Finite element analysis of moment-rotation relationships for human cervical spine

A comprehensive, geometrically accurate, nonlinear C0-C7 FE model of head and cervical spine based on the actual geometry of a human cadaver specimen was developed. The motions of each cervical vertebral level under pure moment loading of 1.0 Nm applied incrementally on the skull to simulate the movements of the head and cervical spine under flexion, tension, axial rotation and lateral bending with the inferior surface of the C7 vertebral body fully constrained were analysed. The predicted range of motion (ROM) for each motion segment were computed and compared with published experimental data. The model predicted the nonlinear moment-rotation relationship of human cervical spine. Under the same loading magnitude, the model predicted the largest rotation in extension, followed by flexion and axial rotation, and least ROM in lateral bending. The upper cervical spines are more flexible than the lower cervical levels. The motions of the two uppermost motion segments account for half (or even higher) of the whole cervical spine motion under rotational loadings. The differences in the ROMs among the lower cervical spines (C3-C7) were relatively small. The FE predicted segmental motions effectively reflect the behavior of human cervical spine and were in agreement with the experimental data. The C0-C7 FE model offers potentials for biomedical and injury studies.     

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

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

Moment-rotation relationships of the ligamentous occipito-atlanto-axial complex

The relationships between applied pure moments at the occiput (C0) and the resulting rotations at the atlanto-occipital (C0-C1) and atlanto-axial (C1-C2) joints are quantified. In axial twist, with a moment of 0.3 Nm, a mean rotation of about 2.5 degrees and 23.3 degrees was observed at C0-C1 and C1-C2 units respectively. Both the atlas and axis contributed to produce lateral bending motion. The ratio between extension and flexion rotations at C0-C1 was 2.5:1. Lateral bending and axial rotations were strongly coupled to each other. The occipito-atlanto-axial complex exhibited a large 'neutral zone' compared to lower cervical spine segments. The likely clinical significance of these findings are discussed.     

Load-displacement properties of lower cervical spine motion segments

The load-displacement behavior of 35 fresh adult cervical spine motion segments was measured in compression, shear, flexion, extension, lateral bending and axial torsion tests. Motion segments were tested both intact and with posterior elements removed. Applied forces ranged to 73.6 N in compression and to 39 N in shear, while applied moments ranged to 2.16 Nm. For each mode of loading, principal and coupled motions were measured and stiffnesses were calculated. The effect of disc degeneration on motion segment stiffnesses and the moments required for motion segment failure were also measured. In compression, the stiffnesses of the cervical motion segments were similar to those of thoracic and lumbar motion segments. In other modes of loading, cervical stiffnesses were considerably smaller than thoracic or lumbar stiffnesses. Removal of the posterior elements decreased cervical motion segment stiffnesses by as much as 50%. Degenerated cervical discs were less stiff in compression and stiffer in shear than less degenerated discs, but in bending or axial torsion, no statistically significant differences were evident. Bending moments causing failure were an order of magnitude lower than those for lumbar segments.     

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

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

Parametric and subject-specific finite element modelling of the lower cervical spine. Influence of geometrical parameters on the motion patterns

Morphometrical and postural features of the cervical spine are supposed to significantly influence its biomechanical behaviour. However, the effects of these geometrical parameters are quite difficult to evaluate. An original numerical method is proposed in order to automatically generate parametric and subject-specific meshes of the lower cervical spine. Sixteen finite element models have been built from cadaver specimens using low dose biplanar X-rays. All the generated meshes fulfilled the quality criteria. A preliminary evaluation was performed on the C5–C6 functional units using a database of previous experimental tests. The principal and coupled motions were simulated. The responses of the numerical models were within the experimental standard deviation corridors in most cases. Rotation–moment relationships were then compared to assess the influence of geometry on the mechanical response. Geometry was found to play a significant role in the motion patterns.     

