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.     

Robust estimation of dominant axis of rotation

A simple method is developed for robustly estimating a fixed dominant axis of rotation (AoR) of anatomical joints from surface marker data. Previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the AoR. However, when there is limited joint range of motion and rotation due to a second degree of freedom, minimizing only the planar error can give poor estimates of the AoR direction. Optimizing a cost function which includes the error component within a plane, instead of only the component orthogonal to a plane, leads to improved estimates of the AoR direction for joints which exhibit additional rotational motion from a second degree of freedom. Results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane-fitting techniques. Estimates of the flexion-extension AoR from empirical motion capture data of the knee and index finger joints were also more anatomically plausible.     

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.     

Comparison of the SCoRE and HA methods for locating in vivo the glenohumeral joint centre

A recent paper has described a new functional method, the symmetrical centre of rotation (SCoRE), for locating joint centre position [Ehrig, R.M., Taylor, W.R., Duda, G.N., Heller, M.O., 2006. A survey of formal methods for determining the centre of rotation of ball joints. Journal of Biomechanics 39 (15), 2798-2809]. For in vitro analyses, the SCoRE method showed better precision than helical axis (HA) or sphere fitting methods. Despites HA determination is very sensitive to small angular velocity, the International Society of Biomechanics has recommended to use HA for locating the glenohumeral joint centre. This paper aims at comparing the SCoRE method with the HA method for locating in vivo the glenohumeral joint centre according to the movement characteristics. Nine subjects performed 10 cycles of three different movements at two different velocities. For each test (combination of movements) the location of the centre of rotation was estimated with both methods (SCoRE and HA). Analyses focused on the 3D location of the glenohumeral joint centre and on the repeatability of location (standard deviation). This study showed that SCoRE and HA methods yielded the same GH location. Nevertheless, with SCoRE method, the location of the glenohumeral joint centre was different according to the test. This study evidenced that the SCoRE method was more precise than HA method (error of 3 mm versus 4.6 mm) and that the GH location with the SCoRE method was not affected by movements with slow velocities.     

Estimation of the axis of a screw motion from noisy data--a new method based on Plücker lines

The problems of estimating the motion and orientation parameters of a body segment from two n point-set patterns are analyzed using the Plücker coordinates of a line (Plücker lines). The aim is to find algorithms less complex than those in conventional use, and thus facilitating more accurate computation of the unknown parameters. All conventional techniques use point transformation to calculate the screw axis. In this paper, we present a novel technique that directly estimates the axis of a screw motion as a Plücker line. The Plücker line can be transformed via the dual-number coordinate transformation matrix. This method is compared with Schwartz and Rozumalski [2005. A new method for estimating joint parameters from motion data. Journal of Biomechanics 38, 107-116] in simulations of random measurement errors and systematic skin movements. Simulation results indicate that the methods based on Plücker lines (Plücker line method) are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements. This investigation yielded practical results, which can be used to locate the axis of a screw motion in a noisy environment. Developing the dual transformation matrix (DTM) from noisy data and determining the screw axis from a given DTM is done in a manner analogous to that for handling simple rotations. A more robust approach to solve for the dual vector associated with DTM is also addressed by using the eigenvector and the singular value decomposition.     

Evolutionary optimization for robust hierarchical computation of the rotation centres of kinematic chains from reduced ranges of motion the lower spine case

A novel technique based on evolutionary optimization is proposed here to compute the average rotation centres (RCs) of ball joints linked into kinematic chains using 3D trajectories of the markers attached to the external surface of the corresponding articulated structures. The chain is hierarchically solved by iteratively minimizing the variance of the marker distances from the actual RC through an evolutional strategy method (ESM) from proximal to distal joints. In particular, the technique is compared to the non-rigid sphere-fitting method, recently proposed in literature and implemented through a closed-form solution (CFS), in conditions of random and systematic noise superimposed to the marker coordinates. Results from simulated motions showed that, in case of small range of motion (5°, 10°) the performance of CFS is really unreliable whereas ESM provided satisfactory accuracy. Error propagation along the kinematic chain was found to be negligible. Also in the case of systematic errors, ESM provides an accuracy that is sensibly better than that of the CFS. As a case study, ESM was applied to the in vivo computation of the RCs of the vertebrae in the lower spine region using a specific marker protocol. A set of spine movements by a normal adult male, recorded by an optoelectronic motion capture system, were processed with the developed method. The variability of the estimated average RCs was small (few millimeters) in agreement with the literature data from cadaveric studies and X-ray imaging.     

