Analysis of the interaction between vertebral lateral deviation and axial rotation in scoliosis

There is a lack of clear biomechanical analyses to explain the interaction of the lateral and axial deformity of the spine in idiopathic scoliosis. A finite element model which represented an isolated ligamentous spine with realistic elastic properties and idealized geometry was used to analyse this interaction. Three variations of this model were used to investigate two different hypotheses about the etiology of scoliosis and to define the forces required to produce a scoliosis deformity. The first hypothesis is that coupling within a motion segment produces the interaction between lateral deviation and axial rotation. The second hypothesis is that posterior tethering by soft tissues in the growing spine produces the observed interaction. Modeling of both hypotheses failed to produce the clinically observed pattern of interaction. Therefore, to find which biomechanical forces were required to produce an idealized scoliosis, prescribed displacements were applied to the model. Production of a double curve scoliosis of 10 degrees Cobb angles required lateral forces on the order of 20 N acting 40 mm anterior to the vertebral body centers. There do not appear to be any anatomic structures capable of producing such forces. Therefore, it seems unlikely that scoliosis deformity can be explained in terms of forces acting on the spine, and understanding of its origins may come from examination of other mechanisms such as asymmetric thoracic growth, or asymmetric vertebral development.     

Dynamic model of the equine hindlimb during the swing phase

A dynamic model is developed to describe the swing phase of the hindlimb of a normally walking horse. The limb was represented by four rigid segments constrained to move in a sagittal plane only. The mathematical equations of motion of this four-element pendulum were formulated using Lagrange's theorem. The morphometric parameters from the hindlimb segments of 3 horses were determined using high-speed film analysis. Five muscle groups were incorporated in the model. Muscle activity was derived from earlier EMG measurements. Optimization of muscle moments resulted in a simulated swing movement that approximated that in the living animal.     

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.     

A model for studies of the deformable rib cage.

An earlier model for the study of rib cage mechanics was modified so that rib deformity in scoliosis could be better represented. The rigid ribs of that model were replaced by five-segment deformable ribs. Literature data on cadaver rib mechanical behavior were used to assign stiffnesses to the new individual model ribs so that experimental and model rib deflections agreed. Shear and tension/compression stiffnesses had little effect on individual rib deformation, but bending stiffnesses had a major effect. Level-to-level differences in mechanical behavior could be explained almost exclusively by level to level differences in the rib shape. The model ribs were then assembled into a whole rib cage. Computer simulations of whole rib cage behaviors, both in vivo and in vitro, showed a reasonable agreement with the measured behaviors. The model was used to study rib cage mechanics in two scolioses, one with a 43 degrees and the other with a 70 degrees Cobb angle. Scoliotic rib cage deformities were quantified by parameters measuring the rib cage lateral offset, rib cage axial rotation, rib cage volume and rib distortion. Rib distortion was quantified both in best-fit and simulated computer tomography (CT) scan planes. Model rib distortion was much smaller in best-fit planes than in CT planes. The total rib cage volume changed little in the presence of the scolioses, but it became asymmetrically distributed.     

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.     

High pressures and asymmetrical stresses in the scoliotic disc in the absence of muscle loading

Background

Loads acting on scoliotic spines are thought to be asymmetric and involved in progression of the scoliotic deformity; abnormal loading patterns lead to changes in bone and disc cell activity and hence to vertebral body and disc wedging. At present however there are no direct measurements of intradiscal stresses or pressures in scoliotic spines. The aim of this study was to obtain quantitative measurements of the intradiscal stress environment in scoliotic intervertebral discs and to determine if loads acting across the scoliotic spine are asymmetric. We performed in vivo measurements of stresses across the intervertebral disc in patients with scoliosis, both parallel (termed horizontal) and perpendicular (termed vertical) to the end plate, using a side mounted pressure transducer (stress profilometry)

Methods

Stress profilometry was used to measure horizontal and vertical stresses at 5 mm intervals across 25 intervertebral discs of 7 scoliotic patients during anterior reconstructive surgery. A state of hydrostatic pressure was defined by identical horizontal and vertical stresses for at least two consecutive readings. Results were compared with similar stress profiles measured during surgery across 10 discs of 4 spines with no lateral curvature and with data from the literature.