Mechanically simulated muscle forces strongly stabilize intact and injured upper cervical spine specimens

Although muscles are assumed to be capable of stabilizing the spinal column in vivo, they have only rarely been simulated in vitro. Their effect might be of particular importance in unstable segments. The present study therefore tests the hypothesis that mechanically simulated muscle forces stabilize intact and injured cervical spine specimens. In the first step, six human occipito-cervical spine specimens were loaded intact in a spine tester with pure moments in lateral bending (+/- 1.5 N m), flexion-extension (+/- 1.5 N m) and axial rotation (+/- 0.5 N m). In the second step, identical flexibility tests were carried out during constant traction of three mechanically simulated muscle pairs: splenius capitits (5 N), semispinalis capitis (5 N) and longus colli (15 N). Both steps were repeated after unilateral and bilateral transection of the alar ligaments. The muscle forces strongly stabilized C0-C2 in all loading and injury states. This was most obvious in axial rotation, where a reduction of range of motion (ROM) and neutral zone to <50% (without muscles=100%) was observed. With increasing injury the normalized ROM (intact condition=100%) increased with and without muscles approximately to the same extend. With bilateral injury this increase was 125-132% in lateral bending, 112%-119% in flexion-extension and 103-116% in axial rotation. Mechanically simulated cervical spine muscles strongly stabilized intact and injured cervical spine specimens. Nevertheless, it could be shown that in vitro flexibility tests without muscle force simulation do not necessarily lead to an overestimation of spinal instability if the results are normalized to the intact state.     

Development and validation of a CO-C7 FE complex for biomechanical study

In this study, the digitized geometrical data of the embalmed skull and vertebrae (C0-C7) of a 68-year old male cadaver were processed to develop a comprehensive, geometrically accurate, nonlinear C0-C7 FE model. The biomechanical response of human neck under physiological static loadings, near vertex drop impact and rear-end impact (whiplash) conditions were investigated and compared with published experimental results. Under static loading conditions, the predicted moment-rotation relationships of each motion segment under moments in midsagittal plane and horizontal plane agreed well with experimental data. In addition, the respective predicted head impact force history and the S-shaped kinematics responses of head-neck complex under near-vertex drop impact and rear-end conditions were close to those observed in reported experiments. Although the predicted responses of the head-neck complex under any specific condition cannot perfectly match the experimental observations, the model reasonably reflected the rotation distributions among the motion segments under static moments and basic responses of head and neck under dynamic loadings. The current model may offer potentials to effectively reflect the behavior of human cervical spine suitable for further biomechanics and traumatic studies.     

Evaluation of the intervertebral neck injury criterion using simulated rear impacts

The Intervertebral Neck Injury Criterion (IV-NIC) is based on the hypothesis that intervertebral motion beyond the physiological limit may injure spinal soft tissues during whiplash, while the Neck Injury Criterion (NIC) hypothesizes that sudden changes in spinal fluid pressure may cause neural injury. Goals of the present study, using a biofidelic whole cervical spine model with muscle force replication, were to correlate IV-NIC with soft-tissue injury, determine the IV-NIC injury threshold, and compare IV-NIC and NIC. Using a bench-top apparatus, rear-impacts were simulated at 3.5, 5, 6.5, and 8 g horizontal accelerations of the T1 vertebra. Pre- and post-whiplash flexibility tests measured the soft tissue injury threshold, i.e. significant increases in the intervertebral neutral zone (NZ) or range of motion (ROM) above corresponding baseline values. Extension IV-NIC peaks correlated well with NZ and ROM increases at C0-C1 and at C3-C4 through C7-T1 (r=0.64 and 0.62 respectively, p<0.001). Average IV-NIC injury thresholds (95% confidence limits) varied among the intervertebral levels and ranged between 1.5 (1.1, 1.9) at C5-C6 and 3.4 (2.4, 4.4) at C7-T1. The NIC injury threshold was 8.7 (7.7, 9.7) m2/s2, substantially less than the proposed threshold of 15 m2/s2. Results support the use of IV-NIC for determining the cervical spine injury threshold and injury severity. Advantages of IV-NIC include the ability to predict the intervertebral level, mode, severity, and time of the cervical spine soft-tissue injury.     

