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PubMed2006

Trajectories of internalizing, externalizing, and grades for children who have and have not experienced their parents' divorce or separation.

This study examined whether the occurrence and timing of parental separation or divorce was related to trajectories of academic grades and mother- and teacher-reported internalizing and externalizing problems. The authors used hierarchical linear models to estimate trajectories for children who did and did not experience their parents' divorce or separation in kindergarten through 10th grade (N = 194). A novel approach to analyzing the timing of divorce/separation was adopted, and trajectories were estimated from 1 year prior to the divorce/separation to 3 years after the event. Results suggest that early parental divorce/separation is more negatively related to trajectories of internalizing and externalizing problems than is later divorce/separation, whereas later divorce/separation is more negatively related to grades. One implication of these findings is that children may benefit most from interventions focused on preventing internalizing and externalizing problems, whereas adolescents may benefit most from interventions focused on promoting academic achievement.

Achievement↗
PubMed2001

Analyzing developmental trajectories of distinct but related behaviors: a group-based method.

This article presents a group-based method to jointly estimate developmental trajectories of 2 distinct but theoretically related measurement series. The method will aid the analysis of comorbidity and heterotypic continuity. Three key outputs of the model are (a) for both measurement series, the form of the trajectory of distinctive subpopulations; (b) the probability of membership in each such trajectory group; and (c) the joint probability of membership in trajectory groups across behaviors. This final output offers 2 novel features. First, the joint probabilities can characterize the linkage in the developmental course of distinct but related behaviors. Second, the joint probabilities can measure differences within the population in the magnitude of this linkage. Two examples are presented to illustrate the application of the method.

Child↗
PubMed1998

Quality of life and psychological distress of bone marrow transplant recipients: the 'time trajectory' to recovery over the first year.

The purpose of this study was to measure the trajectory of psychosocial recovery over the first year after bone marrow transplantation (BMT). BMT patients were assessed at baseline (n = 86), hospital discharge (n = 74), 100 days (n = 64) and at 1 year (n = 45). Participants completed the Functional Assessment of Cancer Therapy-Bone Marrow Transplant Scale (FACT-BMT), the Profile of Mood States Total Mood Disturbance Scale (POMS-TMDS), the Medical Outcomes Social Support Survey (MOS-SSS), the Center for Epidemiologic Studies-Depression (CES-D) scale screener, a performance Status Rating Scale (PSR), and an interview questionnaire. The recovery trajectory in this patient population showed three distinct trends. The trajectory for distress was linear and improved over time with approximately 20% of patients continuing to have psychological distress at 1 year. Secondly, the trend for overall quality of life was parabolic, worsening at discharge, then improving at 100 days and at 1 year. However, there were individual areas of deficit at follow-up, eg fatigue, even while overall quality of life mean scores improved. Thirdly, the trend for patient concerns over time was linear and worsening. These recovery trajectories suggest psychosocial interventions before and after BMT that may prepare patients for increasing and worsening concerns even as physical well-being improves.

Adult↗
PubMed1993

Measuring the similarity between trajectories using clustering techniques.

A clustering method has been developed to group signals that display similar dynamic behavior. The procedure involves using the method of time delay embedding to construct a trajectory in state space from a time series. Certain features that characterize the geometry of the trajectory have been defined. These features were subjected to a series of statistical tests to determine their usefulness in a hierarchical clustering analysis. The latter is aimed at finding groups of similar trajectories. The trajectory-based clustering algorithm has been applied to simulated data, which included both stochastic data generated by a linear AR model, and nonlinear data generated by a Duffing oscillator. The results show that the algorithm works reliably in both cases.

Journal Article↗
PubMed1997

The analysis of ontogenetic trajectories: when a change in size or shape is not heterochrony.

