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PubMed1982

Human arm trajectory formation.

In order to investigate the strategies used to plan and control multijoint arm trajectories, two-degrees-of-freedom arm movements performed by normal adult humans were recorded. Only the shoulder and elbow joints were active. When a subject was told simply to move his hand from one visual target to another, the path of the hand was roughly straight, and the hand speed profile of their straight trajectories was bell-shaped. When the subject was required to produce curved hand trajectories, the path usually had a segmented appearance, as if the subject was trying to approximate a curve with low curvature elements. Hand speed profiles associated with curved trajectories contained speed valleys or inflections which were temporally associated with the local maxima in the trajectory curvature. The mean duration of curved movements was longer than the mean for straight movements. These results are discussed in terms of trajectory control theories which have originated in the fields of mechanical manipulator control and biological motor control. Three explanations for the results are offered.

Adult↗
PubMed1999

Reliability of foot trajectory measures within and between testing sessions.

BACKGROUND: Impaired control of foot trajectory during the swing phase of gait is hypothesized to increase the risk of slipping or tripping. Before assessing the predictive validity of foot trajectory measures with respect to incidence of falls, it is necessary to establish their reliability. The purpose of this study is to assess within- and between-session reliability of foot trajectory measures and traditional temporal-distance measures in healthy elderly women during gait. METHODS: Sixteen healthy, elderly women (ages 65-79 years) completed six sets of five trials each of natural and fast cadence gait during a 3.5-hour period on each of 4 days. An optoelectric motion analysis system and heel switches were used to obtain both foot trajectory (minimum toe clearance during swing, vertical, and horizontal heel contact velocities) and temporal-distance measures (step width, cadence, velocity, stride length, and time). RESULTS: Within-session test-retest reliability of all variables at natural and fast speeds was good to excellent, with intraclass correlation coefficients (ICCs) of greater than 0.9 for all but one measure (fast cadence stride time). ICCs for between-session test-retest reliability were slightly lower, but still greater than 0.9 for all but two measures (fast cadence stride time and natural cadence vertical heel contact velocity). Heel contact velocities quantified at the instant of heel contact correlated strongly with values obtained by averaging over the last 2% of the gait cycle. DISCUSSION: The good to excellent within- and between-session reliability of these foot trajectory measures supports their use as a possible means of assessing subtle changes in gait motor control. Confirmation of an association between alterations in foot trajectory measures and incidence of falls awaits further study.

Aged↗
PubMed1998

Self-rated health and adverse health outcomes: an exploration and refinement of the trajectory hypothesis.

OBJECTIVES: To examine the hypothesis that the relationship between poor self-rated health and adverse health outcomes simply reflects self-assessments of declining health trajectories rather than current health status. METHODS: A 12-month follow-up of 786 disadvantaged adults aged 50-99 years old was conducted. Baseline markers of poor self-rated health and declining health trajectory were used to predict 12-month follow-up reports of the expectations of being hospitalized within one year, being placed in a nursing home within five years, and dying within ten years. Hierarchical multivariable logistic regression was used with poor self-rated health entered first, standard epidemiologic covariates entered next, and declining health trajectory entered last. RESULTS: Poor self-rated health was not independently associated with expectations for being hospitalized, but declining health trajectory independently increased the risk of such expectations by 65-88%. Neither poor self-rated health nor declining health trajectory were independently associated with expectations for being placed in a nursing home, but both were independently associated with expectations for dying, increasing such expectations by 70-105%. DISCUSSION: The relationship between poor self-rated health and adverse outcomes is not a simple reflection of unmeasured self-assessments of impending decline or doom. Rather, the effects of poor self-rated health and declining health trajectory appear to be independent and complementary.

Aged↗
PubMed2004

Trajectories of impairment, social support, and depressive symptoms in later life.

