Principles of measurement of vertebral rotation from frontal projections of the pedicles

Measurement of vertebral rotation from frontal X-ray projections of the pedicles was introduced by Nash and Moe. By the introduction of a vertebral model, their method and different modifications can be described and characterized easily. A geometrical analysis shows, that two parameters are sufficient for this model. When applying an appropriate interpretation of vertebral rotation, rotation measurement can be performed independent of lateral tilting and forward-backward inclination. As a test of the Nash-Moe method 65 vertebrae are each investigated from 15 directions. The measurements are analyzed for each pedicle separately and also compared to the opposite pedicle of the particular vertebra. The results indicate figures for the accuracy of the Nash-Moe method and its modifications for absolute and relative measurements. A simple correction to the Nash-Moe method is proposed.     

Model-guided derivation of lumbar vertebral kinematics in vivo reveals the difference between external marker-defined and internal segmental rotations

This study investigated whether the external marker-defined spine inter-segmental rotation is different from the internal vertebral rotation, and explored how to estimate the latter from limited surface measurement. A kinematic model was first created to elucidate analytically the relation between the external and internal rotations. A novel approach guided by the model was proposed for deriving vertebral centers of rotation (CORs) from measured planar trajectories of skin-surface markers. The approach involved a recursive procedure for establishing local (anatomical) coordinate systems, and an optimization routine that identified the maximum-likelihood circles best fitting the marker trajectories in local coordinate systems. An experiment with 10 subjects (5 males and 5 females) was conducted to test the approach along with the model. Skin-surface markers were strategically placed over individual spinous processes and other body landmarks, and recorded by an opto-electronic system while sagittally symmetric load-lifting movements were being performed. For the majority (89%) of measured motions, the COR locations for lumbar vertebrae (L2-L5) were derived successfully: solutions resulting from the optimization routine met a convergence criterion governed by the model, and were in agreement with existing data from radiographic or cadaveric studies. Empirical results confirmed the differences between the external marker-defined inter-segmental motions and corresponding internal vertebral rotations (1.1-5.8 degrees on average, all statistically significant). The study demonstrated the necessity and viability of quantifying internal vertebral kinematics when utilizing non-invasive marker-based measurement for spine-related clinical diagnosis and biomechanical modeling.     

Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting.

A combined approach involving optimization and the finite element technique was used to predict biomechanical parameters in the lumbar spine during static lifting in the sagittal plane. Forces in muscle fascicles of the lumbar region were first predicted using an optimization-based force model including the entire lumbar spine. These muscle forces as well as the distributed upper body weight and the lifted load were then applied to a three-dimensional finite element model of the thoracolumbar spine and rib cage to predict deformation, the intradiskal pressure, strains, stresses, and load transfer paths in the spine. The predicted intradiskal pressures in the L3-4 disk at the most deviated from the in vivo measurements by 8.2 percent for the four lifting cases analyzed. The lumbosacral joint flexed, while the other lumbar joints extended for all of the four lifting cases studied (rotation of a joint is the relative rotation between its two vertebral bodies). High stresses were predicted in the posterolateral regions of the endplates and at the junctions of the pedicles and vertebral bodies. High interlaminar shear stresses were found in the posterolateral regions of the lumbar disks. While the facet joints of the upper two lumbar segments did not transmit any load, the facet joints of the lower two lumbar segments experienced significant loads. The ligaments of all lumbar motion segments except the lumbosacral junction provided only marginal moments. The limitations of the current model and possible improvements are discussed.     

Cervical spine morphology and ligament property variations: A finite element study of their influence on sagittal bending characteristics

