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PubMed1998

Volumetric spectroscopic imaging with spiral-based k-space trajectories.

Spiral-based k-space trajectories were applied in a spectroscopic imaging sequence with time-varying readout gradients to collect volumetric chemical shift information. In addition to spectroscopic imaging of low signal-to-noise ratio (SNR) brain metabolites, the spiral trajectories were used to rapidly collect reference signals from the high SNR water signal to automatically phase the spectra and to aid the reconstruction of metabolite maps. Spectral-spatial pulses were used for excitation and water suppression. The pulses were designed to achieve stable phase profiles in the presence of up to 20% variation in the radiofrequency field. A gridding algorithm was used to resample the data onto a rectilinear grid before fast Fourier transforms. This method was demonstrated by in vivo imaging of brain metabolites at 1.5 T with 10 slices of 18 x 18 pixels each. Nominal voxel size was 1.1 cc, spectral bandwidth was 400 Hz, scan time was 18 min for the metabolite scan and 3 min for the reference scan.

Aspartic Acid↗

PubMed2004

Single TrAjectory Radial (STAR) imaging.

The number of MRI applications that use radial k-space data acquisition have been increasing because of their inherent robustness to motion-induced reconstruction image artifacts relative to Cartesian acquisition methods. However, images reconstructed from radial data are more prone to image degrading effects due to magnetic field inhomogeneities than images made from Cartesian data. Presented here is a method for acquiring several radial k-space data lines in one trajectory, the Single TrAjectory Radial, or STAR method, that is a variation of radial EPI. The STAR method allows for angular oversampling without the increase in imaging time that occurs with angularly oversampled single line imaging. It is shown that such oversampling potentially reduces the image degrading effect of magnetic field inhomogeneities so that the motion robust features of radial imaging may be realized in a segmented EPI approach.

Artifacts↗

PubMed2006

Direct parallel image reconstructions for spiral trajectories using GRAPPA.

The use of spiral trajectories is an efficient way to cover a desired k-space partition in magnetic resonance imaging (MRI). Compared to conventional Cartesian k-space sampling, it allows faster acquisitions and results in a slight reduction of the high gradient demand in fast dynamic scans, such as in functional MRI (fMRI). However, spiral images are more susceptible to off-resonance effects that cause blurring artifacts and distortions of the point-spread function (PSF), and thereby degrade the image quality. Since off-resonance effects scale with the readout duration, the respective artifacts can be reduced by shortening the readout trajectory. Multishot experiments represent one approach to reduce these artifacts in spiral imaging, but result in longer scan times and potentially increased flow and motion artifacts. Parallel imaging methods are another promising approach to improve image quality through an increase in the acquisition speed. However, non-Cartesian parallel image reconstructions are known to be computationally time-consuming, which is prohibitive for clinical applications. In this study a new and fast approach for parallel image reconstructions for spiral imaging based on the generalized autocalibrating partially parallel acquisitions (GRAPPA) methodology is presented. With this approach the computational burden is reduced such that it becomes comparable to that needed in accelerated Cartesian procedures. The respective spiral images with two- to eightfold acceleration clearly benefit from the advantages of parallel imaging, such as enabling parallel MRI single-shot spiral imaging with the off-resonance behavior of multishot acquisitions.

Algorithms↗

PubMed2002

Trajectories of cognitive recovery following a minor brain injury.

Minor brain injury (MBI) is the most frequently diagnosed head trauma in the United States, with treatment costing more than $1.5 billion annually and many patients incapacitated for months following injury. The purpose of this study was to characterize the brain function disruptions associated with MBI and to determine the time trajectory of recovery, using a theoretical model of attention. Distractibility, impulsivity, irritability, and impaired executive functioning were demonstrated in all participants during the 24 hr after injury. Twenty percent of participants continued to complain of distractibility, impulsivity, and/or irritability throughout the 30-day study. Loss of consciousness was shown to confound participants' healing trajectories. These results suggest that standard emergency room treatment following MBI is inadequate and should include discharge directives to reduce cognitive demands for at least 48 hr at a minimum, for 30 days or longer for those with loss of consciousness.

Adult↗

PubMed1991

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme.

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.

Binding Sites↗

PubMed2002

Spiking structure of amplitude characteristics for ion trajectories in hyperboloidal mass spectrometers: the theory.

