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PubMed2003

Spatial excitation using variable-density spiral trajectories.

PURPOSE: To examine the usefulness of variable-density k-space trajectories for the design of multi-dimensional spatially selective RF pulses. MATERIALS AND METHODS: Experimental phantom and in vivo studies were performed and confirmed by simulations. Two-dimensional spatially selective magnetization patterns were excited using variable-density spiral trajectories and analyzed with respect to the signal excitation outside the excitation field of view (FOX). RESULTS: By using variable-density trajectories, signal excitation outside the FOX was drastically reduced compared to trajectories with a uniform density, while maintaining fairly short pulse durations. CONCLUSION: A main advantage of the method is that unwanted signal excitation outside the nominal FOX can be reduced without significantly increasing the duration of the RF excitation pulse. The variable-density approach is useful for all applications that require a well-defined spatial excitation profile, e.g., to perform imaging in a reduced field of view (FOV), for spatial saturation pulses, for curved slice imaging or in MR spectroscopy.

Computer Simulation↗

PubMed2001

Design of a logarithmic k-space spiral trajectory.

Spiral acquisitions are used in fast cardiac imaging because they traverse k-space efficiently and minimize flow artifacts. A variable pitch logarithmic spiral trajectory is designed to critically sample the low-frequency region in k-space and gradually undersample the high-frequency region. An approximate analytical expression for the trajectory provides a fast means to calculate the gradient waveforms and the sampled data points. A numerical method is introduced based on the trajectory curvature and the rate of change in the gradient magnitude with time for the composite Archimedean-logarithmic trajectory. The pulse sequence is implemented and images are acquired on phantoms and human hearts. The images show improved image resolution and some improvement in image quality as a result of increased extent in k-space and reduction in aliasing artifacts, respectively.

Artifacts↗

PubMed2004

Automatic spatial and temporal temperature control for MR-guided focused ultrasound using fast 3D MR thermometry and multispiral trajectory of the focal point.

Of the different modalities to induce local hyperthermia, focused ultrasound is the only noninvasive technology available at the moment. In addition to the 3D localization of the target region, it has been shown that MRI can provide real-time thermometry and allows online, automatic control of temperature evolution of the focal point. Treatment of a large tissue volume (as compared to the focal spot size, i.e., the ultrasound wavelength) can be achieved rapidly by moving the focal point along an inside-out spiral trajectory. It has been shown previously that under linear conditions of energy deposition versus temperature, the spatial profile of the temperature within a large area can be controlled. In this study, a proportional, integral, and derivative (PID) spatial-and-temporal controller is described for the control of the temperature evolution within the target region under more variable conditions. The aim was to reach a predefined temperature profile after a few successive trajectories. Heat conduction in tissue is exploited to obtain a uniform temperature increase in a volume using discrete sonications without any waiting time. Input data sets consisted of 3D temperature maps provided online by a MR scanner. For each new trajectory, the controller recalculates the number of sonications per surface unit (spatial density of points describing the trajectory) and the applied power. Its performance was tested ex vivo and in vivo. Diameters of the target region ranged from 9 mm to 19 mm. Targeted temperature increase ranged from +8 degrees C to +18 degrees C. Spatiotemporal temperature control showed good stability and fast convergence, for both circular and elliptic ROIs.

Algorithms↗

PubMed2006

Three-dimensional MRI with an undersampled spherical shells trajectory.

The shells trajectory is a 3D data acquisition method with improved efficiency compared to Cartesian sampling. It is a true center-out trajectory that does not repeatedly resample the center of k-space, and also offers advantages for motion correction. This work demonstrates that k-space undersampling can be combined with the shells trajectory to further accelerate the acquisition. The undersampling was implemented by removing selected interleaves from shells with larger radii. Because only the outer portion of k-space was undersampled, the artifacts introduced were of low energy and high spatial frequency. The undersampling rate was determined by a Kaiser window with a variable shape parameter beta. Various undersampling schemes with different beta values were examined. Phantom and volunteer studies demonstrate that when up to a twofold acceleration is achieved, only minor artifacts are introduced by undersampling the shells trajectory. For a fixed acquisition time, the improved efficiency can be used to increase spatial resolution.

Algorithms↗

PubMed2004

Target tissue influences the peripheral trajectory of mouse primary sensory olfactory axons.

