A method for the intravital measurement of interspinous kinematics.

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of +/- 4 degrees rotation and +/- 4 mm translation determined the absolute maximum errors to be 0.2 degree and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1 degrees and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.     

Mandibular kinematics represented by a non-orthogonal floating axis joint coordinate system

There are many methods used to represent joint kinematics (e.g., roll, pitch, and yaw angles; instantaneous center of rotation; kinematic center; helical axis). Often in biomechanics internal landmarks are inferred from external landmarks. This study represents mandibular kinematics using a non-orthogonal floating axis joint coordinate system based on 3-D geometric models with parameters that are "clinician friendly" and mathematically rigorous. Kinematics data for two controls were acquired from passive fiducial markers attached to a custom dental clutch. The geometric models were constructed from MRI data. The superior point along the arc of the long axis of the condyle was used to define the coordinate axes. The kinematic data and geometric models were registered through fiducial markers visible during both protocols. The mean absolute maxima across the subjects for sagittal rotation, coronal rotation, axial rotation, medial-lateral translation, anterior-posterior translation, and inferior-superior translation were 34.10 degrees, 1.82 degrees, 1.14 degrees, 2.31, 21.07, and 6.95 mm, respectively. All the parameters, except for one subject's axial rotation, were reproducible across two motion recording sessions. There was a linear correlation between sagittal rotation and translation, the dominant motion plane, with approximately 1.5 degrees of rotation per millimeter of translation. The novel approach of combining the floating axis system with geometric models succinctly described mandibular kinematics with reproducible and clinician friendly parameters.     

Spinal shape changes resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation

This paper reports the changes in spinal shape resulting from scoliotic spine surgical instrumentation expressed as intervertebral rotations and centers of rotation. The objective is to test the hypothesis that the type of spinal instrumentation system (Cotrel-Dubousset versus Colorado) does not influence these motion parameters. Intervertebral rotations and centers of rotation of the scoliotic spines were computed from the pre- and post-operative radiographs of 82 patients undergoing spinal correction. The three-dimensional (3D) reconstruction of six anatomical landmarks was achieved for each of the thoracic and lumbar vertebrae. A least-squares approach based on singular value decomposition was used to calculate the rigid body transformation parameters. Average centers of rotation for all intervertebral levels are located in the neural canal at the mid-sagittal plane and approximately at the superior endplate level of the inferior vertebra. Intervertebral rotations have components in all planes: 6.7 degrees (frontal), 5.5 degrees (sagittal) and 4.5 degrees (transverse) RMS for all intervertebral levels. Nearly all intervertebral rotations and centers of rotation are not significantly different for the two instrumentation systems. Various intervertebral rotations and 3D reconstruction errors were simulated on a theoretical model of a lumbar functional unit to assess the proposed method. Intervertebral rotation errors were 1.7 degrees when simulating 3D errors of 3mm on the position of the landmarks. Maximum errors for the position of centers of rotation were below 1cm in the case of intervertebral rotations larger than 2.5 degrees (most cases), but were larger (38 mm) for small intervertebral rotations (<1 degrees ). The type of instrumentation system did not influence intervertebral rotations and centers of rotation. These results provide valuable data for the development and validation of simulation models for surgical instrumentation of idiopathic scoliosis.     

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.     

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.     

The sit-up: complex kinematics and muscle activity in voluntary axial movement.

This paper describes the kinematics and muscle activity associated with the standard sit-up, as a first step in the investigation of complex motor coordination. Eight normal human subjects lay on a force table and performed at least 15 sit-ups, with the arms across the chest and the legs straight and unconstrained. Several subjects also performed sit-ups with an additional weight added to the head. Support surface forces were recorded to calculate the location of the center of pressure and center of gravity; conventional motion analysis was used to measure segmental positions; and surface EMG was recorded from eight muscles. While the sit-up consists of two serial components, 'trunk curling' and 'footward pelvic rotation', it can be further subdivided into five phases, based on the kinematics. Phases I and II comprise trunk curling. Phase I consists of neck and upper trunk flexion, and phase II consists of lumbar trunk lifting. Phase II corresponds to the point of peak muscle contraction and maximum postural instability, the 'critical point' of the sit-up. Phases III-V comprise footward pelvic rotation. Phase III begins with pelvic rotation towards the feet, phase IV with leg lowering, and phase V with contact between the legs and the support surface. The overall pattern of muscle activity was complex with times of EMG onset, peak activity, offset, and duration differing for different muscles. This complex pattern changed qualitatively from one phase to the next, suggesting that the roles of different muscles and, as a consequence, the overall form of coordination, change during the sit-up.     