Heterochrony has become a central organizing concept relating development and evolution. Unfortunately, the standard definition of heterochrony--evolutionary change in the rate or timing of developmental processes--is so broad as to apply to any case of phenotypic evolution. Conversely, the standard classes of heterochrony only accurately describe a small subset of the possible ways that ontogeny can change. I demonstrate here that the nomenclature of heterochrony is meaningful only when there is a uniform change in the rate or timing of some ontogenetic process, with no change in the internal structure of that process. Given two ontogenetic trajectories, we can test for this restricted definition of heterochrony by asking if a uniform stretching or translation of one trajectory along the time axis superimposes it on the other trajectory. If so, then the trajectories are related by a uniform change in the rate or timing of development. If not, then there has been change within the ontogenetic process under study. I apply this technique to published data on fossil Echinoids and to the comparison of human and chimpanzee growth curves. For the Echinoids, some characters do show heterochrony (hypermorphosis), while others, which had previously been seen as examples of heterochrony, fail the test--implying that their evolution involved changes in the process of development, not just the rate at which it proceeded. Analysis of human and chimpanzee growth curves indicates a combination of neoteny and sequential hypermorphosis, two processes previously seen as alternate explanations for the differences between these species.

Animals↗
PubMed1999

Effects of Displacement and Trajectory Length on the Variability Pattern of Reaching Movements.

The design of the present study enabled the authors to distinguish between the possible effects of movement displacement and trajectory length on the pattern of final positions of planar reaching movements. With their eyes closed, 9 subjects performed series of fast and accurate movements from different initial positions to the same target. For some series, the movements were unconstrained and were therefore performed along an approximately straight vertical line. For other series, an obstacle was positioned so that trajectory length was increased because of an increase in movement curvature. Ellipses of variability obtained by means of principal component analysis applied to the scatter of movement final positions enabled the authors to assess the pattern of movement variable errors. The results showed that the orientation of the ellipses was not affected by movement displacement or by trajectory length, whereas variable errors increased with movement displacement. An increase in trajectory length as a consequence of increased curvature caused no change in variable error. From the perspective of current motor control theory, that finding was quite unexpected. Further studies are required so that one can distinguish among the possible effects of various kinematics, kinetics, and other variables that could affect the pattern of variable errors of reaching movements.

Journal Article↗
PubMed1997

Optimal trajectory for the basketball free throw.

Using a theoretical approach, we studied the basketball free throw as a function of angle, speed and spin at release. The ball was constrained to the sagittal plane bisecting the hoop and normal to the backboard, and was permitted to bounce and change spin on both backboard and hoop. Combinations of angle, speed and spin resulting in a successful shot were calculated analytically. Standard deviations for a shooter's angle and speed were used to predict the optimal trajectory for a specific position of release. An optimal trajectory was predicted which had an initial angle and speed of approximately 60 degrees and 7.3 m s(-1) respectively over the domain of spins (-2 to +2 m s(-1) surface speed; -16 to +16 rad s[1]). The effect of air resistance and the sagittal plane constraint on the predicted optimal trajectory were discussed and quantified. The optimal trajectory depended on both the anthropometric characteristics and accuracy of the shooter, but generally a high backspin with an angle and speed combination which sent the ball closer to the far rim of the basket than the near rim was advantageous. We provide recommendations for shooters as a function of the height of ball release.

Basketball↗
PubMed2006

Peer and parental influences on longitudinal trajectories of smoking among African Americans and Puerto Ricans.

The purpose of this study was to identify distinct trajectories of smoking behavior during a period extending from adolescence (mean age = 14 years) to young adulthood (mean age = 26 years) among African American and Puerto Rican adolescents/young adults, to examine ethnic and gender differences in group membership, and to assess the ability of peer and parental smoking to distinguish among trajectory groups. A community-based sample of 451 African American and Puerto Rican adolescents was interviewed four times during adolescence and in early adulthood, covering a span of 12 years. For both ethnic/racial groups, four distinct trajectories were identified: Nonsmokers, maturing-out smokers, late-starting smokers, and early-starting continuous smokers. Compared with Puerto Ricans, African Americans were over-represented in the nonsmoking group, whereas Puerto Ricans were over-represented in the early-starting continuous group. Females were more likely than males to be early-starting continuous smokers than late starters. Adolescents who were exposed to peer and parental smoking in early adolescence were more likely to belong to trajectory groups characterized by higher levels of smoking. These findings show that exposure to peer and parental smoking in early adolescence constitutes a risk factor for engaging in elevated levels of smoking behavior at an early age and for continued smoking into adulthood for urban African Americans and Puerto Ricans. To be most effective, smoking prevention programs should address peer group and family influences on adolescent smoking.