Primary olfactory neurons situated in the nasal septum project axons within fascicles along a highly stereotypical trajectory en route to the olfactory bulb. The ventral fascicles make a distinct dorsovental turn at the rear of the septum so as to reach the olfactory bulb. In the present study we have used a brain and nasal septum coculture system to examine the role of target tissue on the peripheral trajectory of olfactory sensory axons. In cultures of isolated embryonic nasal septa, olfactory axons form numerous parallel fascicles that project caudally in the submucosa, as they do in vivo. The ventral axon fascicles in the septum, however, often fail to turn, and do not project dorsally towards the roof of the nasal cavity. The presence of olfactory bulb, cortical, or tectal tissue apposed to the caudal end of the septum rescued this phenotype, causing the ventral fascicles to follow a normal in vivo-like trajectory. Ectopic placements of the explants revealed that brain tissue is not tropic for olfactory axons but appears to maintain the peripheral trajectory of growing axons in the nasal septum. Although primary olfactory axons are able to penetrate into olfactory bulb in vitro, they only superficially enter cortical tissue, whereas they do not grow into tectal explants. The ability of axons to differentially grow into different brain regions was shown to be unrelated to the migratory behavior of olfactory ensheathing cells, indicating that olfactory axons are directly responsive to guidance cues in the brain.

Animals↗

PubMed1997

Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories.

This paper explores the dependence of the molecular dynamics (MD) trajectory of a protein molecule on the titration state assigned to the molecule. Four 100-ps MD trajectories of bovine pancreatic trypsin inhibitor (BPTI) were generated, starting from two different structures, each of which was held in two different charge states. The two starting structures were the X-ray crystal structure and one of the solution structures determined by NMR, and the charge states differed only in the ionization state of N terminus. Although it is evident that the MD simulations were too short to sample fully the equilibrium distribution of structures in each case, standard Poisson-Boltzmann titration state analysis of the resulting configurations shows general agreement between the overall titration behavior of the protein and the charge state assumed during MD simulation: at pH 7, the total net charge of the protein resulting from the titration analysis is consistently lower for the protein with the N terminus assumed to be neutral than for the protein with the N terminus assumed to be charged. For most of the ionizable residues, the differences in the calculated pKaS among the four trajectories are statistically negligible and remain in good agreement with the data obtained by crystal structure titration and by experiment. The exceptions include the N terminus, which responds directly to the change of its imposed charge; the C terminus, which in the NMR structure interacts strongly with the former; and a few other residues (Arg 1, Glu 7, Tyr 35, and Arg 42) whose pKaS reflect the initial structure and the limited trajectory lengths. This study illustrates the importance of the careful assignment of protonation states at the start of MD simulations and points to the need for simulation methods that allow for the variation of the protonation state in the calculation of equilibrium properties.

Aprotinin↗

PubMed1992

Fuzzy cluster analysis of molecular dynamics trajectories.

We propose fuzzy clustering as a method to analyze molecular dynamics (MD) trajectories, especially of proteins and polypeptides. A fuzzy cluster analysis locates classes of similar three-dimensional conformations explored during a molecular dynamics simulation. The method can be readily applied to results from both equilibrium and nonequilibrium simulations, with clustering on either global or local structural parameters. The potential of this technique is illustrated by results from fuzzy cluster analyses of trajectories from MD simulations of various fragments of human parathyroid hormone (PTH). For large molecules, it is more efficient to analyze the clustering of root-mean-square distances between conformations comprising the trajectory. We found that the results of the clustering analysis were unambiguous, in terms of the optimal number of clusters of conformations, for the majority of the trajectories examined. The conformation closest to the cluster center can be chosen as being representative of the class of structures making up the cluster, and can be further analyzed, for example, in terms of its secondary structure. The CPU time used by the cluster analysis was negligible compared to the MD simulation time.

Amino Acid Sequence↗

PubMed1995

Protein conformational landscapes: energy minimization and clustering of a long molecular dynamics trajectory.

