Longitudinal Rotation Axis Research Articles

Angular velocity around the longitudinal axis in combination with head movements of springboard divers during twisted somersaults

ABSTRACT The ability of springboard divers to perform and control difficult elements with multiple twisted somersaults before entering the water is of great interest for coaches and researchers. In order to produce twists within somersaults, divers use both ‘contact’ and ‘aerial’ techniques. After completing body axes rotations, head movements seem to be important, as they enable visual information in the air. The current study aims at investigating angular velocities around the longitudinal axis in combination with head movements of 13 springboard divers during twisted somersaults. Divers performed forward and backward somersaults with different numbers of half twists. The results revealed maximum longitudinal axis angular velocities between 500°/s and 1300°/s. Moreover, results showed that the use of contact technique was greater in twisted somersaults with backward approaches, and thus higher angular velocities could be achieved. While finishing the twists, head movements in the opposite direction to the longitudinal axis rotation occurred, which allow divers to orient themselves. Twist speeds influenced athletes’ head movements to have greater angles and greater rotational velocities. Therefore, it is concluded that fast head movements are necessary in difficult twisted dives to allow orientation in the short phase between finishing the twist and entering the water surface.

CT-based study of vertebral and intravertebral rotation in right thoracic adolescent idiopathic scoliosis

PurposeTo define the longitudinal rotation axis around which individual vertebrae rotate, and to establish the various extra- and intravertebral rotation patterns in thoracic adolescent idiopathic scoliosis (AIS) patients, for better understanding of the 3D development of the rotational deformity.MethodsSeventy high-resolution CT scans from an existing database of thoracic AIS patients (Cobb angle: 46°–109°) were included to determine the vertebral axial rotation, rotation radius, intravertebral axial rotation, and local mechanical torsion for each spinal level, using previously validated image processing techniques.ResultsFor all levels, the longitudinal rotation axis, from which the vertebrae rotate away from the midline, was localized posterior to the spine. The axis became closer to the spine at the apex: apex, r = 11.5 ± 5.1 cm versus two levels above (radius = 15.8 ± 8.5 cm; p < 0.001) and beneath (radius = 14.2 ± 8.2 cm; p < 0.001). The vertebral axial rotation, intravertebral axial rotation, and local mechanical torsion of the vertebral bodies were largest at the apex (21.9° ± 7.4°, 8.7° ± 13.5° and 3.0° ± 2.5°) and decreased toward the neutral, junctional zones (p < 0.001).ConclusionIn AIS, the vertebrae rotate away around an axis that is localized posterior to the spine. The distance between this axis and the spine is minimal at the apex and increases gradually to the neutral zones. The vertebral axial rotation is accompanied by smaller amounts of intravertebral rotation and local mechanical torsion, which increases toward the apical region. The altered morphology and alignment are important for a better understanding of the 3D pathoanatomical development of AIS and better therapeutic planning for bracing and surgical intervention.Graphic abstractThese slides can be retrieved under Electronic Supplementary Material.

Psychomotor Tremor and Proprioceptive Control Problems in Current and Former Stimulant Drug Users: An Accelerometer Study of Heavy Users of Amphetamine, MDMA, and Other Recreational Stimulants.

The recreational use of various stimulant drugs has been implicated in the development of movement disorders through dysregulation of the dopaminergic and serotoninergic neurotransmitter systems. The present study investigated psychomotor differences in current and former recreational stimulant drug users compared with nonusing controls. Sixty participants comprised 3 groups: 20 current stimulant drug users (CSUs; 11 men, aged 31.4 ± 9.1 years), 20 former stimulant drug users (FSUs; 5 men, aged 39.1 ± 8.5 years), and 20 nonuser controls (NUCs; 5 men, aged 35.7 ± 6.4 years). Psychomotor arm steadiness for each participant was assessed with a wrist-attached accelerometer during 5 arm positions with eyes open and then eyes closed. Arm-drop of arm position was indicated by the arm longitudinal rotation axis (ALoRA), and tremor was indicated by the overall vector of dynamic body acceleration (VeDBA). Overall, CSUs performed the most poorly on ALoRA (P < .05) and VeDBA indices (P < .05), and FSUs perform almost as poorly on VeDBA indices (P < .05) compared with NUCs. It was concluded that stimulant drug use, primarily MDMA and amphetamines, may result in acute stimulant-induced tremor as well as long-term proprioceptive deficits in terms of arm-droop.

