A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion-extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

A multibody modelling approach to determine load sharing between passive elements of the lumbar spine

The human spinal segment is an inherently complex structure, a combination of flexible and semi-rigid articulating elements stabilised by seven principal ligaments. An understanding of how mechanical loading is shared among these passive elements of the segment is required to estimate tissue failure stresses. A 3D rigid body model of the complete lumbar spine has been developed to facilitate the prediction of load sharing across the passive elements. In contrast to previous multibody models, this model includes a non-linear, six degrees of freedom intervertebral disc, facet bony articulations and all spinal ligaments. Predictions of segmental kinematics and facet joint forces, in response to pure moment loading (flexion–extension), were compared to published in vitro data. On inclusion of detailed representation of the disc and facets, the multibody model fully captures the non-linear flexibility response of the spinal segment, i.e. coupled motions and a mobile instantaneous centre of rotation. Predicted facet joint forces corresponded well with reported values. For the loading case considered, the model predicted that the ligaments are the main stabilising elements within the physiological motion range; however, the disc resists a greater proportion of the applied load as the spine is fully flexed. In extension, the facets and capsular ligaments provide the principal resistance. Overall patterns of load distribution to the spinal ligaments are in agreement with previous predictions; however, the current model highlights the important role of the intraspinous ligament in flexion and the potentially high risk of failure. Several important refinements to the multibody modelling of the passive elements of the spine have been described, and such an enhanced passive model can be easily integrated into a full musculoskeletal model for the prediction of spinal loading for a variety of daily activities.     

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.     

Effects of the rib cage on thoracic spine flexibility.

Besides protecting the internal organs of the thorax, the rib cage is the site of numerous muscle attachments. It also decreases the overall flexibility of the thoracic spine. This study developed finite element (FE) models of the thoracic spine with and without the rib cage, and the effects of the rib cage on thoracic spine flexibility were determined. The numerical models were validated by comparing the maximum rotation of the models for several loading cases with experimental data in the literature. After adapting the material properties for the discs and ligaments, the calculated maximum rotations differed from the measured median values by less than 1 degrees without the rib cage and by less than 2.5 degrees with it. The rib cage decreased the mean flexibility of the thoracic spine by 23% to 47%, depending on the loading plane. Assuming the ribs to be rigid beams required a corresponding reduction of ligament stiffnesses in order to achieve the same agreement of the maximum rotations with the measured median values. Interconnecting the FE thoracic spine model plus rib cage with the existing detailed FE lumbar spine model improves the simulation of force directions of muscles attached to the rib cage or thoracolumbar spine. In addition, such a model is suitable for determining the effects of lumbar spine implants on spinal balance.     

Investigation of whiplash injuries in the upper cervical spine using a detailed neck model

Whiplash injuries continue to have significant societal cost; however, the mechanism and location of whiplash injury is still under investigation. Recently, the upper cervical spine ligaments, particularly the alar ligament, have been identified as a potential whiplash injury location. In this study, a detailed and validated explicit finite element model of a 50th percentile male cervical spine in a seated posture was used to investigate upper cervical spine response and the potential for whiplash injury resulting from vehicle crash scenarios. This model was previously validated at the segment and whole spine levels for both kinematics and soft tissue strains in frontal and rear impact scenarios. The model predicted increasing upper cervical spine ligament strain with increasing impact severity. Considering all upper cervical spine ligaments, the distractions in the apical and alar ligaments were the largest relative to their failure strains, in agreement with the clinical findings. The model predicted the potential for injury to the apical ligament for 15.2 g frontal or 11.7 g rear impacts, and to the alar ligament for a 20.7 g frontal or 14.4 g rear impact based on the ligament distractions. Future studies should consider the effect of initial occupant position on ligament distraction.     

Comparative role of disc degeneration and ligament failure on functional mechanics of the lumbar spine

Understanding spinal kinematics is essential for distinguishing between pathological conditions of spine disorders, which ultimately lead to low back pain. It is of high importance to understand how changes in mechanical properties affect the response of the lumbar spine, specifically in an effort to differentiate those associated with disc degeneration from ligamentous changes, allowing for more precise treatment strategies. To do this, the goals of this study were twofold: (1) develop and validate a finite element (FE) model of the lumbar spine and (2) systematically alter the properties of the intervertebral disc and ligaments to define respective roles in functional mechanics. A three-dimensional non-linear FE model of the lumbar spine (L3-sacrum) was developed and validated for pure moment bending. Disc degeneration and sequential ligament failure were modelled. Intersegmental range of motion (ROM) and bending stiffness were measured. The prediction of the FE model to moment loading in all three planes of bending showed very good agreement, where global and intersegmental ROM and bending stiffness of the model fell within one standard deviation of the in vitro results. Degeneration decreased ROM for all directions. Stiffness increased for all directions except axial rotation, where it initially increased then decreased for moderate and severe degeneration, respectively. Incremental ligament failure produced increased ROM and decreased stiffness. This effect was much more pronounced for all directions except lateral bending, which is minimally impacted by ligaments. These results indicate that lateral bending may be more apt to detect the subtle changes associated with degeneration, without being masked by associated changes of surrounding stabilizing structures.     