Adolescent↗
PubMed2003

Synchronized moving aperture radiation therapy (SMART): average tumour trajectory for lung patients.

Synchronized moving aperture radiation therapy (SMART) is a new technique for treating mobile tumours under development at Massachusetts General Hospital (MGH). The basic idea of SMART is to synchronize the moving radiation beam aperture formed by a dynamic multileaf collimator (DMLC) with the tumour motion induced by respiration. SMART is based on the concept of the average tumour trajectory (ATT) exhibited by a tumour during respiration. During the treatment simulation stage, tumour motion is measured and the ATT is derived. Then, the original IMRT MLC leaf sequence is modified using the ATT to compensate for tumour motion. During treatment, the tumour motion is monitored. The treatment starts when leaf motion and tumour motion are synchronized at a specific breathing phase. The treatment will halt when the tumour drifts away from the ATT and will resume when the synchronization between tumour motion and radiation beam is re-established. In this paper, we present a method to derive the ATT from measured tumour trajectory data. We also investigate the validity of the ATT concept for lung tumours during normal breathing. The lung tumour trajectory data were acquired during actual radiotherapy sessions using a real-time tumour-tracking system. SMART treatment is simulated by assuming that the radiation beam follows the derived ATT and the tumour follows the measured trajectory. In simulation, the treatment starts at exhale phase. The duty cycle of SMART delivery was calculated for various treatment times and gating thresholds, as well as for various exhale phases where the treatment begins. The simulation results show that in the case of free breathing, for 4 out of 11 lung datasets with tumour motion greater than 1 cm from peak to peak, the error in tumour tracking can be controlled to within a couple of millimetres while maintaining a reasonable delivery efficiency. That is to say, without any breath coaching/control, the ATT is a valid concept for some lung tumours. However, to make SMART an efficient technique in general, it is found that breath coaching techniques are required.

Computer Simulation↗
PubMed2006

View-independent reconstruction algorithms for cone beam CT with general saddle trajectory.

In Yang et al (2006 Phys. Med. Biol. 51 1157-72), an exact filtered backprojection (FBP) reconstruction algorithm was proposed for cone beam tomography with saddle trajectory based on the seminal works of Pack and Noo (2005a Inverse Problems 21 1105-20; 2005b 8th Int. Meeting on Fully 3D Reconstruction in Radiology and Nuclear Medicine (Salt Lake City) ed F Noo, H Kudo and L G Zeng pp 287-90). However, the artefacts due to discretization and/or sampling errors in the reconstructed images by this method were still visible, especially when the pitch is large. In this paper, two view-independent (VI) algorithms, which are similar to the FDK-type algorithms (Feldkamp et al 1984 J. Opt. Soc. Am. A 1 612-19), are proposed for planar detector geometry. The first VI algorithm involves two filtered projections and a small additional term (two-dimensional (2D) Radon transform term). One of the filtered projections is obtained by ramp filtering (as in the FDK algorithm for circular trajectory) and the other one is obtained by Hilbert transform. The 2D Radon transform term is just like the term which was first derived by Hu (1996 Scanning 18 572-81) for a circular trajectory. The second VI algorithm involves only one filtered projection term, which is obtained by differentiation followed by Hilbert transform and the 2D Radon transform term. Both algorithms involve only one backprojection step with a weighting factor as in the FDK algorithm. The simulation studies show that the pixel values of the reconstructed images by the VI algorithms are more accurate than those by the original view differencing (VD) algorithm, the streak artefacts are also reduced, and their computational times are comparable to that of the original VD algorithm. We also generalize the concept of saddle trajectory and the corresponding reconstruction algorithm. The generalized algorithm is also theoretically exact, has a shift-invariant FBP structure, and does not depend on the concept of pi-line.

Algorithms↗
PubMed2003

Developmental typology of trajectories to nighttime bladder control: epidemiologic application of longitudinal latent class analysis.