The micromechanical role of the annulus fibrosus components under physiological loading of the lumbar spine

To date, studies that have investigated the kinematics of spinal motion segments have largely focused on the contributions that the spinal ligaments play in the resultant motion patterns. However, the specific roles played by intervertebral disk components, in particular the annulus fibrosus, with respect to global motion is not well understood in spite of the relatively large literature base with respect to the local ex vivo mechanical properties of the tissue. The primary objective of this study was to implement the nonlinear and orthotropic mechanical behavior of the annulus fibrosus in a finite element model of an L4/L5 functional spinal unit in the form of a strain energy potential where the individual mechanical contributions of the ground substance and fibers were explicitly defined. The model was validated biomechanically under pure moment loading to ensure that the individual role of each soft tissue structure during load bearing was consistent throughout the physiologically relevant loading range. The fibrous network of the annulus was found to play critical roles in limiting the magnitude of the neutral zone and determining the stiffness of the elastic zone. Under flexion, lateral bending, and axial rotation, the collagen fibers were observed to bear the majority of the load applied to the annulus fibrosus, especially in radially peripheral regions where disk bulging occurred. For the first time, our data explicitly demonstrate that the exact fiber recruitment sequence is critically important for establishing the range of motion and neutral zone magnitudes of lumbar spinal motion segments.     

Moderately degenerated lumbar motion segments: Are they truly unstable?

The two main load bearing tissues of the intervertebral disc are the nucleus pulposus and the annulus fibrosus. Both tissues are composed of the same basic components, but differ in their organization and relative amounts. With degeneration, the clear distinction between the two tissues disappears. The changes in biochemical content lead to changes in mechanical behaviour of the intervertebral disc. The aim of the current study was to investigate if well-documented moderate degeneration at the biochemical and fibre structure level leads to instability of the lumbar spine. By taking into account biochemical and ultrastructural changes to the extracellular matrix of degenerating discs, a set of constitutive material parameters were determined that described the individual tissue behaviour. These tissue biomechanical models were then used to simulate dynamic behaviour of the degenerated spinal motion segment, which showed instability in axial rotation, while a stabilizing effect in the other two principle bending directions. When a shear load was applied to the degenerated spinal motion segment, no sign of instability was found. This study found that reported changes to the nucleus pulposus and annulus fibrosus matrix during moderate degeneration lead to a more stable spinal motion segment and that such biomechanical considerations should be incorporated into the general pathophysiological understanding of disc degeneration and how its progress could affect low back pain and its treatments thereof.     

Computation of trunk equilibrium and stability in free flexion-extension movements at different velocities

Velocity of movement has been suggested as a risk factor for low-back disorders. The effect of changes in velocity during unconstrained flexion-extension movements on muscle activations, spinal loads, base reaction forces and system stability was computed. In vivo measurements of kinematics and ground reaction forces were initially carried out on young asymptomatic subjects. The collected kinematics of three subjects representing maximum, mean and minimum lumbar rotations were subsequently used in the kinematics-driven model to compute results during the entire movements at three different velocities. Estimated spinal loads and muscle forces were significantly larger in fastest pace as compared to slower ones indicating the effect of inertial forces. Spinal stability was improved in larger trunk flexion angles and fastest movement. Partial or full flexion relaxation of global extensor muscles occurred only in slower movements. Some local lumbar muscles, especially in subjects with larger lumbar flexion and at slower paces, also demonstrated flexion relaxation. Results confirmed the crucial role of movement velocity on spinal biomechanics. Predictions also demonstrated the important role on response of the magnitude of peak lumbar rotation and its temporal variation.     

Spinal constraint modulates head instantaneous center of rotation and dictates head angular motion

The head is kinematically constrained to the torso through the spine and thus, the spine dictates the amount of output head angular motion expected from an input impact. Here, we investigate the spinal kinematic constraint by analyzing the head instantaneous center of rotation (HICOR) with respect to the torso in head/neck sagittal extension and coronal lateral flexion during mild loads applied to 10 subjects. We found the mean HICOR location was near the C5-C6 intervertebral joint in sagittal extension, and T2-T3 intervertebral joint in coronal lateral flexion. Using the impulse-momentum relationship normalized by subject mass and neck length, we developed a non-dimensional analytical ratio between output angular velocity and input linear impulse as a function of HICOR location. The ratio was 0.65 and 0.50 in sagittal extension and coronal lateral flexion respectively, implying 30% greater angular velocities in sagittal extension given an equivalent impulse. Scaling to subject physiology also predicts larger required impulses given greater subject mass and neck length to achieve equivalent angular velocities, which was observed experimentally. Furthermore, the HICOR has greater motion in sagittal extension than coronal lateral flexion, suggesting the head and spine can be represented with a single inverted pendulum in coronal lateral flexion, but requires a more complex representation in sagittal extension. The upper cervical spine has substantial compliance in sagittal extension, and may be responsible for the complex motion and greater extension angular velocities. In analyzing the HICOR, we can gain intuition regarding the neck’s role in dictating head motion during external loading.     