CINERADIOGRAPHIC STUDIES OF THE NORMAL CERVICAL SPINE

By considering the cervical spine as several segments with relatively different motions, an understanding of the total possible motions of the cervical spine can be more easily attained.Reversal of the cervical lordosis is a normal part of the flexion action and can result from positioning of the patient for radiographic studies.The effect of standing or sitting postures, and methods of initiating flexion of the neck should be considered in the evaluation of routine flexion and extension studies.Evaluation of individual cervical segments may be accomplished by the use of different methods of initiating flexion.     

Response of a human head/neck/upper-torso replica to dynamic loading--II. Analytical/numerical model

A three-dimensional lumped-parameter model of the human head/neck/upper-torso was developed to predict its motion for any specified initial conditions and that could also be used to compare with the results of other investigators. This model consists of ten rigid bodies representing the head, cervical vertebrae C1-C7, T1 and T2 combined with the rest of the torso. These rigid bodies were connected by intervertebral joints described by a stiffness matrix relating the force (moment) and translation (rotation). Fifteen pairs of muscles were incorporated in the model, represented by three-point linear elements with nonlinear constitutive relationships obtained from cadaver test results. The calculated response compared favorably with human volunteer data for both flexion and lateral whiplash. However, tests on an inanimate replica of a human indicated greater flexibility than predicted by the corresponding numerical model. The difference is believed to be due to insufficient mass of the muscles incorporated in the structure.     

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.     

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.     

The effect of follower load on the intersegmental coupled motion characteristics of the human thoracic spine: An in vitro study using entire rib cage specimens

The mechanical coupling behaviour of the thoracic spine is still not fully understood. For the validation of numerical models of the thoracic spine, however, the coupled motions within the single spinal segments are of importance to achieve high model accuracy. In the present study, eight fresh frozen human thoracic spinal specimens (C7-L1, mean age 54 ± 6 years) including the intact rib cage were loaded with pure bending moments of 5 Nm in flexion/extension (FE), lateral bending (LB), and axial rotation (AR) with and without a follower load of 400 N. During loading, the relative motions of each vertebra were monitored. Follower load decreased the overall ROM (T1-T12) significantly (p < 0.01) in all primary motion directions (extension: −46%, left LB: −72%, right LB: −72%, left AR: −26%, right AR: −26%) except flexion (−36%). Substantial coupled motion was found in lateral bending with ipsilateral axial rotation, which increased after a follower load was applied, leading to a dominant axial rotation during primary lateral bending, while all other coupled motions in the different motion directions were reduced under follower load. On the monosegmental level, the follower load especially reduced the ROM of the upper thoracic spine from T1-T2 to T4-T5 in all motion directions and the ROM of the lower thoracic spine from T9-T10 to T11-T12 in primary lateral bending. The facet joints, intervertebral disc morphologies, and the sagittal curvature presumably affect the thoracic spinal coupled motions depending on axial compressive preloading. Using these results, the validation of numerical models can be performed more accurately.     

Examining motion in the cervical spine II: characterization of coupled joint motion using an opto-electronic device to track skin markers

Analysis of coupled motion in the cervical spine may be useful in helping to identify injuries. In order to investigate this possibility, the nature of coupled motion in the spine and previous investigations on this subject are reviewed here. An enhanced set of displays are developed for an existing opto-electronic device employed for the non-invasive measurement of movement in the upper spine. This instrument consists of a high resolution motion analysis system which tracks small infrared emitting diodes (IREDs). Kinematic data for the motion of the markers is processed and absolute coordinates for the location of each IRED at any time are tabulated; coupled motion with respect to a fixed calibration frame, as well as for vertebrae relative to each other, is deduced from these. Overall analysis provided by the original device includes assessment of cervical lordosis, thoracic kyphosis, and inter-segmental mobility. Characterization of coupled motion, in particular, involves a series of plots showing principal versus secondary motion. Principal movements include flexion-extension, lateral bending, and axial rotation, corresponding to motion in the sagittal, transverse, and horizontal planes, respectively. Mobility is represented in terms of the direction angles made by virtual vectors orthogonal to the planes made by markers on the head, neck, and shoulders. Development of the enhanced displays and the required refinements are described. Precision of the deduced angles is found to be approximately 1°. This representation of coupled motion is expected to be valuable in improving the accuracy of attempts to identify normal versus pathological motion in the cervical spine.     

