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On the rotational operators in protein structure simulations.

The reduction of the computational complexity of the algorithms dealing with protein structure analysis and conformation predictions is of prime importance. One common element in most of these algorithms is the process of transforming geometrical information between dihedral angles and Cartesian coordinates of the atoms in the protein using rotational operators. In the literature, the operators used in protein structures are rotation matrices, quaternions in vector and matrix forms and the Rodrigues-Gibbs formula. In the protein structure-related literature, the most widely promoted rotational operator is the quaternions operator. In this work, we studied the computational efficiency of the mathematical operations of the above rotational operators applied to protein structures. A similar study applied to protein structures has not been reported previously. We concluded that the computational efficiency of these rotational operators applied to protein chains is different from those reported for other applications (such as mechanical machinery) and the conclusions are not analogous. Rotation matrices are the most efficient mathematical operators in the protein chains. We examined our findings in two protein molecules: Ab1 tyrosine kinase and heparin-binding growth factor 2. We found that the rotation matrix operator has between 2 and 187% fewer mathematical operations than the other rotational operators.

Computer Simulation↗

Patterns of hip rotation range of motion: a comparison between healthy subjects and patients with low back pain.

The purpose of this study was to characterize and classify the prevalence of passive hip rotation range-of-motion (ROM) asymmetry in healthy subjects (n = 100) and in patients with low back dysfunction (n = 50). We categorized the subjects of both groups as having one of three patterns of hip rotation. Pattern IA existed when all ROM measurements were equal (within 10 degrees). Pattern IB existed when total medial and lateral rotation were equal, but one or more of the individual measurements were unequal. Pattern II existed when total medial rotation ROM was greater than total lateral rotation ROM. Those subjects with total lateral rotation ROM greater than total medial rotation ROM demonstrated pattern III. The distribution of subjects among the ROM pattern categories was significantly different in the patient and healthy subject groups. The frequency of occurrence of pattern III was greater in the patient group than in the healthy subject group. These results suggest an association between hip rotation ROM imbalance and the presence of low back pain.

Adult↗

Imagining rotation by endogenous versus exogenous forces: distinct neural mechanisms.

Previous neuroimaging studies of mental image transformations have sometimes implicated motor processes and sometimes not. In this study, prior to neuroimaging the subjects either viewed an electric motor rotating an angular object, or they rotated the object manually. Following this, they performed the identical mental rotation task in which they compared members of pairs of such figures, but were asked to imagine the figures rotating as they had just seen the model rotate. When results from the two rotation conditions were directly compared, motor cortex (including area M1) was found to be activated only when subjects imagined the rotations as a consequence of manual activity. Thus, there are at least two, qualitatively distinct, ways to imagine objects rotating in images, and these different strategies can be adopted voluntarily.

Adolescent↗

Effect of continuous rotational therapy on intracranial pressure in the severely brain-injured patient.

OBJECTIVE: To determine the effect of continuous rotational therapy on the dynamics of intracranial pressure. DESIGN: A controlled, prospective evaluation of intracranial pressure during continuous rotation therapy. SETTING: Neuroscience intensive care unit in a university hospital. PATIENTS: A total of 58 severely brain-injured patients (Glasgow Coma Score of < or = 9) ranging in age from 14 to 81 yrs. INTERVENTIONS: All patients had intraventricular catheters placed to continuously monitor intracranial pressure and all patients were placed on continuous rotational therapy once stabilized. MEASUREMENTS AND MAIN RESULTS: Intracranial pressure data were measured in each patient during nonrotation and these data were compared with intracranial pressure data during rotation, thus allowing each patient to serve as their own control. In addition, the intracranial pressure during rotation (40 degrees from center) was further analyzed to determine the effect of angulation on the intracranial pressure. Analysis of computer-recorded intracranial pressure data showed no significant difference in intracranial pressure measured during rotation and nonrotation over the first 5 days postinjury. Minimal differences in intracranial pressure (< 1 to 2 mm Hg) were noted in right/center/left positions. It was also determined that intracranial pressure increased up to 6.5 mm Hg (p = .12) in patients who presented with a unilateral lesion on admission computed tomography when they rotated to the side of the lesion. However, these fluctuations did not promote additional intracranial pressure management. CONCLUSIONS: We conclude that the systemic benefits known to be derived from the use of continuous rotation therapy in the severely head-injured patient can be sustained without any deleterious effects on the intracranial pressure.