The authors aimed to characterize developmental trajectories to nighttime continence by applying two latent class models-longitudinal latent class analysis (LLCA) and latent class growth analysis (LCGA)-to data on nighttime bed-wetting from a population-based birth cohort, the Medical Research Council 1946 National Survey of Health and Development cohort. Data on a binary outcome (wetting in the past month vs. not wetting) were available for children at six ages (4, 6, 8, 9, 11, and 15 years) assessed in 1950, 1952, 1954, 1955, 1957, and 1961. For 3,272 children with complete data (62.5% of the cohort), results of sequential model comparisons (T classes vs. T + 1 classes) and chi-square goodness-of-fit tests were evaluated using parametric bootstrapping. At least four trajectory classes (LLCA and LCGA) were identified. Associations between class membership and the prevalence of related measures were examined using a confirmatory latent class analysis approach. Inclusion of 1,483 children with partially incomplete data (n = 4,755; 90.9% of the cohort) enabled the authors to refine trajectories further: normal development (prevalence = 84.0%); delayed acquisition of bladder control ("transient" (8.7%) and "persistent" (1.8%)), capturing primary enuresis; chronic bed-wetting (2.6%), or experiencing night wetting until age 15 years; and a final trajectory (relapse = 2.9%) capturing secondary or onset enuresis. This empirically based, typologic approach to analysis of extensive longitudinal data in a general population sample provides an alternative perspective to that offered by traditional diagnostic criteria.

Adolescent↗
PubMed2005

Individual variation in CD4 cell count trajectory among human immunodeficiency virus-infected men and women on long-term highly active antiretroviral therapy: an application using a Bayesian random change-point model.

The authors evaluated population- and individual-level CD4-positive T-lymphocyte (CD4 cell) count trajectories over a 7-year period (July 1995-March 2004) following initiation of highly active antiretroviral therapy (HAART) in the Multicenter AIDS Cohort Study and the Women's Interagency HIV Study. The study population included 404 human immunodeficiency virus (HIV)-infected men and 609 HIV-infected women who 1) had a CD4 cell count measurement available from their last pre-HAART study visit, 2) provided at least four post-HAART CD4 cell count measurements, and 3) reported HAART usage for at least 80% of the post-HAART visits. The CD4 cell count trajectory was analyzed by means of a Bayesian random change-point model. The results indicated that CD4 cell count trajectories for long-term frequent HAART users can be well modeled with change points at both the population and individual levels. At the population level, regardless of CD4 cell count before HAART initiation, the gains in CD4 cell count ended approximately 2 years after HAART initiation in both men and women. At the individual level, 35% of men in the Multicenter AIDS Cohort Study versus 25% of women in the Women's Interagency HIV Study had a statistically significant change in CD4 cell count trajectory within 7 years after HAART initiation.

Adult↗
PubMed2005

Differential and trajectory methods for time course gene expression data.

MOTIVATION: The issue of high dimensionality in microarray data has been, and remains, a hot topic in statistical and computational analysis. Efficient gene filtering and differentiation approaches can reduce the dimensions of data, help to remove redundant genes and noises, and highlight the most relevant genes that are major players in the development of certain diseases or the effect of drug treatment. The purpose of this study is to investigate the efficiency of parametric (including Bayesian and non-Bayesian, linear and non-linear), non-parametric and semi-parametric gene filtering methods through the application of time course microarray data from multiple sclerosis patients being treated with interferon-beta-1a. The analysis of variance with bootstrapping (parametric), class dispersion (semi-parametric) and Pareto (non-parametric) with permutation methods are presented and compared for filtering and finding differentially expressed genes. The Bayesian linear correlated model, the Bayesian non-linear model the and non-Bayesian mixed effects model with bootstrap were also developed to characterize the differential expression patterns. Furthermore, trajectory-clustering approaches were developed in order to investigate the dynamic patterns and inter-dependency of drug treatment effects on gene expression. RESULTS: Results show that the presented methods performed significant differently but all were adequate in capturing a small number of the potentially relevant genes to the disease. The parametric method, such as the mixed model and two Bayesian approaches proved to be more conservative. This may because these methods are based on overall variation in expression across all time points. The semi-parametric (class dispersion) and non-parametric (Pareto) methods were appropriate in capturing variation in expression from time point to time point, thereby making them more suitable for investigating significant monotonic changes and trajectories of changes in gene expressions in time course microarray data. Also, the non-linear Bayesian model proved to be less conservative than linear Bayesian correlated growth models to filter out the redundant genes, although the linear model showed better fit than non-linear model (smaller DIC). We also report the trajectories of significant genes-since we have been able to isolate trajectories of genes whose regulations appear to be inter-dependent.

