Load sharing among spinal elements of a motion segment in extension and lateral bending

A linear optimization model was formulated using a semi-experimental protocol to estimate the forces in the spinal elements of a lumbar motion segment subjected to an extension or lateral bending moment with and without a 120 N compressive preload. A morphometer was used to acquire the three-dimensional locations of the disk center, facet centers and ligament origin and insertion sites with the specimen in a "neutral" position. The relative motion of the superior vertebra, under the loading conditions tested, was monitored using a Selspot II system. These data allowed the formulation of the static equilibrium equations for the superior vertebra at each of the loading conditions mentioned above. A linear optimization technique was used, along with a suitable cost function, to find an optimum solution for the set of equations and imposed constraints. Results showed that for 6.9 Nm of extension moment, each facet carried a load of 52 N, with the disk carrying an axial tensile load of 104 N. At the 6.9 Nm extension moment coupled with 120 N preload, each facet carried a load of 77.2 N and the disk an axial tensile load of 37 N. In right lateral bending, with and without preload, the load was distributed among the right facet, the disk, the left ligamentum flavum and the left capsular ligament. At the 6.9 Nm load step without preload the right facet carried an axial load of 127.01 N with the disk carrying an axial compressive load of 7.8 N. Ligament forces for this step for the left ligamentum flavum and capsular ligament, respectively, were 61.03 N and 65.14 N. The addition of 120 N of preload reduced the load on the right facet to 83.5 N. The compressive load in the disk increased to 107.5 N. The corresponding ligament forces were 43.2 N (left ligamentum flavum) and 50.7 N (left capsular ligament).     

Effect of annular incision type on the change in biomechanical properties in a herniated lumbar intervertebral disc

The technique used to incise the disc during discectomy may play a role in the subsequent healing and change in biomechanical stiffness of the disc. Several techniques of lumbar disc annulotomy have been described in clinical reports. The purpose of this paper was to study the influence of annulotomy technique on motion segment stiffness using a finite element model. Four incision methods (square, circular, cross, and slit) were compared. The analyses showed that each of the annular incisions produced increase in motions under axial moment loadings with circular incision producing the largest change in the corresponding rotational motion. Under shear loading mode, cross and slit-type annular incisions produced slightly larger changes in the principal motions of the disc than square and circular incisions. All other incision types considered in the current study produced negligibly small increase in motion under rest of the loading conditions. In addition to annulotomy, when nucleotomy was also included in the analyses, once again cross and slit incisions produced larger change in motion under shear loading mode as compared to the other two incision types. A comparison between the four types of annular incisions showed that cross incision produced an increase in motion larger than those produced by the other three incisions under flexion/extension and lateral moment loading and both shear force loadings. Circular incision produced the largest increase in motion under axial moment load in comparison to those produced by square, cross, and slit incisions. Sagittal plane symmetry was influenced by the incision injury to the motion segment leading to coupled motions as well as increased facet loads. From the study it can be concluded that the increase inflexibility of the disc due to annulotomy depends on the type of annulotomy and the annulotomy also produce asymmetrical deformations leading to increased facet loading.     

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.     

A finite element study of a lumbar motion segment subjected to pure sagittal plane moments

A nonlinear finite element program has been developed and applied to the analysis of a three-dimensional model of the lumbar L2-3 motion segment subjected to sagittal plane moments. The analysis accounts for both material and geometric nonlinearities and is based on the Updated Lagrangian approach. The disc nucleus has been considered as an incompressible inviscid fluid and the annulus as a composite of collagenous fibres embedded in a matrix of ground substance. Articulation at the facet joints has been treated as a general moving contact problem and the spinal ligaments have been modelled as a collection of nonlinear axial elements. Effects of the loss of intradiscal pressure in flexion and of facetectomy in extension have been analyzed. Comparison of the predicted gross response characteristics with available measurements indicates satisfactory agreement. In flexion relatively large intradiscal pressures are generated, while in extension negative pressures (i.e. suction) of low magnitude are predicted. The stress distribution results indicate that the load transfer path through the posterior elements of the joint in flexion is different from that in extension. In flexion the ligaments are the means of load transfer, while in extension the load is transmitted through the pedicles, laminae and articular processes. In flexion, the inner annulus fibres at the posterolateral location are subject to maximum tensile strain. It is suggested that large flexion moment in combination with other loads is a likely cause of disc prolapse commonly found at this location of the annulus.     

