The glenohumeral joint rotation centre in vivo

Within the framework of the current call for standardization in upper extremity research, three methods to determine the glenohumeral joint rotation centre in vivo were tested. Therefore, subjects performed humeral movements, while a 3D electromagnetic tracking device registered the motion of the humerus with respect to the scapula. For the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations. The second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis. The experiment consisted of two parts, at first one subject was measured 10 times, subsequently one observer measured 10 subjects twice and another observer measured these subjects once. The first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4 mm, but the location of the centre differed significantly between methods (p<0.001). The second part, showed that inter- and intra-observer reliability was sufficiently for the sphere-fitting method and for the helical-axes method. The two observations of one observer differed significantly (p<0.008) using the regression method. The authors prefer the helical-axes method, it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis, it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research, and calculation time is short.     

The SCoRE residual: a quality index to assess the accuracy of joint estimations

The determination of an accurate centre of rotation (CoR) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. Despite the many functional approaches to estimate CoRs, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. The purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (SCoRE) as a reliable indirect measure of the error of the computed joint centre. To evaluate the SCoRE residual, numerical simulations were performed to evaluate CoR estimations at different ranges of joint motion. A statistical model was developed and used to determine the theoretical relationships among the SCoRE residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the CoR estimations to the known centre of rotation. We found that the equation err=0.5r(s) provides a reliable relationship among the CoR error, err, and the scaled SCoRE residual, r(s), providing that any skin marker artefact is first minimised using the optimal common shape technique (OCST). Measurements on six healthy volunteers showed a reduction of SCoRE residual from 11 to below 6mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. This study also demonstrates the significant benefit of the OCST for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. For the first time, this understanding of the SCoRE residual allows a measure of error in the non-invasive assessment of joint centres. This measure now enables a rapid assessment of the accuracy of the CoR as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.     

Relationship between lordosis and the position of the centre of reaction of the spinal disc

Whenever we stand upright in apparent static equilibrium, we are, in fact, continuously making minor adjustments in order to maintain our balance. For each intervertebral joint, a point must exist at which all moments applied to the joint are continually and dynamically balanced. This point, known as the centre of reaction, is a mathematical invention necessary to perform analyses of spinal motion, but which need not be associated with any real anatomical structure.As the spine flexes and extends, this centre is expected to move; where it moves and the rationale for its motion is worthy of enquiry. In this paper, we propose that the centre of reaction remains confined to the nucleus of the disc, but only if one simple but crucial assumption is made; that the motion of the spine and control of its musculature maintain a minimum and equal stress at each intervertebral joint. This is a simple hypothesis which imposes a very specific relationship between lordosis and the centre of reaction. We investigate this relationship and its consequences on the teaching of lifting.The impossibility of designing experiments adequately to verify this hypothesis prevents in vivo verification, and, therefore, the model's verification must be made through the inferred consequences. For example, the capability of correctly predicting physiological responses of the musculoskeletal system is an indication of the validity of a model; however, this is not universally accepted. In this particular case, additional experimental data are available in the form of the locus of the centre of rotation of a vertebra vis-à-vis its lower neighbour as the spine flexes and extends.It is instructive to compare the predicted locus of the centre of reaction to experimentally determined locus of the centre of rotation; more than just coincidental similarities are found.     

Validation of a video-based motion analysis technique in 3-D dynamic scapular kinematic measurements

BackgroundCurrent non-invasive 3-D scapular kinematic measurement techniques such as electromagnetic tracking are subjected to restrictions of wired sensors and limited capture space. Video-based motion analysis provides greater freedom with relatively less movement restriction. However, video-based motion analysis was rarely used in and not validated for scapular kinematics.MethodsScapular kinematics of five subjects performing abduction, scaption, and internal/external rotation was captured simultaneously with video-based motion analysis and dynamic stereo X-ray, a gold standard for tracking scapular movements. The data from video-based motion analysis was correlated with the data from dynamic stereo X-ray for validity evaluation.FindingsStrong and significant correlations were identified in scapular protraction/retraction and medial/lateral rotation during abduction and scaption, and scapular medial/lateral rotation and anterior/posterior tilt during internal/external rotation.InterpretationVideo-based motion analysis is valid for evaluating a single subject's scapular movement pattern in protraction/retraction during abduction and scaption, and medial/lateral-rotation during internal/external rotation. Anterior/posterior-tilt during abduction and scaption should be investigated with caution. Video motion analysis is also valid for evaluating group average of scapular kinematics except for protraction/retraction during internal/external rotation. While acknowledging the inherent limitations, video-based motion analysis is an appropriate technique for tracking scapular kinematics.     

