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BACKGROUND: Chemotherapy for breast cancer often induces multidimensional adverse reactions such as nausea and vomiting, anxiety, depression, and sleep disturbances. These symptoms are interrelated and may evolve dynamically, impacting patients' treatment outcomes and quality of life. As non-pharmacological interventions, transcutaneous electrical acupoint stimulation (TEAS) and self-acupressure (SA) have shown potential in alleviating symptoms. However, their long-term effects on the joint developmental trajectories of these multidimensional symptoms (nausea and vomiting, anxiety, depression, and sleep disturbances) remain unclear. OBJECTIVE: This study aimed to identify potential trajectory class of multidimensional adverse reactions in breast cancer patients undergoing chemotherapy and to explore the differential effects of TEAS and SA on different trajectory subgroups. METHODS: This was a secondary analysis of a randomized controlled trial. A total of 189 breast cancer patients receiving chemotherapy were included. The Group-Based Multi-Trajectory Model (GBMTM) was employed to identify joint developmental trajectories of acute/delayed chemotherapy-induced nausea and vomiting (CINV), anxiety, depression, and sleep quality during chemotherapy. Subsequently, causal forest was used to analyze the average treatment effects (ATE) of TEAS (vs. control group) and SA (vs. control group) on patients' symptom trajectory. RESULTS: Multidimensional adverse reactions were classified into two heterogeneous trajectories: a "High Symptom Burden-Persistent (HSBP)" type (n = 101) and a "Low Symptom Burden-Relieving (LSBR)" type (n = 88). The persistent high incidence of acute CINV contrasted sharply with the comprehensive relief of other symptoms in the latter group. Causal forest suggested that both TEAS and SA significantly increased the probability of patients being classified into the "LSBR" trajectory. The ATE was 0.147 (95% CI: 0.143, 0.151) for TEAS, slightly lower (P < 0.05) than 0.176 (95% CI: 0.162, 0.190) for SA.  CONCLUSION: Multidimensional adverse reactions in breast cancer patients undergoing chemotherapy exhibit heterogeneity in their trajectories. Both TEAS and SA were associated with a higher probability of patients being classified into a more favorable symptom trajectory-LSBR. The multidimensional trajectory identification with treatment effect estimation may serve as a useful analytical strategy for future longitudinal research in cancer chemotherapy-induced adverse reactions symptom management. CLINICAL TRIAL REGISTRATION: ChiCTR2300077667 (Chinese Clinical Trial Registry, https://www.chictr.org.cn/ ), Registered 15 November 2023.
Magnetocardiograms were recorded from 30 normal (N) subjects, 15 myocardial infarct (MI) patients, and 15 ventricular tachycardia (VT) patients. Discrimination between the groups was affected by iso-integral magnetic field mapping (MFM) and trajectory plotting of MFM extrema. Iso-integral MFM for the QRST, QRS, and ST-T intervals was created for each test group member. A polarity score, based on the number of extrema features present, was assigned to each iso-integral MFM. Differences in group mean integral of QRST map polarity scores were significant (p less than 0.05) between MI and N, between VT and N (p less than 0.005), and between MI and VT (p less than 0.05) subjects. integral of ST-T map polarity scores were significantly (p less than 0.0001) different between VT and N and between MI and VT (p less than 0.001) subjects. Discrimination between MI and VT patients, based on polarity score difference, was 56% accurate using integral of QRS maps and 73% accurate using integral of ST-T maps. For each subject, time-normalized MFM was used to construct trajectory plots of the maxima and minima in the QRS and ST-T intervals. Discrimination between MI and VT patients was based upon intergroup differences in fragmented trajectory plots. When the number of discrete trajectories and/or the total number (F) of trajectory points at which discrete trajectories coexist were considered, QRSmin trajectory plots were significantly (p less than 0.05) different for VT and N, but not for MI and N subjects. The significant (p less than 0.05) difference between MI and VT trajectory plots enabled 76% accuracy for MI and VT identification. ST-Tmax trajectory plots show significantly (p less than 0.0001) higher F values for VT patients facilitating accurate (87%) discrimination between MI and VT patients. These results suggest that the abnormalities of repolarization processes, displayed by MFM as multipolar integral of ST-T maps and/or as fragmented trajectory plots of ST-T extrema, may be useful indicators of the arrhythmia substrate/processes that characterize VT and vulnerable MI patients.
