Morphological aspects and biomechanical properties of the vertebroaxial joint (C2-C3).

The C2-C3 intervertebral joint must be regarded as a transitional area situated between the upper cervical spine where most rotation of the neck and little flexion and extension occur and the lower cervical spaces where chiefly motion in the sagittal plane and also somewhat rotation take place. Under normal circumstances the range of flexion-extension reaches 11 degrees, slighter than below (19.5 degrees at C5-C6); on the opposite, the range of rotation attains 7 degrees; less than above but much more than below (0 degrees at C5-C6). The motion in the sagittal and coronal planes is relatively poor because of the location of Penning's motor-axis of C2 which runs far from the vertebral body and the lowness of the intervertebral disc. However, the rotation of C2 with respect to C3 is fair by the peculiar inclination of the articular facets which slope sagittally but also coronally and trace a sphere whereupon C2 may move around its motor-centre in any plane. When C2-C3 is surgically fixed by bone graft, the lack of motion is completed by a "compensatory movement" in the upper cervical spaces and especially at the atlantooccipital joint for flexion-extension. In the same way, C2-C3 may improve its mobility especially in the sagittal plane when the inferior partner is blocked by surgical or arthritic fusion.     

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.     

Moment arms of the human neck muscles in flexion, bending and rotation

There is a paucity of data available for the moment arms of the muscles of the human neck. The objective of the present study was to measure the moment arms of the major cervical spine muscles in vitro. Experiments were performed on five fresh-frozen human head-neck specimens using a custom-designed robotic spine testing apparatus. The testing apparatus replicated flexion-extension, lateral bending and axial rotation of each individual intervertebral joint in the cervical spine while all other joints were kept immobile. The tendon excursion method was used to measure the moment arms of 30 muscle sub-regions involving 13 major muscles of the neck about all three axes of rotation of each joint for the neutral position of the cervical spine. Significant differences in the moment arm were observed across sub-regions of individual muscles and across the intervertebral joints spanned by each muscle (p<0.05). Overall, muscle moment arms were larger in flexion-extension and lateral bending than in axial rotation, and most muscles had prominent moment arms in at least 2 out of the 3 joint motions investigated. This study emphasizes the importance of detailed representation of a muscle's architecture in prediction of its torque capacity about the individual joints of the cervical spine. The dataset produced may be useful in developing and validating computational models of the human neck.     

In vivo three-dimensional intervertebral kinematics of the subaxial cervical spine during seated axial rotation and lateral bending via a fluoroscopy-to-CT registration approach

Accurate measurement of the coupled intervertebral motions is helpful for understanding the etiology and diagnosis of relevant diseases, and for assessing the subsequent treatment. No study has reported the in vivo, dynamic and three-dimensional (3D) intervertebral motion of the cervical spine during active axial rotation (AR) and lateral bending (LB) in the sitting position. The current study fills the gap by measuring the coupled intervertebral motions of the subaxial cervical spine in ten asymptomatic young adults in an upright sitting position during active head LB and AR using a volumetric model-based 2D-to-3D registration method via biplane fluoroscopy. Subject-specific models of the individual vertebrae were derived from each subject’s CT data and were registered to the fluoroscopic images for determining the 3D poses of the subaxial vertebrae that were used to obtain the intervertebral kinematics. The averaged ranges of motion to one side (ROM) during AR at C3/C4, C4/C5, C5/C6, and C6/C7 were 4.2°, 4.6°, 3.0° and 1.3°, respectively. The corresponding values were 6.4°, 5.2°, 6.1° and 6.1° during LB. Intervertebral LB (ILB) played an important role in both AR and LB tasks of the cervical spine, experiencing greater ROM than intervertebral AR (IAR) (ratio of coupled motion (IAR/ILB): 0.23–0.75 in LB, 0.34–0.95 in AR). Compared to the AR task, the ranges of ILB during the LB task were significantly greater at C5/6 (p=0.008) and C6/7 (p=0.001) but the range of IAR was significantly smaller at C4/5 (p=0.02), leading to significantly smaller ratios of coupled motions at C4/5 (p=0.0013), C5/6 (p<0.001) and C6/7 (p=0.0037). The observed coupling characteristics of the intervertebral kinematics were different from those in previous studies under discrete static conditions in a supine position without weight-bearing, suggesting that the testing conditions likely affect the kinematics of the subaxial cervical spine. While C1 and C2 were not included owing to technical limitations, the current results nonetheless provide baseline data of the intervertebral motion of the subaxial cervical spine in asymptomatic young subjects under physiological conditions, which may be helpful for further investigations into spine biomechanics.     

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.     

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.     