OBJECTIVE: Research has increasingly focused on the dynamic nature of disability and depressive symptoms in later life. Little research, however, has modeled disability and depressive symptoms as dynamic, related processes. Furthermore, virtually no research has considered social support as dynamic across age. Here, we investigate the relationship between long-term patterns of disability, perceived and received social support, and depressive symptoms in later life. METHODS: We use random coefficient (growth) models of four waves of Duke Established Populations for Epidemiologic Studies of the Elderly data to determine whether disability, support, and depressive symptoms follow linear trajectories across age and whether support mediates the relationship between disability and depressive symptoms. RESULT: The results show that (a) trajectories of disability are strongly related to trajectories of depressive symptoms and (b) trajectories of perceived support mediate the relationship between trajectories of disability and depressive symptoms, whereas trajectories of received support do not. DISCUSSION: Disability, social support, and depressive symptoms are strongly interrelated processes in later life. Our results are consistent with previous research in showing that perceived, rather than received, support mediates the relationship between disability and depressive symptoms, but our results extend previous research in showing that this mediation occurs across time.

Age Factors↗
PubMed2005

A safe screw trajectory for atlantoaxial transarticular fixation achieved using an aiming device.

STUDY DESIGN: A retrospective evaluation and characterization of the trajectory of atlantoaxial transarticular screws inserted using an aiming device. OBJECTIVES: To confirm that the screws were inserted through the safest trajectory, which is through the most dorsal and medial part of the isthmus of C2, and to characterize the trajectory on lateral radiograms by comparison with historical controls. SUMMARY OF BACKGROUND DATA: Posterior atlantoaxial transarticular screw fixation entails the potential risk of vertebral artery (VA) injury, which may be lethal. Although much literature recommends that the screws should be inserted aiming at the anterior arch of C1, the authors considered that the safest screw path is via the most dorsal and medial part of the isthmus regardless of the C1 anterior arch, and have used an original aiming device to achieve this trajectory. METHODS: Forty-three consecutive patients who submitted to atlantoaxial transarticular screw fixation using the aiming device were evaluated for screw position using computed tomography (CT) and lateral radiogram. The medialization index (the distance between the screw and the cortex of the spinal canal of C2 on axial CT) and the dorsalization index (the thickness of the bone remaining dorsal to the screw at the isthmus of C2 on sagittal reconstruction CT) were measured. Further, three parameters on the lateral radiograms of these patients were compared with those in the literature and those of our previous cases performed without the aiming device. RESULTS: Neither VA injury nor violation of the spinal canal was encountered, although 12 high-riding VAs were included in this series. The mean medialization index was 0.21 mm, and the indexes of 86.3% of the screws were zero. The mean dorsalization index was 0.36 mm, and the indexes of 76.8% of the screws were zero. These results demonstrated that most of the screws were inserted as aimed, proving the usefulness of the aiming device. The trajectory of these screws on lateral radiograms was characterized by significantly less bone thickness dorsal to the screw at the isthmus compared with the two control groups. As a result, more screws were pointed above the anterior arch of C1. CONCLUSIONS: The atlantoaxial transarticular screw was inserted safely as aimed by using the aiming device. The trajectory was characterized by less bone thickness dorsal to the screw on lateral radiogram, which should be a new intraoperative landmark for screw insertion, in place of the anterior arch of C1.

Adult↗
PubMed2006

Use of spinous processes to determine drill trajectory during placement of lateral mass screws: a cadaveric analysis.