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.     

A light and electron microscopic study of spinal ligament innervation

The innervation of the posterior ligamentous structures of the human lumbar spine was studied by light microscopy, scanning electron microscopy and transmission electron microscopy. Three types of nerve endings were recognized: free nerve endings, Paciniform corpuscles and Ruffini corpuscles. The free nerve endings, which are thought to act as nociceptors, were found in the superficial layers of all ligaments. A few free nerve endings were also identified within the supraspinous and interspinous ligaments. The Paciniform corpuscles were predominantly found in the supraspinous ligament. The Ruffini corpuscles were located in the interspinous and flaval ligaments. These findings suggest that the posterior ligamentous structures could be involved in the spinal control system.     

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.     

Finite element model of the human neck during omni-directional impacts. Part II: relation between cervical curvature and risk of injury

A detailed 3D FE model of the human neck was used to assess a possible relationship between risk of injury and cervical spine curvature for various impacts. A FE model was previously developed, representing the head and neck of a 50th percentile human with a normal lordotic curvature. The model behaviour was omni-directionally validated for various impacts using published results. For the present study, the model was deformed in order to obtain a straight and a kyphotic curvature, and for each geometry, rear-end, frontal, lateral and oblique impact were simulated. Although results showed similar kinematic patterns, significant differences were found in the distribution and peak values of ligament elongations, forces and moments along the cervical spine for the three configurations. It was concluded that the variability observed on the curvature of the human cervical spine may have a significant influence both on the behaviour and on the risk of injury of the neck during impact.     

Finite element model of the human neck during omni-directional impacts. Part II: relation between cervical curvature and risk of injury

A detailed 3D FE model of the human neck was used to assess a possible relationship between risk of injury and cervical spine curvature for various impacts. A FE model was previously developed, representing the head and neck of a 50th percentile human with a normal lordotic curvature. The model behaviour was omni-directionally validated for various impacts using published results. For the present study, the model was deformed in order to obtain a straight and a kyphotic curvature, and for each geometry, rear-end, frontal, lateral and oblique impact were simulated. Although results showed similar kinematic patterns, significant differences were found in the distribution and peak values of ligament elongations, forces and moments along the cervical spine for the three configurations. It was concluded that the variability observed on the curvature of the human cervical spine may have a significant influence both on the behaviour and on the risk of injury of the neck during impact.     

Analysis of simulated single ligament transection on the mechanical behaviour of a lumbar functional spinal unit.

The influence of the different lumbar spinal ligaments on intersegmental rotation is not fully understood. In order to explore this effect, a finite element model of the functional spinal unit L3/L4 was loaded with pure moments in the three main anatomic planes. The two extremes--minimum and maximum--ligament stiffness values reported in the literature were applied. After virtual transection of each of the spinal ligaments in turn, the intersegmental rotation and forces in the remaining ligaments were calculated. On flexion, the highest force was found for the posterior longitudinal ligament; on extension and lateral bending for the anterior longitudinal ligament; and on axial rotation for the facet capsular ligament. The strongest influence on intersegmental rotation is exerted by the interspinous ligament on flexion, by the anterior longitudinal ligament on extension and lateral bending, and by the facet capsular ligaments on axial rotation. Ligament stiffness has a strong influence on intersegmental rotation and forces in the ligaments, so that finite element models of spinal segments must be validated by experimental data. This study should help to elucidate the role of the various ligaments.     

Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine

The objective of this investigation was to develop probabilistic finite element (FE) models of the anterior longitudinal ligament (ALL) and posterior longitudinal ligament (PLL) of the cervical spine that incorporate the natural variability of biological specimens. In addition to the model development, a rigorous validation methodology was developed to quantify model performance. Experimental data for the geometry and dynamic properties of the ALL and PLL were used to create probabilistic FE models capable of predicting not only the mean dynamic relaxation response but also the observed experimental variation of that response. The probabilistic FE model uses a quasilinear viscoelastic material constitutive model to capture the time-dependent behaviour of the ligaments. The probabilistic analysis approach yields a statistical distribution for the model-predicted response at each time point rather than a single deterministic quantity (e.g. ligament force) and that response can be statistically compared to experimental data for validation. A quantitative metric that compares the cumulative distribution functions of the experimental data and model response is computed for both the ALL and PLL throughout the time histories and is used to quantify model performance.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle

Many investigators have performed studies on specific defect situations or determined the contribution on isolated structures. Investigating the contribution of functional structures requires obtaining the kinematic response directly on spinal segments. The purpose of this study was to quantify the function of anatomical components on lumbar segments for different loading magnitudes. Eight spinal segments (L4-5) with a median age of 52 years (ranging from 38 to 59 years) and a low degree of disc degeneration were utilized for the in vitro testing. Specimens were mounted in a custom-built spine tester and loaded with pure moments (1-10 N m) to move within three anatomical planes at a loading rate of 1.0 degrees /s. Anatomy was successively reduced by: ligaments, facet capsules, joints and nucleus. Data were evaluated for range of motion, neutral zone and lordosis angle. Transection of posterior ligaments predominantly increased specimen flexion for all bending moments applied. Supraspinous ligament also indicated to resist in extension slightly, whereas the facet capsules did not. Facet joints contributed to axial rotation, but not in lateral bending. The anterior longitudinal ligament was found to slightly resist in axial rotation, but strongly in extension. Nucleotomy caused largest increase of all movements. The unloaded posture of the specimens changed after ligament dissection, indicating ligament pretension. The region of lumbar spine is interesting for finite element (FE) simulation due to the high evidence of disc degeneration and injuries. This study may help to understand the function of specific anatomical structures and assists in FE model calibration. We suggest to start a calibration procedure for such models with the smallest functional structure (annulus) and to cumulatively add further structures.     