In the framework of the equilibrium-point hypothesis, virtual trajectories and patterns of joint stiffness were reconstructed during voluntary single-joint oscillatory movements in the elbow joint at a variety of frequencies and against two inertial loads. At low frequencies, virtual trajectories were in-phase with the actual joint trajectories. Joint stiffness changed at a doubled frequency. An increase in movement frequency and/or inertial load led to an increase in the difference between the peaks of the actual and virtual trajectories and in both peak and averaged values of joint stiffness. At a certain, critical frequency, virtual trajectory was nearly flat. Further increase in movement frequency led to a 180 degree phase shift between the actual and virtual trajectories. The assessed values of the natural frequency of the system "limb + manipulandum" were close to the critical frequencies for both low and high inertial loads. Peak levels and integrals of the electromyograms of two flexor and two extensor muscles changed monotonically with movement frequency without any special behavior at the critical frequencies. Nearly flat virtual trajectories at the natural frequency make physical sense as hypothetical control signals, unlike the electromyographic recordings, since a system at its natural frequency requires minimal central interference. Modulation of joint stiffness is assumed to be an important adaptive mechanism attenuating difference between the system's natural frequency and desired movement frequency. Virtual trajectory is considered a behavioral observable. Phase transitions between the virtual and actual trajectories are illustrations of behavioral discontinuities introduced by slow changes in a higher level control parameter, movement frequency. Relative phase shift between these two trajectories may be considered an order parameter.
In this paper, we study trajectory planning and control in voluntary, human arm movements. When a hand is moved to a target, the central nervous system must select one specific trajectory among an infinite number of possible trajectories that lead to the target position. First, we discuss what criterion is adopted for trajectory determination. Several researchers measured the hand trajectories of skilled movements and found common invariant features. For example, when moving the hand between a pair of targets, subjects tended to generate roughly straight hand paths with bell-shaped speed profiles. On the basis of these observations and dynamic optimization theory, we propose a mathematical model which accounts for formation of hand trajectories. This model is formulated by defining an objective function, a measure of performance for any possible movement: square of the rate of change of torque integrated over the entire movement. That is, the objective function CT is defined as follows: (formula; see text) We overcome this difficult by developing an iterative scheme, with which the optimal trajectory and the associated motor command are simultaneously computed. To evaluate our model, human hand trajectories were experimentally measured under various behavioral situations. These results supported the idea that the human hand trajectory is planned and controlled in accordance with the minimum torque-change criterion.
BACKGROUND: Functional impairment in psychosis often persists despite symptomatic remission. There is a paucity of research examining early-course psychosocial functioning trajectories, and none has been conducted to examine relationship between the trajectories and prospective long-term functional outcomes in early psychosis sample. METHODS: We conducted 12-year follow-up of a randomized controlled trial on extended early intervention for first-episode psychosis to identify early-course social-occupational functioning trajectories and their baseline predictors and associations with 12-year outcomes. Participants who completed Social and Occupational Functioning Scale (SOFAS) scores at three or more timepoints between baseline and 3-year follow-up were included in the study. Premorbid adjustment, illness characteristics, symptom severity, functioning, and treatment profiles were assessed. Latent growth mixture modeling was employed to derive early-course social-occupational functioning trajectories based on SOFAS scores over 3-year follow-up. RESULTS: A total of 148 participants were included in this study, with 106 patients having completed the 12-year follow-up. Our results identified four distinct trajectories, including persistently-good class, gradually-improved class, suboptimal-stable class, and persistently-poor class. Patients in persistently-poor class had more severe negative symptoms at baseline compared to patients in persistently-good class. Patients with persistently-poor trajectory had worse long-term outcomes than those with other classes in the majority of functional measures at 12-year follow-up. CONCLUSIONS: The majority of patients were classified in early-stage suboptimal or poor functional trajectories. Above one-fourth of the participants exhibited persistently-poor social-occupational functioning trajectory, which predicted worse functional outcomes at 12-year follow-up. These findings highlighted the importance of tracking functional changes during the initial years of illness.