Changes in the rotational axes of the tibiofemoral joint caused by resection of the anterior cruciate ligament.

Kinematic alignment is a method of aligning implants in total knee arthroplasty (TKA) that strives to restore the native flexion-extension (F-E) and longitudinal rotation (LR) axes of the tibiofemoral joint. The anterior cruciate ligament (ACL) is typically resected at the time of TKA, which might change the position, and orientation of these axes from that of the native knee. Our objective was to determine whether resecting the ACL causes changes in the F-E and LR axes. A custom designed and validated instrumented spatial linkage (ISL) measured the F-E and LR axes in nine cadaveric knees before and after ACL resection. Changes in these axes were computed for knee flexion from 0° to 120°. For the F-E axis, the two statistically significant yet relatively small changes were internal rotation of 0.5° (p = 0.02) and posterior translation of 0.3 mm (p = 0.04). For the LR axis, the statistically significant and relatively large change was medial translation of 2.1 mm (p = 0.01). Changes to the LR axis in both medial-lateral position and varus-valgus orientation varied widely; 77% of a population of knees would have a medial-lateral position change greater than 1 mm, and 53% of a population of knees would have a varus-valgus orientation change greater than 1°. Knowledge of changes of the F-E and LR axes caused by resecting the ACL provides an important baseline for determining the changes in these axes caused by kinematic alignment and mechanical alignment of bi-cruciate retaining, posterior cruciate retaining, and posterior cruciate substituting implants. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:886-893, 2017.

体操選手がとびひねり遂行中に行う視線移動パターン

This study aimed to clarify gaze shift patterns in gymnasts during a jump with a half turn by measuring horizontal eye-head movements. We also compared the gaze shift patterns of skilled gymnasts with those of non-gymnasts to examine the patterns characteristic of gymnasts. The participants were 10 skilled male gymnasts and 15 male non-gymnasts. Each participant performed a jump with a half turn, which is an aerial movement with a 180-degree longitudinal axis rotation. Eye movement during the jump was measured using electrooculography. The jump was recorded simultaneously with 2 high-speed digital cameras to determine angular horizontal head movement. Gaze was determined by combining eye and head movement data. The results showed that both gymnasts and non-gymnasts used 2 gaze shift patterns during the jump. In both of these patterns, gaze stabilized before takeoff and immediately before landing. However, in one pattern, termed the single-step gaze shift pattern, gaze moved directly from front to back, whereas in the other pattern, termed the multi-step gaze shift pattern, gaze shift toward the direction of rotation stopped several times even during midair rotation. The single-step gaze shift pattern was used more by gymnasts than by non-gymnasts. Taken together, these results show that gymnasts employ 2 gaze shift patterns when performing a jump with a half turn, but that the single-step gaze shift pattern may be more useful to gymnasts for controlling their movement than other gaze shift patterns.

Design, Calibration and Validation of a Novel 3D Printed Instrumented Spatial Linkage that Measures Changes in the Rotational Axes of the Tibiofemoral Joint