Using energy minimization and cluster analysis, we have analyzed a 1020 ps molecular dynamics trajectory of solvated bovine pancreatic trypsin inhibitor. Elucidation of conformational substates in this way both illustrates the degree of conformational convergence in the simulation and reduces the structural data to a tractable subset. The relative movement of structures upon energy minimization was used to estimate the sizes of features on the protein potential energy surface. The structures were analyzed using their pairwise root-mean-square C alpha deviations, which gave a global measure of conformational changes that would not be apparent by monitoring single degrees of freedom. At time scales of 0.1 ps, energy minimization detected sharp transitions between energy minima separated by 0.1 A rms deviation. Larger conformational clusters containing these smaller minima and separated by 0.25 A were seen at 1 ps time scales. Both of these small features of the conformational landscape were characterized by movements in loop regions associated with small, correlated backbone dihedral angle shifts. On a nanosecond time scale, the main features of the protein energy landscape were clusters separated by over 0.7 A rms deviation, with only seven of these substates visited over the 1 ns trajectory. These substrates, discernible both before and after energy minimization, differ mainly in a monotonic pivot of the loop residues 11-18 over the course of the simulation. This loop contains lysine 17, which specifically binds to trypsin in the active site. The trajectory did not return to previously visited clusters, indicating that this trajectory has not been shown to have completely sampled the conformational substates available to it. Because the apparent convergence to a single region of conformation space depends on both the time scale of observation and the size of the conformational features examined, convergence must be operationally defined within the context of the simulation.

Animals↗

PubMed1990

Trajectory formation of arm movement by cascade neural network model based on minimum torque-change criterion.

We proposed that the trajectory followed by human subject arms tended to minimize the time integral of the square of the rate of change of torque (Uno et al. 1987). This minimum torque-change model predicted and reproduced human multi-joint movement data quite well (Uno et al. 1989). Here, we propose a neural network model for trajectory formation based on the minimum torque-change criterion. Basic ideas of information representation and algorithm are (i) spatial representation of time, (ii) learning of forward dynamics and kinetics model and (iii) relaxation computation based on the acquired model. The model can resolve ill-posed inverse kinematics and inverse dynamics problems for redundant controlled object as well as ill-posed trajectory formation problems. By computer simulation, we show that the model can produce a multi-joint arm trajectory while avoiding obstacles or passing through viapoints.

Algorithms↗

PubMed1995

Head movement trajectory in three-dimensional space during orienting behavior toward visual targets in rhesus monkeys.

Head movement trajectories in three-dimensional space were studied in two monkeys with their heads free during natural and spontaneous orienting behavior toward objects of interest displayed in a horizontal plane. The main interest of this study lies in understanding the process responsible for behavioral variability during the execution of head movements, with special reference to "units of movement." The head movements were recorded by an optoelectronic movement analyzer working with passive markers. Algorithms have been designed to reconstruct the three-dimensional trajectories of the center of gravity of the head. Simultaneously, electromyographic activity in the four pairs of suboccipital muscles was studied. A quantitative evaluation of the involvement of the head in orienting behavior toward visual targets shows that the gaze shift is always produced by eye movements in combination with head movements, even with target eccentricities of less than 10 degrees. On the basis of 80 trials performed by the two monkeys, head trajectories and recruitment patterns of the four pairs of suboccipital muscles have been analyzed. We have been able to identify four elementary kinematic units which can be described as a rightward or leftward turning associated with a contralateral or ipsilateral bending. Each of these four elementary units are underlain by a precise fixed recruitment pattern in the four pairs of suboccipital muscles. These four sets of motor strategies can be combined in order to offer a certain amount of plasticity from which the animal builds its own head trajectory.

Animals↗

PubMed1988

Trajectory control in targeted force impulses. IV. Influences of choice, prior experience and urgency.