Predictions of the minimum-jerk model for a human cyclic motion were given in terms of asymmetry in movement trajectories. A detailed kinematic analysis of cyclic forearm motion, i.e., extension/flexion movements around the elbow joint in a horizontal plane ranging in frequency from 2-5.5 Hz, was made to examine the validity of the predictions. The kinematics of the trajectories were described in terms of deviation from symmetry in velocity and acceleration profiles, and jerk cost. The asymmetry could be accounted for by the solution of the minimum-jerk model using the boundary condition differences between extension and flexion during a movement cycle. The trajectory was asymmetrical at relatively low frequencies, and symmetrical at higher frequencies; the frequency boundary from asymmetrical to symmetrical trajectories differed among subjects with a range of 3-4.3 Hz. It was suggested for the asymmetrical trajectory formation that consecutive extension and flexion in a cycle could be processed as a unit in which speed and acceleration in each direction were differentiated. The shift from asymmetrical to symmetrical trajectories with increasing frequency was accompanied by a reduction in jerk cost and mechanical energy. The oscillators underpinning the high frequency movements were mainly non-linear. The results suggested a shift of control from the "rhythmic" sequencing of extension and flexion which resulted in trajectory asymmetry, to non-linear oscillation with no directional difference.
This paper investigates whether endpoint Cartesian variables or joint variables better describe the planning of human arm movements. For each of the two sets of planning variables, a coordination strategy of linear interpolation is chosen to generate possible trajectories, which are to be compared against experimental trajectories for best match. Joint interpolation generates curved endpoint trajectories called N-leaved roses. Endpoint Cartesian interpolation generates curved joint trajectories, which however can be qualitatively characterized by joint reversal points. Though these two sets of planning variables ordinarily lead to distinct predictions under linear interpolation, three situations are pointed out where the two strategies may be confused. One is a straight line through the shoulder, where the joint trajectories are also straight. Another is any trajectory approaching the outer boundary of reach, where the joint rate ratio always appears to be approaching a constant. A third is a generalization to staggered joint interpolation, where endpoint trajectories virtually identical to straight lines can sometimes be produced. In examining two different sets of experiments, it is proposed that staggered joint interpolation is the underlying planning strategy.
In the preceding study (Gordon and Ghez 1987), we showed that accurately targeted isometric force impulses produced by human subjects are governed by a pulse height control policy. Different peak forces were achieved by modulating the rate of rise of force while force rise time was maintained close to a constant value and independent of peak force. An early measure of the rate of rise of force, peak d2F/dt2, was scaled to the required force (target amplitude) and highly predictive of the peak force achieved. In six subjects examined, peak d2F/dt2 accounted for between 70% and 96% of the total variance in peak force. In the present study, we further examined these targeted responses to determine whether the residual variability not predicted by peak d2F/dt2 could be accounted for by adjustments to the force trajectories which compensated for initial errors in the scaling of the d2F/dt2. A statistical model of the determinants of peak force was tested. This model included two paths by which the target amplitude could independently influence the peak force achieved. The first path was preprogrammed pulse height control. In this path, target amplitude determined the initial rate of rise of force (peak d2F/dt2) which in turn determined the final peak force achieved. The second path was an independent influence of errors in the initial scaling of peak d2F/dt2 on peak force. Multiple regression analysis was performed on trajectory variables within the sets of responses by each subject in each condition to determine whether the second path contributed significantly to explaining the variance in peak force. In each subject and condition, there was a significant independent influence of error in d2F/dt2 on peak force, and the direction of this effect was to decrease the magnitudes of peak force errors. These compensatory adjustments accounted for between 1% and 14% of the total variance in peak force. Further multiple regression analyses revealed that inappropriate scaling of the initial phase of the trajectories was compensated for by shortening or prolonging the force rise time. These trajectory adjustments were in turn implemented by modulation of the timing and magnitude of the contractions in the agonist and antagonist muscles that produced the force trajectories. Because these compensatory adjustments were evident in the EMG pattern at latencies too short to be accounted for by peripheral feedback, we assume that they depend on internal monitoring of the unfolding neural commands. These internal feedback processes act in parallel with the programmed commands, both determining the force trajectory.