Cervical spine finite element models reported in biomechanical literature usually represent a static morphology. Not considering morphology as a model parameter limits the predictive capabilities for applications in personalized medicine, a growing trend in modern clinical practice. The objective of the study was to investigate the influence of variations in spinal morphology on the flexion-extension responses, utilizing mesh-morphing-based parametrization and metamodel-based sensitivity analysis. A C5-C6 segment was used as the baseline model. Variations of intervertebral disc height, facet joint slope, facet joint articular processes height, vertebral body anterior-posterior depth, and segment size were parametrized. In addition, material property variations of ligaments were considered for sensitivity analysis. The influence of these variations on vertebral rotation and forces in the ligaments were analyzed. The disc height, segmental size, and body depth were found to be the most influential (in the cited order) morphology variations; while among the ligament material property variations, capsular ligament and ligamentum flavum influenced vertebral rotation the most. Changes in disc height influenced forces in the posterior ligaments, indicating that changes in the anterior load-bearing column of the spine could have consequences on the posterior column. A method to identify influential morphology variations is presented in this work, which will help automation efforts in modeling to focus on variations that matter. This study underscores the importance of incorporating influential morphology parameters, easily obtained through computed tomography/magnetic resonance images, to better predict subject-specific biomechanical responses for applications in personalized medicine.     

A new method for estimating the axis of rotation and the center of rotation.

A new method is presented for estimating the parameters of two different models of a joint. The two models are: (1) A rotational joint with a fixed axis of rotation, also referred to as a hinge joint and (2) a ball and socket model, corresponding to a spherical joint. Given the motion of a set of markers, it is shown how the parameters can be estimated, utilizing the whole data set. The parameters are estimated from motion data by minimizing two objective functions. The method does not assume a rigid body motion, but only that each marker rotates around the same fixed axis of rotation or center of rotation. Simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present, the proposed method is inferior to methods that utilize the rigid body assumption. However, when there are large skin movement artefacts, simulation results show the proposed method to be more robust.     

Influence of tool rotation on 3D surface topography at the nanometric scale

The influence of the tool rotation on the 3D surface topography produced by the nano-cutting process is investigated using molecular dynamics simulations. The least square mean method is utilized to model the evaluation criteria for the surface roughness parameters. The effects of the tool rotation on the cutting force and the chip formation at the nano-metric scale are also evaluated. It is found that the chip formation produced with tool rotation is dominated by the ploughing and the shearing forces. With increase of the adopted rotation velocity, the cutting force is sharply increased and the smaller elastic recovery of the machined surface is observed. The 3D surface roughness parameters at the nano-metric scale are significantly influenced by the tool rotation velocity and the feed speed, and the surface quality can be improved by decreasing the tool rotation velocity and the feed speed.     

A method for analysis of back shape in scoliosis

The shape of the back is an important factor in the clinical assessment of various spinal disorders, in particular scoliosis. A method of analysis of back surface shape is described which was designed to present most of the numerical parameters needed to assess the progress of the disease as it affects body shape. Measurements of back surface shape and manually marked anatomical landmarks were taken from a television/computer surface measurement system in which a plane of light was scanned over the back and from moiré topographs. The anatomical landmarks were used to define reference planes from which successive analyses were matched. Asymmetry in the transverse plane was illustrated by horizontal cross-sections and skin surface angles. The lateral deformity was shown by an estimate of the line of the vertebral bodies beneath the skin, derived by adding an extra lateral displacement to the palpated positions of the spinous processes, proportional to the rotation of the skin in the transverse plane. This model was used to estimate vertebral end-plate angles and Cobb angles. Lateral sections showed kyphosis and lordosis. Correlations of Lateral Asymmetry from the surface shape analysis with Cobb angle from X-ray measurements in three groups of patients (totalling 119 subjects) were in the range r = 0.77 to r = 0.94, p less than 0.0001. The analysis has reduced follow-up X-ray examinations at the Nuffield Orthopaedic Centre because it indicates quantitatively and with complete safety both lateral asymmetry and deformity in the transverse plane.     

Comparative stability of the "Internal Fixator" and the "Universal Spine System" and the effect of crosslinking transfixating systems. A biomechanical in vitro study.

