Biomechanical implications of lumbar spinal ligament transection

Many lumbar spine surgeries either intentionally or inadvertently damage or transect spinal ligaments. The purpose of this work was to quantify the previously unknown biomechanical consequences of isolated spinal ligament transection on the remaining spinal ligaments (stress transfer), vertebrae (bone remodelling stimulus) and intervertebral discs (disc pressure) of the lumbar spine. A finite element model of the full lumbar spine was developed and validated against experimental data and tested in the primary modes of spinal motion in the intact condition. Once a ligament was removed, stress increased in the remaining spinal ligaments and changes occurred in vertebral strain energy, but disc pressure remained similar. All major biomechanical changes occurred at the same spinal level as the transected ligament, with minor changes at adjacent levels. This work demonstrates that iatrogenic damage to spinal ligaments disturbs the load sharing within the spinal ligament network and may induce significant clinically relevant changes in the spinal motion segment.     

Influence of cervical disc degeneration after posterior surgical techniques in combined flexion-extension--a nonlinear analytical study

Laminectomy and facetectomy are surgical techniques used for decompression of the cervical spinal stenosis. Recent in vitro and finite element studies have shown significant cervical spinal instability after performing these surgical techniques. However, the influence of degenerated cervical disk on the biomechanical responses of the cervical spine after these surgical techniques remains unknown. Therefore, a three-dimensional nonlinear finite element model of the human cervical spine (C2-C7) was created. Two types of disk degeneration grades were simulated. For each grade of disk degeneration, the intact as well as the two surgically altered models simulating C5 laminectomy with or without C5-C6 total facetectomies were exercised under flexion and extension. Intersegmental rotational motions, internal disk annulus, cancellous and cortical bone stresses were obtained and compared to the normal intact model. Results showed that the cervical rotational motion decreases with progressive disk degeneration. Decreases in the rotational motion due to disk degeneration were accompanied by higher cancellous and cortical bone stress. The surgically altered model showed significant increases in the rotational motions after laminectomies and facetectomies when compared to the intact model. However, the percentage increases in the rotational motions after various surgical techniques were reduced with progressive disk degeneration.     

Search for critical loading condition of the spine--a meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2-L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Search for critical loading condition of the spine–A meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2–L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Effect of bone graft characteristics on the mechanical behavior of the lumbar spine

There is little information about the influence of bone graft size, position and elasticity on the mechanical behavior of the lumbar spine. Intersegmental motion, intradiscal pressure and stresses in the lumbar spine were calculated using a three-dimensional, nonlinear finite element model which included an internal spinal fixation device and a bone graft. Cross-sectional area, position, and elastic modulus of the graft were varied in this study. Bone grafts, especially very stiff ones, increase stresses on adjacent endplates. Though larger grafts lead to less contact pressure, it is difficult to judge the quality of different bone graft positions. In general, ventral flexion results in lower maximum contact pressure than lateral bending. There is always little intersegmental rotation in the bridged region compared with that of an intact spine.A larger graft with low stiffness should be favored from a mechanical point of view. Patients should avoid lateral bending of the upper body shortly after surgery.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1-L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Finite element lumbar spine facet contact parameter predictions are affected by the cartilage thickness distribution and initial joint gap size

Current finite element modeling techniques utilize geometrically inaccurate cartilage distribution representations in the lumbar spine. We hypothesize that this shortcoming severely limits the predictive fidelity of these simulations. Specifically, it is unclear how these anatomically inaccurate cartilage representations alter range of motion and facet contact predictions. In the current study, cadaveric vertebrae were serially sectioned, and images were taken of each slice in order to identify the osteochondral interface and the articulating surface. A series of custom-written algorithms were utilized in order to quantify each facet joint's three-dimensional cartilage distribution using a previously developed methodology. These vertebrae-dependent thickness cartilage distributions were implemented on an L1 through L5 lumbar spine finite element model. Moments were applied in three principal planes of motion, and range of motion and facet contact predictions from the variable thickness and constant thickness distribution models were determined. Initial facet gap thickness dimensions were also parameterized. The data indicate that the mean and maximum cartilage thickness increased inferiorly from L1 to L5, with an overall mean thickness value of 0.57 mm. Cartilage distribution and initial facet joint gap thickness had little influence on the lumbar range of motion in any direction, whereas the mean contact pressure, total contact force, and total contact area predictions were altered considerably. The data indicate that range of motion predictions alone are insufficient to establish model validation intended to predict mechanical contact parameters. These data also emphasize the need for the careful consideration of the initial facet joint gap thickness with respect to the spinal condition being studied.     

Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data

Muscle forces stabilize the spine and have a great influence on spinal loads. But little is known about their magnitude. In a former in vitro experiment, a good agreement with intradiscal pressure and fixator loads measured in vivo could be achieved for standing and extension of the lumbar spine. However, for flexion the agreement between in vitro and in vivo measurements was insufficient. In order to improve the determination of trunk muscle forces, a three-dimensional nonlinear finite element model of the lumbar spine with an internal fixation device was created and the same loads were applied as in a previous in vitro experiment. An extensive adaptation process of the model was performed for flexion and extension angles up to 20 degrees and -15 degrees, respectively. With this validated computer model intra-abdominal pressure, preload in the fixators, and a combination of hip- and lumbar flexion angle were varied until a good agreement between analytical and in vivo results was reached for both, intradiscal pressure and bending moments in the fixators. Finally, the fixators were removed and the muscle forces for the intact lumbar spine calculated. A good agreement with the in vivo results could only be achieved at a combination of hip- and lumbar flexion. For the intact spine, forces of 170, 100 and 600 N are predicted in the m. erector spinae for standing, 5 degrees extension and 30 degrees flexion, respectively. The force in the m. rectus abdominus for these body positions is less than 25 N. For more than 10 degrees extension the m. erector spinae is unloaded. The finite element method together with in vivo data allows the estimation of trunk muscle forces for different upper body positions in the sagittal plane. In our patients, flexion of the upper body was most likely a combination of hip- and lumbar spine bending.     

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.     

The role of the facet capsular ligament in providing spinal stability

Abstract

Low back pain (LBP) is the most common type of pain in America, and spinal instability is a primary cause. The facet capsular ligament (FCL) encloses the articulating joints of the spine and is of particular interest due to its high innervation – as instability ensues, high stretch values likely are a cause of this pain. Therefore, this work investigated the FCL's role in providing stability to the lumbar spine. A previously validated finite element model of the L4-L5 spinal motion segment was used to simulate pure moment bending in multiple planes. FCL failure was simulated and the following outcome measures were calculated: helical axes of motion, range of motion (ROM), bending stiffness, facet joint space, and FCL stretch. ROM increased, bending stiffness decreased, and altered helical axis patterns were observed with the removal of the FCL. Additionally, a large increase in FCL stretch was measured with diminished FCL mechanical competency, providing support that the FCL plays an important role in spinal stability.     

Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?--a modeling study

Prior studies have found that primary rotations in the lumbar spine are accompanied by coupled out-of-plane rotations. However, it is not clear whether these accompanying rotations are primarily due to passive (discs, ligaments and facet joints) or active (muscles) spinal anatomy. The aim of this study was to use a finite element (FE) model of the lumbar spine to predict three-dimensional coupled rotations between the lumbar vertebrae, due to passive spinal structures alone. The FE model was subjected to physiologically observed whole lumbar spine rotations about in vivo centres of rotation. Model predictions were validated by comparison of intra-discal pressures and primary rotations with in vivo measurements and these showed close agreement. Predicted coupled rotations matched in vivo measurements for all primary motions except lateral bending. We suggest that coupled rotations accompanying primary motions in the sagittal (flexion/extension) and transverse (axial rotation) planes are primarily due to passive spinal structures. For lateral bending the muscles most likely play a key role in the coupled rotation of the spine.     

Lumbar spine finite element model for healthy subjects: development and validation

Finite element (FE) method is a proven powerful and efficient tool to study the biomechanics of the human lumbar spine. However, due to the large inter-subject variability of geometries and material properties in human lumbar spines, concerns existed on the accuracy and predictive power of one single deterministic FE model with one set of spinal geometry and material properties. It was confirmed that the combined predictions (median or mean value) of several distinct FE models can be used as an improved prediction of behavior of human lumbar spine under identical loading and boundary conditions. In light of this improved prediction, five FE models (L1-L5 spinal levels) of the human lumbar spine were developed based on five healthy living subjects with identical modeling method. The five models were extensively validated through experimental and computational results in the literature. Mesh convergence and material sensitivity analysis were also conducted. We have shown that the results from the five FE models developed in this paper were consistent with the experimental data and simulation results from the existing literature. The validated modeling method introduced in this study can be used in modeling dysfunctional lumber spines such as disc degeneration and scoliosis in future work.     

Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting.

A combined approach involving optimization and the finite element technique was used to predict biomechanical parameters in the lumbar spine during static lifting in the sagittal plane. Forces in muscle fascicles of the lumbar region were first predicted using an optimization-based force model including the entire lumbar spine. These muscle forces as well as the distributed upper body weight and the lifted load were then applied to a three-dimensional finite element model of the thoracolumbar spine and rib cage to predict deformation, the intradiskal pressure, strains, stresses, and load transfer paths in the spine. The predicted intradiskal pressures in the L3-4 disk at the most deviated from the in vivo measurements by 8.2 percent for the four lifting cases analyzed. The lumbosacral joint flexed, while the other lumbar joints extended for all of the four lifting cases studied (rotation of a joint is the relative rotation between its two vertebral bodies). High stresses were predicted in the posterolateral regions of the endplates and at the junctions of the pedicles and vertebral bodies. High interlaminar shear stresses were found in the posterolateral regions of the lumbar disks. While the facet joints of the upper two lumbar segments did not transmit any load, the facet joints of the lower two lumbar segments experienced significant loads. The ligaments of all lumbar motion segments except the lumbosacral junction provided only marginal moments. The limitations of the current model and possible improvements are discussed.     