Quantifying the centre of rotation pattern in a multi-body model of the lumbar spine

Understanding the kinematics of the spine provides paramount knowledge for many aspects of the clinical analysis of back pain. More specifically, visualisation of the instantaneous centre of rotation (ICR) enables clinicians to quantify joint laxity in the segments, avoiding a dependence on more inconclusive measurements based on the range of motion and excessive translations, which vary in every individual. Alternatively, it provides motion preserving designers with an insight into where a physiological ICR of a motion preserving prosthesis can be situated in order to restore proper load distribution across the passive and active elements of the lumbar region. Prior to the use of an unconstrained dynamic musculoskeletal model system, based on multi-body models capable of transient analysis, to estimate segmental loads, the model must be kinematically evaluated for all possible sensitivity due to ligament properties and the initial locus of intervertebral disc (IVD). A previously calibrated osseoligamentous model of lumbar spine was used to evaluate the changes in ICR under variation of the ligament stiffness and initial locus of IVD, when subjected to pure moments from 0 to 15 Nm. The ICR was quantified based on the closed solution of unit quaternion that improves accuracy and prevents coordinate singularities, which is often observed in Euler-based methods and least squares principles. The calculation of the ICR during flexion/extension revealed complexity and intrinsic nonlinearity between flexion and extension. This study revealed that, to accommodate a good agreement between in vitro data and the multi-body model predictions, in flexion more laxity is required than in extension. The results showed that the ICR location is concentrated in the posterior region of the disc, in agreement with previous experimental studies. However, the current multi-body model demonstrates a sensitivity to the initial definition of the ICR, which should be recognised as a limitation of the method. Nevertheless, the current simulations suggest that, due to the constantly evolving path of the ICR across the IVD during flexion–extension, a movable ICR is a necessary condition in multi-body modelling of the spine, in the context of whole body simulation, to accurately capture segmental kinematics and kinetics.     

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.     

Validation of single-segment and three-segment spinal models used to represent lumbar flexion

Changes in spinal posture between the erect and flexed positions were calculated using angular measurements from lateral photographs and radiographs of ten adult male subjects. For photographic measurements, the thoracolumbar vertebral column was modelled as either a single segment or as three segments. In the three-segment model, there was a non-significant correlation between the decrease in lumbar concavity and intervertebral motion. In addition, there was a non-significant negative correlation between the increase in thoracic convexity and lumbar motion determined radiographically. In the single-segment model, the decrease in angulation between the thoracolumbar spine and pelvis was a good representation of lumbar spine flexion as determined by the mean lumbar intervertebral angular change. Therefore, modelling the thoracolumbar vertebral column as a single segment allowed better estimation of lumbar intervertebral angular change during flexion than a three-segment model. The results indicate that large range dynamic motion of the lumbar vertebral column can be represented using photographic analysis of the positions of three easily identified anatomical landmarks: the anterior superior iliac spine, posterior superior iliac spine and the spinous process of the first thoracic vertebra.     

Between-session reliability of opto-electronic motion capture in measuring sagittal posture and 3-D ranges of motion of the thoracolumbar spine

This study evaluated between-session reliability of opto-electronic motion capture to measure trunk posture and three-dimensional ranges of motion (ROM). Nineteen healthy participants aged 24–74 years underwent spine curvature, pelvic tilt and trunk ROM measurements on two separate occasions. Rigid four-marker clusters were attached to the skin overlying seven spinous processes, plus single markers on pelvis landmarks. Rigid body rotations of spine marker clusters were calculated to determine neutral posture and ROM in flexion, extension, total lateral bending (left-right) and total axial rotation (left-right). Segmental spine ROM values were in line with previous reports using opto-electronic motion capture. Intraclass correlation coefficients (ICC) and standard error of measurement (SEM) were calculated as measures of between-session reliability and measurement error, respectively. Retroreflective markers showed fair to excellent between-session reliability to measure thoracic kyphosis, lumbar lordosis, and pelvic tilt (ICC = 0.82, 0.63, and 0.54, respectively). Thoracic and lumbar segments showed highest reliabilities in total axial rotation (ICC = 0.78) and flexion-extension (ICC = 0.77–0.79) ROM, respectively. Pelvic segment showed highest ICC values in flexion (ICC = 0.78) and total axial rotation (ICC = 0.81) trials. Furthermore, it was estimated that four or fewer repeated trials would provide good reliability for key ROM outcomes, including lumbar flexion, thoracic and lumbar lateral bending, and thoracic axial rotation. This demonstration of reliability is a necessary precursor to quantifying spine kinematics in clinical studies, including assessing changes due to clinical treatment or disease progression.     

