osteoporosis by changing the Young's modulus of cortical bone, cancellous bone, and endplate. Four finite element models of normal lumbar, osteoporotic lumbar, normal AIS lumbar and osteoporotic AIS lumbar were established, and the same load and boundary conditions were applied respectively. The displacement, stress, and intervertebral disc strain of the four models were compared to explore the effect of osteoporosis on the stability and injury risk of AIS.Results: After suffering from osteoporosis, under the same load, the displacement of lumbar spine increases, the stability decreases, and the stability of AIS lumbar spine decrease more obviously, especially under extension load. Suffering from osteoporosis will increase the stress of lumbar spine, AIS lumbar spine increases more obviously, and the stress is more concentrated, Osteoporotic lumbar spine only affects the strain of intervertebral disc when AIS lumbar spine bends on the concave side, resulting in greater strain behind the concave side of intervertebral disc.Conclusions: AIS patients with OP have lower lumbar stability, a higher risk of fracture of lumbar vertebrae, and spinal nerves are more likely to be compressed by intervertebral discs. OP can aggravate the scoliosis of lumbar vertebrae.

Biomechanical Comparison between Isobar and Dynamic-Transitional Optima (DTO) Hybrid Lumbar Fixators: A Lumbosacral Finite Element and Intersegmental Motion Analysis

Biomechanical performance of longitudinal component in dynamic hybrid devices was evaluated to display the load-transfer effects of Dynesys cord spacer or Isobar damper-joint dynamic stabilizer on junctional problem based on various disc degenerations. The dynamic component was adapted at the mildly degenerative L3–L4 segment, and the static component was fixed at the moderately degenerative L4–L5 segment under a displacement-controlled mode for the finite element study. Furthermore, an intersegmental motion behavior was analyzed experimentally on the synthetic model under a load-controlled mode. Isobar or DTO hybrid fixator could reduce stress/motion at transition segment, but compensation was affected at the cephalic adjacent segment more than the caudal one. Within the trade-off region (as a motion-preserving balance between the transition and adjacent segments), the stiffness-related problem was reduced mostly in flexion by a flexible Dynesys cord. In contrast, Isobar damper afforded the effect of maximal allowable displacement (more than peak axial stiffness) to reduce stress within the pedicle and at facet joint. Pedicle-screw travel at transition level was related to the extent of disc degeneration in Isobar damper-joint (more than Dynesys cord spacer) attributing to the design effect of axial displacement and angular rotation under motion. In biomechanical characteristics relevant to clinical use, longitudinal cord/damper of dynamic hybrid lumbar fixators should be designed with less interface stress occurring at the screw-vertebral junction and facet joint to decrease pedicle screw loosening/breakage under various disc degenerations.

Optimization of a lumbar interspinous fixation device for the lumbar spine with degenerative disc disease

Interspinous spacer devices used in interspinous fixation surgery remove soft tissues in the lumbar spine, such as ligaments and muscles and may cause degenerative diseases in adjacent segments its stiffness is higher than that of the lumbar spine. Therefore, this study aimed to structurally and kinematically optimize a lumbar interspinous fixation device (LIFD) using a full lumbar finite element model that allows for minimally invasive surgery, after which the normal behavior of the lumbar spine is not affected. The proposed healthy and degenerative lumbar spine models reflect the physiological characteristics of the lumbar spine in the human body. The optimum number of spring turns and spring wire diameter in the LIFD were selected as 3 mm and 2 turns, respectively—from a dynamic range of motion (ROM) perspective rather than a structural maximum stress perspective—by applying a 7.5 N∙m extension moment and 500 N follower load to the LIFD-inserted lumbar spine model. As the spring wire diameter in the LIFD increased, the maximum stress generated in the LIFD increased, and the ROM decreased. Further, as the number of spring turns decreased, both the maximum stress and ROM of the LIFD increased. When the optimized LIFD was inserted into a degenerative lumbar spine model with a degenerative disc, the facet joint force of the L3-L4 lumbar segment was reduced by 56%–98% in extension, lateral bending, and axial rotation. These results suggest that the optimized device can strengthen the stability of the lumbar spine that has undergone interspinous fixation surgery and reduce the risk of degenerative diseases at the adjacent lumbar segments.

Finite element analysis of the effect of anterior dynamic plating on two-level anterior cervical discectomy fusion biomechanics

BACKGROUND

Limitations of anterior cervical discectomy and fusion (ACDF) relate to mechanical failure of the construct after recurring subsidence and migration. This study aims to evaluate the effect of the maximum rotation of variable angle screws on the range of motion (ROM), cage migration, and subsidence.

METHODS

Five finite element (FE) models were developed from a C2-C7 cervical spine model. The first model was an intact C2-C7 spine model, and the second model was an altered C2-C7 model with C4-C6 cage insertion and a 2-level static plate. The other three models were altered C2-C7 models with the same C4-C6 cage insertion and a 2-level dynamic plate.

RESULTS

ROM of C4-C6 in the static plate model was reduced by about 14º from the intact model, while only reduced by about 9^o in dynamic plate models. The maximum migration and subsidence at the cage-endplate interface in the dynamic plate models were lower than that in the static plate model under all moments. The von-Mises stress of the C3-C4 and C6-C7 discs in the dynamic plate models was lower than that in the static plate model.

CONCLUSION

Results indicate dynamic plating has promising potential (higher ROM and lower von Mises stress of discs) for stabilization in multilevel ACDF than static plate, though both dynamic plate and static plate has lower ROM than the intact model. Lower screw rotational angle has superior biomechanical performance (lower migration and subsidence) to higher rotational angle in multilevel applications regardless of loading.

Biphasic Properties of PVAH (Polyvinyl Alcohol Hydrogel) Reflecting Biomechanical Behavior of the Nucleus Pulposus of the Human Intervertebral Disc

PVAH is a mixture of solid and fluid, but its mechanical behavior has usually been described using solid material models. The purpose of this study was to obtain material properties that can reflect the mechanical behavior of polyvinyl alcohol hydrogel (PVAH) using finite element analysis, a biphasic continuum model, and to optimize the composition ratio of PVAH to replace the nucleus pulposus (NP) of the human intervertebral disc. Six types of PVAH specimens (3, 5, 7, 10, 15, 20 wt%) were prepared, then unconfined compression experiments were performed to acquire their material properties using the Holmes–Mow biphasic model. With an increasing weight percentage of PVA in PVAH, the Young’s modulus increased while the permeability parameter decreased. The Young’s modulus and permeability parameter were similar to those of the NP at 15 wt% and 20 wt%. The range of motion, facet joint force, and NP pressures measured from dynamic motional analysis of the lumbar segments with the NP model also exhibited similar values to those with 15~20 wt% PVAH models. Considering the structural stability and pain of the lumbar segments, it appears that 20 wt% PVAH is most suitable for replacing the NP.