Biomechanical comparison between fusion of two vertebrae and implantation of an artificial intervertebral disc

Surgical treatments for lower back pain can be distributed into two main groups: fusion (arthrodesis) and disc replacement (arthroplasty). The objective of this study was to compare, under severe loading conditions, the biomechanics of the lumbar spine treated either by fusion or total disc replacement (TDR). A three-dimensional model of a two-level ligamentous lumbar segment was created and simulated through static analyses with the finite-element method (FEM) software ABAQUS. The model was validated by comparing mobility, pressure on the facets, force in the ligaments, maximum stresses, disc bulge, and endplate deflection with measured data given in the literature. The FEM analysis predicted that the mobility of the model after arthrodesis on the upper level was reduced in all rotational degrees of freedom by an average of approximately 44%, relative to healthy normal discs. Conversely, the mobility of the model after TDR on the upper level was increased in all rotational degrees of freedom by an average of approximately 52%. The level implanted with the artificial disc showed excessive ligament tensions (greater than 500 N), high facet pressures (greater than 3 MPa), and a high risk of instability. The mobility and the stresses in the level adjacent to the arthroplasty were also increased. In conclusion, the model for an implanted movable artificial disc illustrated complications common to spinal arthroplasty and showed greater risk of instability and further degeneration than predicted for the fused model. This modeling technique provides an accurate means for assessing potential biomechanical risks and can be used to improve the design of future artificial intervertebral discs.     

Neuromuscular disorders associated with static lumbar flexion: a feline model.

Static flexion of the lumbar spine with constant load applied to the viscoelastic structures for 20 minutes and for 50 minutes resulted in development of spasms and inhibition in the multifidus muscles (e.g., deep erector spinae) and in creep of the supraspinous ligament in the feline model. The development of spasms and inhibition was not dependent on load magnitude. It is suggested that occupational and sports activities which require prolonged static lumbar flexion within the physiological range can cause a "sprain"-like injury to the ligaments, which in turn reflexively induce spasms and inhibition in some erector spinae muscles. Such disorder may take a long time to recover, in the order of days to weeks, depending on the level of creep developed in the tissues.     

A real-time computational model for estimating kinematics of ankle ligaments

Background: An accurate assessment of ankle ligament kinematics is crucial in understanding the injury mechanisms and can help to improve the treatment of an injured ankle, especially when used in conjunction with robot-assisted therapy. A number of computational models have been developed and validated for assessing the kinematics of ankle ligaments. However, few of them can do real-time assessment to allow for an input into robotic rehabilitation programs. Method: An ankle computational model was proposed and validated to quantify the kinematics of ankle ligaments as the foot moves in real-time. This model consists of three bone segments with three rotational degrees of freedom (DOFs) and 12 ankle ligaments. This model uses inputs for three position variables that can be measured from sensors in many ankle robotic devices that detect postures within the foot–ankle environment and outputs the kinematics of ankle ligaments. Validation of this model in terms of ligament length and strain was conducted by comparing it with published data on cadaver anatomy and magnetic resonance imaging. Results: The model based on ligament lengths and strains is in concurrence with those from the published studies but is sensitive to ligament attachment positions. Conclusions: This ankle computational model has the potential to be used in robot-assisted therapy for real-time assessment of ligament kinematics. The results provide information regarding the quantification of kinematics associated with ankle ligaments related to the disability level and can be used for optimizing the robotic training trajectory.     

Modelling the behaviour of ligaments: a technical note

Experimental observations suggest that during a ligament tensile strain test, water and glycosaminoglycans are exuded. Many attempts have been tried to model this behaviour using continuum mechanics. We have investigated this unique behaviour and have established three mechanisms which may contribute to the experimental observations: the slackness of the fibres before stretching can lead to a decrease in volume upon straightening; a Poisson's ratio higher than 0.5 from the axial to the lateral direction (as recorded in the literature [Hewitt, J., Guilak, F., Glisson, R. and Parker Vail, T. (2001) "Regional material properties of the human hip joint capsule ligaments", Journal of Orthopaedic Research 19(3), 359-364]) due to the very high level of anisotropy of the tissue; and an osmotic pressure, with a certain level of anisotropy, that causes the swelling of the tissue before loading [Thornton, G.M., Shrive, N.G. and Frank, C.B. (2001) "Altering ligament water content affects ligament pre-stress and creep behaviour", Journal of Orthopaedic Research 19(5), 845-851]. There may be other mechanisms that also contribute in the observed fluid exudation on tensile loading.