Results

Profiles across scoliotic discs were very different from those of normal, young, healthy discs of equivalent age previously presented in the literature. Hydrostatic pressure regions were only seen in 14/25 discs, extended only over a short distance. Non-scoliotic discs of equivalent age would be expected to show large centrally placed hydrostatic nuclear regions in all discs. Mean pressures were significantly greater (0.25 MPa) than those measured in other anaesthetised patients (<0.07 MPa). A stress peak was seen in the concave annulus in 13/25 discs. Stresses in the concave annulus were greater than in the convex annulus indicating asymmetric loading in these anaesthetised, recumbent patients.

Conclusion

Intradiscal pressures and stresses in scoliotic discs are abnormal, asymmetrical and high in magnitude even in the absence of significant applied muscle loading. The origin of these abnormal stresses is unclear.     

Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method

Compared to a healthy intervertebral disc, the geometry and the material properties of the involved tissues are altered in a degenerated disc. It is not completely understood how this affects the mechanical behaviour of a motion segment. In order to study the influence of disc degeneration on motion segment mechanics a three-dimensional, nonlinear finite element model of the L3/L4 functional unit was used. Different grades of disc degeneration were simulated by varying disc height and bulk modulus of the nucleus pulposus. The model was loaded with pure moments of 10Nm in the three main anatomic planes. The finite element model predicted the same trends for intersegmental rotation and intradiscal pressure as described in the literature for in vitro studies. A comparison between calculated intersegmental rotation and experimental data showed a mean difference of 1.9 degrees while the mean standard deviation was 2.5 degrees . A mildly degenerated disc increases intersegmental rotation for all loading cases. With further increasing disc degeneration intersegmental rotation is decreased. For axial rotation the decrease takes place in the final stage. Intradiscal pressure is lower while facet joint force and maximum von Mises stress in the annulus are higher in a degenerated compared to a healthy disc.     

The effect of three-dimensional geometrical changes during adolescent growth on the biomechanics of a spinal motion segment

During adolescent growth, vertebrae and intervertebral discs undergo various geometrical changes. Although such changes in geometry are well known, their effects on spinal stiffness remains poorly understood. However, this understanding is essential in the treatment of spinal abnormalities during growth, such as scoliosis.A finite element model of an L3–L4 motion segment was developed, validated and applied to study the quantitative effects of changing geometry during adolescent growth on spinal stiffness in flexion, extension, lateral bending and axial rotation. Height, width and depth of the vertebrae and intervertebral disc were varied, as were the width of the transverse processes, the length of the spinous process, the size of the nucleus, facet joint areas and ligament size. These variations were based on average growth data for girls, as reported in literature.Overall, adolescent growth increases the stiffness with 36% (lateral bending and extension) to 44% (flexion). Two thirds of this increase occurs between 10 and 14 years of age and the last third between 14 years of age and maturity.Although the height is the largest geometrical change during adolescent growth, its effect on the biomechanics is small. The depth increase of the disc and vertebrae significantly affects the stiffness in all directions, while the width increase mainly affects the lateral bending stiffness. Hence, when analysing the biomechanics of the growing adolescent spine (for instance in scoliosis research), the inclusion of depth and width changes, in addition to the usually implemented height change, is essential.     