The three-dimensional kinematics and flexibility characteristics of the human ankle and subtalar joints--Part I: Kinematics

The in-vitro, three dimensional kinematic characteristics of the human ankle and subtalar joint were investigated in this study. The main goals of this investigation were: 1) To determine the range of motion of the foot-shank complex and the associated range of motion of the ankle and subtalar joints; 2) To determine the kinematic coupling characteristics of the foot-shank complex, and 3) To identify the relationship between movements at the ankle and subtalar joints and the resulting motion produced between the foot and the shank. The tests were conducted on fifteen fresh amputated lower limbs and consisted of incrementally displacing the foot with respect to the shank while the motion of the articulating bones was measured through a three dimensional position data acquisition system. The kinematic analysis was based on the helical axis parameters describing the incremental displacements between any two of the three articulating bones and on a joint coordinate system used to describe the relative position between the bones. From the results of this investigation it was concluded that: 1) The range of motion of the foot-shank complex in any direction (dorsiflexion/plantarflexion, inversion/eversion and internal rotation/external rotation) is larger than that of either the ankle joint or the subtalar joint.; 2) Large kinematic coupling values are present at the foot-shank complex in inversion/eversion and in internal rotation/external rotation. However, only a slight amount of coupling was observed to occur in dorsiflexion/plantarflexion.; 3) Neither the ankle joint nor the subtalar joint are acting as ideal hinge joints with a fixed axis of rotation.; 4) Motion of the foot-shank complex in any direction is the result of rotations at both the ankle and the subtalar joints. However, the contribution of the ankle joint to dorsiflexion/plantarflexion of the foot-shank complex is larger than that of the subtalar joint and the contribution of the subtalar joint to inversion/eversion is larger than that of the ankle joint.; 5) The ankle and the subtalar joints have an approximately equal contribution to internal rotation/external rotation movements of the foot-shank complex.     

The physical basis of gravity stimulus nullification by clinostat rotation

The question of how rotation on a horizontal axis clinostat removes plants from the influence of the gravitational stimulus is answered. It is shown that appropriate horizontal axis clinostat rotation restricts the fall of intracellular particles to a quasi-circular path such that the position of the particle remains virtually stationary within cells. The displacement of the path of fall, due to centrifugal force, is then considered, and a method of determining the optimal rotation rate is developed from physical principles. This method selects the rotation rate which minimizes the volume of cytoplasm through which particles pass under the joint influence of centrifugal and gravitational forces. With the recognition that single axis clinostats are ineffective with large plants or for long experiments, a new type of clinostat is proposed on which intracellular conditions can be rendered virtually identical to those of plants in satellite free fall regardless of plant size or duration of experiment.     

Cervical helical axis characteristics and its center of rotation during active head and upper arm movements-comparisons of whiplash-associated disorders, non-specific neck pain and asymptomatic individuals

The helical axis model can be used to describe translation and rotation of spine segments. The aim of this study was to investigate the cervical helical axis and its center of rotation during fast head movements (side rotation and flexion/extension) and ball catching in patients with non-specific neck pain or pain due to whiplash injury as compared with matched controls. The aim was also to investigate correlations with neck pain intensity. A finite helical axis model with a time-varying window was used. The intersection point of the axis during different movement conditions was calculated. A repeated-measures ANOVA model was used to investigate the cervical helical axis and its rotation center for consecutive levels of 15 degrees during head movement. Irregularities in axis movement were derived using a zero-crossing approach. In addition, head, arm and upper body range of motion and velocity were observed. A general increase of axis irregularity that correlated to pain intensity was observed in the whiplash group. The rotation center was superiorly displaced in the non-specific neck pain group during side rotation, with the same tendency for the whiplash group. During ball catching, an anterior displacement (and a tendency to an inferior displacement) of the center of rotation and slower and more restricted upper body movements implied a changed movement strategy in neck pain patients, possibly as an attempt to stabilize the cervical spine during head movement.     