Computational modelling of the scoliotic spine: A literature review

Scoliosis is a deformity of the spine that in severe cases requires surgical treatment. There is still disagreement among clinicians as to what the aim of such treatment is as well as the optimal surgical technique. Numerical models can aid clinical decision-making by estimating the outcome of a given surgical intervention. This paper provided some background information on the modelling of the healthy spine and a review of the literature on scoliotic spine models, their validation, and their application. An overview of the methods and techniques used to construct scoliotic finite element and multibody models was given as well as the boundary conditions used in the simulations. The current limitations of the models were discussed as well as how such limitations are addressed in non-scoliotic spine models. Finally, future directions for the numerical modelling of scoliosis were addressed.

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.

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

INTRODUCTION

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

METHODS

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

RESULTS

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

CONCLUSION

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

The Role of Biological Fusion and Anterior Column Support in a Long Lumbopelvic Spinal Fixation and Its Effect on the S1 Screw-An In Silico Biomechanics Analysis

STUDY DESIGN

Finite element analysis.

OBJECTIVE

The aim of this study was to determine the role of biological fusion and anterior column support in a long lumbopelvic spinal fixation.

SUMMARY OF BACKGROUND DATA

Retrospective studies have shown that adding anterior column support is not sensitive to construct failure, highlighting that posterior fusion quality may be a more important factor.

METHODS

Finite element models were created to match the average spinal-pelvic parameters of two patient cohorts reported in the literature: major failure and nonfailure. A moment load was applied at the T10 superior endplate to simulate gravimetric loading in a standing position. Effects of three factors on the biomechanical behavior of a fused spine were evaluated: sagittal alignment; posterior fusion versus no fusion; and anterior support at L4-S1 versus no anterior support.

RESULTS

Sagittal balance of the major failure group was positively correlated with 15% higher translation, 14% higher rotation, and 16% higher stress than in the nonfailure group. Simulated posterior fusion-only decreased motion by 32% and 29%, and alleviated rod stress by 15% and 5% and S1 screw stress by 26% and 35%, respectively, in major failure and non-failure groups. The addition of anterior fusion without posterior fusion did not help with rod stress alleviation but dramatically decreased S1 screw stress (by 57% and 41%), respectively. With both posterior fusion and anterior support, screw stress at the S1 was decreased by additional 30% and 6%, respectively.

CONCLUSION

The spinopelvic parameters of the major failure group produced increased gravity load, resulting in increased stresses in comparison to the nonfailure group. Simulated posterior "solid" fusion in the lumbar region helped reduce stresses in both major failure and nonfailure patients. Anterior column support was an important factor in reducing S1 screw stress, with or without posterior fusion, and should be considered for patients with poor alignment.Level of Evidence: N/A.

Biomechanical analysis of a newly developed interspinous process device conjunction with interbody cage based on a finite element model

Purpose

This study aimed to investigate the biomechanical effects of a newly developed interspinous process device (IPD), called TAU. This device was compared with another IPD (SPIRE) and the pedicle screw fixation (PSF) technique at the surgical and adjacent levels of the lumbar spine.

Materials and methods

A three-dimensional finite element model analysis of the L1-S1 segments was performed to assess the biomechanical effects of the proposed IPD combined with an interbody cage. Three surgical models—two IPD models (TAU and SPIRE) and one PSF model—were developed. The biomechanical effects, such as range of motion (ROM), intradiscal pressure (IDP), disc stress, and facet loads during extension were analyzed at surgical (L3-L4) and adjacent levels (L2-L3 and L4-L5). The study analyzed biomechanical parameters assuming that the implants were perfectly fused with the lumbar spine.

Results

The TAU model resulted in a 45%, 49%, 65%, and 51% decrease in the ROM at the surgical level in flexion, extension, lateral bending, and axial rotation, respectively, when compared to the intact model. Compared to the SPIRE model, TAU demonstrated advantages in stabilizing the surgical level, in all directions. In addition, the TAU model increased IDP at the L2-L3 and L4-L5 levels by 118.0% and 78.5% in flexion, 92.6% and 65.5% in extension, 84.4% and 82.3% in lateral bending, and 125.8% and 218.8% in axial rotation, respectively. Further, the TAU model exhibited less compensation at adjacent levels than the PSF model in terms of ROM, IDP, disc stress, and facet loads, which may lower the incidence of the adjacent segment disease (ASD).

Conclusion

The TAU model demonstrated more stabilization at the surgical level than SPIRE but less stabilization than the PSF model. Further, the TAU model demonstrated less compensation at adjacent levels than the PSF model, which may lower the incidence of ASD in the long term. The TAU device can be used as an alternative system for treating degenerative lumbar disease while maintaining the physiological properties of the lumbar spine and minimizing the degeneration of adjacent segments.

The role of sagittal alignment in predicting major failure of lumbopelvic instrumentation: a biomechanical validation of lumbopelvic failure classification

STUDY DESIGN

Finite element analysis.

OBJECTIVES

To biomechanically validate the classification of lumbopelvic fixation failure using an in silico model. Even though major failure of lumbopelvic constructs has occurred more often in patients with suboptimal lumbar lordosis and sagittal balance, there has been no biomechanical validation of this classification.

METHODS

Finite element models (T10-pelvis) were created to match the average spinal-pelvic parameters of two cohorts of patients reported in Cho et al. (J Neurosurg Spine 19:445-453, 2013): major failure group (defined as rod breakage between L4 and S1, failure of S1 screws and prominence of iliac screws requiring removal) and non-failure group. A moment was applied at the T10 superior endplate to simulate gravimetric loading in a standing position.

RESULTS

Due to differences in the alignment of spinopelvic parameters between normal and failed spines in the presence of a fixed gravity line, the major failure cohort in this study observed a 20% higher load and 18% greater instability. As a result, the rod and screw stress in the major failure cohort increased by 20% and 42%, respectively, in comparison to the non-failure cohort.

CONCLUSIONS

The greater mechanical demand on the posterior rods in the lower lumbar spine in the major failure cohort further emphasizes the importance of proper sagittal alignment. This finite element analysis validates the classification of lumbopelvic fixation failure.

Finite Element Study to Evaluate the Biomechanical Performance of the Spine After Augmenting Percutaneous Pedicle Screw Fixation With Kyphoplasty in the Treatment of Burst Fractures

Percutaneous pedicle screw fixation (PPSF) is a well-known minimally invasive surgery (MIS) employed in the treatment of thoracolumbar burst fractures (TBF). However, hardware failure and loss of angular correction are common limitations caused by the poor support of the anterior column of the spine. Balloon kyphoplasty (KP) is another MIS that was successfully used in the treatment of compression fractures by augmenting the injured vertebral body with cement. To overcome the limitations of stand-alone PPSF, it was suggested to augment PPSF with KP as a surgical treatment of TBF. Yet, little is known about the biomechanical alteration occurred to the spine after performing such procedure. The objective of this study was to evaluate and compare the immediate post-operative biomechanical performance of stand-alone PPSF, stand-alone-KP, and KP-augmented PPSF procedures. Novel three-dimensional (3D) finite element (FE) models of the thoracolumbar junction that describes the fractured spine and the three investigated procedures were developed and tested under mechanical loading conditions. The spinal stiffness, stresses at the implanted hardware, and the intradiscal pressure at the upper and lower segments were measured and compared. The results showed no major differences in the measured parameters between stand-alone PPSF and KP-augmented PPSF procedures, and demonstrated that the stand-alone KP may restore the stiffness of the intact spine. Accordingly, there was no immediate post-operative biomechanical advantage in augmenting PPSF with KP when compared to stand-alone PPSF, and fatigue testing may be required to evaluate the long-term biomechanical performance of such procedures.