According to the equilibrium trajectory hypothesis, multi-joint arm movements are achieved by gradually shifting the hand equilibrium positions defined by the neuromuscular activity. The magnitude of the force exerted on the arm, at any time, depends on the difference between the actual and equilibrium hand positions and the stiffness and viscosity about the equilibrium position. The purpose of this paper is to test the validity and implications of this hypothesis in the context of reaching movements. A mathematical description of the behavior of an arm tracking the equilibrium trajectory was developed and implemented in computer simulations. The joint stiffness parameters used in these simulations were derived from experimentally measured static stiffness values. The kinematic features of hand equilibrium trajectories which were derived from measured planar horizontal movements gave rise to the suggestion that the generation of reaching movements involves explicit planning of spatially and temporally invariant hand equilibrium trajectories. This hypothesis was tested by simulating actual arm movements based on hypothetical equilibrium trajectories. The success of the predicted behavior in capturing both the qualitative features and the quantitative kinematic details of the measured movements supports the equilibrium trajectory hypothesis. The control strategy suggested here may allow the motor system to avoid some of the complicated computational problems associated with multi-joint arm movements.
Three orthogonally derived voltage-time records, when plotted simultaneously on three-dimensional voltage-voltage-voltage coordinates, produce a 3-Channel Lissajous' Trajectory (3CLT). 3CLTs of short latency visual evoked potentials (SVEP) were obtained for 8 adult humans (16 eyes) in response to monocular flash stimulation. Intersubject variability of 3CLT of SVEP was small enough to enable identification along the trajectory of comparable planar-segments of approx. 3-5 ms duration across subjects. In each planar-segment, the point at which the trajectory exhibited marked bending was noted. These points were called apices and they corresponded to maxima in the trajectory's distance from the origin (Trajectory Amplitude). Intersubject variability in apex latencies was comparable to, or smaller than, peak latency variability of single-channel records. 3CLT of SVEP consisted of 8 planar-segments in each of the latency ranges of 0-40, 40-70 and 70-100 ms. Analysis of 3CLT, combining the criteria of segment planarity, apices and trajectory amplitude peaks, enabled differentiation between components that had been considered the same in surface distribution studies. 3CLT of SVEP seemed to be influenced by the direction of propagation along the visual pathway.
A novel method for analysing molecular dynamics trajectories has been developed, which filters out high frequencies using digital signal processing techniques and facilitates focusing on the low-frequency collective motions of proteins. These motions involve low energy slow motions, which lead to important biological phenomena such as domain closure and allosteric effects in enzymes. The filtering method treats each of the atomic trajectories obtained from the molecular dynamics simulation as a "signal". The trajectories of each of the atoms in the system (or any subset of interest) are Fourier transformed to the frequency domain, a filtering function is applied and then an inverse transformation back to the time domain yields the filtered trajectory. The filtering method has been used to study the dynamics of the enzyme phospholipase A2. In the filtered trajectory, all the high frequency bond and valence angle vibrations were eliminated, leaving only low-frequency motion, mainly fluctuations in torsions and conformational transitions. Analysis of this trajectory revealed interesting motions of the protein, including concerted movements of helices, and changes in shape of the active site cavity. Unlike normal mode analysis, which has been used to study the motion of proteins, this method does not require converged minimizations or diagonalization of a matrix of second derivatives. In addition, anharmonicity, multiple minima and conformational transitions are treated explicitly. Thus, the filtering method avoids most of the approximations implicit in other investigations of the dynamic behaviour of large systems.
PURPOSE: "Abrazos, no balazos" (Hugs, not gunshots) is the approach to violence used by the Federal Mexican government from 2018 to 2024. This study identifies distinct conceptually useful latent class growth trajectories in the annual intensity of risk for exposure to events and fatalities from violence against civilians and battles for adolescents and young adults (AYAs) in México from 2018 to 2024. METHODS: Data are from the Armed Conflict Location and Event Data project. Latent class growth analyses were conducted with four longitudinal dependent variables assessed in seven sequential years (2018-2024). RESULTS: In most of the Mexican states, AYAs experienced low intensity-flat trajectories (p >.096) in the annual intensity of risk for exposure to events and fatalities from violence against civilians and battles. AYAs who lived in states with extremely, markedly, or moderately elevated 2018 intensities of risk for exposure to violence experienced decreasing trajectories (p =.000). One latent class with a mildly elevated-increasing trajectory (p =.000) in the annual intensity of risk for exposure to violence was identified for each of the four longitudinal dependent variables. DISCUSSION: During the time that the Federal Mexican government used the "Abrazos, no balazos" approach, AYAs in the majority of the states in México had intensity of risk for exposure to violence and armed conflict trajectories that were consistent with the goals of primary and secondary violence prevention. Violence prevention efforts should be augmented in states with unfavorable trajectories.