An accurate axis-finding technique is required to measure any changes from normal caused by total knee arthroplasty in the flexion-extension (F-E) and longitudinal rotation (LR) axes of the tibiofemoral joint. In a previous paper, we computationally determined how best to design and use an instrumented spatial linkage (ISL) to locate the F-E and LR axes such that rotational and translational errors were minimized. However, the ISL was not built and consequently was not calibrated; thus the errors in locating these axes were not quantified on an actual ISL. Moreover, previous methods to calibrate an ISL used calibration devices with accuracies that were either undocumented or insufficient for the device to serve as a gold-standard. Accordingly, the objectives were to (1) construct an ISL using the previously established guidelines,(2) calibrate the ISL using an improved method, and (3) quantify the error in measuring changes in the F-E and LR axes. A 3D printed ISL was constructed and calibrated using a coordinate measuring machine, which served as a gold standard. Validation was performed using a fixture that represented the tibiofemoral joint with an adjustable F-E axis and the errors in measuring changes to the positions and orientations of the F-E and LR axes were quantified. The resulting root mean squared errors (RMSEs) of the calibration residuals using the new calibration method were 0.24, 0.33, and 0.15 mm for the anterior-posterior, medial-lateral, and proximal-distal positions, respectively, and 0.11, 0.10, and 0.09 deg for varus-valgus, flexion-extension, and internal-external orientations, respectively. All RMSEs were below 0.29% of the respective full-scale range. When measuring changes to the F-E or LR axes, each orientation error was below 0.5 deg; when measuring changes in the F-E axis, each position error was below 1.0 mm. The largest position RMSE was when measuring a medial-lateral change in the LR axis (1.2 mm). Despite the large size of the ISL, these calibration residuals were better than those for previously published ISLs, particularly when measuring orientations, indicating that using a more accurate gold standard was beneficial in limiting the calibration residuals. The validation method demonstrated that this ISL is capable of accurately measuring clinically important changes (i.e. 1 mm and 1 deg) in the F-E and LR axes.

Optimized Design of an Instrumented Spatial Linkage that Minimizes Errors in Locating the Rotational Axes of the Tibiofemoral Joint: A Computational Analysis

An accurate method to locate of the flexion-extension (F-E) axis and longitudinal rotation (LR) axis of the tibiofemoral joint is required to accurately characterize tibiofemoral kinematics. A method was recently developed to locate these axes using an instrumented spatial linkage (ISL) (2012, "On the Estimate of the Two Dominant Axes of the Knee Using an Instrumented Spatial Linkage," J. Appl. Biomech., 28(2), pp. 200-209). However, a more comprehensive error analysis is needed to optimize the design and characterize the limitations of the device before using it experimentally. To better understand the errors in the use of an ISL in finding the F-E and LR axes, our objectives were to (1) develop a method to computationally determine the orientation and position errors in locating the F-E and LR axes due to transducer nonlinearity and hysteresis, ISL size and attachment position, and the pattern of applied tibiofemoral motion, (2) determine the optimal size and attachment position of an ISL to minimize these errors, (3) determine the best pattern of pattern of applied motion to minimize these errors, and (4) examine the sensitivity of the errors to range of flexion and internal-external (I-E) rotation. A mathematical model was created that consisted of a virtual "elbow-type" ISL that measured motion across a virtual tibiofemoral joint. Two orientation and two position errors were computed for each axis by simulating the axis-finding method for 200 iterations while adding transducer errors to the revolute joints of the virtual ISL. The ISL size and position that minimized these errors were determined from 1080 different combinations. The errors in locating the axes using the optimal ISL were calculated for each of three patterns of motion applied to the tibiofemoral joint, consisting of a sequential pattern of discrete tibiofemoral positions, a random pattern of discrete tibiofemoral positions, and a sequential pattern of continuous tibiofemoral positions. Finally, errors as a function of range of flexion and I-E rotation were determined using the optimal pattern of applied motion. An ISL that was attached to the anterior aspect of the knee with 300-mm link lengths had the lowest maximum error without colliding with the anatomy of the joint. A sequential pattern of discrete tibiofemoral positions limited the largest orientation or position error without displaying large bias error. Finally, the minimum range of applied motion that ensured all errors were below 1 deg or 1 mm was 30 deg flexion with ±15 deg I-E rotation. Thus a method for comprehensive analysis of error when using this axis-finding method has been established, and was used to determine the optimal ISL and range of applied motion; this method of analysis could be used to determine the errors for any ISL size and position, any applied motion, and potentially any anatomical joint.