Internal Biomechanical Study of a 70-Year-Old Female Human Lumbar Bi-Segment Finite Element Model and Comparison with a Middle-Aged Male Model

The main purpose of this article is to study the biomechanics of spine tissue in elderly female. In this study, the L3-L5 lumbar bi-segmental finite element model for elderly female was obtained from the Advanced Human Modeling Laboratory of the Bioengineering Center at Wayne State University. The effects of flexion and extension on bone geometry, distribution of ligament fibers, location of nucleus, and changes in intervertebral disc height were studied by comparing the results obtained before and after the update of older female and middle-aged male models. For the purpose of comparing the calculated range of motion (ROM) with the experimental data, additional calculations for axial rotation and lateral bending were performed. The study found that the parameters of the model affected the deformation of the disc herniation, ligament and intervertebral disc, and the axial force carrying capacity of the model. The three predicted ROMs are usually similar to the experimental results. Only the older female model has a slightly larger ROM. Therefore, older women are more vulnerable to lumbar spine injuries than men.

The Path to Deliver the Most Realistic Follower Load for a Lumbar Spine in Standing Posture: A Finite Element Study

A spine is proven to be subjected to a follower load which is a compressive load of physiologic magnitude acting on the whole spine. The path of the follower load approximates the tangent to the curve of the spine in in vivo neutral standing posture. However, the specific path location of the follower load is still unclear. The aim of this study is to find out the most realistic location of the follower load path (FLP) for a lumbar spine in standing. A three-dimensional (3D) nonlinear finite element model (FEM) of lumbosacral vertebrae (L1-S1) with consideration of the calibrated material properties was established and validated by comparing with the experimental data. We show that the shape of the lumbosacral spine is strongly affected by the location of FLP. An evident nonlinear relationship between the FLP location and the kinematic response of the L1-S1 lumbosacral spine exists. The FLP at about 4 and 3 mm posterior to the curve connecting the center of the vertebral bodies delivers the most realistic location in standing for healthy people and patients having low back pains (LPBs), respectively. Moreover, the “sweeping” method introduced in this study can be applicable to all individualized FEM to determine the location of FLP.

Spinal biomechanics modeling and finite element analysis of surgical instrument interaction

When the spinal surgery robot assists the surgeon perform the surgery, the patient is prone on the operating table. However, due to the force of the surgical instruments on the spine, there is a corresponding deformation in the surgical field, which affects the accuracy of the operation. In order to improve the accuracy and safety of the operation, this paper reconstructs the three-dimensional model of the lumbar spine which includes the vertebral body and the intervertebral disc based on the CT scan data, and then the lumbar spine is analyzed by the finite element method. The mathematical model of the relationship between force and displacement is established by using response surface methodology based on the simulation results. After that, the position control system is constructed based on the mathematical model. Through the simulation of the control system, the trajectory curve of the end of the manipulator is compared and the validity of the mathematical model is verified.

Validation of an In Vivo Medical Image-Based Young Human Lumbar Spine Finite Element Model

Mathematical models of the human spine can be used to investigate spinal biomechanics without the difficulties, limitations, and ethical concerns associated with physical experimentation. Validation of such models is necessary to ensure that the modeled system behavior accurately represents the physics of the actual system. The goal of this work was to validate a medical image-based nonlinear lumbosacral spine finite element model of a healthy 20-yr-old female subject under physiological moments. Range of motion (ROM), facet joint forces (FJF), and intradiscal pressure (IDP) were compared with experimental values and validated finite element models from the literature. The finite element model presented in this work was in good agreement with published experimental studies and finite element models under pure moments. For applied moments of 7.5 N·m, the ROM in flexion–extension, axial rotation, and lateral bending were 39 deg, 16 deg, and 28 deg, respectively. Excellent agreement was observed between the finite element model and experimental data for IDP under pure compressive loading. The predicted FJFs were lower than those of the experimental results and validated finite element models for extension and torsion, likely due to the nondegenerate properties chosen for the intervertebral disks and morphology of the young female spine. This work is the first to validate a computational lumbar spine model of a young female subject. This model will serve as a valuable tool for predicting orthopedic spinal injuries, studying the effect of intervertebral disk replacements using advanced biomaterials, and investigating soft tissue degeneration.

Estimating Lumbar Load During Motion with an Unknown External Load Based on Back Muscle Activity Measured with a Muscle Stiffness Sensor

A forward bending motion is essential in everyday tasks, such as carrying objects, shoveling snow, and performing farm work. However, many people suffer from lumbar pain resulting from forward bending motion, which causes a lumbar disc load owing to the changing of the lumbar shape. We have developed a wearable lumbar load estimation system, which measures the skin shape on the back using a curvature sensor. Because the lumbar load varies with the external load, the lumbar load should be estimated based on the external load. Therefore, we have developed a method for estimating an unknown external force using a muscle stiffness sensor. Muscle strength can be estimated by measuring the muscle hardness from the surface, and the relationship between the external force and the muscle force can be modeled. Using this method, we estimate the dependence of the lumbar load on external forces in real time. In addition, we simplify the calculation by converting the external load into a load resulting from a person’s own weight. We incorporate the proposed method into our wearable sensor system, estimate the lumbar load, and compare this with the results of a musculoskeletal dynamics simulation.

The Effect of Muscle Direction on the Predictions of Finite Element Model of Human Lumbar Spine

The normal physiological loads from muscles experienced by the spine are largely unknown due to a lack of data. The aim of this study is to investigate the effects of varying muscle directions on the outcomes predicted from finite element models of human lumbar spine. A nonlinear finite element model of L3–L5 was employed. The force of the erector spinae muscle, the force of the rectus abdominis muscle, follower loads, and upper body weight were applied. The model was fixed in a neural standing position and the direction of the force of the erector spinae muscle and rectus abdominis muscle was varied in three directions. The intradiscal pressure, reaction moments, and intervertebral rotations were calculated. The intradiscal pressure of L4-L5 was 0.56–0.57 MPa, which agrees with the in vivo pressure of 0.5 MPa from the literatures. The models with the erector spinae muscle loaded in anterior-oblique direction showed the smallest reaction moments (less than 0.6 Nm) and intervertebral rotations of L3-L4 and L4-L5 (less than 0.2 degrees). In comparison with loading in the vertical direction and posterior-oblique direction, the erector spinae muscle loaded in the anterior-oblique direction required lower external force or moment to keep the lumbar spine in the neutral position.

Effect of Lumbar Lordosis on the Adjacent Segment in Transforaminal Lumbar Interbody Fusion: A Finite Element Analysis

OBJECTIVE

We used a finite element (FE) analysis to investigate the biomechanical changes caused by transforaminal lumbar interbody fusion (TLIF) at the L4-L5 level by lumbar lordosis (LL) degree.