OBJECTIVE: Prior cadaveric research showed that the lateral mass and facets are landmarks to determine the initial starting point for lateral mass screws and that the optimum screw trajectory was 30 degrees lateral and 15 degrees cephalad. The missing link was an intraoperative landmark to guide the trajectory for drilling according to these angles. The authors hypothesized that spinous processes can be used to guide the trajectory for lateral mass screw placement. METHODS: The authors analyzed 144 lateral masses of 72 cervical vertebrae in 18 cadavers (7 males and 11 females). The lateral and cephalocaudad angles were measured for each lateral mass from C3 to C6 while using the spinous processes of the adjacent three caudad vertebrae at each level to guide the starting trajectories for a total of 864 angles. The lateral and cephalad trajectory angles at each spinous process relative to the starting hole were compared with 30 degrees and 15 degrees . For each angle measured at a particular level, the same starting hole was used in the lateral mass, and the superolateral cortex of each spinous process was the most medial point. RESULTS: When drilling for the C3 and C4 lateral mass screws, the C4 and C5 spinous processes provided an accurate starting point, respectively, for the lateral angle but moderately overestimated the cephalocaudad angle. For C5 and C6 lateral mass screws, the C6 and C7 spinous processes provided an accurate starting point, respectively, for both the lateral and the cephalocaudad angles. CONCLUSION: The spinous processes can be an accurate local anatomic guide for lateral mass screw trajectory and will allow greater safety while drilling before performing laminectomies. These guides may change in patients with cervical spinal deformities.

Bone Screws↗
PubMed2006

Biomechanical comparison of anatomic trajectory pedicle screw versus injectable calcium sulfate graft-augmented pedicle screw for salvage in cadaveric thoracic bone.

Many salvage options for failed thoracic pedicle screws exist including the use of a different trajectory or the augmentation of the screw with polymethylmethacrylate cement. Although polymethylmethacrylate immediately increases the construct stiffness and the pull-out strength, it may cause bone necrosis, toxin relaxation, and/or neural injury. On the other hand, calcium sulfate bone grafts have a high potential for biologic incorporation and no thermal damage effect. In the current study, polyaxial pedicle screws were first inserted with a straightforward approach on both sides in 17 fresh human cadaveric thoracic vertebrae. The maximal insertion torque for each screw was measured and then the pull-out strengths were recorded. Afterward, these pedicle screws were randomly assigned to be replaced either by graft augmentation or by anatomic trajectory technique for salvage. The graft-augmented screws were placed using the previous holes. The maximum insertional torque for each anatomic trajectory screw was measured. Finally, the pull-out strengths of the revision screws were recorded. The mean maximum insertional torque decreased with the anatomic trajectory salvage technique when compared with the straightforward approach, 0.23 versus 0.38 Nm, respectively (P=0.003). The anatomic trajectory revision resulted in decreased pull-out strength when compared with the pull-out strength of the straightforward technique, 297 versus 469 N, respectively (P=0.003). The calcium sulfate graft augmentation increased the pull-out strength when compared with the pull-out strength of the straightforward technique, 680 versus 477 N, respectively (P=0.017). The mean pull-out strength ratio of revised screw to original was 0.71 for anatomic trajectory and 1.8 for graft-augmented screws, a statistically significant difference (P=0.002).

Aged↗
PubMed2006

Major depression and physical illness trajectories in heart failure and pulmonary disease.

The purpose of this study was to examine conjoint trajectories of depression-physical illness in elderly medical inpatients with heart failure and/or chronic pulmonary disease and major depression (MDD), and to identify baseline predictors of trajectory. Consecutive medically hospitalized patients over age 50 with heart failure and/or chronic pulmonary disease were screened for MDD using the Structured Clinical Interview for Depression. Patients were re-evaluated at 6, 12, 18, and 24 weeks. Four depression-physical illness conjoint trajectories were examined: depression better, illness better; depression better, illness same; depression same, illness better; and depression same, illness same. Baseline predictors of trajectory were examined. MDD was identified in 413 patients; 352 had at least one follow-up. By 6 weeks, 22.3% improved on both depression and illness and 38.1% improved on neither. By 24 weeks, 45.0% had improved on both and 24.8% on neither. Short-term baseline predictors of trajectory (6 weeks) differed from long-term (12-24 weeks); past psychiatric history, overall medical illness severity, and education were short-term predictors, whereas past psychiatric history, depression treatments, and physical functioning were long-term. Improvements in MDD and physical illness track closely together. Characteristics during baseline hospitalization predict outcome trajectory after discharge, and may be useful in understanding etiology and directing treatment.