Contact pressure in the facet joint during sagittal bending of the cadaveric cervical spine

The facet joint contributes to the normal biomechanical function of the spine by transmitting loads and limiting motions via articular contact. However, little is known about the contact pressure response for this joint. Such information can provide a quantitative measure of the facet joint's local environment. The objective of this study was to measure facet pressure during physiologic bending in the cervical spine, using a joint capsule-sparing technique. Flexion and extension bending moments were applied to six human cadaveric cervical spines. Global motions (C2-T1) were defined using infra-red cameras to track markers on each vertebra. Contact pressure in the C5-C6 facet was also measured using a tip-mounted pressure transducer inserted into the joint space through a hole in the postero-inferior region of the C5 lateral mass. Facet contact pressure increased by 67.6 ± 26.9 kPa under a 2.4 Nm extension moment and decreased by 10.3 ± 9.7 kPa under a 2.7 Nm flexion moment. The mean rotation of the overall cervical specimen motion segments was 9.6 ± 0.8° and was 1.6 ± 0.7° for the C5-C6 joint, respectively, for extension. The change in pressure during extension was linearly related to both the change in moment (51.4 ± 42.6 kPa/Nm) and the change in C5-C6 angle (18.0 ± 108.9 kPa/deg). Contact pressure in the inferior region of the cervical facet joint increases during extension as the articular surfaces come in contact, and decreases in flexion as the joint opens, similar to reports in the lumbar spine despite the difference in facet orientation in those spinal regions. Joint contact pressure is linearly related to both sagittal moment and spinal rotation. Cartilage degeneration and the presence of meniscoids may account for the variation in the pressure profiles measured during physiologic sagittal bending. This study shows that cervical facet contact pressure can be directly measured with minimal disruption to the joint and is the first to provide local pressure values for the cervical joint in a cadaveric model.     

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.     

An experimental method for measuring force on the spinal facet joint: description and application of the method.

A technique is described for measuring load magnitude and resultant load contact location in the facet joint in response to applied loads and moments, and the technique applied to the canine lumbar spine motion segment. Due to the cantilever beam geometry of the cranial articular process, facet joint loads result in surface strains on the lateral aspect of the cranial articular process. Strains were quantified by four strain gages cemented to the bony surface of the process. Strain measured at any one gage depended on the loading site on the articular surface of the caudal facet and on the magnitude of the facet load. Determination of facet loads during in vitro motion segment testing required calibration of the strains to known loads of various magnitudes applied to multiple sites on the caudal facet. The technique is described in detail, including placement of the strain gages. There is good repeatability of strains to applied facet loads and the strains appear independent of load distribution area. Error in the technique depends on the location of the applied facet loads, but is only significant in nonphysiologic locations. The technique was validated by two independent methods in axial torsion. Application of the technique to five in vitro canine L2-3 motion segments testing resulted in facet loads (in newtons, N) of 74+ / -23 N (mean + / -STD) in 2 newton-meter, Nm, extension, to unloaded in flexion. Lateral bending resulted in loads in the right facet of 40+ / -32 N for 1 Nm right lateral bending and 54+ / -29 N for 1 Nm left lateral bending. 4 Nm Torsion with and without 100 N axial compression resulted in facet loads of 92+ / -27 N and 69+ / -19 N, respectively. The technique is applicable to dynamic and in vivo studies.     

Biomechanical contributions of upper cervical ligamentous structures in Type II odontoid fractures

Fractures of the odontoid present frequently in spinal trauma, and Type II odontoid fractures, occurring at the junction of the odontoid process and C2 vertebrae, represent the bulk of all traumatic odontoid fractures. It is currently unclear what soft-tissue stabilizers contribute to upper cervical motion in the setting of a Type II odontoid fracture, and evaluation of how concomitant injury contributes to cervical stability may inform surgical decision-making as well as allow for the creation of future, accurate, biomechanical models of the upper cervical spine. The objective of the current study was to determine the contribution of soft-tissue stabilizers in the upper cervical spine following a Type II odontoid fracture. Eight cadaveric C0-C2 specimens were evaluated using a robotic testing system with motion tracking. The unilateral facet capsule (UFC) and anterior longitudinal ligament (ALL) were serially resected to determine their biomechanical role following odontoid fracture. Range of motion (ROM) and moment at the end of intact specimen replay were the primary outcomes. We determined that fracture of the odontoid significantly increases motion and decreases resistance to intact motion for flexion–extension (FE), axial rotation (AR), and lateral bending (LB). Injury to the UFC increased AR by 3.2° and FE by 3.2°. ALL resection did not significantly increase ROM or decrease end-point moment. The UFC was determined to contribute to 19% of intact flexion resistance and 24% of intact AR resistance. Overall, we determined that Type II fracture of the odontoid is a significant biomechanical destabilizer and that concurrent injury to the UFC further increases upper cervical ROM and decreases resistance to motion in a cadaveric model of traumatic Type II odontoid fractures.     

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.     

