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.     

Structural behavior of human lumbar spinal motion segments

The objectives of this study were to obtain linearized stiffness matrices, and assess the linearity and hysteresis of the motion segments of the human lumbar spine under physiological conditions of axial preload and fluid environment. Also, the stiffness matrices were expressed in the form of an 'equivalent' structure that would give insights into the structural behavior of the spine. Mechanical properties of human cadaveric lumbar L2-3 and L4-5 spinal motion segments were measured in six degrees of freedom by recording forces when each of six principal displacements was applied. Each specimen was tested with axial compressive preloads of 0, 250 and 500 N. The displacements were four slow cycles of +/-0.5mm in anterior-posterior and lateral displacements, +/-0.35 mm axial displacement, +/-1.5 degrees lateral rotation and +/-1 degrees flexion-extension and torsional rotations. There were significant increases with magnitude of preload in the stiffness, hysteresis area (but not loss coefficient) and the linearity of the load-displacement relationship. The mean values of the diagonal and primary off-diagonal stiffness terms for intact motion segments increased significantly relative to values with no preload by an average factor of 1.71 and 2.11 with 250 and 500 N preload, respectively (all eight tests p<0.01). Half of the stiffness terms were greater at L4-5 than L2-3 at higher preloads. The linearized stiffness matrices at each preload magnitude were expressed as an equivalent structure consisting of a truss and a beam with a rigid posterior offset, whose geometrical properties varied with preload. These stiffness properties can be used in structural analyses of the lumbar spine.     

Separating brain motion into rigid body displacement and deformation under low-severity impacts

The relative motion of the brain with respect to the skull has been widely studied to investigate brain injury mechanisms under impacts, but the motion patterns are not yet thoroughly understood. This work analyzes brain motion patterns using the most recent and advanced experimental relative brain/skull motion data collected under low-severity impacts. With a minimum total pseudo-strain energy, the closed-form solutions for rigid body translation and rotation were obtained by matching measured neutral density target (NDT) positions with initial NDT positions. The brain motion was thus separated into rigid body displacement and deformation. The results show that the brain has nearly pure rigid body displacement at low impact speed. As the impact becomes more severe, the increased brain motion primarily is due to deformation, while the rigid body displacement is limited in magnitude for both translation and rotation. Under low-severity impacts in the sagittal plane, the rigid body brain translation has a magnitude of 4-5 mm, and the whole brain rotation is on the order of +/-5 degrees.     

Validation of vibration testing for the assessment of the mechanical properties of human lumbar motion segments

Experimental modal analysis is a non-destructive measurement technique, which applies low forces and small deformations to assess the integrity of a structure. It is therefore a promising method to study the mechanical properties of the spine in vivo. Previously, modal parameters successfully revealed artificially induced spinal injuries. The question remains however, whether experimental modal analysis can be applied successfully in human spinal segments with mechanical changes due to physiological processes. Since quasi-static mechanical testing is considered the "gold standard" for assessing intervertebral stiffness, the purpose of our study was to examine if the mechanical properties derived from vibration testing and quasi-static testing correlate. Six cadaver human spines (L1-L5) were loaded quasi-statically in bending and torsion, while an optical system measured the angular rotations of the individual motion segments. Subsequently, the polysegmental spines were divided into L2-L3 and L4-L5 segments and a shaker was used to vibrate the upper vertebra, while its response was obtained from accelerometers in anteroposterior and mediolateral directions. From the resulting frequency response function the eigenfrequencies (ratio between stiffness and mass) and vibration modes (pattern of motion) were determined. The vibration results showed clear eigenfrequencies for flexion-extension (mean 121.83Hz, SD 40.05Hz), lateroflexion (mean 132.17, SD 34.80Hz) and axial rotation (mean 236.17Hz, SD 81.45Hz). Furthermore, the correlation between static and dynamic tests was significant (r=0.73, p=0.01). In conclusion, the findings from this study show that experimental modal analysis is a valid method to assess the mechanical properties of human lumbar motion segments.     

The feasibility of modal testing for measurement of the dynamic characteristics of goat vertebral motion segments

Structural vibration testing might be a promising method to study the mechanical properties of spinal motion segments as an alternative to imaging and spinal manipulation techniques. Structural vibration testing is a non-destructive measurement technique that measures the response of a system to an applied vibration as a function of frequency, and allows determination of modal parameters such as resonance frequencies (ratio between stiffness and mass), vibration modes (pattern of motion) and damping. The objective of this study was to determine if structural vibration testing can reveal the resonance frequencies that correspond to the mode shapes flexion-extension, lateroflexion and axial rotation of lumbar motion segments, and to establish whether resonance frequencies can discriminate specific structural alterations of the motion segment. Therefore, a shaker was used to vibrate the upper vertebra of 16 goat lumbar motion segments, while the response was obtained from accelerometers on the transverse and spinous processes and the anterior side of the upper vertebra. Measurements were performed in three conditions: intact, after dissection of the ligaments and after puncturing the annulus fibrosus. The results showed clear resonance peaks for flexion-extension, lateral bending and axial rotation for all segments. Dissection of the ligaments did not affect the resonance frequencies, but puncturing the annulus reduced the resonance frequency of axial rotation. These results indicate that vibration testing can be utilised to assess the modal parameters of lumbar motion segments, and might eventually be used to study the mechanical properties of spinal motion segments in vivo.     

