Proposal of a thorax segment coordinate system for the 3D kinematical analysis of the cervical spine

The International Society of Biomechanics detailed the recommendations for 3D kinematics of intervertebral movements (Wu, et al. 2002. J Biomech. 35:543–548), but does not specify how to adapt this proposal to describe the kinematics of the cervical spine, between the head and the thorax. The analysis of the literature shows that no consensus exists at the present time on this subject. The objective of our study was to identify the reference points that formed the most rigid triplet allowing building an optimal thorax segment coordinate system (SCS). We thus measured the variations of distances between markers placed on various anatomical landmarks, and then the deformations of the combinations of three markers on different cervical movements of a sample of 10 asymptomatic subjects. The results show that the triplet formed by the sternum and both acromions undergoes less deformation on the flexion–extension movement. For all the other movements (lateral bending, axial rotation and complex movements), the triplet formed by sternum, T3 and TH (positioned on the thoracic spinal column, in a horizontal plane containing the sternal marker), undergoes less deformation. As a conclusion, the optimal triplet to define the thorax SCS for 3D kinematical analysis of the cervical spine is that formed by the markers: sternum, T3 and TH. This triplet makes it possible to define an orthonormal SCS, the axes of which coincide with anatomical directions, i.e. with the functional axes of the movement.     

Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

Evidence for IHA migration during axial rotation of a lumbar spine segment by using a novel high-resolution 6D kinematic tracking system

The biomechanical properties of the lumbar spine have long been studied. However, despite its enormous importance, basic functional and morphological properties have been not well understood and require further experimental analysis since data concerning the spatial instantaneous segmental motions are hardly available. This study describes the theoretical background and the technical properties of an innovative method for tracking the instantaneous 3D motion of human spinal segments in vitro at high spatial resolution. This new acquisition system allows to scrutinise closely the location and alignment of the segmental instantaneous helical axis (IHA) and the respective screw pitch as functions of the absolute rotational angle. The required precision of the measuring device was attained (a) by six highly resolving linear inductive displacement sensors in a special spatially configuration (3-2-1), (b) by a method to apply torque and force independently of each other without counteraction, and (c) by suppression of vibrations. The validity and reliability of the experimental set-up and the numerical method of data analysis were tested by subjects of known mechanical properties. In vitro experiments with a human lumbar segment (L3/L4, autopsy material) demonstrated that (a) the IHA migrated during axial rotation from one segmental articulatio zygapophysialis to the other joint, (b) the IHA tilted medial-laterally, and (c) the pitch of the screw altered linearly as a function of the rotational angle. This phenomenon is traced back to the guidance of the articluationes zygapophysiales. The validation of the method allows to map segments of the entire vertebral column. The results can be used as benchmarks for future models of the human spine.     

A biomechanical model for the analysis of the cervical spine in static postures.

To gain a better understanding of the forces working on the cervical spine, a spatial biomechanical computer model was developed. The first part of our research was concerned with the development of a kinematic model to establish the axes of rotation and the mutual position of the head and vertebrae with regard to flexion, extension, lateroflexion and torsion. The next step was the introduction of lines of action of muscle forces and an external load, created by gravity and accelerations in different directions, working on the centre of gravity of the head and possibly a helmet. Although the results of our calculations should be interpreted cautiously in the present stage of our research, some conclusions can be drawn with respect to different head positions. During flexion muscle forces and joint reaction forces increase, except the force between the odontoid and the ligamentum transversum atlantis. This force shows a minimum during moderate flexion. The joint reaction forces on the levels C0-C1, C1-C2, and C7-T1 reach minimum values during extension, each in different stages of extension. Axial rotation less than 35 degrees does not need great muscle forces, axial rotation further than 35 degrees causes muscle forces and joint reaction forces to increase fast. While performing, lateral flexion muscle forces and joint reaction forces must increase rapidly to balance the head. We obtained some indications that the order of magnitude of the calculated forces is correct.     