Load-bearing role of facets in a lumbar segment under sagittal plane loadings

In the present work, the load-bearing role of the facet joints in a lumbar I2-3 segment is quantitatively determined by means of a three dimensional nonlinear finite element program. The analysis accounts for both material and geometric nonlinearities and treats the facet articulation as a nonlinear moving contact problem. The disc nucleus is considered as an inviscid incompressible fluid and the annulus as a composite of collagenous fibres embedded in a matrix of ground substance. The spinal ligaments are modelled as a collection of nonlinear axial elements. The loadings consist of axial compression and sagittal plane shears and bending moments, acting alone or combined. The results show that in pure compression, the external axial force is transmitted primarily by the intervertebral disc. The facet joints carry only a small percentage of the force. However, the facet joints carry large forces in extension, whereas in small flexion they carry none. Addition of compression tends to increase these contact forces in extension while it has no effect on them in flexion. In extension, the forces on the facet joints are transmitted by both the articular surfaces and the capsular ligaments. Although in small flexion the facets carry no load, large contact forces are predicted to develop as the segment is flexed beyond 7-8 degrees. These forces are of the same magnitude as those computed under large extension rotation and are oriented nearly in the horizontal plane with negligible component in the axial direction. The horizontal components of the contact forces generated during articulation are often larger than the axial components which directly resist the applied compressive force. The axial components of the contact forces, therefore, grossly underestimate the total forces acting on the facets. The transfer of forces from one facet to the adjacent one occurs through distinct areas in flexion and in extension loadings. That is, on the superior articular surface, the contact area shifts from the upper tip in large flexion to the lower margin in extension. On the inferior articular surface, the contact area shifts from the upper and central regions in large flexion to the lower tip in extension.     

Design of next generation total disk replacements

To improve the treatments for low back pain, new designs of total disk replacement have been proposed. The question is how well these designs can act as a functional replacement of the intervertebral disk. Four finite element models were made, for four different design concepts, to determine how well they can mimic the physiological intervertebral disk mechanical function. The four designs were a homogenous elastomer, a multi-stiffness elastomer, an elastomer with fiber jacket, and a hydrogel with fiber jacket. The best material properties of the four models were determined by optimizing the model behavior to match the behavior of the intervertebral disk in flexion-extension, axial rotation, and lateral bending. It was shown that neither a homogeneous elastomer nor a multi-stiffness elastomer could mimic the non-linear behavior within the physiological range of motion. Including a fiber jacket around an elastomer allowed for physiological motion in all degrees of freedom. Replacing the elastomer by a hydrogel yielded similar good behavior. Mimicking the non-linear behavior of the intervertebral disk, in the physiological range of motion is essential in maintaining and restoring spinal motion and in protecting surrounding tissues like the facet joints or adjacent segments. This was accomplished with designs mimicking the function of the annulus fibrosus.     

Influence of single-level lumbar degenerative disc disease on the behavior of the adjacent segments—A finite element model study

The current study investigated mechanical predictors for the development of adjacent disc degeneration. A 3-D finite element model of a lumbar spine was modified to simulate two grades of degeneration at the L4–L5 disc. Degeneration was modeled by changes in geometry and material properties. All models were subjected to follower preloads of 800 N and moment loads in the three principal directions of motion using a hybrid protocol. Degeneration caused changes in the loading and motion patterns of the segments above and below the degenerated disc. At the level (L3–L4) above the degenerated disc, the motion increased due to moderate degeneration by 21% under lateral bending, 26% under axial rotation and 28% under flexion/extension. At the level (L5-S1) below the degenerated disc, motion increased only during lateral bending by 20% due to moderate degeneration. Both the L3–L4 and L5-S1 segment showed a monotonic increase in both the maximum von Mises stress and shear stress in the annulus as degeneration progressed for all loading directions, expect extension at L3–L4. The most significant increase in stress was observed at the L5-S1 level during axial rotation with nearly a ten-fold increase in the maximum shear stress and 103% increase in the maximum von Mises stress. The L5-S1 segment also showed a progressive increase in facet contact force for all loading directions with degeneration. Nucleus pressure did not increase significantly for any loading direction at either the caudal or cephalic adjacent segment. Results suggest that single-level degeneration can increase the risk for injury at the adjacent levels.     