Calculation of the instantaneous centre of rotation for a rigid body

The mathematical procedure presented is used for the calculation of the instantaneous centre of rotation for a rigid body based on kinematic measurement data. For every rotation angle interval observed an average centre of rotation is calculated by an appropriate optimizing calculation similar to data approximation by moving average. Practical applicability of this procedure has been proved by means of two planar and one three-dimensional test measurements of known movements (pure rotation, rolling motion and motion of a ball-and-socket joint.     

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.     

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.     

Validation of lumbar spine loading from a musculoskeletal model including the lower limbs and lumbar spine

Low back mechanics are important to quantify to study injury, pain and disability. As in vivo forces are difficult to measure directly, modeling approaches are commonly used to estimate these forces. Validation of model estimates is critical to gain confidence in modeling results across populations of interest, such as people with lower-limb amputation. Motion capture, ground reaction force and electromyographic data were collected from ten participants without an amputation (five male/five female) and five participants with a unilateral transtibial amputation (four male/one female) during trunk-pelvis range of motion trials in flexion/extension, lateral bending and axial rotation. A musculoskeletal model with a detailed lumbar spine and the legs including 294 muscles was used to predict L4-L5 loading and muscle activations using static optimization. Model estimates of L4-L5 intervertebral joint loading were compared to measured intradiscal pressures from the literature and muscle activations were compared to electromyographic signals. Model loading estimates were only significantly different from experimental measurements during trunk extension for males without an amputation and for people with an amputation, which may suggest a greater portion of L4-L5 axial load transfer through the facet joints, as facet loads are not captured by intradiscal pressure transducers. Pressure estimates between the model and previous work were not significantly different for flexion, lateral bending or axial rotation. Timing of model-estimated muscle activations compared well with electromyographic activity of the lumbar paraspinals and upper erector spinae. Validated estimates of low back loading can increase the applicability of musculoskeletal models to clinical diagnosis and treatment.     

Moiré patterns: an accurate technique for determination of the locus of the centres of rotation

This study describes an accurate technique for the determination of the centre of rotation of small angles. The moiré fringe method localizes the centre of rotation by defining two primary fringes, each of which is found by the intersection of three lines. The primary fringes intersect at the centre of rotation at 90 degrees to each other, the angle least likely to produce an error in measurement. By utilizing joints with known centres of rotation, we have found that the method is extremely accurate and reproducible to within 2 mm of the real centre for angular changes as small as 3 degrees. This technique is useful in evaluating whether a joint is a simple hinge, i.e. rotating about a single axis of rotation or whether the joint moves about a changing axis of rotation referred to as a locus or centrode.     

A videofluoroscopy-based tracking algorithm for quantifying the time course of human intervertebral displacements

The motions of individual intervertebral joints can affect spine motion, injury risk, deterioration, pain, treatment strategies, and clinical outcomes. Since standard kinematic methods do not provide precise time-course details about individual vertebrae and intervertebral motions, information that could be useful for scientific advancement and clinical assessment, we developed an iterative template matching algorithm to obtain this data from videofluoroscopy images. To assess the bias of our approach, vertebrae in an intact porcine spine were tracked and compared to the motions of high-contrast markers. To estimate precision under clinical conditions, motions of three human cervical spines were tracked independently ten times and vertebral and intervertebral motions associated with individual trials were compared to corresponding averages. Both tests produced errors in intervertebral angular and shear displacements no greater than 0.4° and 0.055 mm, respectively. When applied to two patient cases, aberrant intervertebral motions in the cervical spine were typically found to correlate with patient-specific anatomical features such as disc height loss and osteophytes. The case studies suggest that intervertebral kinematic time-course data could have value in clinical assessments, lead to broader understanding of how specific anatomical features influence joint motions, and in due course inform clinical treatments.     

Applying a follower load delivers realistic results for simulating standing

The exact loads acting on the lumbar spine during standing remain hitherto unknown. It is for this reason that different loads are applied in experimental and numerical studies. The aim of this study was to compare intersegmental rotations, intradiscal pressures and facet joint forces for different loading modes simulating standing in order to ascertain, the results for which loading modes are closest to data measured in vivo.A validated osseoligamentous finite element model of the lumbar spine ranging from L1 to the disc L5–S1, was used. Six load application modes were investigated as to how they could simulate standing. This posture was simulated by applying a vertical force of 500 N at the centre of the L1 vertebral endplate with different boundary conditions, by applying a follower load, and by applying upper body weight and muscle forces. The calculated intersegmental rotations and intradiscal pressures were compared to in vivo values.Intersegmental rotations at one level vary by up to 8° for the different loading modes simulating standing. The overall rotation in the lumbar spine varies between 2.2° and 19.5°. With a follower load, the difference to the value measured in vivo is 3.3°. For all other loading cases studied, the difference is greater than 6.6°. Intradiscal pressures vary slightly with the loading mode. Calculated forces in the facet joints vary between 0 and nearly 80 N.Applying a follower load of 500 N is the only loading mode simulating standing for which the calculated values for intervertebral rotations and intradiscal pressures agreed well with in vivo data from literature.     