Adaptation, Psychological↗
PubMed2001

Quantum trajectory analysis of multimode subsystem-bath dynamics.

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Journal Article↗
PubMed2004

Semiclassical approximations based on complex trajectories.

The semiclassical limit of the coherent state propagator involves complex classical trajectories of the Hamiltonian H(u,v) = satisfying u(0) = z' and v(T) = z"*. In this work we study mostly the case z' = z". The propagator is then the return probability amplitude of a wave packet. We show that a plot of the exact return probability brings out the quantal images of the classical periodic orbits. Then we compare the exact return probability with its semiclassical approximation for a soft chaotic system with two degrees of freedom. We find two situations where classical trajectories satisfying the correct boundary conditions must be excluded from the semiclassical formula. The first occurs when the contribution of the trajectory to the propagator becomes exponentially large as Planck's over 2 pi goes to zero. The second occurs when the contributing trajectories undergo bifurcations. Close to the bifurcation the semiclassical formula diverges. More interestingly, in the example studied, after the bifurcation, where more than one trajectory satisfying the boundary conditions exist, only one of them in fact contributes to the semiclassical formula, a phenomenon closely related to Stokes lines. When the contributions of these trajectories are filtered out, the semiclassical results show excellent agreement with the exact calculations.

Journal Article↗
PubMed2005

Polynomial dispersion of trajectories in sticky dynamics.

Hamiltonian chaotic dynamics is, in general, not ergodic and the boundaries of the ergodic or quasiergodic area (stochastic sea, stochastic layers, stochastic webs, etc.) are sticky, i.e., trajectories can spend an arbitrarily long time in the vicinity of the boundaries with a nonexponentially small probability. Segments of trajectories imposed by the stickiness are called flights. The flights have polynomial dispersion that can lead to non-Gaussian statistics of displacements and to anomalous transport in phase space. In particular, the presence of flights influences the distribution of Poincaré recurrences. We use the distribution function of (l,t;epsilon, epsilon0) -separation of trajectories that at time instant t and trajectory length l are separated for the first time by epsilon<<1, being initially at a distance epsilon0 <<epsilon. The connection of this function, called the complexity function [Afraimovich and Zaslavsky, Chaos 13, 519 (2003)], with the distribution of Poincaré recurrences is established for three cases: (i) for the case of superdiffusion in standard and web maps for which the stickiness is defined by the boundaries of hierarchical sets of islands; (ii) for the case of the Sinai billiard with infinite horizon, where the stickiness is defined by zero-measure slits in the phase space; (iii) for the square billiard with a slit (bar-in-square billiard) where the Lyapunov exponent is zero and the stickiness is defined by the vicinity of the trajectory to the closest periodic trajectories obtained from the Diophantine approximation. Finally, the powerwise asymptotics of the Poincaré recurrences can be connected, in some cases, to the anomalous transport exponent.

Journal Article↗
PubMed2004

Trajectory priming with dynamic fuzzy networks in nonlinear optimal control.

Fuzzy logic systems have been recognized as a robust and attractive alternative to some classical control methods. The application of classical fuzzy logic (FL) technology to dynamic system control has been constrained by the nondynamic nature of popular FL architectures. Many difficulties include large rule bases (i.e., curse of dimensionality), long training times, etc. These problems can be overcome with a dynamic fuzzy network (DFN), a network with unconstrained connectivity and dynamic fuzzy processing units called "feurons." In this study, DFN as an optimal control trajectory priming system is considered as a nonlinear optimization with dynamic equality constraints. The overall algorithm operates as an autotrainer for DFN (a self-learning structure) and generates optimal feed-forward control trajectories in a significantly smaller number of iterations. For this, DFN encapsulates and generalizes the optimal control trajectories. By the algorithm, the time-varying optimal feedback gains are also generated along the trajectory as byproducts. This structure assists the speeding up of trajectory calculations for intelligent nonlinear optimal control. For this purpose, the direct-descent-curvature algorithm is used with some modifications [called modified-descend-controller (MDC) algorithm] for the nonlinear optimal control computations. The algorithm has numerically generated robust solutions with respect to conjugate points. The minimization of an integral quadratic cost functional subject to dynamic equality constraints (which is DFN) is considered for trajectory obtained by MDC tracking applications. The adjoint theory (whose computational complexity is significantly less than direct method) has been used in the training of DFN, which is as a quasilinear dynamic system. The updating of weights (identification of DFN parameters) are based on Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Simulation results are given for controlling a difficult nonlinear second-order system using fully connected three-feuron DFN.