We present a theory that describes a 'spiking' structure of the amplitude characteristics for trajectories of ions within a hyperboloidal mass spectrometer (HMS) discovered and reported recently. This effect, as well as modulation parametric resonance, relates directly to a fine structure of the stability diagram for a HMS. A method of extremum characteristic solutions of the Hill equation (developed in our laboratory earlier) has been used in this work. Simple expressions determined the shape of narrow dips (or reversed peaks) in the amplitude of ion oscillation versus stability parameter curves and conditions of their appearance are presented. The results that were calculated from analytical expressions are compared with those obtained from direct computations of ion trajectories in a HMS. This effect with respect to a nature of 'black holes' or 'black canyons' observed earlier in investigations of trapping efficiency and ion trapping within ion traps is discussed.

Electrodes↗

PubMed2000

Numerical simulation of flow fields and particle trajectories in ciliary suspension feeding.

A model describing the ciliary driven flow and motion of suspended particles in downstream suspension feeders is developed. The quasi-steady Stokes equations for creeping flow are solved numerically in an unbounded fluid domain around cylindrical bodies using a boundary integral formulation. The time-dependent flow is approximated with a continuous sequence of steady state creeping flow fields, where metachronously beating ciliary bands are modelled by linear combinations of singularity solutions to the Stokes equations. Generally, the computed flow fields can be divided into an unsteady region close to the driving ciliary bands and a steady region covering the remaining fluid domain. The size of the unsteady region appears to be comparable to the metachronal wavelength of the ciliary band. A systematic investigation is performed of trajectories of infinitely small (fluid) particles in the simulated unsteady ciliary driven flow. A fraction of particles appear to follow trajectories, that resemble experimentally observed particle capture events in the downstream feeding system of the polycheate Sabella penicillus, indicating that particles can be captured by ciliary systems without mechanical contact between particle and cilia. A local capture efficiency is defined and its value computed for various values of beat frequencies and other parameters. The results indicate that the simulated particle capture process is most effective when the flow field oscillates within timescales comparable to transit timescales of suspended particles passing the unsteady region near the ciliary bands. However, the computed retention efficiencies are found to be much lower than those obtained experimentally.

Animals↗

PubMed1999

Bet-hedging when targets may disappear: optimal mate-seeking or prey-catching trajectories and the stability of leks and herds

When a female frog moves towards a calling male, the male may suddenly stop calling and the female have to switch to another male. Analogous situations where "hunters" move towards "targets" that can disappear unpredictably include predators stalking prey and plants growing towards gaps in the canopy. I use dynamic programming to show that when the hunter has a choice of such targets it is optimal to take a curved bet-hedging trajectory, initially heading between two targets so that if one target disappears the other is closer. Also hunters should prefer groups of targets, even if a solitary target is somewhat closer, because it is unlikely that all targets in a group will disappear. Assuming that hunters follow these optimal trajectories I then ask whether it will pay targets to form herds or leks. The extra attractiveness of groups in this model turns out not to be sufficient to outweigh the advantages of herding, but the net benefits of herding are considerably reduced. Copyright 1999 Academic Press

Journal Article↗

PubMed1989

Transposition of image-defined trajectories into arc-quadrant centered stereotactic systems.

A methodology and computer program used for transposition of image-defined trajectories into stereotactic space is presented. Arc-quadrant centered stereotactic frames (Leksell, modified by us Komai) are based on the principle of aiming a target point from any entry of a formed sphere of known radius. Frames adapted isocentrically to CT gantry and parallel to the scanning plane allow interactive selection of targets and trajectories based on multiplanar reformatted images. The mathematical fundaments to calculate angle A in the coronal plane and angle B in the saggital plane based on the geometrical configuration of arc-quadrant centered stereotactic devices are presented.

Brain Diseases↗

PubMed1994

Is a virtual trajectory necessary in reaching movements?

The mass-spring model of limb control was extended to two-joint arm movements in the horizontal plane and tested against kinematic data from human subjects. Two versions of the model were compared in order to test the idea that the equilibrium position of the hand moves along a "virtual" trajectory as demonstrated in single-joint arm movements (Bizzi et al. 1982, 1984; Latash and Gottlieb 1991). In the peripheral version, the equilibrium position was shifted abruptly, while the torques generated at the joints are gated by rise-time functions. In the central version, the equilibrium position was updated gradually according to a predefined trajectory. The paths and tangential velocity profiles of the hand generated by these two versions were compared to Morasso's (1981) experimental data. The central version generally performed better throughout the workspace except in certain special directions. Moreover, its paths exhibited more stability as the movement speed was varied.

Arm↗

PubMed1996

A biologically inspired neural net for trajectory formation and obstacle avoidance.