Adult↗

Computer-assisted quantification of periaxial bone rotation from X-ray CT.

PURPOSE: Numerous orthopedic disorders involve periaxial rotation of long bones. We have developed and evaluated a computer-assisted method that segments a bone from X-ray CT, graphically unwraps the bone around its long axis into a surface plot (signature landscape), and measures periaxial rotation as the translation shift of the landscape. Bones in known rotations and partially segmented surfaces were used, respectively, to test accuracy and problematic situations in bone segmentation. METHOD: CT images of three chicken femora at known rotations were analyzed to determine their relative periaxial rotations, which were compared with the known rotations. RESULTS: The regression slope between measured and expected periaxial rotations was 1.005 +/- 0.003, with a maximum discrepancy of 2 degrees for same-bone and 3 degrees for interbone comparisons. Rasterization artifacts and the use of partial surfaces (with < 40% surface omission) resulted in a < 3 and < 1 degree error, respectively. CONCLUSION: The current method provides accurate and objective periaxial rotation measurements of a long bone.

Animals↗

Manual rotational testing of the vestibulo-ocular reflex.

OBJECTIVES/HYPOTHESIS: Manual whole-body and head-on-body rotational testing of the vestibuloocular reflex (VOR) is comparable to conventional rotary chair methods with and without visual fixation from 0.025 to 1 Hz. STUDY DESIGN: Summary of four previously published trials from our laboratory and a fifth prospective blinded study comparing whole-body and head-on-body rotation with rotational chair results from 0.025 to 1 Hz in 10 patients with bilateral vestibular dysfunction. METHODS: Subjects were fitted with standard electro-oculogram (EOG) electrodes and placed in the rotary chair for testing at 0.025, 0.05, 0.1, 0.25, 0.5, and 1 Hz in the dark (VOR) and in the light with a stationary target (VVOR). They were then placed in an otolaryngology examination, chair where an adjustable headband containing the velocity sensor and an opaque visor were placed on the forehead. Whole-body rotational trials from 0.025 to 1 Hz and both passive and active head-on-body trials from 0.25 to 1 Hz were performed with and without visual fixation. Data from each frequency were analyzed cycle-by-cycle and averaged for gain, phase, and asymmetry. These values were then compared to the results obtained during rotational chair testing. RESULTS: Throughout the five studies, no systematic differences were noted between the manual rotational methods and the rotary chair results. Specifically, no consistent effect of volition or cervico-ocular reflex (COR) enhancement was demonstrated. CONCLUSIONS: Manual rotational testing is a reliable technique for measuring the VOR up to 1 Hz as compared with standard rotary chair methods. Advantages to this technique include portability, lower equipment costs, and potential application up to 6 Hz using head-on-body rotation.

Electronystagmography↗

Axial rotation of the lumbar spine and the effect of flexion. An in vitro and in vivo biomechanical study.

A series of experiments were performed on eight whole, cadaveric lumbar spines and on eight male volunteers to determine whether axial rotation changed with subjects bending forward compared with being in a neutral posture and whether rotation was affected by articular tropism. Kirschner wires were inserted into the spinous processes of the eight cadaveric lumbar spines, and the axial rotation of the wires was measured while the spine was rotated in a torsion apparatus. Similarly, Steinmann pins were inserted into the spinous processes of L3, L4, and L5 of the eight volunteers, and the axial rotation of the pins was measured while the subjects rotated in a torsion apparatus. Axial rotation was found to be less when combined with forward flexion, and articular tropism did not influence the amplitude of rotation.

Adult↗

The effect of injury on rotational coupling at the lumbosacral joint. A biomechanical investigation.