Fuzzy Logic↗
PubMed2006

Trajectory tracking of piezoelectric positioning stages using a dynamic sliding-mode control.

Trajectory tracking performance of a piezoelectric positioning stage almost depends on whether the tracking controller can effectively compensate the inherent hysteresis phenomenon. In this paper, a dynamic sliding-mode control (DSMC) with backstepping is proposed for the trajectory tracking of the piezoelectric positioning stage, which is suitable for a component of scanning microscopes. An equivalent model developed from a linear motion dynamics with addition of the hysteresis nonlinearity and strain-dependent function first is proposed to approximately represent the dynamics of motion of a one-dimensional piezoelectric positioning stage. Then, based on the equivalent model, the DSMC with an asymptotical sliding surface is proposed for the trajectory tracking control of the piezoelectric positioning stage. Moreover, the analysis of stability can be completed by mathematics, and the convergence rate of the tracking error can be governed by the choice of the control parameter values. Using the DSMC to trajectory tracking control, the piezoelectric positioning stage becomes more suitable for practical applications, especially with the need of various trajectories tracking in microscopy. To validate the proposed control scheme, a computer-based controller and a piezoelectric positioning stage with a capacitive displacement sensor are implemented. Experimental results illustrate the feasibility of the proposed controller for trajectory tracking applications.

Journal Article↗
PubMed2005

Developmental trajectories of conduct problems and hyperactivity from ages 2 to 10.

BACKGROUND: Conduct problems (CP) and hyperactivity/attention problems (HAP) are thought to covary with regularity, yet few studies have examined their co-occurrence or risk factors that discriminate their trajectories beginning in early childhood. METHOD: The present study sought to advance our understanding of this issue by examining separate trajectories of overt CP and HAP symptomatology among 284 boys from urban, low-income families followed from ages 1.5 to 10. We also investigated the co-occurrence of persistent CP and HAP and explored risk factors that discriminate CP and HAP trajectories. RESULTS: Four similar trajectory groups were identified for both CP and HAP symptoms. Chronic CP was differentiated from persistent low CP by risk factors in child, parenting, and family domains, while chronic trajectories of HAP were typified by elevated maternal depressive symptoms compared to children with persistent low HAP. CONCLUSIONS: The findings extend previous research with older children of HAP and/or CP, highlighting the effects of proximal family and child risk factors that are identifiable in the first two years of children's lives and associated with trajectories of disruptive behavior.

Attention Deficit Disorder with Hyperactivity↗
PubMed1992

Formant trajectory characteristics of males with amyotrophic lateral sclerosis.

The purpose of this study was to describe the formant trajectories produced by males with amyotrophic lateral sclerosis (ALS), a degenerative neuromuscular disease that is typically associated with dysarthria. Formant trajectories of 25 males with ALS and 15 neurologically normal geriatric males were compared for 12 words selected from the speech intelligibility task developed by Kent et al. [J. Speech. Hear. Disord. 54, 482-499 (1989)]. The results indicated that speakers with ALS (1) produced formant transitions having shallower slopes than transitions of normal speakers, (2) tended to produce exaggerations of formant trajectories at the onset of vocalic nuclei, and (3) had greater interspeaker variability of formant transition characteristics than normal speakers. Within the group of ALS speakers, those subjects who were less than 70% intelligible produced distinctly more aberrant trajectory characteristics than subjects who were more than 70% intelligible. ALS subjects who were less than 70% intelligible produced many trajectories that were essentially flat, or that had very shallow slopes. These results are discussed in terms of the speech production deficit in the dysarthria associated with ALS, and with respect to the potential influence of aberrant trajectories on speech intelligibility.