Representation of planar motion of complex joints by means of rolling pairs. Application to neck motion

We propose to model planar movements between two human segments by means of rolling-without-slipping kinematic pairs. We compute the path traced by the instantaneous center of rotation (ICR) as seen from the proximal and distal segments, thus obtaining the fixed and moving centrodes, respectively. The joint motion is then represented by the rolling-without-slipping of one centrode on the other. The resulting joint kinematic model is based on the real movement and accounts for nonfixed axes of rotation; therefore it could improve current models based on revolute pairs in those cases where joint movement implies displacement of the ICR. Previous authors have used the ICR to characterize human joint motion, but they only considered the fixed centrode. Such an approach is not adequate for reproducing motion because the fixed centrode by itself does not convey information about body position. The combination of the fixed and moving centrodes gathers the kinematic information needed to reproduce the position and velocities of moving bodies. To illustrate our method, we applied it to the flexion-extension movement of the head relative to the thorax. The model provides a good estimation of motion both for position variables (mean R(pos)=0.995) and for velocities (mean R(vel)=0.958). This approach is more realistic than other models of neck motion based on revolute pairs, such as the dual-pivot model. The geometry of the centrodes can provide some information about the nature of the movement. For instance, the ascending and descending curves of the fixed centrode suggest a sequential movement of the cervical vertebrae.     

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.     

Design of next generation total disk replacements

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

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.     

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.     

Prehistoric mongoloid dispersals. Edited by Takeru Akazawa and Emöke J. E. Szathmáry. New York: Oxford University Press. 1996. 387 pp. ISBN 0-19-852318-1 $150.00 (cloth)

Studies of the dynamics of locomotor performances depend on knowledge of the distribution of body mass within and between limb segments. However, these data are difficult to derive. Segment mass properties have generally been estimated by modelling limbs as truncated cones, but this approach fails to take into account that some segments are of elliptical, not circular, cross section; and further, the profiles of real segments are generally curved. Thus, they are more appropriately modelled as solids of revolution, described by the rotation in space of convex or concave curves, and the possibility of an elliptical cross section needs to be taken into account. In this project we have set out to develop a general geometric model which can take these factors into account, and permit segment inertial properties to be derived from cadavers by segmentation, and from living individuals using linear external measurements. We present a model which may be described by up to four parameters, depending o the profile and serial cross section (circular or ellipsoidal) of the individual segments. The parameters are obtained from cadavers using a simplified complex-pendulum technique, and from intact specimens by calculation from measurements of segment diameters and lengths. From the parameters, the center of mass, moments of inertia, and radii of gyration may be derived, using simultaneous equations. Inertial properties of the body segments of four Pan troglodytes and a single Pongo were determined, and contrasted to comparable findings for humans. Using our approach, the mass distribution characteristics of any individual or species may be represented by a rigid-link segment model or “android.” If this is made to move according to motion functions derived from a real performance of the individual represented, we show that recordings of resulting ground reaction forces may be quite closely simulated by predictive dynamic modelling. © 1996 Wiley-Liss, Inc.     

Changes in axial stiffness of the trunk as a function of walking speed

Research suggests that abnormal coordination patterns between the thorax and pelvis in the transverse plane observed in patients with Parkinson's disease and the elderly might be due to alteration in axial trunk stiffness. The purpose of this study was to develop a tool to estimate axial trunk stiffness during walking and to investigate its functional role. Fourteen healthy young subjects participated in this study. They were instructed to walk on the treadmill and kinematic data was collected by 3D motion analysis system. Axial trunk stiffness was estimated from the angular displacement between trunk segments and the amount of torque around vertical axis of rotation. The torque due to arm swing cancelled out the torque due to the axial trunk stiffness during walking and the thoracic rotation was of low amplitude independent of changes in walking speeds within the range used in this study (0.85-1.52 m/s). Estimated axial trunk stiffness increased with increasing walking speed. Functionally, the suppression of axial rotation of thorax may have a positive influence on head stability as well as allowing recoil between trunk segments. Furthermore, the increased stiffness at increased walking speed would facilitate the higher frequency rotation of the trunk in the transverse plane required at the higher walking speeds.     