On the Estimate of the Two Dominant Axes of the Knee Using an Instrumented Spatial Linkage

This article presents the validation of a technique to assess the appropriateness of a 2 degree-of-freedom model for the human knee, and, in which case, the dominant axes of flexion/extension and internal/external longitudinal rotation are estimated. The technique relies on the use of an instrumented spatial linkage for the accurate detection of passive knee kinematics, and it is based on the assumption that points on the longitudinal rotation axis describe nearly circular and planar trajectories, whereas the flexion/extension axis is perpendicular to those trajectories through their centers of rotation. By manually enforcing a tibia rotation while bending the knee in flexion, a standard optimization algorithm is used to estimate the approximate axis of longitudinal rotation, and the axis of flexion is estimated consequently. The proposed technique is validated through simulated data and experimentally applied on a 2 degree-of-freedom mechanical joint. A procedure is proposed to verify the fixed axes assumption for the knee model. The suggested methodology could be possibly valuable in understanding knee kinematics, and in particular for the design and implant of customized hinged external fixators, which have shown to be effective in knee dislocation treatment and rehabilitation.

Validation of a New Method for Finding the Rotational Axes of the Knee Using Both Marker-Based Roentgen Stereophotogrammetric Analysis and 3D Video-Based Motion Analysis for Kinematic Measurements

In a previous paper, we reported the virtual axis finder, which is a new method for finding the rotational axes of the knee. The virtual axis finder was validated through simulations that were subject to limitations. Hence, the objective of the present study was to perform a mechanical validation with two measurement modalities: 3D video-based motion analysis and marker-based roentgen stereophotogrammetric analysis (RSA). A two rotational axis mechanism was developed, which simulated internal-external (or longitudinal) and flexion-extension (FE) rotations. The actual axes of rotation were known with respect to motion analysis and RSA markers within ± 0.0006 deg and ± 0.036 mm and ± 0.0001 deg and ± 0.016 mm, respectively. The orientation and position root mean squared errors for identifying the longitudinal rotation (LR) and FE axes with video-based motion analysis (0.26 deg, 0.28 m, 0.36 deg, and 0.25 mm, respectively) were smaller than with RSA (1.04 deg, 0.84 mm, 0.82 deg, and 0.32 mm, respectively). The random error or precision in the orientation and position was significantly better (p=0.01 and p=0.02, respectively) in identifying the LR axis with video-based motion analysis (0.23 deg and 0.24 mm) than with RSA (0.95 deg and 0.76 mm). There was no significant difference in the bias errors between measurement modalities. In comparing the mechanical validations to virtual validations, the virtual validations produced comparable errors to those of the mechanical validation. The only significant difference between the errors of the mechanical and virtual validations was the precision in the position of the LR axis while simulating video-based motion analysis (0.24 mm and 0.78 mm, p=0.019). These results indicate that video-based motion analysis with the equipment used in this study is the superior measurement modality for use with the virtual axis finder but both measurement modalities produce satisfactory results. The lack of significant differences between validation techniques suggests that the virtual sensitivity analysis previously performed was appropriately modeled. Thus, the virtual axis finder can be applied with a thorough understanding of its errors in a variety of test conditions.

테니스 양손 백핸드 스트로크 방법에 따른 어깨와 힙의 회전운동 변화

The purpose of this study was to examine differences between players who bend the left elbow and those who stretch it during the forward swing from BST to BC in a 2-handed backhand stroke among outstanding high school tennis players, and to assess the detailed 3D rotational kinematic characteristics of the shoulder and the hip. Statistically significant differences were observed between groups in the longitudinal axis rotation angle of the shoulder and the angle between the shoulder and the arm at BST, and in the side to side movement of the shoulder, the up and down movement of the hip, the side tilt angular velocity of the shoulder, the side tilt angular velocity of the hip, and the front tilt angular velocity of the hip at BC. The difference in the longitudinal axis rotation angle of the shoulder between the 2 groups suggests a difference in the flexibility of the joint in the shoulder arm racquet system. The longitudinal axis rotation angular velocity of the shoulder reached its peak at 75 % of the duration of the analyzed segment and then decreased little by little until BC. This time is considered the stage for increasing the angular velocity of the upper arm, the forearm, the hand and then the racquet, which are more distal segments than the shoulder.