Flexion and extension structural properties and strengths for male cervical spine segments

New vehicle safety standards are designed to limit the amount of neck tension and extension seen by out-of-position motor vehicle occupants during airbag deployments. The criteria used to assess airbag injury risk are currently based on volunteer data and animal studies due to a lack of bending tolerance data for the adult cervical spine. This study provides quantitative data on the flexion-extension bending properties and strength on the male cervical spine, and tests the hypothesis that the male is stronger than the female in pure bending. An additional objective is to determine if there are significant differences in stiffness and strength between the male upper and lower cervical spine. Pure-moment flexibility and failure testing was conducted on 41 male spinal segments (O-C2, C4-C5, C6-C7) in a pure-moment test frame and the results were compared with a previous study of females. Failures were conducted at approximately 90 N-m/s. In extension, the male upper cervical spine (O-C2) fails at a moment of 49.5 (s.d. 17.6)N-m and at an angle of 42.4 degrees (s.d. 8.0 degrees). In flexion, the mean moment at failure is 39.0 (s.d. 6.3 degrees) N-m and an angle of 58.7 degrees (s.d. 5.1 degrees). The difference in strength between flexion and extension is not statistically significant. The difference in the angles is statistically significant. The upper cervical spine was significantly stronger than the lower cervical spine in both flexion and extension. The male upper cervical spine was significantly stiffer than the female and significantly stronger than the female in flexion. Odontoid fractures were the most common injury produced in extension, suggesting a tensile mechanism due to tensile loads in the odontoid ligamentous complex.     

Biomechanical analysis of the anterior cervical fusion

This paper presents a biomechanical analysis of the cervical C5-C6 functional spine unit before and after the anterior cervical discectomy and fusion. The aim of this work is to study the influence of the medical procedure and its instrumentation on range of motion and stress distribution. First, a three-dimensional finite element model of the lower cervical spine is obtained from computed tomography images using a pipeline of image processing, geometric modelling and mesh generation software. Then, a finite element study of parameters' influence on motion and a stress analysis at physiological and different post-operative scenarios were made for the basic movements of the cervical spine. It was confirmed that the results were very sensitive to intervertebral disc properties. The insertion of an anterior cervical plate influenced the stress distribution at the vertebral level as well as in the bone graft. Additionally, stress values in the graft decreased when it is used together with a cage.     

An in-vitro study of the kinematics of the normal, injured and stabilized cervical spine

The relative motion between various vertebrae of multi-level cervical ligamentous spinal segments (C2-T2), using Bryant angles, is described. A three-dimensional sonic digitizer was utilized to study the motion in flexion, extension, right lateral bending and right axial rotation. Effects of a number of injuries and stabilization (interspinous wiring and acrylic cement, PMMA) on the motion behavior of C5-C6 (injured) and C4-C5 (superior to injured) levels were investigated. The data were normalized with respect to intact specimens. The injury to capsular ligaments at C5-C6 produced a significant increase in the relative motion at C4-C5. Although the interspinous wiring reduced the motion at C5-C6 the C4-C5 motion was still higher. The application of PMMA made the motion at C4-C5 comparable to the intact specimen.     

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.     

Comparative strengths and structural properties of the upper and lower cervical spine in flexion and extension

The purpose of this study is to test the hypothesis that the upper cervical spine is weaker than the lower cervical spine in pure flexion and extension bending, which may explain the propensity for upper cervical spine injuries in airbag deployments. An additional objective is to evaluate the relative strength and flexibility of the upper and lower cervical spine in an effort to better understand injury mechanisms, and to provide quantitative data on bending responses and failure modes. Pure moment flexibility and failure testing was conducted on 52 female spinal segments in a pure-moment test frame. The average moment at failure for the O-C2 segments was 23.7+/-3.4Nm for flexion and 43.3+/-9.3Nm for extension. The ligamentous upper cervical spine was significantly stronger in extension than in flexion (p=0.001). The upper cervical spine was significantly stronger than the lower cervical spine in extension. The relatively high strength of the upper cervical spine in tension and in extension is paradoxical given the large number of upper cervical spine injuries in out-of-position airbag deployments. This discrepancy is most likely due to load sharing by the active musculature.