METHODS

A lumbar FE model (L1-S5) was constructed based on computed tomography scans of a 30-year-old healthy male volunteer (pelvic incidence,= 50°; LL, 52°). We investigated the influence of LL on the biomechanical behavior of the lumbar spine after TLIF in L4-L5 fusion models with 57°, 52°, 47°, and 40° LL. The LL was defined as the angle between the superior end plate of L1 and the superior end plate of S1. A 150-N vertical axial preload was imposed on the superior surface of L3. A 10-N/m moment was simultaneously applied on the L3 superior surface along the radial direction to simulate the 4 basic physiologic motions of flexion, extension, lateral bending, and torsion in the numeric simulations. The range of motion (ROM) and intradiscal pressure (IDP) of L3-L4 were evaluated and compared in the simulated cases.

RESULTS

In all motion patterns, the ROM and IDP were both increased after TLIF. In addition, the decrease in lordosis generally increased the ROM and IDP in all motion patterns.

CONCLUSIONS

This FE analysis indicated that decreased spinal lordosis may evoke overstress of the adjacent segment and increase the risk of the pathologic development of adjacent segment degeneration; thus, adjacent segment degeneration should be considered when planning a spinal fusion procedure.

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.

Effect of sacral slope on the biomechanical behavior of the low lumbar spine

The present study investigated the influence of sacral slope (SS) on the biomechanical responses of the lumbar spine under specific physiological conditions. Firstly, based on computed tomography scan images of a 30-year-old healthy male volunteer (SS, 55°), a three-dimensional finite element (FE) model including the L4-S1 segment was established. Flexion, extension, lateral bending and torsion motions were simulated and compared with cadaveric test data in the literature to validate the lumbar spine FE model. The model was then modified with different SS values (40 and 25°) for the same simulations to describe the process of structural compensation. Numerical results showed that with the reduction of SS, the range of motions (ROMs) reduced for flexion and lateral bending, but increased for extension and torsion. For displacement, the maximum magnitudes of L4/5 annulus fibrosus (AF) reduced by 10-25% in flexion, lateral bending and torsion, but less effect was observed for extension with only a 4% drop. Nearly the same displacement distribution appeared on the L5/S1 AF with small changes in the four motions. For the stress field of L4/5 AF, in contrast to flexion, the magnitudes for extension and lateral bending varied markedly, and under torsion the value increased by ~10%. For L5/S1 AF, the stresses changed little under flexion, extension and lateral bending, but strongly declined for torsion by ~71.8%. In conclusion, the present study indicates that the change in SS due to structural compensation affects the biomechanical behavior of the spine structure, and attention should be paid to SS when conducting surgical procedures or selecting intervertebral fusion implants.

Effects of sudden walking perturbations on neuromuscular reflex activity and three-dimensional motion of the trunk in healthy controls and back pain symptomatic subjects

Background

Back pain patients (BPP) show delayed muscle onset, increased co-contractions, and variability as response to quasi-static sudden trunk loading in comparison to healthy controls (H). However, it is unclear whether these results can validly be transferred to suddenly applied walking perturbations, an automated but more functional and complex movement pattern. There is an evident need to develop research-based strategies for the rehabilitation of back pain. Therefore, the investigation of differences in trunk stability between H and BPP in functional movements is of primary interest in order to define suitable intervention regimes. The purpose of this study was to analyse neuromuscular reflex activity as well as three-dimensional trunk kinematics between H and BPP during walking perturbations.

Methods

Eighty H (31m/49f;29±9yrs;174±10cm;71±13kg) and 14 BPP (6m/8f;30±8yrs;171±10cm;67±14kg) walked (1m/s) on a split-belt treadmill while 15 right-sided perturbations (belt decelerating, 40m/s², 50ms duration; 200ms after heel contact) were randomly applied. Trunk muscle activity was assessed using a 12-lead EMG set-up. Trunk kinematics were measured using a 3-segment-model consisting of 12 markers (upper thoracic (UTA), lower thoracic (LTA), lumbar area (LA)). EMG-RMS ([%],0-200ms after perturbation) was calculated and normalized to the RMS of unperturbed gait. Latency (T_ON;ms) and time to maximum activity (T_MAX;ms) were analysed. Total motion amplitude (ROM;[°]) and mean angle (A_mean;[°]) for extension-flexion, lateral flexion and rotation were calculated (whole stride cycle; 0-200ms after perturbation) for each of the three segments during unperturbed and perturbed gait. For ROM only, perturbed was normalized to unperturbed step [%] for the whole stride as well as the 200ms after perturbation. Data were analysed descriptively followed by a student´s t-test to account for group differences. Co-contraction was analyzed between ventral and dorsal muscles (V:R) as well as side right:side left ratio (S_right:S_left). The coefficient of variation (CV;%) was calculated (EMG-RMS;ROM) to evaluate variability between the 15 perturbations for all groups. With respect to unequal distribution of participants to groups, an additional matched-group analysis was conducted. Fourteen healthy controls out of group H were sex-, age- and anthropometrically matched (group H_matched) to the BPP.

Results

No group differences were observed for EMG-RMS or CV analysis (EMG/ROM) (p>0.025). Co-contraction analysis revealed no differences for V:R and S_rigth:S_left between the groups (p>0.025). BPP showed an increased T_ON and T_MAX, being significant for Mm. rectus abdominus (p = 0.019) and erector spinae T9/L3 (p = 0.005/p = 0.015). ROM analysis over the unperturbed stride cycle revealed no differences between groups (p>0.025). Normalization of perturbed to unperturbed step lead to significant differences for the lumbar segment (LA) in lateral flexion with BPP showing higher normalized ROM compared to H_matched (p = 0.02). BPP showed a significant higher flexed posture (UTA (p = 0.02); LTA (p = 0.004)) during normal walking (A_mean). Trunk posture (A_mean) during perturbation showed higher trunk extension values in LTA segments for H/H_matched compared to BPP (p = 0.003). Matched group (BPP vs. H_matched) analysis did not show any systematic changes of all results between groups.

Conclusion

BPP present impaired muscle response times and trunk posture, especially in the sagittal and transversal planes, compared to H. This could indicate reduced trunk stability and higher loading during gait perturbations.

The effects of muscle weakness on degenerative spondylolisthesis: A finite element study

BACKGROUND

Whether muscle weakness is a cause, or result, of degenerative spondylolisthesis is not currently well understood. Little biomechanical evidence is available to offer an explanation for the mechanism behind exercise therapy. Therefore, the aim of this study is to investigate the effects of back muscle weakness on degenerative spondylolisthesis and to tease out the biomechanical mechanism of exercise therapy.

METHODS

A nonlinear 3-D finite element model of L3-L5 was constructed. Forces representing global back muscles and global abdominal muscles, follower loads and an upper body weight were applied. The force of the global back muscles was reduced to 75%, 50% and 25% to simulate different degrees of back muscle weakness. An additional boundary condition which represented the loads from other muscles after exercise therapy was set up to keep the spine in a neutral standing position. Shear forces, intradiscal pressure, facet joint forces and von Mises equivalent stresses in the annuli were calculated.