The lumbosacral joint is frequently indicated as a source of low-back pain, a cause of which may be abnormal patterns of vertebral motions. The goal of this study was to describe the influence of injury on the coupled motions of the L5-S1 joint in a human cadaveric model. Nine whole lumbosacral spine specimens were studied under the application of flexion, extension, left/right axial torque and right/left lateral bending pure moments. Injuries to the posterior ligaments, intervertebral disc, and articular facets at L5-S1 were produced, and the motion at L5-S1 was determined after each sequential injury. No significant coupled rotations were observed under flexion or extension moments. Under axial torque, lateral rotation at L5-S1 occurred to the same side as the applied torque and increased significantly only after injury to the intervertebral disc. Also coupled to axial torque was flexion rotation in the intact specimen, which became extension rotation after facetectomy. Under lateral bending moments, coupled axial rotation was to the opposite side of the applied moment and increased significantly only after removal of the facets of L5. Based on these results, it was concluded that intervertebral disc most resisted the coupled motion of lateral rotation under the application of axial torque, whereas the articular facets most resisted the coupled axial rotation under the application of lateral bending at the lumbosacral joint. Also, the facets were the structures that produced the flexion rotation of L5 on S1 under axial torque loading.

Back Pain↗

Three-dimensional motion analysis of the upper cervical spine during axial rotation.

Rotational motion of the normal upper cervical spine was analyzed in 20 men using biplanar roentgenograms, a system digitizer, and a personal computer. To detect the bony landmarks of the atlas, the subjects' heads were fixed and their trunks rotated in the reference frame while these biplanar studies were obtained. Coupling motions observed included 10 degrees extension at C0-C1, with 11 degrees of lateral bending between C1-C2. Almost all (80%) cervical axial rotation took place at C1-C2, whereas only 4 degrees of rotation occurred at C0-C1. Furthermore, as C1-C2 axial rotation increased, so did rotation in the opposite direction at C0-C1 while less rotation was noted below C2. The instantaneous axis of rotation was located anterior to the foramen magnum at the C0-C1 level, in the central portion of the dens at C1-C2.

Adult↗

Axial rotation strength in seated neutral and prerotated postures of young adults.

STUDY DESIGN: To determine the trunk-twisting capability from neutral and prerotated postures, a study was designed to measure torque generated in isometric and isokinetic activities of 50 young adults. OBJECTIVES: To determine the isometric and isokinetic axial rotation strengths of male and female subjects in neutral and asymmetric postures and to quantify the effect of velocity of rotation on the isokinetic trunk strength profile. METHODS: A specially designed axial rotation tester was employed using specially written modular software for data collection and analysis. The isometric strengths were measured in neutral, 15 degrees, and 30 degrees prerotated trunk postures. The isokinetic strength was measured in activities starting from the neutral position to fully rotated and from a fully rotated position to neutral positions at 10 degrees, 20 degrees, and 40 degrees per second angular velocity. The data obtained were subjected to multivariate and univariate analyses of variances with multiple comparisons and multiple regression analyses. RESULTS: All study participants were significantly stronger in isometric twisting activities than in the isokinetic activities. In isometric activities, participants were 20-25% weaker in prerotated postures when twisting in the direction of prerotation and were approximately 30% stronger in the opposite direction. For isokinetic activities, the trunk rotation from neutral to asymmetric positions produced lesser torques compared with torques from rotated positions to the neutral position. The torque-producing capability declined with increasing velocity of activity. CONCLUSION: This study adds to the data base of rotational strength.

Adolescent↗

A multicenter analysis of axial femorotibial rotation after total knee arthroplasty.

A multicenter analysis was done to determine in vivo femorotibial axial rotation magnitudes and patterns in 1,027 knees (normal knees, nonimplanted ACL-deficient knees, and multiple designs of total knee arthroplasty). All knees were analyzed using fluoroscopy and a three-dimensional computer model-fitting technique during a deep knee bend and/or gait. Normal knees showed 16.5 degrees and 5.7 degrees of internal tibial rotation during a deep knee bend and gait, respectively. Rotation magnitudes and the percent having normal axial rotation patterns decreased in all total knee arthroplasty groups during a deep knee bend. During gait, all knee arthroplasty groups had similar rotational patterns (limited magnitudes). Average axial rotational magnitudes in gait and a deep knee bend were similar among major implant categories (ie, fixed-bearing versus mobile-bearing, etc). Average values in normal knees and ACL-retaining total knee arthroplasty patients (16.5 degrees and 8.1 degrees , respectively) were higher than in groups in which the ACL was absent (< 4.0 degrees ). All total knee arthroplasty groups had at least 19% of patients have a reverse axial rotational pattern during a deep knee bend and at least 31% during gait. Normal axial rotation patterns are essential for good patellar tracking, reduction of patellofemoral shear forces, and maximization of knee flexion.