Computational biomechanics of a lumbar motion segment in pure and combined shear loads

Anterior shear has been implicated as a risk factor in spinal injuries. A 3D nonlinear poroelastic finite element model study of a lumbar motion segment L4-L5 was performed to predict the temporal shear response under various single and combined shear loads. Effects of nucleotomy and facetectomy as well as changes in the posture and facet gap distance were analyzed as well.     

Minimizing errors during in vitro testing of multisegmental spine specimens: considerations for component selection and kinematic measurement

Apparatus-induced artifacts may invalidate standard spine testing protocols. Kinematic measurements may be compromised by the configuration of motion capture equipment. This study has determined: (1) the influence of machine design (component friction) on in vitro spinal kinetics; (2) the sensitivity of kinematic measurements to variations in the placement of motion capture markers. A spinal loading simulator has been developed to dynamically apply pure bending moments (three axes) with or without a simultaneous compressive preload. Two linear slider types with different friction coefficients, one with caged ball bearings and one with high-precision roller bearings on rails, were mounted and specimen response compared in sequential tests. Three different optoelectronic marker cluster configurations were mounted on the specimen and motion data was captured simultaneously from all clusters during testing. A polymer tube with a uniform bending stiffness approximately equivalent to a polysegmental lumbar spine specimen was selected to allow reproducible behavior over multiple tests. The selection of sliders for linear degrees of freedom had a marked influence on parasitic shear forces. Higher shear forces were recorded with the caged-bearing design than with the high-precision rollers and consequently a higher moment was required to achieve a given rotation. Kinematic accuracy varied with each marker configuration, but in general higher accuracy was achieved with larger marker spacings and situations where markers moved predominantly parallel to the camera's imaging plane. Relatively common alternatives in the mechanical components used in an apparatus for in vitro spine testing can have a significant influence on the measured kinematic and kinetics. Low-magnitude parasitic shear forces due to friction in sliders induces a linearly increasing moment along the length of the specimen, precluding the ideal of pure moment application. This effect is compounded in polysegmental specimens. Kinematic measurements are highly sensitive to marker design and placement, despite equivalent absolute precision of individual marker measurements, however marker configurations can be designed to minimize errors related to spatial distribution and system bias.     

Biomechanical analysis of Graf's dynamic spine stabilisation system ex vivo.

The most frequent causes of chronic lumbar spine instability are of degenerative or traumatic origin. Numerous anterior and posterior stabilisation devices were developed for anatomical reconstruction of the spinal alignment and fusion of the spine to restore stability. Fusion of the spine results in increased load of adjacent segments with an increased risk of secondary degeneration which might result in instability or stenosis. To avoid the disadvantages of static devices, Graf developed a method of dynamic surgical treatment of spinal column instabilities, which is based on the principle of flexible stabilisation. This study is analysing the kinematics of discoligamentary intact motion segments compared with the experimentally destabilised human lumbar spine and the influence of Graf's stabilisation. According to our results, rotational instabilities cannot be satisfactorily stabilised by Graf's ligamentoplasty. With the present ex vivo study, it could be shown that it is possible to restore stability after discoligamentary lesion and after facetectomy using Graf's dynamic lordosis ligamentoplasty.     

Uncertainty analysis of material properties and morphology parameters in numerical models regarding the motion of lumbar vertebral segments

Abstract

The kinematics of a spinal motion segment is determined by the material properties of the soft-tissue and the morphology. The material properties can vary within subjects and between vertebral levels, leading to a wide possible range of motion of a spinal segment independently on its morphology. The goal of this numerical study was to identify the most influential material parameters concerning the kinematics of a spinal motion segment and their plausible ranges. Then, a method was tested to deduce the material properties automatically, based on a given ROM and morphology. A fully parametric finite element model of the morphology and material properties of a lumbar spinal motion segment was developed. The impact of uncertainty of twelve spinal material parameters, as well as the size of the gap between the articular surfaces of the facet joints was examined. The simulation results were compared to our own in vitro data. The flexibility of a lumbar segment was especially influenced by the properties of the anterior annulus region, the facet gap size and the interspinous ligament. The high degree of uncertainty in the material properties and facet gap size published in the literature can lead to a wide scatter in the motion of a spinal segment, with a range of 6°-17° in the intact condition in flexion/extension, from 5°-22° in lateral bending and from 3°-14° in axial rotation. Statistical analysis of the variability might help to estimate the sensitivity and total uncertainty propagated through biomechanical simulations, affecting the reliability of the predictions.