FINDINGS

The intervertebral rotations of L3-L4 and L4-L5 were within the range of in vitro experimental data. The calculated intradiscal pressure of L4-L5 for standing was 0.57MPa, which is similar to previous in vivo data. With the back muscles were reduced to 75%, 50% and 25% force, the shear force moved increasingly in a ventral direction. Due to the additional stabilizing force and moment provided by boundary conditions, the shear force varied less than 15%.

INTERPRETATION

Reducing the force of global back muscles might lead to, or aggravate, degenerative spondylolisthesis with forward slipping from biomechanical point of view. Exercise therapy may improve the spinal biomechanical environment. However, the intrinsic correlation between back muscle weakness and degenerative spondylolisthesis needs more clinical in vivo study and biomechanical analysis.

Musculoskeletal Modeling of the Lumbar Spine to Explore Functional Interactions between Back Muscle Loads and Intervertebral Disk Multiphysics

During daily activities, complex biomechanical interactions influence the biophysical regulation of intervertebral disks (IVDs), and transfers of mechanical loads are largely controlled by the stabilizing action of spine muscles. Muscle and other internal forces cannot be easily measured directly in the lumbar spine. Hence, biomechanical models are important tools for the evaluation of the loads in those tissues involved in low-back disorders. Muscle force estimations in most musculoskeletal models mainly rely, however, on inverse calculations and static optimizations that limit the predictive power of the numerical calculations. In order to contribute to the development of predictive systems, we coupled a predictive muscle model with the passive resistance of the spine tissues, in a L3-S1 musculoskeletal finite element model with osmo-poromechanical IVD descriptions. The model included 46 fascicles of the major back muscles that act on the lower spine. The muscle model interacted with activity-related loads imposed to the osteoligamentous structure, as standing position and night rest were simulated through distributed upper body mass and free IVD swelling, respectively. Calculations led to intradiscal pressure values within ranges of values measured in vivo. Disk swelling led to muscle activation and muscle force distributions that seemed particularly appropriate to counterbalance the anterior body mass effect in standing. Our simulations pointed out a likely existence of a functional balance between stretch-induced muscle activation and IVD multiphysics toward improved mechanical stability of the lumbar spine understanding. This balance suggests that proper night rest contributes to mechanically strengthen the spine during day activity.

Kinematic and mechanical comparisons of lumbar hybrid fixation using Dynesys and Cosmic systems

STUDY DESIGN

The biomechanical effects of Dynesys and Cosmic fixators on transition and adjacent segments were evaluated using the finite-element method.

OBJECTIVE

This study investigated the load-transferring mechanisms of 2 dynamic fixators and the fixator-induced effects on the junctional problem of the adjacent segments.

SUMMARY OF BACKGROUND DATA

The mobility and flexibility of Dynesys screw-spacer and Cosmic screw-hinge joints preserve motion and share loads for the transition segment. However, the differences in tissue responses and fixator mechanisms among these 2 fixators have not been investigated extensively.

METHODS

A lumbosacral model from L1 to S1 levels was developed and subjected to muscular contraction, ligamentous interconnection, compressive force, and trunk moment. A static fixator was instrumented at the moderately degenerative L4-L5 segment to serve as a comparison baseline. Subsequently, the 2 fixators were instrumented at the mildly degenerative L3-L4 segment. The tissue responses of the adjacent segments and the load transmission at the screw-spacer and bone-screw interfaces were compared.

RESULTS

Both systems show the ability to protect the transition segment but deteriorate the adjacent segments. The screw-hinge joint and the stiffer rod of the Cosmic system significantly constrained the motion pattern of the transition segment. Comparatively, the Dynesys screw-spacer interfaces make contact with and depart from each other during motion; thus providing higher mobility to the transition segment. However, the highly stressed distribution at the Cosmic bone-screw causes the screw and hinge prone to pullout and fatigue failures.

CONCLUSION

Cosmic fixation can better protect the disc and facet joint of the transition segment than can the Dynesys. However, the screw-hinge joint strictly constrains intersegmental motion and deteriorates the junctional problem. The Cosmic system can be chosen to treat more severely degenerative transition segments. With higher flexibility, the Dynesys system is recommended for the transition segment that is healthy or mildly degenerative.

LEVEL OF EVIDENCE

N/A.

Biomechanical analysis of two-step traction therapy in the lumbar spine

Traction therapy is one of the most common conservative treatments for low back pain. However, the effects of traction therapy on lumbar spine biomechanics are not well known. We investigated biomechanical effects of two-step traction therapy, which consists of global axial traction and local decompression, on the lumbar spine using a validated three-dimensional finite element model of the lumbar spine. One-third of body weight was applied on the center of the L1 vertebra toward the superior direction for the first axial traction. Anterior translation of the L4 vertebra was considered as the second local decompression. The lordosis angle between the superior planes of the L1 vertebra and sacrum was 44.6° at baseline, 35.2° with global axial traction, and 46.4° with local decompression. The fibers of annulus fibrosus in the posterior region, and intertransverse and posterior longitudinal ligaments experienced stress primarily during global axial traction, these stresses decreased during local decompression. A combination of global axial traction and local decompression would be helpful for reducing tensile stress on the fibers of the annulus fibrosus and ligaments, and intradiscal pressure in traction therapy. This study could be used to develop a safer and more effective type of traction therapy.

Discrepancies in anthropometric parameters between different models affect intervertebral rotations when loading finite element models with muscle forces from inverse static analyses

In only a few published finite element (FE) simulations have muscle forces been applied to the spine. Recently, muscle forces determined using an inverse static (IS) model of the spine were transferred to a spinal FE model, and the effect of methodical parameters was investigated. However, the sensitivity of anthropometric differences between FE and IS models, such as body height and spinal orientation, was not considered. The aim of this sensitivity study was to determine the influence of those differences on the intervertebral rotations (IVRs) following the transfer of muscle forces from an IS model to a FE model. Muscle forces were estimated for 20° flexion and 10° extension of the upper body using an inverse static musculoskeletal model. These forces were subsequently transferred to a nonlinear FE model of the spino-pelvic complex, which includes 243 muscle fascicles. Deviations of body height (±10 cm), spinal orientation in the sagittal plane (±10°), and body weight (±10 kg) between both models were intentionally generated, and their influences on IVRs were determined. The changes in each factor relative to their corresponding reference value of the IS model were calculated. Deviations in body height, spinal orientation, and body weight resulted in maximum changes in the IVR of 19.2%, 26% and 4.2%, respectively, relative to T12-S1 IVR. When transferring muscle forces from an IS to a FE model, it is crucial that both models have the same spinal orientation and height. Additionally, the body weight should be equal in both models.

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.

What have we learned from finite element model studies of lumbar intervertebral discs in the past four decades?