The present study examines the influences of target predictability, level of practice and response urgency upon the latency and trajectory of a simple motor response. This response is an impulse of isometric force produced by the index finger and aimed to match a step change in a visual target. As expected (Welford 1980), the responses of naive subjects responding as soon as possible after target presentation were initiated at longer latencies when the target steps were of unpredictable amplitudes (choice condition) than when their amplitudes were all the same (simple condition). This choice effect on response latency diminished progressively with practice and eventually disappeared. The trajectories of urgently produced choice responses, however, differed from those of simple responses, and this difference was not reduced by practice. Choice trajectories were more variable and showed a systematic distortion in scaling: response amplitudes exhibited a central tendency bias, or range effect. When targets were equiprobable, responses were biased towards the middle sized target while responses aimed at targets of unequal probability were biased towards the most probable. This effect was independent of the absolute amplitudes of the responses required and was not associated with deviations from the pulse height control policy (Gordon and Ghez 1987a) that human subjects use to vary the amplitude of force impulses. The distortion in scaling and the increased variability of responses aimed at individual targets were markedly reduced when urgency was relaxed and subjects could respond when ready. Then, both simple and choice responses were proportionally scaled to the target, but choice responses were initiated at longer latencies. The changes in trajectory of urgent responses suggests that their inaccuracy occurs because the subjects initiate their responses before the specification of amplitude is complete. The central tendency bias of such incompletely specified responses suggests further that, prior to target presentation, subjects prepare a default response reflecting their expectations. This default may then be modified by information obtained from the target in a process that lasts longer than a minimal reaction time.

Adult↗

PubMed2004

Distractor modulation of saccade trajectories: spatial separation and symmetry effects.

The trajectories of saccadic eye movements can be modulated by the presence of a competing visual distractor. In the present study the trajectories of vertical saccades curved away from a single visual distractor presented in one visual field, but tended to be straight when two distractors were presented at mirror symmetric locations in both visual fields. The spatial nature of the mirror distractor effect was examined by presenting a second distractor at mirror and non-mirror locations. Saccade trajectories also tended to be straight with both mirror and non-mirror symmetrical distractors. The relationship between the distractor location and saccade curvature was examined in a third experiment by manipulating the distractor-to-target spatial separation. Although there was a tendency for greater curvature when the distractor was presented in the same hemifield as the target there was no clear relationship between curvature and distractor location. The results show that the distractor modulation of saccade trajectory is not highly spatially specific and that it can be balanced by a second bilateral distractor in the opposite visual field. The results are interpreted in terms of a model in which the initial saccade direction and curvature back towards the saccade goal are controlled by separate processes. Initial saccade direction is modulated by the inhibition of distractor locations within a 'motor map' specifying saccade direction. Curvature back towards the saccade goal may be attributed to a feedback system, with a separate representation of the visual target location, that enables an on-line correction of the saccade during mid-flight.

Adult↗

PubMed2004

Keeping with the beat: movement trajectories contribute to movement timing.

Previous studies of paced repetitive movements with respect to an external beat have either emphasised (a) the form of movement trajectories or (b) timing errors made with respect to the external beat. The question of what kinds of movement trajectories assist timing accuracy has not previously been addressed. In an experiment involving synchronisation or syncopation with an external auditory metronome we show that the nervous system produces trajectories that are asymmetric with respect to time and velocity in the out and return phases of the repeating movement cycle. This asymmetry is task specific and is independent of motor implementation details (finger flexion vs. extension). Additionally, we found that timed trajectories are less smooth (higher mean squared jerk) than unpaced ones. The degree of asymmetry in the flexion and extension movement times is positively correlated with timing accuracy. Negative correlations were observed between synchronisation timing error and the movement time of the ensuing return phase, suggesting that late arrival of the finger is compensated by a shorter return phase and conversely for early arrival. We suggest that movement asymmetry in repetitive timing tasks helps satisfy requirements of precision and accuracy relative to a target event.

Acoustic Stimulation↗

PubMed2005

Determining natural arm configuration along a reaching trajectory.

Owing to the flexibility and redundancy of neuromuscular and skeletal systems, humans can trace the same hand trajectory in space with various arm configurations. However, the joint trajectories of typical unrestrained movements tend to be consistent both within and across subjects. In this paper we propose a method to solve the 3-D inverse kinematics problem based on minimizing the magnitude of total work done by joint torques. We examined the fit of the joint-space trajectories against those observed from human performance in a variety of movement paths in 3-D workspace. The results showed that the joint-space trajectories produced by the method are in good agreement with the subjects' arm movements (r2>0.98), with the exception of shoulder adduction/abduction (where, in the worst case, r2 approximately 0.8). Comparison of humeral rotation predicted by our algorithm with other models showed that the correlation coefficient r2) between actual data and our predictions is extremely high (mostly >0.98, 11 out of 15 cases, with a few exceptions, 4 of 15, in the range of 0.8-0.9) and the slope of linear regression is much closer to one (<0.05 distortion in 12 out of 15 cases, with only one case >0.15). However, the discrepancy in shoulder adduction/abduction indicated that when only the hand path is known, additional constraint(s) may be required to generate a complete match with human performance.