Adult↗
PubMed1989

The evolution of growth trajectories and other complex quantitative characters.

Growth trajectories differ from many other quantitative characters in that they are characterized by a continuous function rather than by a finite number of discrete measurements. We review here recently developed methods for predicting the evolution of growth trajectories under the influence of natural or artificial selection. Using our method, analysis of genetic data from mice shows that the patterns of genetic variation arising from developmental processes impose constraints on evolution of growth trajectories. These constraints can be quantified to reveal the families of growth trajectories that can be produced by selection and those families that cannot. The data suggest there may be relatively few evolutionary degrees of freedom for growth trajectories despite the presence of abundant additive genetic variation to alter size and (or) growth rate at every age. The description of these constraints may be useful to both biologists who would like to determine the evolutionary options available to natural populations and to breeders who would like to alter growth trajectories to economically improve domesticated species. Our methods and conclusions can be generalized to other kinds of "infinite-dimensional" or complex characters, including morphological shapes and norms of reaction.

Age Factors↗
PubMed2001

Unsupervised learning and temporal context to recall complex robot trajectories.

An unsupervised neural network is proposed to learn and recall complex robot trajectories. Two cases are considered: (i) A single trajectory in which a particular arm configuration (state) may occur more than once, and (ii) trajectories sharing states with each other. Ambiguities occur in both cases during recall of such trajectories. The proposed model consists of two groups of synaptic weights trained by competitive and Hebbian learning laws. They are responsible for encoding spatial and temporal features of the input sequences, respectively. Three mechanisms allow the network to deal with repeated or shared states: local and global context units, neurons disabled from learning, and redundancy. The network reproduces the current and the next state of the learned sequences and is able to resolve ambiguities. The model was simulated over various sets of robot trajectories in order to evaluate learning and recall, trajectory sampling effects and robustness.

Algorithms↗
PubMed1998

Reversible inactivation of monkey superior colliculus. I. Curvature of saccadic trajectory.

The neurons in the intermediate layers of the monkey superior colliculus (SC) that discharge before saccadic eye movements can be divided into at least two types, burst and buildup neurons, and the differences in their characteristics are compatible with different functional contributions of the two cell types. It has been suggested that a spread of activity across the population of the buildup neurons during saccade generation may contribute to the control of saccadic eye movements. The influence of any such spread should be on both the horizontal and vertical components of the saccade because the map of the movement fields on the SC is a two-dimensional one; it should affect the trajectory of saccade. The present experiments used muscimol injections to inactivate areas within the SC to determine the functional contribution of such a spread of activity on the trajectory of the saccades. The analysis concentrated on saccades made to areas of the visual field that should be affected primarily by alteration of buildup neuron activity. Muscimol injections produced saccades with altered trajectories; they became consistently curved after the injection, and successive saccades to the same targets had similar curvatures. The curved saccades showed changes in their direction and speed at the very beginning of the saccade, and for those saccades that reached the target, the direction of the saccade was altered near the end to compensate for the initially incorrect direction. Postinjection saccades had lower peak speeds, longer durations, and longer latencies for initiation. The changes in saccadic trajectories resulting from muscimol injections, along with the previous observations on changes in speed of saccades with such injections, indicate that the SC is involved in influencing the eye position during the saccade as well as at the end of the saccade. The changes in trajectory when injections were made more rostral in the SC than the most active burst neurons also are consistent with a contribution of the buildup neurons to the control of the eye trajectory. The results do not, however, support the hypothesis that the buildup neurons in the SC act as a spatial integrator.

Animals↗