In this study, the three-dimensional stabilizing capabilities of the AO-Internal Fixator (IF) and the new Universal Spine System (USS) were investigated. Both devices were tested without and with the cross-link system (IF, IFC, USS, USSC). To determine biomechanical characteristics, a human thoracolumbar spine instability model with resection of the vertebral body Th12 was created. The vertebral body was replaced by a spacer and transpedicular posterior stabilization was performed from Th11 to L1. All devices reduced the range of motion (ROM) significantly compared to the values of the intact specimen. In flexion the IFC showed the highest reduction of ROM (85% of intact), followed by the USSC, USS and IF (79% of intact). In extension the ROM was restored again most by the IFC (52% of intact), followed by the USSC, IF and USS (44% of intact). In lateral bending stability was provided by the USSC (right 78% and left 81% of intact), followed in right lateral bending by the IF, IFC and USS and in left lateral bending by the USS, IF and IFC. In axial rotation the ROM was reduced primary by the IFC (right 51% and left 46% of intact), followed in right axial rotation by the USS, USSC and IF, in left axial rotation by the USSC, USS and IF. Additional stability by crosslinking has been provided in the IF and the USS in flexion and extension, in the USS in lateral bending and in the IF in axial rotation nonsignificantly. The neutral zone (NZ) was reduced by posterior instrumentation in flexion/extension and right/left lateral bending significantly. In axial rotation only the USSC decreased the NZ below intact levels. The study showed no statistical significant differences in the stabilizing capabilities of the USS compared to the IF. For both implants the cross-link system increased stability in the chosen instability model insignificantly only.     

Spine kineamtics: a digital videofluoroscopic technique

It is notoriously difficult to quantify the kinematic behaviour of vertebral segments in the assessment and localization of mechanical disorders of the spine. This paper describes the use of an image processor and an X-ray machine with image intensifier for the measurement of lumbar spine angular rotation and instantaneuous centres of rotation in the coronal plane. The system was calibrated against a model under realistic conditions employing multiplanar motion and X-ray scatter.     

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.     

A segmental radiological study of the spine and rib – cage in children with progressive Infantile Idiopathic Scoliosis

Background

The role of rib cage in the development of progressive infantile idiopathic scoliosis (IIS) has not been studied previously. No report was found for rib growth in children with IIS. These findings caused us to undertake a segmental radiological study of the spine and rib-cage in children with progressive IIS. The aim of the present study is to present a new method for assessing the thoracic shape in scoliotics and in control subjects and to compare the findings between the two groups.

Materials and methods

In the posteroanterior (PA) spinal radiographs of 24 patients with progressive IIS, with a mean age of 4.1 years old, the Thoracic Ratios (TRs) (segmental convex and concave TRs), the Cobb angle, the segmental vertebral rotation and vertebral tilt were measured. In 233 subjects, with a mean age of 5.1 years old, who were used as a control group, the segmental left and right TRs and the total width of the chest (left plus right TRs) were measured in PA chest radiographs. Statistical analysis included Mann-Whitney, Spearman correlation coefficient, multiple linear regression analysis and ANOVA.

Results

The comparison shows that the scoliotic thorax is significantly narrower than that of the controls at all spinal levels. The upper chest in IIS is funnel-shaped and the vertebral rotation at T4 early in management correlates significantly with the apical vertebral rotation at follow up.

Conclusion

The IIS thorax is narrower than that of the controls, the upper chest is funnel-shaped and there is a predictive value of vertebral rotation at the upper limit of the thoracic curve of IIS, which reflects, impaired rib control of spinal rotation possibly due to neuromuscular factors, which contribute also to the funnel-shaped chest.     

A new approach to the determination of cardiac potential distributions: application to the analysis of electrode configurations

This paper presents a mathematical model and new solution technique for studying the electric potential in a slab of cardiac tissue. The model is based on the bidomain representation of cardiac tissue and also allows for the effects of fibre rotation between the epicardium and the endocardium. A detailed solution method, based on Fourier Series and a simple one-dimensional finite difference scheme, for the governing equations for electric potential in the tissue and the blood, is also presented. This method has the advantage that the potential can be calculated only at points where it is required, such as the measuring electrodes. The model is then used to study various electrode configurations which have been proposed to determine cardiac tissue conductivity parameters. Three electrode configurations are analysed in terms of electrode spacing, placement position and the effect of including fibre rotation: the usual surface four-electrode configuration; a single vertical analogue of this and a two probe configuration, which has the current electrodes on one probe and the measuring electrodes on the other, a fixed distance away. It is found that including fibre rotation has no effect on the potentials measured in the first two cases; however, in the two probe case, non-zero fibre rotation causes a significant drop in the voltage measured. This leads to the conclusion that it is necessary to include the effects of fibre rotation in any model which involves the use of multiple plunge electrodes.     