The accuracy of measuring glenohumeral motion with a surface humeral cuff

Conclusions about normal and pathologic shoulder motion are frequently made from studies using skin surface markers, yet accuracy of such sensors representing humeral motion is not well known. Nineteen subjects were investigated with flock of birds electromagnetic sensors attached to transcortical pins placed into the scapula and humerus, and a thermoplastic cuff secured on the arm. Subjects completed two repetitions of raising and lowering the arm in the sagittal, scapular and coronal planes, as well as shoulder internal and external rotation with the elbow at the side and abducted to 90°. Humeral motion was recorded simultaneously from surface and bone fixed sensors. The average magnitude of error was calculated for the surface and bone fixed measurements throughout the range of motion. ANOVA tested for differences across angles of elevation, raising and lowering, and differences in body mass index. For all five motions tested, the plane of elevation rotation average absolute error ranged from 0-2°, while the humeral elevation rotation average error ranged from 0-4°. The axial rotation average absolute error was much greater, ranging from 5° during elevation motions to approaching 30° at maximum excursion of internal/external rotation motions. Average absolute error was greater in subjects with body mass index greater than 25. Surface sensors are an accurate way of measuring humeral elevation rotations and plane of elevation rotations. Conversely, there is a large amount of average error for axial rotations when using a humeral cuff to measure glenohumeral internal/external rotation as the primary motion.     

Calculating the 2D motion of lumbar vertebrae using splines

In this study we investigate the use of splines and the ICP method [Besl, P., McKay, N., 1992. A method for registration of 3d shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 239-256.] for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane. We demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion/extension radiographs of the lumbar spine. In an in vitro error study, the method displayed an average error of rotation of 0.44 +/- 0.45 degrees, and an average error in FCR calculation of 7.6 +/- 8.5 mm. The method was shown to be superior to that of Crisco et al. [Two-dimensional rigid-body kinematics using image contour registration. Journal of Biomechanics 28(1), 119-124.] and Brinckmann et al. [Quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace: Part i - the shape of vertebrae and intervertebral discs - study of a yound, healthy population and a middle-aged control group. Clinical Biomechanics Supplement 1, S5-S83.] for the tests performed here. In general, we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons. First, with appropriate software, splines require less effort to define and are a compact representation, with most vertebra outlines using less than 30 control points. Second, splines are inherently sub-pixel representations of curves, even if the control points are limited to pixel resolutions. Third, there is a well-defined method (the ICP algorithm) for registering shapes represented as splines. Finally, like digitised curves, splines are able to represent a large class of shapes with little effort, but reduce potential segmentation errors from two dimensions (parallel and perpendicular to the image gradient) to just one (parallel to the image gradient). We have developed an application for performing all the necessary computations which can be downloaded from http://www.claritysmart.com.     

构象耦合作用下驱动蛋白的定向运动

用电偶极子的转动来描述驱动蛋白的构象变化。把微管的构象简化为若干电偶极子的线性排列。驱动蛋白和微管之间的相互作用可看作偶极子－偶极子的耦合作用。计算结果表明：这种耦合作用能够产生沿微管的定向粒子流,并且粒子平均位移反映了驱动蛋白实验结果的主要特征。     

Kinematics of the upper cervical spine during high velocity-low amplitude manipulation. Analysis of intra- and inter-operator reliability for pre-manipulation positioning and impulse displacements