Finite element analysis is a powerful tool routinely used to study complex biological systems. For the last four decades, the lumbar intervertebral disc has been the focus of many such investigations. To understand the disc functional biomechanics, a precise knowledge of the disc mechanical, structural and biochemical environments at the microscopic and macroscopic levels is essential. In response to this need, finite element model studies have proven themselves as reliable and robust tools when combined with in vitro and in vivo measurements. This paper aims to review and discuss some salient findings of reported finite element simulations of lumbar intervertebral discs with special focus on their relevance and implications in disc functional biomechanics. Towards this goal, the earlier investigations are presented, discussed and summarized separately in three distinct groups of elastic, multi-phasic transient and transport model studies. The disc overall response as well as the relative role of its constituents are markedly influenced by loading rate, magnitude, combinations/preloads and posture. The nucleus fluid content and pressurizing capacity affect the disc compliance, annulus strains and failure sites/modes. Biodynamics of the disc is affected by not only the excitation characteristics but also preloads, existing mass and nucleus condition. The role of fluid pressurization and collagen fiber stiffening diminish with time during diurnal loading. The endplates permeability influences the time-dependent response of the disc in both loaded and unloaded recovery phases. The transport of solutes is substantially influenced by the disc size, tissue diffusivity and endplates permeability.

Biomechanical analysis of C4-C6 spine segment considering anisotropy of annulus fibrosus

Based on computed tomography scanning images of human cervical spine, this paper develops a detailed and anatomically accurate finite element model for C4-C6 motion segment to investigate its biomechanical responses. The model includes vertebrae, intervertebral disc, and various ligaments. The annulus fibrosus is characterized by using a previously developed nonlinear, anisotropic, hyperelastic fiber-reinforced model with fiber-matrix shear interaction considered. Other materials are simplified as linear or nonlinear elastic. The proposed cervical model is first validated by comparing numerical force-displacement relationship and intradiscal pressure under axial compression with experimental data available in the literature. The biomechanical responses of the spine segment under axial compression and rotation are then investigated. It is found that the fiber matrix-shear interaction of the annulus fibrosis plays an important role on appropriately predicting the biomechanical behavior of the cervical spine segment.

Parameters influencing the outcome after total disc replacement at the lumbosacral junction. Part 1: misalignment of the vertebrae adjacent to a total disc replacement affects the facet joint and facet capsule forces in a probabilistic finite element analysis

PURPOSE

After total disc replacement with a ball-and-socket joint, reduced range of motion and progression of facet joint degeneration at the index level have been described. The aim of the study was to test the hypothesis that misalignment of the vertebrae adjacent to the implant reduces range of motion and increases facet joint or capsule tensile forces.

METHODS

A probabilistic finite element analysis was performed using a lumbosacral spine model with an artificial disc at level L5/S1. Misalignment of the L5 vertebra, the gap size of the facet joints, the transection of the posterior longitudinal ligament, and the spinal shape were varied. The model was loaded with pure moments.

RESULTS

Misalignment of the L5 vertebra reduced the range of motion up to 2°. A 2-mm displacement of the L5 vertebra in the anterior direction already led to facet joint forces of approximately 240 N. Extension, lateral bending, and axial rotation caused maximum facet joint forces between 280 and 380 N, while flexion caused maximum forces of approximately 200 N. A 2-mm displacement in the posterior direction led to capsule forces of approximately 80 N. Additional moments increased the maximum facet capsule forces to values between 120 and 230 N.

CONCLUSIONS

Misalignment of the vertebrae adjacent to an artificial disc strongly increases facet joint or capsule forces. It might, therefore, be an important reason for unsatisfactory clinical results. In an associated clinical study (Part 2), these findings are validated.

Pretension effects of the Dynesys cord on the tissue responses and screw-spacer behaviors of the lumbosacral construct with hybrid fixation

STUDY DESIGN

The pretension of the Dynesys cord was varied to evaluate its effects on both tissue responses and screw-spacer behaviors by the finite-element method.

OBJECTIVE

This study aimed to provide detailed information about the motion-preserving and load-shielding mechanisms of the Dynesys screw-spacer joint.

SUMMARY OF BACKGROUND DATA

Intuitively, higher cord pretension aims to ensure the occurrence of screw-spacer contact, thus making the spacer the transmitter of the vertebral loads. However, detailed investigations of the cord-pretension effects have not yet been carried out. METHODS.: Using a validated lumbosacral model, the moderately degenerative L4-L5 segment was instrumented by a static fixator and the Dynesys fixator was further used to bridge a mildly degenerative L3-L4 segment. The pre-tended cord was modeled as an elastic spring with 0- and 300-N pretensions. The disc range-of-motion, disc stress, facet force, bone-screw stress, and screw-spacer force were chosen as comparison indices. RESULTS.: At the transition and adjacent segments, the range-of-motion differences between the 2 pretensions were 7.7% and 2.0% on average, respectively. The mechanical differences at the transition and adjacent segments were 9.0% and 5.2% (disc stress) and 9.4% and 9.1% (facet force), respectively. The results indicated that the cord pretension has a minor effect on the adjacent segments in comparison with the transition segment. However, the stress at the screw hub and force of the screw-spacer contact of the 300-N pretension were increased by 33.7% and 316.5% on average than without pretension, respectively.

CONCLUSION

The moment arm from the screw-cord center to the fulcrum is significantly less than that of vertebral loads. This leads to the minor effect of increasing the cord pretension on the responses of the adjacent segments. However, the cord pretension can significantly affect both screw-spacer force and bone-screw stress.

LEVEL OF EVIDENCE

4.

Comparison among load-, ROM-, and displacement-controlled methods used in the lumbosacral nonlinear finite-element analysis

STUDY DESIGN

For lumbosacral nonlinear analysis, the characteristics and differences between the load- and range-of-motion (ROM)-controlled methods (LCM and RCM) were compared using the numerical approach.

OBJECTIVE

This study aimed to discuss the LCM and RCM problems inherent in the method assumption and calculation procedure. A displacement-controlled method (DCM) based on the nodal movement at the lumbosacral top was proposed to offer a more efficient and equivalent comparison between the evaluated models.

SUMMARY OF BACKGROUND DATA

Both LCM and RCM have been extensively used to evaluate the biomechanical performance of lumbosacral implants. The LCM models were subject to the same loads as the intact model. The ROMs of the RCM models were controlled in the same way by iteratively adjusting some of the applied loads. However, the different strategies for adjusting lumbar loads might affect the predicted results and the execution might be inefficient. To the best of the authors' knowledge, the kinematic, mechanical, and computational comparisons between the 2 methods have still not been extensively investigated.

METHODS

An intact lumbosacral model was developed and validated with the cadaveric and numerical data from the literature studies. The intact model was then modified as a degenerative model, in which the moderately dehydrated L4-L5 segment was instrumented with transpedicular fixation. Lumbosacral flexion was simulated by ligament interconnection, muscular contraction, and weight compression. One LCM, 3 RCM, and 1 DCM models were developed to evaluate their effects on biomechanical results and the computational efficiency of the lumbosacral nonlinear analysis.