Capacities of angiography in the imaging of abnormal changes in the cerebral arteries

The study was based on the angiographic examination of 233 patients with prior subarachnoidal hemorrhage. Angiographic study was performed using the Seldinger technique by contrasting both carotid and vertebral arteries. Twenty-three patients in whom arterial aneurysm had been detected by digital subtraction angiography underwent 3D angiography. The authors improved a procedure during which a contrast agent was manually injected into the internal carotid or vertebral artery, by using a 20-ml disposal syringe with controlled maximum developed pressure and flow increase rate up to 2.0 ml/sec for 4-5 sec during rotary scanning and the administration of the radiocontrast medium was stopped when an image appeared on the monitor at 190 degrees (190.0, 200.0) C-arm rotation. This procedure could decrease significantly the volume of the administered contrast agent from 18 to 8 (8.0, 10.0) ml and reduce the time of radiation exposure from 6 to 4 (4.0, 5.0) sec. The improved angiographic modes for the right vertebral and right carotid artery could visualize pathological changes in these arteries and establish a relationship, namely: due to degenerative dystrophic processes of the cervical spine there is a tendency for higher pathological changes in the vertebral arteries with an increased stage of osteochondrosis in the cervical spine (R = 0.95; p = 0.014).     

Evaluation of frontal radiographs of scoliotic spines—Part II. Relations between lateral deviation, lateral tilt and axial rotation of vertebrae

The shape of scoliotic spines as measured from frontal radiographs (see Part I of this paper) is analysed with respect to interrelations between lateral deviation, lateral tilt and axial rotation of the vertebrae. These parameters are represented by sinusoidal functions of the longitudinal coordinate. The interrelations can, therefore, be expressed in terms of amplitude and phase relations. Two additional functions—‘spinal tilt’ and (local) curvature—are calculated from the first and second derivatives of lateral deviation. The method has been applied to three patient groups with different aetiology: 113 patients with idiopathic scoliosis (478 radiographs, partially follow-up examinations), 23 patients with scoliosis secondary to Wilms' tumour irradiation and 18 patients with scoliosis secondary to poliomyelitis. The amplitude and phase relations of all functions reveal a characteristic pattern which is apparently independent of the specific aetiology. The results show that the available biomechanic explanations of coupling of vertebral motions are questionable.     

The construction of the scoliosis 3D finite element model and the biomechanical analysis of PVCR orthopaedy

ObjectiveThe objective is to investigate the biomechanical conditions of the Posterior Vertebral Column Resection (PVCR) of the constructed scoliosis 3D finite element model.MethodsA patient with scoliosis was selected; before the PVCR orthopaedy, the patient was submitted to the radiography of normal and lateral full-length vertebral column scans and the total magnetic resonance imaging (MRI) scans; then, the idiopathic scoliosis model was constructed by the 3D finite element method, and the 3D finite element software utilized in the process of model construction included Mimics software, Geomagic Studio 12 software, and Unigraphic 8.0 (UG 8.0) software; in addition, PVCR orthopaedy was utilized to correct the scoliosis of the patient, and the biomechanical parameters, such as orthodontic force, vertebral body displacement, orthopedic rod stress, stress on the pin-bone interface of the vertebral body surface, and the stress on the intervertebral disc, were studied.ResultsThe 3D effective finite element model of scoliosis was successfully constructed by the Mimics software, the Geomagic Studio 12 software, and the UG 8.0 software, and the effectiveness was tested. PVCR orthopaedy could effectively solve the problem of scoliosis. The magnitude of the orthodontic force that a patient needed depended on the physical conditions and the personal orthodontic requirements of the patient. The maximum vertebral body displacement on the X-axis was the vertebral body L1, the maximum displacement on the Y-axis was the vertebral body T3, the maximum displacement on the Z-axis was the vertebral body T1, and the rang of orthopedic rod stress was 0.0050214e⁷ MPa to 0.045217e⁷ MPa, in which the maximum stress of 2 vertebral bodies in, above, and below the osteotomy area reached 0.045217e⁷ MPa, the stress on the pin-bone interface of the T10 vertebral body surface reached 11.83 MPa, and the stress of T8/T9 intervertebral disc reached 13.84 MPa.ConclusionThe 3D finite element model based on 3D finite element software was highly efficient, and its numerical simulation was accurate, which was important for the subsequent biomechanical analysis of PVCR orthopaedy. In addition, the vertebral stress of PVCR orthopaedy was different in each body part, which was mainly affected by the applied orthodontic force and the sites of the orthodontic area.     