In this paper we present a biologically inspired two-layered neural network for trajectory formation and obstacle avoidance. The two topographically ordered neural maps consist of analog neurons having continuous dynamics. The first layer, the sensory map, receives sensory information and builds up an activity pattern which contains the optimal solution (i.e. shortest path without collisions) for any given set of current position, target positions and obstacle positions. Targets and obstacles are allowed to move, in which case the activity pattern in the sensory map will change accordingly. The time evolution of the neural activity in the second layer, the motor map, results in a moving cluster of activity, which can be interpreted as a population vector. Through the feedforward connections between the two layers, input of the sensory map directs the movement of the cluster along the optimal path from the current position of the cluster to the target position. The smooth trajectory is the result of the intrinsic dynamics of the network only. No supervisor is required. The output of the motor map can be used for direct control of an autonomous system in a cluttered environment or for control of the actuators of a biological limb or robot manipulator. The system is able to reach a target even in the presence of an external perturbation. Computer simulations of a point robot and a multi-joint manipulator illustrate the theory.

Avoidance Learning↗

PubMed1992

Three-dimensional drawings in isometric conditions: planar segmentation of force trajectory.

Normal human subjects grasped an isometric handle with an unrestrained, pronated hand. They were asked to exert forces continuously to draw lemniscates (figure eights) in specified or self-chosen planes and in the presence or absence of a three-dimensional visual feedback cursor and a visual template. In every condition, the mean plane orientation in the force space differed appreciably between the two loops of the figure, as described previously by Soechting and Terzuolo (1987a) for free drawing arm movements. These findings suggest that the planar segmentation of the motor trajectory is not a consequence of joint motion but arises from central constraints related to the production of motor trajectory in space.

Feedback↗

PubMed1996

Differential influence of the visual framework on end point accuracy and trajectory specification of arm movements.

In this study the influence of visual scene on both arm end point accuracy and spatial path kinematics was evaluated. Eight subjects, immersed in a virtual environment, were required to point to one of ten targets located at two distances and in five directions. Targets were presented in frameworks of different complexity. The simplest framework was constituted by a uniform background, the most complex framework was constituted by a perspective-arranged grid. In the other two conditions it consisted of lines having a direction parallel to either the subject's sagittal or frontal body axis. Movements were executed without vision of both target and framework. The results showed that pointing movements were hypometric in all conditions. No difference in end point localization was observed between movements executed after presentation of the simplest and the most complex scenes. However, hypometria significantly increased when the scene was formed by lines parallel to the subject's sagittal axis. Visual information on the scene was also used to specify hand path parameters. Trajectory curvature increased with decreasing complexity of the framework. Correspondingly, the pointing kinematics varied. Taken together, these results suggest that visual analysis of cues surrounding the target can influence both target localisation and hand path planning. However, scene complexity is directly related only to determining trajectory curvature. We conclude that planning an arm movement consists of at least two processes: target localisation and hand path specification. Environmental visual cues forming the scene are taken into account differently during the two processes.

Adult↗

PubMed1993

Motor cortical activity preceding a memorized movement trajectory with an orthogonal bend.

Two monkeys were trained to make an arm movement with an orthogonal bend, first up and then to the left ([symbol: see text]), following a waiting period. They held a two-dimensional manipulandum over a spot of light at the center of a planar working surface. When this light went off, the animals were required to hold the manipulandum there for 600-700 ms and then move the handle up and to the left to receive a liquid reward. There were no external signals concerning the "go" time or the trajectory of the movement. It was hypothesized that during that period signs of directional processing relating to the upcoming movement would be identified in the motor cortex. Following 20 trials of the memorized movement trajectory, 40 trials of visually triggered movements in radially arranged directions were performed. The activity of 137 single cells in the motor cortex was recorded extracellularly during performance of the task. It was found that 62.8% of the cells changed activity during the memorized waiting period. During the waiting period, the population vector (Georgopoulos et al. 1983, 1984) began to grow approximately 130 ms after the center light was turned off; it pointed first in the direction of the second part of the memorized movement (<--) and then rotated clockwise towards the direction of the initial part of the movement (increases). These findings indicate processing of directional information during the waiting period preceding the memorized movement. This conclusion was supported by the results of experiments in ten human subjects, who performed the same memorized movement ([symbol: see text]). In 10% of the trials a visual stimulus was shown in radially arranged directions in which the subjects had to move; this stimulus was shown at 0, 200, and 400 ms from the time the center light was turned off. We found that as the interval increased the reaction time shortened for the visual stimulus that was in the same direction as the upward component of the memorized movement.

Animals↗

PubMed1993

Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories.