Algorithms↗

PubMed2004

Optimal trajectory formation of constrained human arm reaching movements.

Opening a door, turning a steering wheel, and rotating a coffee mill are typical examples of human movements that are constrained by the physical environment. The constraints decrease the mobility of the human arm and lead to redundancy in the distribution of actuator forces (either joint torques or muscle forces). Due to this actuator redundancy, there is an infinite number of ways to form a specific arm trajectory. However, humans form trajectories in a unique way. How do humans resolve the redundancy of the constrained motions and specify the hand trajectory? To investigate this problem, we examine human arm movements in a crank-rotation task. To explain the trajectory formation in constrained point-to-point motions, we propose a combined criterion minimizing the hand contact force change and the actuating force change over the course of movement. Our experiments show a close matching between predicted and experimental data.

Adult↗

PubMed1997

Two-arm trajectory planning in a manipulation task.

This paper addresses the trajectory planning problem for a task which requires positioning and orienting an object firmly grasped by two hands at a visually specified goal configuration in the horizontal plane. The motor task involves three degrees of freedom (two translational and one rotational), and the motions of the arms are constrained by the physical coupling through the held object. Experimentally measured trajectories of two arms in the coordinated positioning/orienting task are presented. The hypothesis that the rotational and translational components of motions are decoupled and independently planned is tested. Two explicit mathematical models to account for the kinematic features of the two-arm motions are formulated, and the predictions of the models are compared with the experimental data. Both models extend the minimum-jerk model to the two-arm coordinated motions case. The trajectories predicted by the models were found to be in qualitative agreement with the experimental data. However, neither model could account for the observed configuration dependence of the motions, nor for some of the properties of the measured velocity components of the motions. Our findings support the idea that the rotational and translational components of two-arm motions in the positioning/orienting task are independently planned in extra-personal space, and are further combined in a hierarchical fashion to produce the observed motions. The tested models may serve as a basis for further investigations of issues pertinent to the generation of two-arm trajectories.

Arm↗

PubMed2006

Neighborhood disadvantage, parent-child conflict, neighborhood peer relationships, and early antisocial behavior problem trajectories.

This study examined relations among neighborhood disadvantage, parent-child conflict, deviant peer involvement in the neighborhood, and early-starting antisocial trajectories. Antisocial group patterns were identified in 218 low-income boys followed from ages 5 to 11, and neighborhood and family variables were evaluated as predictors in early and middle childhood. Four trajectory groups emerged: one increasing pattern that corresponded with developmental theories of early-starting antisocial behavior; one with initially high and decreasing problems over time; and two low antisocial groups. Parent-child conflict and neighborhood disadvantage were significantly associated with trajectory patterns, with youth in the 2 higher antisocial behavior groups characterized by more neighborhood problems and parent-child conflict than other groups. The results suggest that in early childhood, neighborhood disadvantage and family conflict place children at risk for early-starting trajectories, and that involvement with deviant peers in the neighborhood takes on an increasingly important role in patterns of antisocial behavior over middle childhood.

Adolescent↗

PubMed2006

The proxy effect: gender and gambling problem trajectories of iowa gambling treatment program participants.

Recent research has found that men and women who end up in gambling treatment tend to follow different trajectories to that endpoint: women generally begin gambling later in life, but progress to problems and seek treatment more quickly. With women's prevalence rates of gambling and disordered gambling increasing, it has become important to identify the causes and consequences of these trajectory differences. The current study used a sample of 2,256 gamblers enrolled in the Iowa Gambling Treatment Program to examine the relationship of gender and other demographic, economic and health-related (i.e., psychosocial) factors to empirically-identified gambling problem trajectories. The results indicated that gender made a statistically significant contribution to the prediction of trajectory, but increased predictive accuracy by only 1-2% beyond a model with psychosocial predictors. Gender's contribution was limited to its relationship to age of initiation; men and women's problem progression did not differ meaningfully once age of gambling initiation was taken into account. Gender is a unique contributor to the development of gambling problems among treatment seekers, but it is only one small part of the myriad psychosocial characteristics that influence gambling problem development.

Aged↗