RESULTS

Both solution feasibility and calculation time were closely related to the loading sequence that was defined as the time curves of the load-incremental control. The calculation of the RCM models was the most time-consuming. The calculation time of the DCM model was about 17 times faster than that of the RCM counterparts. Apart from the LCM model, the total ROM of the other models could be consistently controlled with the same value as that of the intact model. The intersegmental ROMs of all models were quite comparable. However, the LCM model predicted the least value of the screw stress and averaged 15.6% and 19.9% less than the RCM and DCM models. In general, the computational efficiency between the models was the most different, followed by the mechanical stress; the kinematic results were the most comparable.

CONCLUSION

The superiority of the computational efficiency of the DCM compared with its counterparts makes it the improved strategy for executing lumbosacral nonlinear analysis.

Biomechanical effects of disc degeneration and hybrid fixation on the transition and adjacent lumbar segments: trade-off between junctional problem, motion preservation, and load protection

STUDY DESIGN

The biomechanical effects of disc degeneration and hybrid fixation on the transition and adjacent segments were evaluated using a numerical approach.

OBJECTIVE

This study aimed to evaluate the rigidity-rising effects of the dehydrated disc and bridged fixator on the kinematic and mechanical redistribution of the transition and adjacent segments.

SUMMARY OF BACKGROUND DATA

After static fixation, a dynamic fixator can be used to preserve motion and share loads for the transition segments. However, the hybrid use of both static and dynamic fixators and its effects on the biomechanical behavior of the transition and adjacent segments were not investigated extensively.

METHODS

A nonlinear and osseoligamentous lumbar model from L1 vertebra to S1 vertebrae was developed. Ligament interconnection, muscular contraction, and weight compression were all used to simulate lumbar flexion. The static fixator was instrumented at the degenerative L4-L5 segment and the dynamic fixators (Dynesys system) with different stiffness were subsequently applied to the degenerative or healthy L3-L4 segment. A healthy lumbar model was used as a reference point for further comparison and evaluation. The predicted results were validated with the cadaveric and numerical values of the literature studies. Among the 21 models, the junctional problem at the adjacent (L2/L3 and L5/S1) discs as well as the motion preservation and stress distribution at the transition (L3/L4) disc were compared.

RESULTS

Static fixation and the degenerative disc deteriorated the junctional problem at adjacent segments. On average, the hybrid fixation of the original Dynesys cord constrained the range of motion (ROM) by 65%. Furthermore, it shared 43% of the stress on the transition disc. However, this resulted in the adjacent discs increasing about 50% ROM and 40% stress. The term "trade-off stiffness" was used to express the concept that the decreased stiffness of the original cord could balance the junctional problem, motion preservation, and load protection of the transition and adjacent segments. The trade-off stiffness of the degenerative transition disc was higher than that of the healthy disc. Compared with the original design, the increased ROM and stress of the adjacent segments can be reduced by about 43% using the trade-off stiffness.

CONCLUSION

The use of the hybrid fixator should involve a certain trade-off between the protection of the transition segment and the deterioration of the adjacent segments. This trade-off stiffness, which largely depends on both fixator design and disc degeneration, provides the improved rigidity and flexibility of the transition and adjacent segments.

Comparison of four reconstruction methods after total sacrectomy: a finite element study

BACKGROUND

After total sacrectomy, it is mandatory to reconstruct the continuity between the lumbar spine and the pelvis. Only few biomechanical analyses exist which compare different reconstructions. Therefore, the aim of this study was to compare the lumbo-pelvic motion and the relative risk of implant breakage for four different reconstructions after total sacrectomy.

METHOD

Finite element analyses were performed for four general different reconstructions after total sacrectomy: sacral-rod reconstruction, four-rod reconstruction, bilateral fibular flaps reconstruction, and improved compound reconstruction. The rotations between L5 vertebra and ilium, the L5 shift-down displacement, and the maximum von Mises stress in the implants were calculated and evaluated for flexion, extension, lateral bending and axial rotation.

FINDINGS

The decreasing order of the rotations between L5 vertebra and ilium as well as of the L5 shift-down displacement for the studied reconstruction methods was four-rod reconstruction>sacral-rod reconstruction>bilateral fibular flaps reconstruction>improved compound reconstruction. The decreasing order of the maximum von Mises stress in the implants was sacral-rod reconstruction>four-rod reconstruction>bilateral fibular flaps reconstruction>improved compound reconstruction.

INTERPRETATION

From the mechanical point of view, improved compound reconstruction is superior to the other methods studied here as it shows the highest stability and the lowest maximum von Mises stress. However, clinical aspects must also be regarded when choosing a reconstruction method for a specific patient.

Modeling Degenerative Disk Disease in the Lumbar Spine: A Combined Experimental, Constitutive, and Computational Approach

Using a continuum approach for modeling the constitutive mechanical behavior of the intervertebral disk’s annulus fibrosus holds the potential for facilitating the correlation of morphology and biomechanics of this clinically important tissue. Implementation of a continuum representation of the disk’s tissues into computational models would yield a particularly valuable tool for investigating the effects of degenerative disease. However, to date, relevant efforts in the literature towards this goal have been limited due to the lack of a computationally tractable and implementable constitutive function. In order to address this, annular specimens harvested from a total of 15 healthy and degenerated intervertebral disks were tested under planar biaxial tension. Predictions of a strain energy function, which was previously shown to be unconditionally convex, were fit to the experimental data, and the optimized coefficients were used to modify a previously validated finite element model of the L4/L5 functional spinal unit. Optimization of material coefficients based on experimental results indicated increases in the micro-level orientation dispersion of the collagen fibers and the mechanical nonlinearity of these fibers due to degeneration. On the other hand, the finite element model predicted a progressive increase in the stress generation in annulus fibrosus due to stepwise degeneration of initially the nucleus and then the entire disk. Range of motion was predicted to initially increase with the degeneration of the nucleus and then decrease with the degeneration of the annulus in all rotational loading directions, except for axial rotation. Overall, degeneration was observed to specifically impact the functional effectiveness of the collagen fiber network of the annulus, leading to changes in the biomechanical behavior at both the tissue level and the motion-segment level.

A combined numerical and experimental technique for estimation of the forces and moments in the lumbar intervertebral disc

Evaluation of the loads on lumbar intervertebral discs (IVD) is critically important since it is closely related to spine biomechanics, pathology and prosthesis design. Non-invasive estimation of the loads in the discs remains a challenge. In this study, we proposed a new technique to estimate in vivo loads in the IVD using a subject-specific finite element (FE) model of the disc and the kinematics of the disc endplates as input boundary conditions. The technique was validated by comparing the forces and moments in the discs calculated from the FE analyses to the in vitro experiment measurements of three corresponding lumbar discs. The results showed that the forces and moments could be estimated within an average error of 20%. Therefore, this technique can be a promising tool for non-invasive estimation of the loads in the discs and may be extended to be used on living subjects.