Computer Simulation↗
PubMed1990

Analysis of the inheritance, selection and evolution of growth trajectories.

We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.

Animals↗
PubMed2005

Theory of cathode trajectory characterization by canonical mapping transformation.

The paraxial lens theory cannot directly be applied to the cathode trajectories inside the gun. This inconvenience makes the interpretation of cathode trajectories difficult since one cannot use the physical concepts familiar in the paraxial lens theory, such as focal length and magnification factor. We have proposed the canonical mapping transformation (CMT) to describe the electron trajectories inside the gun by relating the ray conditions on the cathode surface to those in the crossover plane. The method takes as variables the distance along the surface and the sine of the ray angle with respect to the surface normal to define ray conditions. It has been shown that the CMT can be characterized by a small number of optical parameters. One of the parameters is the 'electron gun focal length', an extension of the image side focal length in the paraxial lens theory. The crossover size of a triode gun can be calculated from the electron gun focal length and the initial transverse energy spread. The calculation predicts the dependence of the crossover size on the grid voltage due to the change in the electron gun focal length. The prediction is compared with the measurement and shows good agreement with it. Since the CMT optical parameters can be calculated from the representative trajectories only and as they predict practically all the necessary source properties of guns, the CMT can be used as a practical tool in the designing of various types of electron guns.

Journal Article↗
PubMed1994

Successive roles of the cerebellum and premotor cortices in trajectorial learning.

The structures of the human brain engaged during learning of unilateral trajectorial hand movements were mapped by measurements of regional cerebral blood flow. Trajectorial movement velocity accelerated moderately after short-term training p < 0.025 and increased further after long-term training p < 0.01. During the early phase of learning there was a significant activation p < 0.001 of the ipsilateral dentate nucleus. By contrast, after overlearning the premotor cortical areas in both cerebral hemispheres were maximally activated p < 0.001, while the dentate nucleus was no longer activated. It is suggested that learning of new movement trajectories involves the cerebellum, while overlearned trajectorial movements engage the premotor cortex.

Cerebellum↗
PubMed1997

A test of the fit between the Corbin and Strauss Trajectory Model and care provided to older patients after cancer surgery.

The Corbin and Strauss Trajectory Model proposed that nursing care should differ along a trajectory of eight phases to meet patients' and families' needs. Seventy-nine patients with breast, prostate, or gastrointestinal cancer were determined to be in either the stable or the unstable phase of their illness. Contrary to expectations, documented nursing interventions did not significantly differ between stable and unstable trajectory phases, although significant differences were found when comparisons were made across cancer sites. These findings suggest that the trajectory framework may require modification for use with oncology patients.

Aged↗
PubMed2002

Pedal trajectory alters maximal single-leg cycling power.

PURPOSE: Muscular power produced during in vitro cyclic contraction has been reported to vary with muscle-length trajectory. The purpose of this study was to determine whether maximal human single-leg cycling power could be similarly altered by manipulating pedal trajectory. METHOD: Seven trained cyclists performed maximal single-leg cycle ergometry. Pedal trajectory was manipulated by repositioning the ergometer drive sprocket off-center with respect to the crank axle, such that the leg-extension phase occupied 42, 50, or 58% of the cycle time (LEP42, LEP50, and LEP58, respectively). RESULTS: Maximum instantaneous power was 12% greater for LEP58 (1984 +/- 143 W) than LEP50 (1838 +/- 126 W), which was 8% greater than that for LEP42 (1645 +/- 112 W). Maximum power, averaged over a complete revolution of the crank, was 4% greater for LEP58 (636 +/- 59 W) than for LEP50 (613 +/- 53 W), which was 18% greater than that for LEP42 (520 +/- 43 W). CONCLUSIONS: These findings, paralleling those for an in vitro model, confirmed our hypothesis that maximal single-leg cycling power could be altered by manipulating pedal trajectory. Alterations in power were likely due to concomitant effects of muscle-shortening velocity, muscle excitation, and biomechanical constraints. Additional research is needed to determine whether greater leg-extension phase ratios can elicit further increases in power and whether similar results can be obtained during bilateral cycling.

Adult↗