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Local hyperthermia with MR-guided focused ultrasound: spiral trajectory of the focal point optimized for temperature uniformity in the target region.

The objective of hyperthermia treatment is to deliver a similar therapeutic thermal dose throughout the target volume within a minimum amount of time. We describe a noninvasive approach to this goal based on magnetic resonance imaging (MRI)-guided focused ultrasound (FUS) with a spherical transducer that can be moved along two directions inside the bed of a clinical MR imager and that has an adjustable focal length in the third dimension. Absorption of FUS gives rise to a highly localized thermal buildup, which then spreads by heat diffusion and blood perfusion. A uniform temperature within a large target volume can be obtained using a double spiral trajectory of the transducer focal point together with constant and maximum FUS power. Differences between the real and target temperatures during the first spiral are evaluated in real time with temperature MRI and corrected for during the second spiral trajectory employing FUS focal point velocity modulation. Once a uniform temperature distribution is reached within the entire volume, FUS heating is applied only at the region's boundaries to maintain the raised temperature levels. Heat conduction, together with the design and timing of the trajectories, therefore ensures a similar thermal dose for the entire target region. Good agreement is obtained between theory and experimental results in vitro on gel phantoms, ex vivo on meat samples, and in vivo on rabbit thigh muscle. Edema in muscle was visible 1 hour after hyperthermia as a spatially uniform rise of the signal intensity in T(2)-weighted images.

Animals↗

Patterns of exercise across the cancer trajectory in brain tumor patients.

BACKGROUND: Exercise may represent a supportive intervention that may complement existing neurooncologic therapies and address a multitude of therapy-induced debilitating side effects in patients with brain tumors. Given the limited evidence, the authors conducted a survey to examine the exercise patterns of brain tumor patients across the cancer trajectory. METHODS: Using a cross-sectional design, 386 brain tumor patients who received treatment at the Brain Tumor Center at Duke University were sent a questionnaire that assessed self-reported exercise behavior prior to diagnosis, during adjuvant therapy, and after the completion of therapy. RESULTS: The response rate was 28% (106 of 383 patients). Descriptive analyses indicated that 42%, 38%, and 41% of participants, respectively, met national exercise prescription guidelines prior to diagnosis, during treatment, and after the completion of adjuvant therapy. Repeated measures analyses indicated no significant changes in the majority of exercise behavior outcomes over the cancer trajectory. However, exploratory analyses indicated that males and younger participants may be at the greatest risk of reducing exercise levels after a brain tumor diagnosis. These analyses remained unchanged after controlling for relevant demographic and medical covariates. CONCLUSIONS: A relatively high percentage of brain tumor patients are exercising at recommended levels across the cancer trajectory. Moreover, these patients have unique exercise patterns that may be modified by select demographic variables. This preliminary study provides important informative data for future studies examining the potential role of exercise in patients diagnosed with neurologic malignancies.

Adult↗

Axon diameters and intradural trajectories of the dural innervation in the rat.

Neurophysiological studies have characterized the sensory responses of primary afferent nociceptors that innervate the intracranial dura. The present study used anatomical methods to examine in greater detail the axonal trajectories within the dura, as well as the axonal size distribution of the dural innervation. Immunostaining for CGRP in dural wholemounts revealed a network of fibers extending across the entire dura, with an especially dense plexus running along the borders of the transverse and superior sagittal sinuses. The plexus along the caudal border of the transverse sinus partially overlapped the dural area that shows the greatest density of mast cells. Visualization of axon bundles by DiI application in formalin-fixed tissue revealed two separate systems of fibers in the dura that could be distinguished by the orientation of their trajectories: one that runs parallel to the middle meningeal artery (MMA), and another with a more or less orthogonal orientation that runs rostromedially from the transverse sinus across the MMA. Axons traversed large distances across the dura, but the majority of the branching and arborization was usually concentrated in the distal part of the trajectory. In separate animals, measurement of myelinated axon diameters with electron microscopy showed that approximately one-third of the myelinated axons in the nerves supplying the dura (nervus spinosus and tentorial nerves) could be classified as A-beta, since they were comparable in size to the majority of axons in the trochlear nerve and the upper end of the size range in the trigeminal nerve (i.e., > 5 microm).

Animals↗

Axon trajectories and pattern of terminal arborization during the prenatal development of the cat's retinogeniculate pathway.

In this study we have examined the trajectories taken by populations of ganglion cell axons and the spatial gradients of terminal arbor maturity within the lateral geniculate nucleus (LGN) during the prenatal development of the cat's visual system. To do so, an in vitro method of labeling optic tract axons from fetal brains between embryonic day 37 (E37) and postnatal day 2 (P2) with horseradish peroxidase (HRP) was used. At the earliest ages studied (E37-E53), optic axons leave the optic tract to run across the LGN toward their sites of termination in straight trajectories parallel to each other. At later ages (E57-P2), however, axons with abrupt changes in their course across the nucleus can be clearly identified. When the detailed terminal arbor morphology of the set of retinogeniculate axons filled with HRP at a given age was examined, two different spatial gradients of maturation could be detected. The terminal arbors of axons within LGN layer A are always more mature than those ending in layer A1, an observation consistent with previous findings that axons from the contralateral eye arrive within the LGN several days before those from the ipsilateral eye. Moreover, the terminal arbors of axons projecting to the medial portions of each layer are always more mature than their more lateral counterparts. These gradients are likely to be a direct reflection of the central-first, peripheral-last gradient associated with the neurogenesis of the retinal ganglion cells themselves. In the oldest animals studied (E58-P2), a remarkable periodic pattern of terminal arbor labeling was seen following a localized HRP injection into the optic tract. Within the labeled portions of the LGN, densely filled axon terminal arbors are separated by unlabeled gaps of similar width. This pattern of labeling could reflect local topographic disorder within the optic tract or could arise if axons of different classes of retinal ganglion cells run in separate portions of the optic tract. Taken together, all of these observations suggest that there may be a fair degree of topographic order in the retinogeniculate projection within the cat's LGN early on in development. However, when topographic errors are present, some can be corrected by minor readjustments in axonal trajectories.