Subcortical rotation in Xenopus eggs: an early step in embryonic axis specification

The amphibian egg undergoes a rotation of its subcortical cytoplasm relative to its surface during the first cell cycle. Nile blue spots applied to the egg periphery move with the subcortical cytoplasm and make rotation directly observable (J.-P. Vincent, G.F. Oster, and J. C. Gerhart (1986). Dev. Biol. 113, 484). We have previously shown that the direction of rotation accurately predicts the orientation of the embryonic axis developed by the egg. This suggests an important role for subcortical rotation in axis specification. In this report, we provide two kinds of experimental evidence for the essential role of rotation, and against a role for other concurrent cytoplasmic movements such as the convergence of subcortical cytoplasm toward the sperm entry point in the animal hemisphere. First, dispermic eggs develop only one embryonic axis, which is oriented accurately in line with the direction of the single rotation movement and not with the two convergence foci that form in the animal hemisphere. Rotation probably modifies the vegetal, not animal, hemisphere since axial development is normal in dispermic eggs despite highly altered animal subcortical movement. Second, we show that the amount of rotation correlates with the extent of dorsal development. UV irradiation of the vegetal hemisphere, or cold shock of the egg, inhibits rotation effectively. When there is no rotation, there is no dorsal development. On average within the egg population, increasing amounts of rotation correlate with the increasingly anterior limit of the dorsal structures of the embryonic body axis. However, individual partially inhibited eggs vary greatly in the amount of axis formed following a given amount of movement. Furthermore, the egg normally rotates more than is necessary for the development of a complete axis. These findings suggest that rotation, although essential, does not directly pattern the antero-posterior dimension of the body axis, but triggers a response system which varies from egg to egg in its sensitivity to rotation. This system is artificially sensitized by exposure of the egg to D2O shortly before rotation. We show that D2O-treated eggs produce extensive axes despite very limited rotation, often developing into hyperdorsal embryos. However, like normal eggs, they depend on rotation and cannot form dorsal structures if it is eliminated.     

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.     

The effects of rotation and positional change of stump tissues upon morphogenesis of the regenerating axolotl limb.

Rotation of a skin cuff 180° around the proximodistal axis of the upper arm in the axolotl results in the formation of multiple regenerates in about 80° of cases after amputation of the limb through the rotated skin. Rotation of the dermis or the flexor and extensor muscles folowed by amputation produced similar percentages of multiple regenerates. Rotated bone produced no abnormalities, and rotated stump epidermis was minimally effective in stimulating multiple regeneration. A thin strip of normally oriented skin interposed between a rotated skin cuff and the amputation surface blocks the morphogenetic effect of the rotated stump skin whereas removal of the normal skin between a rotated proximal skin cuff and the amputation surface allows the formation of a low percentage of multiple regenerates. Gross rotation of stump tissue components can be broken down into axial rotation per se and positional dislocation. Experiments conducted upon skin and muscle have shown that positional dislocation along the anteroposterior axis rather than axial rotation is the manipulation that leads to the formation of multiple regenerates. The first morphological indication of multiple regeneration is the appearance of a triaxial apical ridge on the blastema. Subsequently, digits form along the apical ridges.     