Stepwise reduction of functional spinal structures increase vertebral translation and intradiscal pressure

To date, there are only a few studies that provide data to efficiently calibrate finite element models for the spine due to its complexity. In a recent study, we quantified the range of motion rotation and the lordosis angle. This paper provides complementary results regarding two more parameters, intradiscal pressure and vertebral translation. All parameters were obtained as a function of stepwise anatomical reduction, loading direction and magnitude. Eight lumbar spinal segments (L4-5) with a median age of 52 years (38-59 years) and no signs of disc degeneration were used for the in vitro testing. A miniaturized pressure probe was implanted into the nucleus. An ultrasound-based motion-tracking system was employed to record spatial movements of several landmarks on the specimens. The center of L4, the anterior, posterior, left and right point of the lower endplate of L4 were digitized as landmarks and its translation was determined. Specimens were loaded with pure moments (1-10Nm) in the three principal anatomical planes at a loading rate of 1.0 degrees /s. Anatomy was stepwise reduced by cutting different ligaments, facet capsules and joints and removing nucleus. Translation analysis showed that the L4 center point had its largest displacement in sagittal direction and almost none vertically. Removal of the supra- and interspinous, flaval ligaments showed a slight increase and further removal of structures, a higher increase of translation. Axial rotation also was accompanied with L4 to elevate when torsion was applied. This effect was found to be larger with progressing defects. Nucleotomy exhibited the most unstable situation for specimens. Results of the intradiscal pressure indicated a large increase after removing the facet capsules and joints. Furthermore, it was found that intradiscal pressure correlated well with data of range of motion for rotation. Predicting and simulating clinical defects, surgical intervention or treatment methods requires a well performed calibration based on in vitro data, whereas it is important to adapt all including structures with as many known parameters as possible. Results provided by these studies may be used as a database for researchers aiming to calibrate or validate finite element models of L4-5 segments.     

The role of the nucleus pulposus in neutral zone human lumbar intervertebral disc mechanics

To study the effect of denucleation on the mechanical behavior of the human lumbar intervertebral disc through a 2mm incision, two groups of six human cadaver lumbar spinal units were tested in axial compression, axial rotation, lateral bending and flexion/extension after incremental steps of "partial" denucleation. Neutral zone, range of motion, stiffness, intradiscal pressure and energy dissipation were measured; the results showed that the contribution of the nucleus pulposus to the mechanical behavior of the intervertebral disc was more dominant through the neutral zone than at the farther limits of applied loads and moments.     

Using Skin Markers for Spinal Curvature Quantification in Main Thoracic Adolescent Idiopathic Scoliosis: An Explorative Radiographic Study

Background and Purpose

Although the relevance of understanding spinal kinematics during functional activities in patients with complex spinal deformities is undisputed among researchers and clinicians, evidence using skin marker-based motion capture systems is still limited to a handful of studies, mostly conducted on healthy subjects and using non-validated marker configurations. The current study therefore aimed to explore the validity of a previously developed enhanced trunk marker set for the static measurement of spinal curvature angles in patients with main thoracic adolescent idiopathic scoliosis. In addition, the impact of inaccurate marker placement on curvature angle calculation was investigated.

Methods

Ten patients (Cobb angle: 44.4±17.7 degrees) were equipped with radio-opaque markers on selected spinous processes and underwent a standard biplanar radiographic examination. Subsequently, radio-opaque markers were replaced with retro-reflective markers and the patients were measured statically using a Vicon motion capture system. Thoracolumbar / lumbar and thoracic curvature angles in the sagittal and frontal planes were calculated based on the centers of area of the vertebral bodies and radio-opaque markers as well as the three-dimensional position of the retro-reflective markers. To investigate curvature angle estimation accuracy, linear regression analyses among the respective parameters were used. The impact of inaccurate marker placement was explored using linear regression analyses among the radio-opaque marker- and spinous process-derived curvature angles.

Results and Discussion

The results demonstrate that curvatures angles in the sagittal plane can be measured with reasonable accuracy, whereas in the frontal plane, angles were systematically underestimated, mainly due to the positional and structural deformities of the scoliotic vertebrae. Inaccuracy of marker placement had a greater impact on thoracolumbar / lumbar than thoracic curvature angles. It is suggested that spinal curvature measurements are included in marker-based clinical gait analysis protocols in order to enable a deeper understanding of the biomechanical behavior of the healthy and pathological spine in dynamic situations as well as to comprehensively evaluate treatment effects.     

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.     

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.