To date, kinematics data analyzing continuous 3D motion of upper cervical spine (UCS) manipulation is lacking. This in vitro study aims at investigating inter- and intra-operator reliability of kinematics during high velocity low amplitude manipulation of the UCS.Three fresh specimens were used. Restricted dissection was realized to attach technical clusters to each bone (skull to C₂). Motion data was obtained using an optoelectronic system during manipulation. Kinematics data were integrated into specific-subject 3D models to provide anatomical motion representation during thrust manipulation. The reliability of manipulation kinematics was assessed for three practitioners performing two sessions of three repetitions on two separate days.For pre-manipulation positioning, average UCS ROM (SD) were 10° (5°), 22° (5°) and 14° (4°) for lateral bending, axial rotation and flexion–extension, respectively. For the impulse phase, average axial rotation magnitude ranged from 7° to 12°. Reliability analysis showed average RMS up to 8° for pre-manipulation positioning and up to 5° for the impulse phase.As compared to physiological ROM, this study supports the limited angular displacement during manipulation for UCS motion components, especially for axial rotation. Kinematics reliability confirms intra- and inter-operator consistency although pre-manipulation positioning reliability is slightly lower between practitioners and sessions.     

Moiré patterns: an accurate technique for determination of the locus of the centres of rotation

This study describes an accurate technique for the determination of the centre of rotation of small angles. The moiré fringe method localizes the centre of rotation by defining two primary fringes, each of which is found by the intersection of three lines. The primary fringes intersect at the centre of rotation at 90 degrees to each other, the angle least likely to produce an error in measurement. By utilizing joints with known centres of rotation, we have found that the method is extremely accurate and reproducible to within 2 mm of the real centre for angular changes as small as 3 degrees. This technique is useful in evaluating whether a joint is a simple hinge, i.e. rotating about a single axis of rotation or whether the joint moves about a changing axis of rotation referred to as a locus or centrode.     

Centre of resistance and centre of rotation of a tooth: experimental determination,computer simulation and the effect of tissue nonlinearity

The centre of resistance and centre of rotation of a tooth are key concepts in orthodontics. Determining the coordinates of these points is essential for planning orthodontic tooth movement. The paper proposes a procedure for experimental determination of the two centres, verifies a previously developed mathematical theory through computer simulations and evaluates the effect of nonlinearity of the periodontal ligament on the parameters related to the centres. The paper relies on the mathematical theory of a rigid body embedded in an elastic medium, physical experiment, finite element method and a simple nonlinear theory of the tooth. The concept of the centre of resistance requires a revision if nonlinearity is taken into account.     

Effects of gleno-humeral joint centre mislocation on gleno-humeral kinematics and kinetics

The gleno-humeral (GH) rotation centre is typically estimated using predictive or functional methods, however these methods may lead to location errors. This study aimed at determining a location error threshold above which statistically significant changes in the values of kinematic and kinetic GH parameters occur. The secondary aims were to quantify the effects of the direction of mislocation (X, Y or Z axis) of the GH rotation centre on GH kinematic and kinetic parameters.

Shoulder flexion and abduction movements of 11 healthy volunteers were recorded using a standard motion capture system (Vicon, Oxford Metrics Ltd, Oxford, UK), then GH kinematic and kinetic parameters were computed. The true position of the GH rotation centre was determined using a low dose x-ray scanner (EOS? imaging, France) and this position was transferred to the motion data. GH angles and moments were re-computed for each position of the GH rotation centre after errors of up to ± 20?mm were added in increments of ± 5?mm to each axis. The three-dimensional error range was 5?mm to 34.65?mm.

GH joint angle and moment values were significantly altered from 10?mm of three-dimensional error, and from 5?mm of error on individual axes. However, errors on the longitudinal and antero-posterior axes only caused very small alterations of GH joint angle and moment values respectively. Future research should develop methods of GH rotation centre estimation that produce three-dimensional location errors of less than 10?mm to reduce error propagation on GH kinematics and kinetics.     