Calculating the axes of rotation for the subtalar and talocrural joints using 3D bone reconstructions

Orientation of the subtalar joint axis dictates inversion and eversion movements of the foot and has been the focus of evolutionary and clinical studies for a number of years. Previous studies have measured the subtalar joint axis against the axis of the whole foot, the talocrural joint axis and, recently, the principal axes of the talus. The present study introduces a new method for estimating average joint axes from 3D reconstructions of bones and applies the method to the talus to calculate the subtalar and talocrural joint axes. The study also assesses the validity of the principal axes as a reference coordinate system against which to measure the subtalar joint axis. In order to define the angle of the subtalar joint axis relative to that of another axis in the talus, we suggest measuring the subtalar joint axis against the talocrural joint axis. We present corresponding 3D vector angles calculated from a modern human skeletal sample. This method is applicable to virtual 3D models acquired through surface-scanning of disarticulated 'dry' osteological samples, as well as to 3D models created from CT or MRI scans.     

Use of roentgen-television film for the analysis of physical exercises]

Biochemical investigation of movements of man is based on precise registration of movements of body links in space and time. The popular method of filming is almost unsuitable for studying exact movements in small joints, rotation movements and movements performed simultaneously in several joints. The use of rentgen-television filming of movement in the joints broadens the possibilities of biomechanical investigations of movements of man.     

Drosophila Myosin II, Zipper, is essential for ommatidial rotation

The adult Drosophila retina is a highly polarized epithelium derived from a precursor tissue that is initially symmetric across its dorsoventral axis. Specialized 90 degrees rotational movements of subsets of cells, the ommatidial precursors, establish mirror symmetry in the retinal epithelium. Myosin II, or Zipper (Zip), a motor protein, regulates the rate at which ommatidia rotate: in zip mutants, the rate of rotation is significantly slowed. Zip is concentrated in the cells that we show to be at the likely interface between rotating and non-rotating cells: the boundary between differentiated and undifferentiated cells. Zip is also robust in newly added ommatidial cells, consistent with our model that the machinery that drives rotation should shift to newly recruited cells as they are added to the growing ommatidium. Finally, cell death genes and canonical Wnt signaling pathway members genetically modify the zip phenotype.     

Improvements in measuring vertebral rotation from the projections of the pedicles

In radiological assessment of scoliosis, some prognostic value is given to vertebral rotation. An improved method for measuring vertebral rotation is introduced. It differs from the known methods by a specific selection of vertebral model parameters describing location of pedicles relative to the vertebral body. Vertebral model parameters have been determined from 150 axial X-rays of vertebral specimens. Application of measured parameters yields accuracy of about +/- 5 degrees in assessing vertebral rotation. Good agreement is found with parameters of six scoliotic vertebrae, investigated by CT-scans. A method for clinical presentation of measurement results is proposed.     

New determinations of the eye rotation center and criteria for the formation of its membrane in terms of the floating eye model and experimental support of the latter

It is well known that the eye is a phylogenetically stabilized body with rotation properties. The eye has an elastic cover and is filled with uniform fluid. According to the theory of covers and other concepts on the configuration of turning fluid mass we concluded that the eyeball has an elliptic configuration. Classification of the eyeball is here presented with simultaneous studies of the principles of the eye situation. The parallelism between the state and different types of heterophory and orthophory was studied. To determine normal configuration it is necessary to have in mind some principles of achieving advisable correct situation of the eye in orbit. We determined the centre of the eye rotation and showed that it is impossible to situate it out of the geometrical centre of the eyeball. It was pointed out that for adequate perception the rotation centre must be situated on the visual axis. Using the well known theory of floating we experimentally determined that the centre of the eye rotation lies on the level of the floating eye, just on the point of cross of the visual line with the optical axis. It was shown experimentally on the basis of recording the eye movements in the process of eyelid closing that weakening of the eye movements is of gravitational pattern and proceeds under the action of stability forces, which directly indicates the floating state of the eye. For the first time using the model of the floating eye it was possible to show the formation of extraeye vacuum by straining the back wall. This effect can be obtained without any difficulty, if the face is turned down. The role of negative pressure in the formation of the eye ametropy, as well as new conclusions and prognostications about this new model are discussed.     

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.