Load-sharing in the lumbosacral spine in neutral standing & flexed postures – A combined finite element and inverse static study

Understanding load-sharing in the spine during in-vivo conditions is critical for better spinal implant design and testing. Previous studies of load-sharing that considered actual spinal geometry applied compressive follower load, with or without moment, to simulate muscle forces. Other studies used musculoskeletal models, which include muscle forces, but model the discs by simple beams or spherical joints and ignore the articular facet joints.This study investigated load-sharing in neutral standing and flexed postures using a detailed Finite Element (FE) model of the ligamentous lumbosacral spine, where muscle forces, gravity loads and intra-abdominal pressure, as predicted by a musculoskeletal model of the upper body, are input into the FE model. Flexion was simulated by applying vertebral rotations following spine rhythm measured in a previous in-vivo study, to the musculoskeletal model. The FE model predicted intradiscal pressure (IDP), strains in the annular fibers, contact forces in the facet joints, and forces in the ligaments. The disc forces and moments were determined using equilibrium equations, which considered the applied loads, including muscle forces and IDP, as well as forces in the ligaments and facet joints predicted by the FE model. Load-sharing was calculated as the portion of the total spinal load carried along the spine by each individual spinal structure. The results revealed that spinal loads which increased substantially from the upright to the flexed posture were mainly supported by the discs in the upright posture, whereas the ligaments’ contribution in resisting shear, compression, and moment was more significant in the flexed posture.     

Effect of a pedicle-screw-based motion preservation system on lumbar spine biomechanics: A probabilistic finite element study with subsequent sensitivity analysis

Pedicle-screw-based motion preservation systems are often used to support a slightly degenerated disc. Such implants are intended to reduce intradiscal pressure and facet joints forces, while having a minimal effect on the motion patterns.In a probabilistic finite element study with subsequent sensitivity analysis, the effects of 10 input parameters, such as elastic modulus and diameter of the elastic rod, distraction of the segment, level of bridged segments, etc. on the output parameters intervertebral rotations, intradiscal pressures, and facet joint forces were determined. A validated finite element model of the lumbar spine was employed. Probabilistic studies were performed for seven loading cases: upright standing, flexion, extension, left and right lateral bending and left and right axial rotation.The simulations show that intervertebral rotation angles, intradiscal pressures and facet joint forces are in most cases reduced by a motion preservation system. The influence on intradiscal pressure is small, except in extension. For many input parameter combinations, the values for intervertebral rotations and facet joint forces are very low, which indicates that the implant is too stiff in these cases. The output parameters are affected most by the following input parameters: loading case, elastic modulus and diameter of the elastic rod, distraction of the segment, and angular rigidity of the connection between screws and rod.The designated functions of a motion preservation system can best be achieved when the longitudinal rod has a low stiffness, and when the connection between rod and pedicle screws is rigid.     

Investigation of impact loading rate effects on the ligamentous cervical spinal load-partitioning using finite element model of functional spinal unit C2–C3

The cervical spine functions as a complex mechanism that responds to sudden loading in a unique manner, due to intricate structural features and kinematics. The spinal load-sharing under pure compression and sagittal flexion/extension at two different impact rates were compared using a bio-fidelic finite element (FE) model of the ligamentous cervical functional spinal unit (FSU) C2–C3. This model was developed using a comprehensive and realistic geometry of spinal components and material laws that include strain rate dependency, bone fracture, and ligament failure. The range of motion, contact pressure in facet joints, failure forces in ligaments were compared to experimental findings. The model demonstrated that resistance of spinal components to impact load is dependent on loading rate and direction. For the loads applied, stress increased with loading rate in all spinal components, and was concentrated in the outer intervertebral disc (IVD), regions of ligaments to bone attachment, and in the cancellous bone of the facet joints. The highest stress in ligaments was found in capsular ligament (CL) in all cases. Intradiscal pressure (IDP) in the nucleus was affected by loading rate change. It increased under compression/flexion but decreased under extension. Contact pressure in the facet joints showed less variation under compression, but increased significantly under flexion/extension particularly under extension. Cancellous bone of the facet joints region was the only component fractured and fracture occurred under extension at both rates. The cervical ligaments were the primary load-bearing component followed by the IVD, endplates and cancellous bone; however, the latter was the most vulnerable to extension as it fractured at low energy impact.     

A finite element model of the L5-S1 functional spinal unit: development and comparison with biomechanical tests in vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro. Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

A Finite Element Model of the L5-S1 Functional Spinal Unit: Development and Comparison with Biomechanical Tests In Vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro . Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

Vibrissal kinematics in 3D: tight coupling of azimuth, elevation, and torsion across different whisking modes

Perception is usually an active process by which action selects and affects sensory information. During rodent active touch, whisker kinematics influences how objects activate sensory receptors. In order to fully characterize whisker motion, we reconstructed whisker position in 3D and decomposed whisker motion to all its degrees of freedom. We found that, across behavioral modes, in both head-fixed and freely moving rats, whisker motion is characterized by translational movements and three rotary components: azimuth, elevation, and torsion. Whisker torsion, which has not previously been described, was large (up to 100 degrees), and torsional angles were highly correlated with whisker azimuths. The coupling of azimuth and torsion was consistent across whisking epochs and rats and was similar along rows but systematically varied across rows such that rows A and E counterrotated. Torsional rotation of the whiskers enables contact information to be mapped onto the circumference of the whisker follicles in a predictable manner across protraction-retraction cycles.     

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.