Analysis of Variance↗

Differential activation of the thoracic multifidus and longissimus thoracis during trunk rotation.

STUDY DESIGN: Cross-sectional study. OBJECTIVE: To develop a technique to measure electromyographic (EMG) activity of deep and superficial paraspinal muscles at different thoracic levels and to investigate activity of these muscles during seated trunk rotation. SUMMARY OF BACKGROUND DATA: Few studies have compared activity of deep and superficial paraspinal muscles of the thorax during trunk rotation, and conflicting results have been presented. Conflicting data may result from recording techniques or variation in activity between thoracic regions. METHODS: EMG recordings were made from deep (multifidus/rotatores) and superficial (longissimus) paraspinal muscles at T5, T8, and T11 using selective intramuscular electrodes. Ten subjects rotated the trunk to end of range in each direction. EMG amplitude was measured in neutral, at end of range, and during four epochs, which represented four quarters of the movement. RESULTS: During trunk rotation in sitting, longissimus EMG either increased with ipsilateral rotation (T5) or decreased with contralateral rotation (T5, T8, T11). In contrast, multifidus EMG was more variable and was either active with rotation in both directions (particularly T5) or with one movement direction. CONCLUSIONS: The deep and superficial muscles of the thorax are differentially active, and the patterns of activity differ between the regions of the thorax. Data from this study support the hypothesis that multifidus may have a role in control of segmental motion at T5. Variability in multifidus activity at T8 and T11 suggests that this muscle may also control coupling between rotation and lateral flexion.

Adult↗

A six-degree-of-freedom acoustic transducer for rotation and translation measurements across the knee.

An acoustic transducer design to measure the relative translations and rotations across the knee with no mechanical coupling between the tibia and femur is presented. Platforms attached to femoral and tibial tracking fixtures hold acoustic sources and receivers, respectively. The distance from each source to each receiver is measured by the acoustic transit time and the translations and rotations across the knee joint are computed. For rotations less than 30 deg around the expected operating position, the resolution of the transducer is 0.3 deg; for translations less than 1.5 cm around the expected operating position, the resolution is 0.03 cm. Theoretical error analysis using a Monte Carlo method shows that the uncertainty in the measurement depends on the relative position of the sources and receivers. The analysis predicts the worst case resolution of the transducer as 0.09 cm in translation and 0.6 deg in rotation when the receiver platform is translated 8.0 cm parallel to the source platform. The transducer and fixturing system are demonstrated on a cadaver specimen for applied anterior force and applied internal-external rotation. Errors due to (soft tissue) motion of the transducer relative to the bone during in vivo measurements are assessed on the cadaver specimen. For internal-external rotation the error due to soft tissue motion is a maximum of 0.5 cm in translation and 1.8 deg in rotation. For applied anterior force the error due to soft tissue motion is a maximum of 0.16 cm in translation and 2.7 deg in rotation.

Biomechanical Phenomena↗

A novel method for automatic detection of patient out-of-plane rotation by comparing a single portal image to a reference image.

A novel method for detecting out-of-plane patient rotation by comparing a single portal image to its reference image is presented. Out-of-plane rotation results in an apparent distortion of the anatomy in a portal image. This distortion can be mathematically predicted with the magnification varying at each point in the image. While scaling of points at equal depth is invariant under in-plane rotation or translation, and changes equally in both dimensions for an axial shift of the patient, a change of scaling in only one dimension can be ascribed to an out-of-plane rotation. For the two conditions that are used in this study, it is shown that out-of-plane rotation yields a different scaling of the image in two perpendicular directions and therefore it is feasible to calculate the scale factors as a function of out-of-plane rotation. Conversely the recovery of scale factors in two different directions at the same time would enable the magnitude of the out-of-plane rotation to be recovered. The properties of the Fourier transform of the image are used to align the portal image with the reference image (a simulator image or first approved portal image) prior to the recovery of the scale factors. Correlating the Fourier transform of the portal image on a log-scale with that of the reference image enables the scale factors to be automatically extracted from a single portal image. In the two approaches investigated, out-of-plane rotations of up to 41 degrees and 20 degrees (respectively) have been recovered with a maximum error of 2.4 degrees. This technique could be used to automatically detect patient roll or tilt prior to or during a treatment session.