The effect of coordinate system choice and segment reference on RSA-based knee translation measures

Roentgen stereophotogrammetric analysis (RSA) can be utilized to accurately describe joint kinematics, but even when measuring small displacements within radiographically discernible structures, standardized reference frames are imperative for useful comparison across patients and across studies. In the current paper, accurately controlled laboratory models demonstrated the considerable influence that a mere 1.9-cm offset of the origin of the coordinate system from the rotation axes could exert on translation measures when rotations were occurring. In addition, the use of two different coordinate systems to gauge translation on a radiographic anterior-posterior (A-P) knee laxity exam resulted in a significant correlation (R(2)=0.562) between the two systems; however, differences of up 9.28 mm were found between corresponding measurements. This implies that clinical conclusions can potentially be upheld or refuted, based on the same data set, subject to coordinate system definition. Although the data analyzed presently involved the knee joint, similar issues surround the RSA motion analysis of other joints as well.     

A new coordinate system using the orbital axis for morphological analysis of primate skulls

A new coordinate system for primate skulls was defined by the orbital axis and the validity of the system was examined. This system is thought to be equivalent throughout the primates. With the aid of photogrammetry the three-dimensional coordinates of 39 points on the skulls of 479 individuals comprising 54 species including man were accurately measured. The orbital structure is morphologically stable and its axis represents a comparative horizontal. The midsagittal plane and the bilateral symmetry of the cranium are also stable. The morphological stability in angular dimensions is confirmed by a standard deviation smaller than 2.0°. The major evolutionary change in the neurocranium is the inclination of the cranial base from the orbital horizon, and the inclination is related to the neurocranial size. The ear-eye plane is generally inapplicable to the primates, because it is affected by the orbital size and the descent of the auricular part due to the inclination of the cranial base. The clivus line or the vestibular coordinate system is not desirable as the horizontal, either. The evolutionary development of the facial part of the cranium is independent of that of the neurocranium and these two parts are separated by the orbital horizon.     

Failure analysis of a beam-column under oblique-eccentric loading: potential failure surfaces for cervical spine trauma.

For a cantilever beam-column with one end built-in and the free end subjected to an oblique-eccentric arbitrary concentrated force, general formulas to produce failure were derived. The original generalized uniform solution to the oblique-eccentric buckling problem was obtained. The Secant formula and Euler's formula were proved to be specific cases in this general solution. The load ratio, F/aE, was derived as functions of the force acting direction, alpha, the slenderness ratio, L/r, as well as the eccentricity ratio, ec/r2. Material and buckling failures aspects were combined in a uniform structural failure analysis. Safe regions for the load ratio, F/aE, were visualized in the three-dimensional (F/aE)-alpha-(L/r) space with the eccentricity ratios, ec/r2, as a parameter. The column failure factor, kL, was shown to be a key index controlling both aspects of failure as well as the orientation of the second stiffest region. The angle alpha E = tan-1 (2L/pi e) for kL = pi/2 is the singular point for both strength and buckling failure, and alpha II = tan-1 (2L/3e) for KL = 0 is the upper bound of the second stiffest region. The feasible domain of the second stiffest region is bounded by alpha E and alpha II both of which are only functions of geometrical properties. The implications of these analyses for the experimental validation of cervical spine trauma are discussed.     

UNIQUIMER 3D, a software system for structural DNA nanotechnology design, analysis and evaluation

A user-friendly software system, UNIQUIMER 3D, was developed to design DNA structures for nanotechnology applications. It consists of 3D visualization, internal energy minimization, sequence generation and construction of motif array simulations (2D tiles and 3D lattices) functionalities. The system can be used to check structural deformation and design errors under scaled-up conditions. UNIQUIMER 3D has been tested on the design of both existing motifs (holiday junction, 4 × 4 tile, double crossover, DNA tetrahedron, DNA cube, etc.) and nonexisting motifs (soccer ball). The results demonstrated UNIQUIMER 3D's capability in designing large complex structures. We also designed a de novo sequence generation algorithm. UNIQUIMER 3D was developed for the Windows environment and is provided free of charge to the nonprofit research institutions.     

Numerical simulation of flow field around a cow using 3-D body-fitted coordinate system

A 3-D theoretical model that characterizes the flow field around a single cow or multiple cows was developed. A general computer code that simulates the flow field that takes into account the shape of a cow and the boundary conditions of the enclosure was developed. A system of visualization of flow field that provides theoretical basis for the study of heat and mass transfer between a cow and its environment was developed. Qualitative and quantitative analyses were performed to determine the effect of cow orientation with respect to direction of airflow on convective heat exchange between the cow and its environment. The direction of air movement is not an important factor in influencing convective heat transfer between a cow and its environment.     