A new conceptual and theoretical framework for studying the human postural control system is introduced. Mathematical techniques from statistical mechanics are developed and applied to the analysis and interpretation of stabilograms. This work was based on the assumption that the act of maintaining an erect posture could be viewed, in part, as a stochastic process. Twenty-five healthy young subjects were studied under quite-standing conditions. Center-of-pressure (COP) trajectories were analyzed as one-dimensional and two-dimensional random walks. This novel approach led to the extraction of repeatable, physiologically meaningful parameters from stabilograms. It is shown that although individual stabilograms for a single subject were highly variable and random in appearance, a consistent, subject-specific pattern emerged with the generation of averaged stabilogram-diffusion plots (mean square COP displacement vs time interval). In addition, significant inter-subject differences were found in the calculated results. This suggests that the steady-state behavior of the control mechanisms involved in maintaining erect posture can be quite variable even amongst a population of age-matched, anthropometrically similar, healthy individuals. These posturographic analyses also demonstrated that COP trajectories could be modelled as fractional Brownian motion and that at least two control systems-a short-term mechanism and a long-term mechanism-were operating during quit standing. More specifically, the present results suggest that over short-term intervals open-loop control schemes are utilized by the postural control system, whereas over long-term intervals closed-loop control mechanisms are called into play. This work strongly supports the position that much can be learned about the functional organization of the postural control system by studying the steady-state behavior of the human body during periods of undisturbed stance.

Adult↗

PubMed1975

Responses of primate dentate neurons to different trajectories of the limb.

The activity of neurons in the dentate nucleus of the squirrel monkey was studied during the execution of a controlled, sequential movement that required different trajectories of the forearm. Examination of 207 dentate neurons ipsilateral to the performing limb revealed that over 80% of the neurons isolated were distinctly correlated with performance. The majority of these neurons had a tonic discharge pattern that usually increased coincident with the start of the movement and was maintained throughout most of the performance. A smaller group of cells ahd a burst of activity that was restricted only to a narrow part of the performance. About 30% of the tonic neurons altered their pattern of discharge whenever different limb trajectories were required, but burst cells showed exxentially no change. Detailed analysis of spike patterns revealed that no dentate neurons were phasically correlated with individual flexion-extension cycles of the performance sequence. Dentate neurons appear to be related to some general function of motor performance rather than the actions of joints or muscles used to execute the task.

Animals↗

PubMed1982

Arm trajectory formation in monkeys.

The formation of forearm trajectories of moderate velocities (0.3-1.3 rad/s) was studied in monkeys performing a simple visuomotor task. The experiments were designed to test the hypothesis that the transition from one position to another is subserved by a rapid shift to a final equilibrium of forces in agonist and antagonist muscles. This idea is attractive because it suggests the possibility that in simple movements the trajectory is determined by the inherent inertial and viscoelastic properties of the limb and muscles around a joint. The results indicate that these moderate speed movements are controlled by a gradual, and not a step-like, shift to the final equilibrium position.

Afferent Pathways↗

PubMed1988

Trajectory control in targeted force impulses. V. Gradual specification of response amplitude.

This study was undertaken in order to determine the time course of the process by which information derived from a visual target is used to accurately set the amplitude of a simple motor response. We refer to this process as response specification. Separate auditory and visual cues were given to the subjects in order to independently control the moment of response initiation and the time available for processing amplitude information from the target. Six subjects initiated impulses of isometric force in synchrony with the last of predictable series of regular tones. Response amplitudes were to match one of three visual target steps occurring at random times between 0 and 400 ms before the response-synchronizing tone. Using these separate auditory and visual cues, we were able to systematically vary the time interval between target presentation and response onset, termed here Stimulus-Response or S-R interval. Target steps were presented in blocks of either predictable (simple condition) or unpredictable (choice condition) amplitudes. The peak forces and the peaks of their time derivatives were analyzed to determine how subjects achieved accuracy under the different conditions and at different S-R intervals. The trajectories of responses produced in the simple condition were independent of the S-R interval. In contrast, when targets were presented in unpredictable order, the distribution of the peak forces of the subjects' responses depended on the S-R interval. At short S-R intervals (less than 125 ms), subjects made responses whose peak forces were distributed around the center of the range of target steps. These responses formed a unimodal, but broad distribution which was independent of actual target amplitude. With increasing S-R interval (greater than 125 ms), the distributions of peak forces gradually shifted toward the correct target amplitudes, with the means reaching the appropriate amplitudes at S-R intervals of 250-400 ms. At S-R intervals comparable to a reaction time, the range of peak forces was constricted to a similar extent as previously observed in a reaction time task (Hening et al. 1988). We found that the gradual improvement of accuracy was not achieved through changes in trajectory control: at all S-R intervals, subjects utilized a pulse-height control policy (Gordon and Ghez 1987a). Different peak forces were achieved by varying the rate of rise of force, while force rise time was held relatively invariant.(ABSTRACT TRUNCATED AT 400 WORDS)

Acoustic Stimulation↗