Algorithms↗

Axial rotation in Parkinson's disease.

AIMS: To investigate the ability of patients with Parkinson's disease to perform a rotation around the longitudinal axis of the body. Three questions were raised. Is body rotation impaired in Parkinson's disease? Is there a level of the kinematic chain from the head to the foot at which the impairment is more severe? Is the deficit related to the general slowness of movement in Parkinson's disease? METHODS: Kinematic data were recorded. The temporal organisation of body rotation during gait initiation was analysed in 10 patients with Parkinson's disease, who were all at an advanced stage of the disease and had all experienced falls and freezing during their daily life, and in five controls. The latency of the onset of the rotation of each segment was measured by taking the onset of the postural phase of step initiation as reference value. Locomotor variables were also analysed. RESULTS: Body rotation was found to be impaired in patients with Parkinson's disease, as the delay in the onset of the rotation of each segment is greater than that in controls. Moreover, a specific uncoupling in the onset of shoulder and pelvis segment rotation was seen in patients. This impairment of rotation is not related only to the general slowness of movements. CONCLUSION: Patients with Parkinson's disease were found to have an impairment of posturo-kinetic coordination and impaired capacity to exert appropriate ground reaction forces to orient the pelvis in space.

Aged↗

Effects of eye rotation on visually guided behavior.

Visually guided behavior was examined in cats reared with one eye intorted, one eye extorted, or monocular section of the extraocular muscles. Kittens from 2 to 4 mo old jumped from a tower onto a platform in a pan of water. They refused to jump or missed the platform more often when forced to use the rotated eye than when forced to use the unoperated eye. This deficit was eliminated if the non-rotated eye was sutured at the time of eye rotation. Further, when the extraocular muscles were cut but the eye was not rotated, jumping was normal. Acuity was measured using an alley box in which the cats were required to distinguish between horizontal and vertical stripes. No cats were blind when tested with the operated eye. Although not conclusive, the data suggest that the acuity of the rotated eye was slightly lower than that of the unoperated eye. The visual field of the rotated eye was also abnormal. Regardless of the direction of eye rotation, the cats appeared blind in the contralateral and lower visual quadrants. This field deficit was much less severe in animals with extraocular muscle section alone and did not occur in rotation-plus-suture animals. The visual-field deficits in the contralateral field can be explained by assuming that each collicular or cortical region always controls orienting to the same region of the visual field. We are, however, unable to explain the deficits in the lower field in terms of the mapping data from the previous paper (4).

Animals↗

Three-dimensional vector analysis of the human vestibuloocular reflex in response to high-acceleration head rotations. II. responses in subjects with unilateral vestibular loss and selective semicircular canal occlusion.