A three-dimensional model of the human cervical spine for impact simulation

A three-dimensional analytical model of the cervical spine is described. The cervical vertebrae and the head are modeled as rigid bodies which are interconnected by deformable elements representing the intervertebral disks, facet joints, ligaments and muscles. A special pentahedral continuum element for representing the articular facets is described which effectively maintains stability of the cervical spine in both lateral and frontal plane accelerations, which is very difficult with multi-spring models of the facets. A simplified representation is used for the spine and body below the level of T1. The neck musculature is modeled by over 100 muscle elements representing 22 major muscle groups in the neck. The model has been validated for frontal and sideways impact accelerations by simulating published experimental data. Results are also presented to show the effects of the stretch reflex response on the dynamics of the head and neck under moderate acceleration.     

Evaluation of alternative technical markers for the pelvic coordinate system

In this study, we evaluated alternative technical markers for the motion analysis of the pelvic segment. Thirteen subjects walked eight times while tri-dimensional kinematics were recorded for one stride of each trial. Five marker sets were evaluated, and we compared the tilt, obliquity, and rotation angles of the pelvis segment: (1) standard: markers at the anterior and posterior superior iliac spines (ASIS and PSIS); (2) markers at the PSIS and at the hip joint centers, HJCs (estimated by a functional method and described with clusters of markers at the thighs); (3) markers at the PSIS and HJCs (estimated by a predictive method and described with clusters of markers at the thighs); (4) markers at the PSIS and HJCs (estimated by a predictive method and described with skin-mounted markers at the thighs based on the Helen-Hayes marker set); (5) markers at the PSIS and at the iliac spines. Concerning the pelvic angles, evaluation of the alternative technical marker sets evinced that all marker sets demonstrated similar precision across trials (about 1°) but different accuracies (ranging from 1° to 3°) in comparison to the standard marker set. We suggest that all the investigated marker sets are reliable alternatives to the standard pelvic marker set.     

The second stiffest axis of a beam-column: implications for cervical spine trauma

Based on an idealized model of a homogeneous, isotropic beam-column, the second stiffest axis under static loading was derived. The maximum allowable force for the second stiffest axis was then examined. The ratio of the maximum allowable forces of the second stiffest axis to the stiffest axis was established. The stiffness ratio of the second stiffest axis to the stiffest axis was also found. Taking buckling into consideration, the safe load region for all possible acting directions was derived. The implications of the idealized model for cervical spine trauma are discussed.     

Evaluation of a robot-assisted testing system for multisegmental spine specimens

Mono- and multi-segmental testing methods are required to identify segmental motion patterns and evaluate the biomechanical behaviour of the spine. This study aimed to evaluate a new testing system for multisegmental specimens using a robot combined with an optical motion analysis system. After validation of the robotic system for accuracy, two groups of calf specimens (six monosegmental vs. six multisegmental) were mounted and the functional unit L3-4 was observed. Using rigid body markers, range of motion (ROM), elastic zone (EZ) and neutral zone (NZ), as well as stiffness properties of each functional spine unit (FSU) was acquired by an optical motion capture system. Finite helical axes (FHA) were calculated to analyse segmental movements. Both groups were tested in flexion and extension. A pure torque of 7.5 Nm was applied. Statistical analyses were performed using the Mann-Whitney U-test. Repeatability of robot positioning was -0.001±0.018 mm and -0.025±0.023° for translations and rotations, respectively. The accuracy of the optical system for the proposed set-up was 0.001±0.034 mm for translations and 0.075±0.12° for rotations. No significant differences in mean values and standard deviations of ROM for L3-4 compared to literature data were found. A robot-based facility for testing multisegmental spine units combined with a motion analysis system was proposed and the reliability and reproducibility of all system components were evaluated and validated. The proposed set-up delivered ROM results for mono- and multi-segmental testing that agreed with those reported in the literature. Representing the FHA via piercing points determined from ROM was the first attempt showing a relationship between ROM and FHA, which could facilitate the interpretation of spine motion patterns in the future.