IMU: Inertial sensing of vertical CoM movement

The purpose of this study was to use a quaternion rotation matrix in combination with an integration approach to transform translatory accelerations of the centre of mass (CoM) from an inertial measurement unit (IMU) during walking, from the object system onto the global frame. Second, this paper utilises double integration to determine the relative change in position of the CoM from the vertical acceleration data. Five participants were tested in which an IMU, consisting of accelerometers, gyroscopes and magnetometers was attached on the lower spine estimated centre of mass. Participants were asked to walk three times through a calibrated volume at their self-selected walking speed. Synchronized data were collected by an IMU and an optical motion capture system (OMCS); both measured at 100 Hz. Accelerations of the IMU were transposed onto the global frame using a quaternion rotation matrix. Translatory acceleration, speed and relative change in position from the IMU were compared with the derived data from the OMCS. Peak acceleration in vertical axis showed no significant difference (p?0.05). Difference between peak and trough speed showed significant difference (p<0.05) but relative peak-trough position between the IMU and OMCS did not show any significant difference (p?0.05). These results indicate that quaternions, in combination with Simpsons rule integration, can be used in transforming translatory acceleration from the object frame to the global frame and therefore obtain relative change in position, thus offering a solution for using accelerometers in accurate global frame kinematic gait analyses.     

New least squares solutions for estimating the average centre of rotation and the axis of rotation.

A new method is proposed for estimating the parameters of ball joints, also known as spherical or revolute joints and hinge joints with a fixed axis of rotation. The method does not require manual adjustment of any optimisation parameters and produces closed form solutions. It is a least squares solution using the whole 3D motion data set. We do not assume strict rigidity but only that the markers maintain a constant distance from the centre or axis of rotation. This method is compared with other methods that use similar assumptions in the cases of random measurement errors, systematic skin movements and skin movements with random measurement noise. Simulation results indicate that the new method is superior in terms of the algorithm used, the closure of the solution, consistency and minimal manual parameter adjustment. The method can also be adapted to joints with translational movements.     

Error reduction in the finite helical axis for knee kinematics

Traditionally the FHA is calculated stepwise between data points (sFHA), requiring down sampling to achieve a sufficiently large step size to minimize error. This paper proposes an alternate FHA calculation approach (rFHA), using a unique reference position to reduce error associated with small rotation angles. This study demonstrated error reduction using the rFHA approach relative to the sFHA approach. Furthermore, the rFHA in the femur is defined at each time point providing a continuous representation of joint motion. These characteristics enable the rFHA to quantify small differences in knee joint motion, providing an excellent measure to quantify knee joint stability.     

SED88: a Pascal program for the analysis of sedimentation equilibrium data

Analytical ultracentrifugation is commonly used for the determinationof molecular weights (sedimentation equilibrium) and sedimentationcoefficients (sedimentation rate) of biological macromoleculesin solution. A Turbo Pascal program for the analysis of sedimentationequilibrium centrifugation data produced by absorbance opticalsystems is described. The user may enter data from a scan ofabsorbance versus distance from the centre of rotation, viaa graphics tablet (or ASCII file). This is subsequently manipulatedto yield an apparent weight average molecular weight for thegiven sample. Plots of In (absorbance) versus (radius²) mayalso be produced. The method described uses readily availablecomputational equipment requiring only a graphics tablet inaddition to an IBM PC compatible computer. This technique andthe software developed have been used to investigate the molecularweight range of two International Humic Substances Society (IHSS)reference samples from the Suwannee River. Received on October 7, 1988; accepted on December 12, 1988     

A MR imaging procedure to measure tarsal bone rotations

Magnetic resonance imaging offers unique insights into three-dimensional foot bone motion. Thereby, adequate devices enabling defined loading and positioning of the foot are needed to profit from this noninvasive procedure. Tarsal bone positions of three healthy subjects were repeatedly measured in a pronated and a supinated foot excursion under bodyweight with a newly developed MR imaging procedure. The quantification of the transferred motion from the loading and positioning device to the calcaneus and an estimation of the required degrees to distinguish between tarsal joint rotations were used to evaluate the applicability of the procedure to investigate tarsal joint motion. It was found that 45-70% (75-95%) of the externally applied 15 deg foot pronation (supination) were transferred to the calcaneus. Furthermore, the talonavicular joint showed the largest amount of rotation up to 20 deg eversion-inversion and abadduction, followed by the subtalar joint showing nearly half of that motion. Considerably less motion was found between the cuboid and calcaneus (about 2-6 deg) and the cuboid nearly did not rotate relative to the navicular (on average 1 deg). The estimated necessary differences between tarsal joint movements to identify individual kinematic behavior were in the order of 2 deg (4 deg related to the talonavicular joint). Since the results were in agreement with the literature, it is concluded that the applicability of the presented procedure to investigate tarsal bone mechanics is warranted. The possibility to evaluate 3D tarsal joint motion in combination with bone morphology (e.g., joint curvature) may provide new insights in the still uncertain relationship between foot function and foot morphology.     