The three dimensional analysis of the Sforzesco brace correction

Background

The historical view of scoliosis as a primary rotation deformity led to debate about the pathomechanic role of paravertebral muscles; particularly multifidus, thought by some to be scoliogenic, counteracting, uncertain, or unimportant. Here, we address lateral lumbar curves (LLC) and suggest a pathomechanic role for quadrates lumborum, (QL) in the light of a new finding, namely of 12th rib bilateral length asymmetry associated with idiopathic and small non-scoliosis LLC.

Methods

Group 1: The postero-anterior spinal radiographs of 14 children (girls 9, boys 5) aged 9–18, median age 13 years, with right lumbar idiopathic scoliosis (IS) and right LLC less that 10°, were studied. The mean Cobb angle was 12° (range 5–22°). Group 2: In 28 children (girls 17, boys 11) with straight spines, postero-anterior spinal radiographs were evaluated similarly to the children with the LLC, aged 8–17, median age 13 years. The ratio of the right/left 12th rib lengths and it’s reliability was calculated. The difference of the ratio between the two groups was tested; and the correlation between the ratio and the Cobb angle estimated. Statistical analysis was done using the SPSS package.

Results

The ratio’s reliability study showed intra-observer +/−0,036 and the inter-observer error +/−0,042 respectively in terms of 95 % confidence limit of the error of measurements. The 12th rib was longer on the side of the curve convexity in 12 children with LLC and equal in two patients with lumbar scoliosis. The 12th rib ratios of the children with lumbar curve were statistically significantly greater than in those with straight spines. The correlation of the 12th rib ratio with Cobb angle was statistically significant. The 12th thoracic vertebrae show no axial rotation (or minimal) in the LLC and no rotation in the straight spine group.

Conclusions

It is not possible, at present, to determine whether the 12th convex rib lengthening is congenitally lengthened, induced mechanically, or both. Several small muscles are attached to the 12th ribs. We focus attention here on the largest of these muscles namely, QL. It has attachments to the pelvis, 12th ribs and transverse processes of lumbar vertebrae as origins and as insertions. Given increased muscle activity on the lumbar curve convexity and similar to the interpretations of earlier workers outlined above, we suggest two hypotheses, relatively increased activity of the right QL muscle causes the LLCs (first hypothesis); or counteracts the lumbar curvature as part of the body’s attempt to compensate for the curvature (second hypothesis). These hypotheses may be tested by electrical stimulation studies of QL muscles in subjects with lumbar IS by revealing respectively curve worsening or correction. We suggest that one mechanism leading to relatively increased length of the right 12 ribs is mechanotransduction in accordance with Wolff’s and Pauwels Laws.

     

Finite element investigation of the loading rate effect on the spinal load-sharing changes under impact conditions

Sudden deceleration and frontal/rear impact configurations involve rapid movements that can cause spinal injuries. This study aimed to investigate the rotation rate effect on the L2–L3 motion segment load-sharing and to identify which spinal structure is at risk of failure and at what rotation velocity the failure may initiate?Five degrees of sagittal rotations at different rates were applied in a detailed finite-element model to analyze the responses of the soft tissues and the bony structures until possible fractures. The structural response was markedly different under the highest velocity that caused high peaks of stresses in the segment compared to the intermediate and low velocities. Under flexion, the stress was concentrated at the upper pedicle region of L2 and fractures were firstly initiated in this region and then in the lower endplate of L2. Under extension, maximum stress was located in the lower pedicle region of L2 and fractures started in the left facet joint, then they expanded in the lower endplate and in the pedicle region of L2. No rupture has resulted at the lower or intermediate velocities. The intradiscal pressure was higher under flexion and decreased when the endplate was fractured, while the contact forces were greater under extension and decreased when the facet surface was cracked. The highest ligaments stresses were obtained under flexion and did not reach the rupture values. The endplate, pedicle and facet surface represented the potential sites of bone fracture. Results showed that spinal injuries can result at sagittal rotation velocity exceeding 0.5°/ms.