Optimised in vitro applicable loads for the simulation of lateral bending in the lumbar spine

In in vitro studies of the lumbar spine simplified loading modes (compressive follower force, pure moment) are usually employed to simulate the standard load cases flexion-extension, axial rotation and lateral bending of the upper body. However, the magnitudes of these loads vary widely in the literature. Thus the results of current studies may lead to unrealistic values and are hardly comparable. It is still unknown which load magnitudes lead to a realistic simulation of maximum lateral bending. A validated finite element model of the lumbar spine was used in an optimisation study to determine which magnitudes of the compressive follower force and bending moment deliver results that fit best with averaged in vivo data. The best agreement with averaged in vivo measured data was found for a compressive follower force of 700 N and a lateral bending moment of 7.8 Nm. These results show that loading modes that differ strongly from the optimised one may not realistically simulate maximum lateral bending. The simplified but in vitro applicable loading cannot perfectly mimic the in vivo situation. However, the optimised magnitudes are those which agree best with averaged in vivo measured data. Its consequent application would lead to a better comparability of different investigations.

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.

Geometry strongly influences the response of numerical models of the lumbar spine--a probabilistic finite element analysis

Typical FE models of the human lumbar spine consider a single, fixed geometry. Such models cannot account for potential effects of the natural variability of the spine's geometry. In this study, we performed a probabilistic uncertainty and sensitivity analysis of a fully parameterized, geometrically simplified model of the L3-L4 segment. We examined the impact of the uncertainty in all 40 geometry parameters, estimated lower and upper bounds for the required sample size and determined the most important geometry parameters. The natural variability of the spine's geometry indeed strongly affects intradiscal pressure, range of motion and facet joint contact forces. Deriving generalized statements from fixed-geometry models as well as transferring those results to different cases thus can easily lead to wrong conclusions and should only be performed with extreme caution. We recommend a sample size of ≈ 100 to obtain reasonable accurate point estimates and a sufficient overview of the remaining uncertainties. Yet, only few parameters, especially those determining the disc geometry (disc height, end-plate width and depth) and the facets' position (intra-articular space, pedicle length, facet angles), proved to be truly important. Accurate measurement and modeling of those structures should therefore be prioritized.

Which postures are most suitable in assessing spinal fusion using radiostereometric analysis?

BACKGROUND

Up to now, plain radiographs are not well suited to assess spinal fusion. Radiostereometric analysis performed for two postures may deliver more reliable results. However, it is unknown, which postures are most suitable for this procedure.

METHODS

In a finite element study, spinal fusion at the level L4-5 was simulated assuming a posterior approach and the implantation of two cages and a spinal fixation device. The change of the distance between markers in vertebrae adjacent to the cages was calculated for moving from one of the following postures standing, flexion, extension, axial rotation, lying, and extension in a lying position to another. The changes of marker distances were calculated for the intact model, as well as for the situations: directly after surgery before fusion started, in the early-fusion-phase and in the late-fusion-phase. Differences in the marker motion between two postoperative situations were also calculated.

FINDINGS

The most anteriorly placed markers showed the greatest motion between two postures. The greatest differences in marker motions between the two situations before-fusion and early-fusion-phase (0.54 mm) as well as between early-fusion-phase and late-fusion-phase (0.34 mm) were found for the two postures flexion while standing and extension in a lying position.

INTERPRETATION

Pairs of X-rays taken while standing with maximum flexed upper body and while lying with maximum extended trunk are most suited for the assessment of spinal fusion when using radiostereometric analysis.

Pedicle-screw-based dynamic implants may increase posterior intervertebral disc bulging during flexion

Abstract Posterior disc bulging may lead to nerve root compression and radicular pain, and in extreme cases to a local pressure on the dural sac and thus to back pain. Compared to when standing, posterior disc bulging is increased during extension and decreased during flexion, in an uninstrumented spine. The aim of this study was to determine the effect of a pedicle-screw-based dynamic implant on posterior disc bulging. A finite element model of the lumbosacral spine was used to calculate posterior disc bulging before and after implantation of a dynamic implant for different loading cases. The elastic modulus of the longitudinal rod was varied, and the influence of distraction of the bridged segment on disc bulging was also determined. In addition, the centre of rotation (CoR) was determined. Due to a dynamic implant, the magnitude of posterior disc bulging was reduced compared to that for "standing without an implant" during extension, lateral bending, and axial rotation. During flexion, however, disc bulging was usually increased. With increasing stiffness of the dynamic implant, the CoR moved towards the longitudinal rod. This posterior shift of the CoR led to a compression of the entire intervertebral disc during flexion and thus to an increase of disc bulging.

Optimal stiffness of a pedicle-screw-based motion preservation implant for the lumbar spine

PURPOSE

Pedicle-screw-based dynamic implants are intended to preserve intervertebral mobility while releasing certain spinal structures. The aim of the study was to determine the as yet unknown optimal stiffness value of the longitudinal rods that fulfils best these opposing tasks.

METHODS

A finite element model of the lumbar spine was used which includes the posterior implant at level L4/5. More than 250 variations of this model were generated by varying the diameter of the longitudinal rods between 6 and 12 mm and their elastic modulus between 10 MPa and 200 MPa. The loading cases flexion, extension, lateral bending and axial rotation were simulated. Evaluated optimization criteria were the ranges of motion, forces in the facet joints, posterior bulgings of the intervertebral disc and the intradiscal pressures. Various objective functions were evaluated.

RESULTS

The results show that the objective values depend more on the axial stiffness of the rods than on bending and torsional stiffness, rod diameter and elastic modulus. The optimal stiffness value for most of the investigated objective functions is approximately 50 N/mm and is achieved, e.g. using a rod diameter of 6 mm and an elastic modulus of 50 MPa. The design with the least axial stiffness was the best one with regard to the mobility. The forces in the facet joints and the intradiscal pressures were reduced mostly by an implant with the highest axial stiffness. When minimal posterior disc bulging was the criterion, the optimal axial stiffness was also approximately 50 N/mm.

CONCLUSIONS

The optimal axial stiffness of a pedicle-screw-based motion preservation implant for the lumbar spine is approximately 50 N/mm.

Optimised loads for the simulation of axial rotation in the lumbar spine

Simplified loading modes (pure moment, compressive force) are usually applied in the in vitro studies to simulate flexion-extension, lateral bending and axial rotation of the spine. The load magnitudes for axial rotation vary strongly in the literature. Therefore, the results of current investigations, e.g. intervertebral rotations, are hardly comparable and may involve unrealistic values. Thus, the question 'which in vitro applicable loading mode is the most realistic' remains open. A validated finite element model of the lumbar spine was employed in two sensitivity studies to estimate the ranges of results due to published load assumptions and to determine the input parameters (e.g. torsional moment), which mostly affect the spinal load and kinematics during axial rotation. In a subsequent optimisation study, the in vitro applicable loading mode was determined, which delivers results that fit best with available in vivo measurements. The calculated results varied widely for loads used in the literature with potential high deviations from in vivo measured values. The intradiscal pressure is mainly affected by the magnitude of the compressive force, while the torsional moment influences mainly the intervertebral rotations and facet joint forces. The best agreement with results measured in vivo were found for a compressive follower force of 720N and a pure moment of 5.5Nm applied to the unconstrained vertebra L1. The results reveal that in many studies the assumed loads do not realistically simulate axial rotation. The in vitro applicable simplified loads cannot perfectly mimic the in vivo situation. However, the optimised values lead to the best agreement with in vivo measured values. Their consequent application would lead to a better comparability of different investigations.