椎动脉狭窄内血液两相流动数值模拟分析

目的:对应用三维重构得到的人体真实椎动脉进行血液两相流数值模拟,与经典单相流牛顿血液模型对比,分析动脉粥样硬化等病因与椎动脉狭窄处的血流动力学关系。方法:把考虑血细胞和血浆的两相流血液模型应用到逆向工程方法构建的基于人体生理解剖特征的椎动脉三维几何模型中去进行数值模拟,分析血细胞分布情况等血流动力学参数,并与单相流模型的模拟结果进行对比。结果:通过瞬态模拟计算,得到了椎动脉在心动周期内不同时刻的两相流和单相流模型的血流动力学参数。结论:通过对比单相流数值模拟结果,得出血管狭窄处血细胞出现聚集,血流更加复杂和低壁面切应力分布等与动脉粥样硬化及血栓的形成相关的结论。并且与两相流模型相比,单相流模型存在如无法获得如血细胞分布等不足,为进一步深入研究椎动脉等疾病的发病机理提供方法和理论支持。     

Parameter identification of the human lower limb under dynamic, transient torsional loading

The response of the lower limb to dynamic, transient torsional loading applied at the foot has been measured for a male test subject. The dynamic loading was provided by a computer controlled pneumatic system which applied single haversine (i.e. half cycle of a sine wave) axial moment pulses of variable amplitude (0-100 Nm) and duration (50-600 ms). Potentiometers measured the absolute rotations of the three leg segments. Test variables included rotation direction, weight bearing and joint flexion. Two approaches were explored for specifying parameters (i.e. inertia, damping, stiffness) of a three degree-of-freedom dynamic system model which best duplicated the measured response. One approach involved identification of linear parameters by means of optimization while the other approach entailed estimation. Parameter estimates, which included non-linear, asymmetric stiffness functions, were derived from the literature. The optimization was undertaken so as to identify parameter dependence on test variables. Results indicate that parameter values are influenced by test variables. Results also indicate that the non-linear, estimated model better approximates the experimental data than the linear, identified model. In addition to identifying parameters of a three degree-of-freedom model, parameters were also identified for a single degree-of-freedom model where the motion variable was intended to indicate the rotation of the in vivo knee. It is concluded that the simpler model offers good accuracy in predicting both magnitude and time of occurrence of peak knee axial rotations. Model motion fails to track the measured knee rotation subsequent to the peak, however.     

Cineradiographic study of forelimb movements during quadrupedal walking in the brown lemur (Eulemur fulvus, Primates: Lemuridae)

Movements of forelimb joints and segments during walking in the brown lemur (Eulemur fulvus) were analyzed using cineradiography (150 frames/sec). Metric gait parameters, forelimb kinematics, and intralimb coordination are described. Calculation of contribution of segment displacements to stance propulsion shows that scapular retroversion in a fulcrum near the vertebral border causes more than 60% of propulsion. The contribution by the shoulder joint is 30%, elbow joint 5%, and wrist joint 1%. Correlation analysis was applied to reveal the interdependency between metric and kinematic parameters. Only the effective angular movement of the elbow joint during stance is speed-dependent. Movements of all other forelimb joints and segments are independent of speed and influence, mainly, linear gait parameters (stride length, stance length). Perhaps the most important result is the hitherto unknown and unexpected degree of scapular mobility. Scapular movements consist of ante-/retroversion, adduction/abduction, and scapular rotation about the longitudinal axis. Inside rotation of the scapula (60 degrees -70 degrees ), together with flexion in the shoulder joint, mediates abduction of the humerus, which is not achieved in the shoulder joint, and is therefore strikingly different from humeral abduction in man. Movements of the shoulder joint are restricted to flexion and extension. At touch down, the shoulder joint of the brown lemur is more extended compared to that of other small mammals. The relatively long humerus and forearm, characteristic for primates, are thus effectively converted into stride length. Observed asymmetries in metric and kinematic behavior of the left and right forelimb are caused by an unequal lateral bending of the spinal column.