Early-childhood temperament is associated with later mental health. Temperament continues to develop throughout the first years of life, and a single assessment cannot capture its trajectory. Whether departures from an individual's developmental trajectory carry psychiatric risk remains unknown. Using data from more than 50,000 children in the Norwegian Mother, Father and Child Cohort Study, we modeled longitudinal temperament at 1.5, 3, and 5 years of age with the FEMA-Long mixed-effects framework. We then quantified each child's departures from their predicted trajectories. Multivariate analysis revealed two transdiagnostic dimensions linking trajectory departures to psychiatric diagnoses across childhood and adolescence. Higher scores on the first dimension were associated with an increased hazard of subsequent ADHD diagnosis (hazard ratio = 1.54), and higher scores on the second with an increased hazard of Asperger syndrome (hazard ratio = 1.64). To examine the genetic basis of these associations, we performed longitudinal GWAS of temperament and conjunctional FDR analysis to detect loci shared with the associated diagnoses. The effects of these loci changed across early childhood, with some strengthening and others attenuating with age. These findings show that departures from predicted temperament trajectories reflect transdiagnostic psychiatric risk with a shared genetic basis. Longitudinal, trajectory-based monitoring could help identify children at elevated psychiatric risk.
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.
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.
The force trajectories of isometric wrist flexor efforts and corresponding EMG activity of forearm muscles were studied in healthy subjects. A target effort of 50 N was developed after the sound signal: the target level and force trajectory were displayed on the TV indicator. Force trajectories under conditions of visual control, kinesthetic control (without a visual target) and with random alternation of these regimens were compared. Wrist flexor EMG latencies were approximately equal under visual and kinesthetic control and noticeably longer when these conditions were alternated randomly. Relative error of the target effort reproduction and duration of late components of force trajectories were higher in absence of the visual target. When visual and kinesthetic regimes were alternated randomly the delay between EMG onset and force trajectory initiation increased; its values correlated positively with the duration of the first force derivative increase. Formation of different strategies for force trajectory correction under different experimental conditions is discussed.
The functional role of opposing muscles in the production of isometric force trajectories was studied in six adult subjects producing impulses and steps of elbow flexor force, with different rise times and amplitudes. Rapidly rising forces were invariably associated with an alternating pattern of EMG activity in agonist and antagonist muscles: an agonist burst (AG1) initiated the development of force in the desired direction while a reciprocal burst in the antagonist (ANT-R) led to the deceleration of the force trajectory prior to the peak force. The temporal pattern of agonist and antagonist activation was dependent on force rise time. Force trajectories with long rise times (greater than 200 ms) were entirely controlled by the agonist, and EMG activity closely followed the contours of the rising force trajectory. For rise times of about 120 to 200 ms, agonist activation formed a discrete EMG burst, and force continued to rise during the subsequent silent period. For brief force rise times (less than 120 ms), reciprocal activation of the antagonist muscle occurred at about the time of the peak dF/dt. The integrated magnitude of AG1 was dependent on peak force but was independent of force rise time. AG1 duration varied directly with both peak force and force rise time. The integrated value of ANT-R varied as an inverse function of force rise time and was minimally influenced by peak force. ANT-R was present with the same magnitude and timing in both force impulses and steps when rise times were equal; therefore it did not serve to return force to baseline. Rather it served to truncate the rising force when very brief rise times were required, thus compensating for the low-pass filter properties of the agonist muscle. Subjects were able to voluntarily suppress ANT-R in rapidly accelerated force trajectories, indicating that the linkage between the commands controlling agonist and antagonist is not obligatory; however AG1 was then prolonged. Our findings emphasize that neuronal commands to opposing muscles acting at a joint must be adapted to constraints imposed by the properties of the neuromuscular plant.