Fast and Easy Reach-Cone Joint Limits

We describe a simple and fast method of creating and using joint sinus reach cones to limit the range of motion on universal and ball-and-socket joints. Reach cones can be created interactively or based on results from biomechanics. A reach cone is specified as a spherical polygon on the surface of a reach sphere that defines all positions the longitudinal segment axis beyond the joint can take. Reach polygons can be concave or convex, and cover more than one hemisphere. Longitudinal axis rotation limits can also be defined for locations in the reach cone. Calculations to determine whether a segment is within the reach cone are based on the relation of the segment longitudinal axis to the planes defining the reach cone and are done in the local coordinate space of the segment. The calculations have no discernible effect on the speed of interactive display or animation.

The transepicondylar axis approximates the optimal flexion axis of the knee.

The traditional understanding of knee kinematics holds that no single fixed axis of rotation exists in the knee. In contrast, a recent hypothesis suggests that knee kinematics are better described simply as two simultaneous rotations occurring about fixed axes. Knee flexion and extension occurs about an optimal flexion axis fixed in the femur, whereas tibial internal and external rotations occur about a longitudinal rotation axis fixed in the tibia. No other translations or rotations exist. This hypothesis has been tested. Tibiofemoral kinematics were measured for 15 cadaveric knees undergoing a realistic loadbearing activity (simulated squatting). An optimization technique was used to identify the locations of the optimal flexion and longitudinal rotation axes such that simultaneous rotations about them could best represent the measured kinematics. The optimal flexion axis was compared with the transepicondylar axis defined by bony landmarks. The longitudinal rotation axis was found to pass through the medial joint compartment. The optimal flexion axis passed through the centers of the posterior femoral condyles. No significant difference was found between the optimal flexion and transepicondylar axes. To an average accuracy of better than 3.4 mm in translation, and 2.9 degrees in orientation, knee kinematics were represented successfully by simple rotations about the optimal flexion and longitudinal rotation axes. The optimal flexion axis is fixed in the femur and can be considered the true flexion axis of the knee. The transepicondylar axis axis, which is identified easily by palpation, closely approximates the optimal flexion axis.

Codman's paradox of the arm rotations is not a paradox: mathematical validation

Movement of a straight arm centred at the shoulder joint in three successive 90° rotations, each around the respective orthogonal coordinate axis, leads to an apparently unrelated 90° rotation around the longitudinal arm axis. This empirical fact is known as Codman's paradox, after a Bostonian surgeon who first reported it in 1934. However, by means of homogeneous coordinates, it is herein demonstrated that the phenomenon is just a mechanical property mathematically described by the equivalence between the matricial product of three orthogonal rotation matrices applied to a position vector and the matricial product of a single rotation matrix applied to the same vector. The latter rotation matrix corresponds to the middle one in the former group of three. When polar coordinates are used, the demonstration is even simpler, for the total shift vector clearly shows a single net effect on the longitudinal axis rotation. Thus, Codman's paradox is not a paradox. This property improves the muscle dynamics arm knowledge and might find applications in robotics.

The Axes of Rotation of the Knee

Knee motion is believed to occur about a variable flexion-extension (FE) axis perpendicular to the sagittal plane and a longitudinal rotation (LR) axis. The authors used a mechanical device to locate the FE and the LR axes of six fresh anatomic specimen knees. The motion of points on the LR axis produced circular, planar paths about the fixed FE axis. Magnetic resonance (MR) images in planes perpendicular to the FE axis showed a circular profile for the femoral condyles. The FE axis is constant and directed from anterosuperior on the medial side to posteroinferior on the lateral side, passing through the origins of the medial and lateral collateral ligaments and superior to the crossing point of the cruciates. The LR axis is anterior and not perpendicular to the FE axis, the anatomic planes. This offset produces the valgus and external rotation observed with extension. The implications of two fixed offset axes for knee motion on prosthetic design, braces, gait analysis, and reconstructive surgery are profound.

Analysis of pulmonary function and axis rotation in adolescent and young adult idiopathic scoliosis patients treated with Cotrel-Dubousset instrumentation.