Three-dimensional computer simulation of radiostereometric analysis (RSA) in distal radius fractures

Physical phantom models have conventionally been used to determine the accuracy and precision of radiostereometric analysis (RSA) in various orthopaedic applications. Using a phantom model of a fracture of the distal radius it has previously been shown that RSA is a highly accurate and precise method for measuring both translation and rotation in three-dimensions (3-D). The main shortcoming of a physical phantom model is its inability to mimic complex 3-D motion. The goal of this study was to create a realistic computer model for preoperative planning of RSA studies and to test the accuracy of RSA in measuring complex movements in fractures of the distal radius using this new model. The 3-D computer model was created from a set of tomographic scans. The simulation of the radiographic imaging was performed using ray-tracing software (POV-Ray). RSA measurements were performed according to standard protocol. Using a two-part fracture model (AO/ASIF type A2), it was found that for simple movements in one axis, translations in the range of 25microm-2mm could be measured with an accuracy of +/-2microm. Rotations ranging from 16 degrees to 2 degrees could be measured with an accuracy of +/-0.015 degrees . Using a three-part fracture model the corresponding values of accuracy were found to be +/-4microm and +/-0.031 degrees for translation and rotation, respectively. For complex 3-D motion in a three-part fracture model (AO/ASIF type C1) the accuracy was +/-6microm for translation and +/-0.120 degrees for rotation. The use of 3-D computer modelling can provide a method for preoperative planning of RSA studies in complex fractures of the distal radius and in other clinical situations in which the RSA method is applicable.     

Assessment of screw displacement axis accuracy and repeatability for joint kinematic description using an electromagnetic tracking device

Screw displacement axes (SDAs) have been employed to describe joint kinematics in biomechanical studies. Previous reports have investigated the accuracy of SDAs combining various motion analysis techniques and smoothing procedures. To our knowledge, no study has assessed SDA accuracy describing the relative movement between adjacent bodies with an electromagnetic tracking system. This is important, since in relative motion, neither body is fixed and consequently sensitivity to potential measurement errors from both bodies may be significant. Therefore, this study assessed the accuracy of SDAs for describing relative motion between two moving bodies. We analyzed numerical simulated data, and physical experimental data recorded using a precision jig and electromagnetic tracking device. The numerical simulations demonstrated SDA position accuracy (p=0.04) was superior for single compared to relative body motion, whereas orientation accuracy (p=0.2) was similar. Experimental data showed data-filtering (Butterworth filter) improved SDA position and orientation accuracies for rotation magnitudes smaller or equal to 5.0 degrees, with no effect at larger rotation magnitudes (p<0.05). This suggests that in absence of a filter, SDAs should only be calculated at rotations of greater than 5.0 degrees. For rotation magnitudes of 0.5 degrees (5.0 degrees ) about the SDA, SDA position and orientation error measurements determined from filtered experimental data were 3.75+/-0.30 mm (3.31+/-0.21 mm), and 1.10+/-0.04 degrees (1.04+/-0.03 degrees ), respectively. Experimental accuracy values describing the translation along and rotation about the SDA, were 0.06+/-0.00 mm and 0.09+/-0.01 degrees, respectively. These small errors establish the capability of SDAs to detect small translations, and rotations. In conclusion, application of SDAs should be a useful tool for describing relative motion in joint kinematic studies.     

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.     

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.     

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.     

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.     

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.     

退行性腰椎滑脱临近节段椎间盘退变和关节突关节角度相关研究

目的:探讨退行性腰椎滑脱(DLS)临近节段椎间盘退变程度和关节突关节角度之间的关系。方法:选取我院2012年6月至2016年6月收治的120例DLS患者作为DLS组,另外选取来我院接受体检的健康者120例作为对照组,选择CT进行关节突关节角和腰椎滑脱度的测量,使用MRI的T2像对椎间盘进行Pfirrmann退变分级。结果:DLS组的各节段关节突关节角度均小于对照组(P0.05);DLS组不同滑脱程度的L2/3、L3/4、L5/S1节段关节突关节角度的比较,差异无统计学意义(P0.05);DLS组L2/3、L3/4、L5/S1节段不同椎间盘退变等级间的滑脱程度无显著性差异(P0.05)。L2/3和L3/4节段不同椎间盘退变程度间关节突关节角度差无显著性差异(P0.05),L5/S1节段不同椎间盘退变程度间关节突关节角度差有统计学差异(P0.05)。结论:退行性腰椎滑脱临近节段关节突关节角度明显小于正常人,且临近节段关节突关节的角度并未随着腰椎滑脱程度的加重而改变,退行性腰椎滑脱患者滑脱临近节段椎间盘退变与关节突关节的矢状化程度无关,但L5/S1关节突关节角度不对称性会影响到同节段椎间盘退变程度。     

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.     