1. We studied the three-dimensional input-output human vestibuloocular reflex (VOR) kinematics after selective loss of semicircular canal (SCC) function either through total unilateral vestibular deafferentation (uVD) or through single posterior SCC occlusion (uPCO), and showed large deficits in magnitude and direction in response to high-acceleration head rotations (head "impulses"). 2. A head impulse is a passive, unpredictable, high-acceleration (3,000-4,000 degrees/s2) head rotation through an amplitude of 10-20 degrees in roll, pitch, or yaw. The subjects were tested while seated in the upright position and focusing on a fixation target. Head and eye rotations were measured with the use of dual search coils, and were expressed as rotation vectors. A three-dimensional vector analysis was performed on the input-output VOR kinematics after uVD, to produce two indexes in the time domain: magnitude and direction. Magnitude is expressed as speed gain (G) and direction as misalignment angle (delta). 3. G. after uVD, was significantly lower than normal in both directions of head rotation during roll, pitch, and yaw impulses, and were much lower during ipsilesional than during contralesional roll and yaw impulses. At 80 ms from the onset of an impulse (i.e., near peak head velocity), G was 0.23 +/- 0.08 (SE) (ipsilesional) and 0.56 +/- 0.08 (contralesional) for roll impulses, 0.61 +/- 0.09 (up) and 0.72 +/- 0.10 (down) for pitch impulses, and 0.36 +/- 0.06 (ipsilesional) and 0.76 +/- 0.09 (contralesional) for yaw impulses (mean +/- 95% confidence intervals). 4. delta, after uVD, was significantly different from normal during ipsilesional roll and yaw impulses and during pitch-up and pitch-down impulses. delta was normal during contralesional roll and yaw impulses. At 80 ms from the onset of the impulse, delta was 30.6 +/- 4.5 (ipsilesional) and 13.4 +/- 5.0 (contralesional) for roll impulses, 23.7 +/- 3.7 (up) and 31.6 +/- 4.4 (down) for pitch impulses, and 68.7 +/- 13.2 (ipsilesional) and 11.0 +/- 3.3 (contralesional) for yaw impulses (mean +/- 95% confidence intervals). 5. VOR gain (gamma), after uVD, were significantly lower than normal for both directions of roll, pitch, and yaw impulses and much lower during ipsilesional than during contralesional roll and yaw impulses. At 80 ms from the onset of the head impulse, the gamma was 0.22 +/- 0.08 (ipsilesional) and 0.54 +/- 0.09 (contralesional) for roll impulses, 0.55 +/- 0.09 (up) and 0.61 +/- 0.09 (down) for pitch impulses, and 0.14 +/- 0.10 (ipsilesional) and 0.74 +/- 0.06 (contralesional) for yaw impulses (mean +/- 95% confidence intervals). Because gamma is equal to [G*cos (delta)], it is significantly different from its corresponding G during ipsilesional roll and yaw, and during all pitch impulses, but not during contralesional roll and yaw impulses. 6. After uPCO, pitch-vertical gamma during pitch-up impulses was reduced to the same extent as after uVD; roll-torsional gamma during ipsilesional roll impulses was significantly lower than normal but significantly higher than after uVD. At 80 ms from the onset of the head impulse, gamma was 0.32 +/- 0.13 (ipsilesional) and 0.55 +/- 0.16 (contralesional) for roll impulses, 0.51 +/- 0.12 (up) and 0.91 +/- 0.14 (down) for pitch impulses, and 0.76 +/- 0.06 (ipsilesional) and 0.73 +/- 0.09 (contralesional) for yaw impulses (mean +/- 95% confidence intervals). 7. The eye rotation axis, after uVD, deviates in the yaw plane, away from the normal interaural axis, toward the nasooccipital axis, during all pitch impulses. After uPCO, the eye rotation axis deviates in same direction as after uVD during pitch-up impulses, but is well aligned with the head rotation axis during pitch-down impulses.

Adult↗

Reaching during virtual rotation: context specific compensations for expected coriolis forces.

Subjects who are in an enclosed chamber rotating at constant velocity feel physically stationary but make errors when pointing to targets. Reaching paths and endpoints are deviated in the direction of the transient inertial Coriolis forces generated by their arm movements. By contrast, reaching movements made during natural, voluntary torso rotation seem to be accurate, and subjects are unaware of the Coriolis forces generated by their movements. This pattern suggests that the motor plan for reaching movements uses a representation of body motion to prepare compensations for impending self-generated accelerative loads on the arm. If so, stationary subjects who are experiencing illusory self-rotation should make reaching errors when pointing to a target. These errors should be in the direction opposite the Coriolis accelerations their arm movements would generate if they were actually rotating. To determine whether such compensations exist, we had subjects in four experiments make visually open-loop reaches to targets while they were experiencing compelling illusory self-rotation and displacement induced by rotation of a complex, natural visual scene. The paths and endpoints of their initial reaching movements were significantly displaced leftward during counterclockwise illusory rotary displacement and rightward during clockwise illusory self-displacement. Subjects reached in a curvilinear path to the wrong place. These reaching errors were opposite in direction to the Coriolis forces that would have been generated by their arm movements during actual torso rotation. The magnitude of path curvature and endpoint errors increased as the speed of illusory self-rotation increased. In successive reaches, movement paths became straighter and endpoints more accurate despite the absence of visual error feedback or tactile feedback about target location. When subjects were again presented a stationary scene, their initial reaches were indistinguishable from pre-exposure baseline, indicating a total absence of aftereffects. These experiments demonstrate that the nervous system automatically compensates in a context-specific fashion for the Coriolis forces associated with reaching movements.

Adaptation, Physiological↗