Forty-eight patients with idiopathic scoliosis underwent posterior spinal fusion with Cotrel-Dubousset instrumentation (CDI). Each patient was given preoperative and postoperative pulmonary function tests (PFTs). Pulmonary volume improved a mean 0.40 L (16%), and pulmonary flow improved a mean 0.33 L (15%). Differences between preoperative and postoperative PFT values were shown to be statistically significant and correlated well with coronal side-bending correction. Twenty patients had preoperative and postoperative CT scans through the apical vertebra. Vertebral rotation was assessed on CT scan by the method of Aaro and Dahlborn (1,2). At the apex, the mean percentage improvements in the longitudinal axis rotation relative to the midline (16%) and to the sagittal plane (10%), the rib hump index (8%), and the kyphosis-lordosis index (0%) were minimal. Radiographically, the 66% mean improvement in apical vertebral translation was more substantial and consistent than the 10% mean improvement in apical vertebral rotation. Therefore, at the apex the CDI "derotation maneuver" may be more of a "translational maneuver."

Radiographic measurement of the lumbar spine. A clinical and experimental study in man.

The accuracy of radiographic measurements of lumbosacral lordosis, vertebral size, spondylolisthesis, and disc height were studied. Errors caused by lateral tilt or longitudinal axis rotation of the lumbosacral spine were assessed in an experimental study on 12 cadavers. In a series of 170 normal individuals, the distribution of radiographic variables describing lumbosacral lordosis, size of vertebrae, and disc height was investigated. The interobserver measurement variation was studied with respect to all measured variables. The differences between radiographs of 125 spondylolytic patients in the recumbent and standing positions were analyzed with respect to vertebral slipping and lumbosacral lordosis. There were only minor projectional and interobserver measurement errors in the variables describing vertebral size and lumbosacral lordosis, which make these variables suitable for radiographic assessment at repeated examination. The absolute measurements of disc height were too inaccurate to be used as a basis for conclusions. A semiquantitative approach is more reliable, and can be recommended for the comparison of radiographic assessments of disc height. In adults, the radiographic evaluation of vertebral slipping and lumbosacral lordosis is equally reliable in the recumbent and standing positions.

The effect of Harrington instrumentation on the longitudinal axis rotation of the apical vertebra and on the spinal and rib-cage deformity in idiopathic scoliosis studied by computer tomography.

The effects of Harrington instrumentation on the longitudinal axis rotation of the vertebra, the kyphosis-lordosis, and the rib-cage deformity were investigated by computer tomography in 33 patients. No significant derotation was achieved. The sagittal diameter of the rib cage was reduced significantly with distraction rod instrumentation and further by additional application of a compression rod. The rib hump was reduced significantly only with distraction rod instrumentation. The obtained results indicate that despite instrumentation, the spine preserves an almost unchanged peripheral position in the rib cage.

The longitudinal axis rotation of the apical vertebra, the vertebral, spinal, and rib cage deformity in idiopathic scoliosis studied by computer tomography.

The correlation between the lateral curve, the location and the length of the curve, and the longitudinal axis rotation of the apical vertebra has been studied in 65 patients with idiopathic scoliosis using computer-assisted tomography. This method provides the opportunity to describe the relationship between the rib hump, the longitudinal axis rotation, the lateral curve, and the kyphosis-lordosis with exceedingly small radiation doses. The vertebral rotation was found to be correlated to the lateral curve but not to the location of the length of the curve. The longitudinal axis rotation of the vertebrae is the most important factor for the development of the rib hump which is further accentuated by increased lordosis.

Correction of scoliosis by muscle stimulation: biomechanical analyses.

Quantitative theoretical analyses of the ability of trunk muscle contraction forces to reduce lateral curves in the spine are presented. The effects of contraction of each of 68 muscle slips on each of 13 configurations of scoliosis were examined using biomechanical models of the trunk. The lateral curve, sagittal curve, and longitudinal axis rotation changes that resulted from contraction of these muscles were determined in each case. The muscles best able, from a biomechanical viewpoint, to reduce different lateral curves are listed. Effects of initial postural configurations and the consequences of reflex attempts to right the trunk after contracting a trunk muscle are described. Substantial changes in spine configuration can result from trunk muscle contractions of even modest intensity.