A new in vivo technique for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint

Patello-femoral disorders are often caused by changes of patello-femoral and/or tibio-femoral kinematics. However, until now there has been no quantitative in vivo technique, that is able to obtain 3D kinematics and contact areas of all knee compartments simultaneously on a non-invasive basis. The aim of this study was therefore to develop and apply a technique which allows for determination of 3D kinematics and contact areas of the patello-femoral and tibio-femoral joint during different knee flexion angles and under neuromuscular activation patterns. One knee of each of the 10 healthy volunteers was examined in an open MR system under flexing isometric muscle activity at 30 degrees and 90 degrees. Three-dimensional kinematics and contact areas of the patello-femoral and tibio-femoral joints were analyzed by 3D image postprocessing. The reproducibility of the imaging technique yielded a coefficient of variation of 4.6% for patello-femoral, 4.7% for femoro-tibial displacement and 8.6% for contact areas. During knee flexion (30-90 degrees ), patella tilt (opened to medial) decreased (8.8+/-3.4 degrees vs. 4.6+/-3.1 degrees, p<0.05), while lateral patellar shift increased significantly (1.6+/-2.3mm vs. 3.4+/-3.0mm, p<0.05). Furthermore, a significant posterior translation and external rotation of the femur relative to the tibia was observed. Patello-femoral contact areas increased significantly in size (134+/-60mm(2) vs. 205+/-96 mm(2)) during knee flexion. This technique shows a high reproducibility and provides physiologic in vivo data of 3D kinematics and contact areas of the patello-femoral and the tibio-femoral joint during knee flexion. This allows for advanced in vivo diagnostics, and may help to improve therapy of patello-femoral disorders in the future.     

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.     

Measurement of spinal sagittal curvatures using the laser triangulation method

The purpose of the first part of the study was to establish the variability of repeated measurements in different measuring conditions. In the second part, we performed in a large number of patients, a measurement of thoracic kyphosis and lumbar lordosis and compared them to age, gender, and level of nourishment. In the first part, measurements were performed on a plastic model of the back of a patient with a rigid and a normal spine. In the second part, 250 patients participated in the study (126 men and 124 women). For measuring spinal curvatures we used an apparatus for laser triangulation constructed at the Faculty of Mechanical Engineering, University of Ljubljana. A comparison of 30 repeated measurements was shown as the average value +/- 2 SD which included 95% of the results. Thirty repeated readings of one 3D measurement: thoracic kyphosis 41.2 degrees +/- 0.6 degrees, lumbar lordosis 4.4 degrees +/- 1.2 degrees; 30 measurements on a plastic model: thoracic kyphosis 36.8 degrees +/- 1.2 degrees, lumbar lordosis 30.9 degrees +/- 2.0 degrees; 30 measurements on a patient with a rigid spine: thoracic kyphosis 41.5 degrees +/- 2.4 degrees, lumbar lordosis 4.0 degrees +/- 1.8 degrees; 30 measurements on a patient with a normal spine: thoracic kyphosis 48.8 degrees +/- 7.4 degrees, lumbar lordosis 21.1 degrees +/- 4.4 degrees. The average size of thoracic kyphosis in 250 patients was 46.8 degrees (SD 10.1 degrees) and lumbar lordosis 31.7 degrees (SD 12.5 degrees). The angle size was statistically significantly correlated to gender (increased thoracic kyphosis and lumbar lordosis in women) and body mass index (increased thoracic kyphosis and lumbar lordosis in more nourished patients). Age was not significantly correlated to the observed angles. During measurements of the spinal angles it was important to pay attention to relaxation and the patient's position as well as to perform more measurements providing the average value. The age and the level of nourishment influence the size of the sagittal spinal angles. In the observed sample the effect of age was not confirmed.     

Uncertainty analysis of material properties and morphology parameters in numerical models regarding the motion of lumbar vertebral segments

Abstract

The kinematics of a spinal motion segment is determined by the material properties of the soft-tissue and the morphology. The material properties can vary within subjects and between vertebral levels, leading to a wide possible range of motion of a spinal segment independently on its morphology. The goal of this numerical study was to identify the most influential material parameters concerning the kinematics of a spinal motion segment and their plausible ranges. Then, a method was tested to deduce the material properties automatically, based on a given ROM and morphology. A fully parametric finite element model of the morphology and material properties of a lumbar spinal motion segment was developed. The impact of uncertainty of twelve spinal material parameters, as well as the size of the gap between the articular surfaces of the facet joints was examined. The simulation results were compared to our own in vitro data. The flexibility of a lumbar segment was especially influenced by the properties of the anterior annulus region, the facet gap size and the interspinous ligament. The high degree of uncertainty in the material properties and facet gap size published in the literature can lead to a wide scatter in the motion of a spinal segment, with a range of 6°-17° in the intact condition in flexion/extension, from 5°-22° in lateral bending and from 3°-14° in axial rotation. Statistical analysis of the variability might help to estimate the sensitivity and total uncertainty propagated through biomechanical simulations, affecting the reliability of the predictions.