In-vivo measurement of dynamic joint motion using high speed biplane radiography and CT: application to canine ACL deficiency

Dynamic assessment of three-dimensional (3D) skeletal kinematics is essential for understanding normal joint function as well as the effects of injury or disease. This paper presents a novel technique for measuring in-vivo skeletal kinematics that combines data collected from high-speed biplane radiography and static computed tomography (CT). The goals of the present study were to demonstrate that highly precise measurements can be obtained during dynamic movement studies employing high frame-rate biplane video-radiography, to develop a method for expressing joint kinematics in an anatomically relevant coordinate system and to demonstrate the application of this technique by calculating canine tibio-femoral kinematics during dynamic motion. The method consists of four components: the generation and acquisition of high frame rate biplane radiographs, identification and 3D tracking of implanted bone markers, CT-based coordinate system determination, and kinematic analysis routines for determining joint motion in anatomically based coordinates. Results from dynamic tracking of markers inserted in a phantom object showed the system bias was insignificant (-0.02 mm). The average precision in tracking implanted markers in-vivo was 0.064 mm for the distance between markers and 0.31 degree for the angles between markers. Across-trial standard deviations for tibio-femoral translations were similar for all three motion directions, averaging 0.14 mm (range 0.08 to 0.20 mm). Variability in tibio-femoral rotations was more dependent on rotation axis, with across-trial standard deviations averaging 1.71 degrees for flexion/extension, 0.90 degree for internal/external rotation, and 0.40 degree for varus/valgus rotation. Advantages of this technique over traditional motion analysis methods include the elimination of skin motion artifacts, improved tracking precision and the ability to present results in a consistent anatomical reference frame.     

Fractal rotation isolates mechanisms for form-dependent motion in human vision

Here, we describe a motion stimulus in which the quality of rotation is fractal. This makes its motion unavailable to the translation-based motion analysis known to underlie much of our motion perception. In contrast, normal rotation can be extracted through the aggregation of the outputs of translational mechanisms. Neural adaptation of these translation-based motion mechanisms is thought to drive the motion after-effect, a phenomenon in which prolonged viewing of motion in one direction leads to a percept of motion in the opposite direction. We measured the motion after-effects induced in static and moving stimuli by fractal rotation. The after-effects found were an order of magnitude smaller than those elicited by normal rotation. Our findings suggest that the analysis of fractal rotation involves different neural processes than those for standard translational motion. Given that the percept of motion elicited by fractal rotation is a clear example of motion derived from form analysis, we propose that the extraction of fractal rotation may reflect the operation of a general mechanism for inferring motion from changes in form.     

Three-dimensional in vivo motion of adult hind foot bones

Knowledge of hind foot bone motion is important for understanding gait as well as various foot pathologies, but the three-dimensional (3D) motion of these bones remains incompletely understood. The purpose of this study was to quantify the motion of the talus, calcaneus, navicular, and cuboid in normal adult feet during open chain quasi-static uniplanar plantar flexion motion. Magnetic resonance images of the right feet of six normal young adult males were taken from which 3D virtual models were made of each hind foot bone. The 3D motion of these models was analyzed. Each hind foot bone rotated in the same plane about half as much as the foot (mean 0.54 degrees of bone rotation per degree of foot motion, range 0.40-0.73 degrees per degree of foot motion as measured relative to the fixed tibia). Talar motion was primarily uniaxial, but the calcaneus, navicular, and cuboid bones exhibited biplanar (sometimes triplanar) translation in addition to biaxial rotation. Net translational motions of these bones averaged 0.39 mm of bone translation per degree of foot motion (range 0.06-0.62 mm per degree of foot motion). These data reflect the functional anatomy of the foot, extend the findings of prior studies, provide a standard for comparison to patients with congenital or acquired foot deformities, and establish an objective reference for quantitatively assessing the efficacy of various hind foot therapies.