Artificial Cervical Vertebra and Intervertebral Complex Replacement through the Anterior Approach in Animal Model: A Biomechanical and In Vivo Evaluation of a Successful Goat Model

This was an in vitro and in vivo study to develop a novel artificial cervical vertebra and intervertebral complex (ACVC) joint in a goat model to provide a new method for treating degenerative disc disease in the cervical spine. The objectives of this study were to test the safety, validity, and effectiveness of ACVC by goat model and to provide preclinical data for a clinical trial in humans in future. We designed the ACVC based on the radiological and anatomical data on goat and human cervical spines, established an animal model by implanting the ACVC into goat cervical spines in vitro prior to in vivo implantation through the anterior approach, and evaluated clinical, radiological, biomechanical parameters after implantation. The X-ray radiological data revealed similarities between goat and human intervertebral angles at the levels of C2-3, C3-4, and C4-5, and between goat and human lordosis angles at the levels of C3-4 and C4-5. In the in vivo implantation, the goats successfully endured the entire experimental procedure and recovered well after the surgery. The radiological results showed that there was no dislocation of the ACVC and that the ACVC successfully restored the intervertebral disc height after the surgery. The biomechanical data showed that there was no significant difference in range of motion (ROM) or neural zone (NZ) between the control group and the ACVC group in flexion-extension and lateral bending before or after the fatigue test. The ROM and NZ of the ACVC group were greater than those of the control group for rotation. In conclusion, the goat provides an excellent animal model for the biomechanical study of the cervical spine. The ACVC is able to provide instant stability after surgery and to preserve normal motion in the cervical spine.     

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.     

Effect of arm swinging on lumbar spine and hip joint forces

During level walking, arm swing plays a key role in improving dynamic stability. In vivo investigations with a telemeterized vertebral body replacement showed that spinal loads can be affected by differences in arm positions during sitting and standing. However, little is known about how arm swing could influence the lumbar spine and hip joint forces and motions during walking. The present study aims to provide better understanding of the contribution of the upper limbs to human gait, investigating ranges of motion and joint reaction forces.A three-dimensional motion analysis was carried out via a motion capturing system on six healthy males and five patients with hip instrumented implant. Each subject performed walking with different arm swing amplitudes (small, normal, and large) and arm positions (bound to the body, and folded across the chest). The motion data were imported in a commercial musculoskeletal analysis software for kinematic and inverse dynamic investigation.The range of motion of the thorax with respect to the pelvis and of the pelvis with respect to the ground in the transversal plane were significantly associated with arm position and swing amplitude during gait. The hip external-internal rotation range of motion statistically varied only for non-dominant limb. Unlike hip joint reaction forces, predicted peak spinal loads at T12-L1 and L5-S1 showed significant differences at approximately the time of contralateral toe off and contralateral heel strike.Therefore, arm position and swing amplitude have a relevant effect on kinematic variables and spinal loads, but not on hip loads during walking.     

Distributed Body Weight Over the Whole Spine for Improved Inference in Spine Modelling

Numerous models used to investigate the causes of low back pain are based upon the concept of the lever model that considers equilibrium of forces and moments about a single intervertebral joint. Consideration of forces and moments at each intervertebral joint is essential if a more realistic idea of the loading on the spine is to be obtained. This will also allow the role of the curvature of the spine to be investigated. A distributed loading pattern for forces due to body weight for the whole spine has not been investigated before. In this paper, a distributed loading pattern for the whole spine for various postures is investigated and the potential impact on the calculations is discussed.     

The SCoRE residual: a quality index to assess the accuracy of joint estimations

The determination of an accurate centre of rotation (CoR) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. Despite the many functional approaches to estimate CoRs, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. The purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (SCoRE) as a reliable indirect measure of the error of the computed joint centre. To evaluate the SCoRE residual, numerical simulations were performed to evaluate CoR estimations at different ranges of joint motion. A statistical model was developed and used to determine the theoretical relationships among the SCoRE residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the CoR estimations to the known centre of rotation. We found that the equation err=0.5r(s) provides a reliable relationship among the CoR error, err, and the scaled SCoRE residual, r(s), providing that any skin marker artefact is first minimised using the optimal common shape technique (OCST). Measurements on six healthy volunteers showed a reduction of SCoRE residual from 11 to below 6mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. This study also demonstrates the significant benefit of the OCST for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. For the first time, this understanding of the SCoRE residual allows a measure of error in the non-invasive assessment of joint centres. This measure now enables a rapid assessment of the accuracy of the CoR as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.