Animals↗

Improvement of spiral MRI with the measured k-space trajectory.

The k-space trajectory of a spiral imaging sequence was measured with a self-encoding technique. The image quality improved dramatically when reconstructed with the measured k-space trajectory. There were substantial artifacts in images reconstructed with the derived k-space trajectory under the assumption of gradient system linearity. The results indicated the non-linearity of the gradient system and the effectiveness of the correction technique.

Analog-Digital Conversion↗

Advances in sensitivity encoding with arbitrary k-space trajectories.

New, efficient reconstruction procedures are proposed for sensitivity encoding (SENSE) with arbitrary k-space trajectories. The presented methods combine gridding principles with so-called conjugate-gradient iteration. In this fashion, the bulk of the work of reconstruction can be performed by fast Fourier transform (FFT), reducing the complexity of data processing to the same order of magnitude as in conventional gridding reconstruction. Using the proposed method, SENSE becomes practical with nonstandard k-space trajectories, enabling considerable scan time reduction with respect to mere gradient encoding. This is illustrated by imaging simulations with spiral, radial, and random k-space patterns. Simulations were also used for investigating the convergence behavior of the proposed algorithm and its dependence on the factor by which gradient encoding is reduced. The in vivo feasibility of non-Cartesian SENSE imaging with iterative reconstruction is demonstrated by examples of brain and cardiac imaging using spiral trajectories. In brain imaging with six receiver coils, the number of spiral interleaves was reduced by factors ranging from 2 to 6. In cardiac real-time imaging with four coils, spiral SENSE permitted reducing the scan time per image from 112 ms to 56 ms, thus doubling the frame-rate.

Brain↗

Reduction of motion artifacts in cine MRI using variable-density spiral trajectories.

Dynamic cardiac imaging in MRI is a very challenging task. To obtain high spatial resolution, temporal resolution, and signal-to-noise ratio (SNR), single-shot imaging is not sufficient. Use of multishot techniques resolves this problem but can cause motion artifacts because of data inconsistencies between views. Motion artifacts can be reduced by signal averaging at some cost in increased scan time. However, for the same increase in scan time, other techniques can be more effective than simple averaging in reducing the artifacts. If most of the energy of the inconsistencies is limited to a certain region of kappa-space, increased sampling density (oversampling) in this region can be especially effective in reducing motion artifacts. In this work, several variable-density spiral trajectories are designed and tested. Their efficiencies for artifact reduction are evaluated in computer simulations and in scans of normal volunteers. The SNR compromise of these trajectories is also investigated. The authors conclude that variable-density spiral trajectories can effectively reduce motion artifacts with a small loss in SNR as compared with a uniform density counterpart.

Artifacts↗

A novel k-space trajectory measurement technique.

A new k-space trajectory measurement technique is proposed and demonstrated. This technique measures the k-space trajectory, in seconds, using only a few readout lines, using phase values of acquired MR signals. As a result of the technique's efficiency, k-space trajectory measurement using patient data becomes possible. The utility of this techniques is demonstrated in phantom and human studies at 4.1 T.

Biophysical Phenomena↗

Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories.

A simple iterative algorithm, termed deconvolution-interpolation gridding (DING), is presented to address the problem of reconstructing images from arbitrarily-sampled k-space. The new algorithm solves a sparse system of linear equations that is equivalent to a deconvolution of the k-space with a small window. The deconvolution operation results in increased reconstruction accuracy without grid subsampling, at some cost to computational load. By avoiding grid oversampling, the new solution saves memory, which is critical for 3D trajectories. The DING algorithm does not require the calculation of a sampling density compensation function, which is often problematic. DING's sparse linear system is inverted efficiently using the conjugate gradient (CG) method. The reconstruction of the gridding system matrix is simple and fast, and no regularization is needed. This feature renders DING suitable for situations where the k-space trajectory is changed often or is not known a priori, such as when patient motion occurs during the scan. DING was compared with conventional gridding and an iterative reconstruction method in computer simulations and in vivo spiral MRI experiments. The results demonstrate a stable performance and reduced root mean square (RMS) error for DING in different k-space trajectories.

Algorithms↗

Some properties of ion trajectories in the radial plane of an axially symmetric ion trap.

In this article we analyse the trajectories of externally generated ions injected in the radial plane into the ion trap. The shape of the envelope curves for two-dimensional (2D) ion trajectories is determined. Conditions under which these envelope curves can be transformed into circles are found. We show that the amplitude of ion oscillations is a minimum in this case and that this mode corresponds to optimised ion trapping conditions. Also we discuss a ring-shaped ion trap mass spectrometer electrode system which consists of two ring electrodes, and which utilises ion trajectories with circular envelope curves.

Ions↗

A framework to monitor environment-induced major genes for developmental trajectories: implication for a prenatal cocaine exposure study.

Whether there are specific genes involved in response to different environmental agents and how such genes regulate developmental trajectories during lifetime are of fundamental importance in health, clinical and pharmaceutical research. In this article, we present a novel statistical model for monitoring environment-induced genes of major effects on longitudinal outcomes of a trait. This model is derived within the maximum likelihood framework, incorporated by mathematical aspects of growth and developmental processes. A typical structural model is implemented to approximate time-dependent covariance matrices for the longitudinal trait. This model allows for a number of biologically meaningful hypothesis tests regarding the effects of major genes on overall growth trajectories or particular stages of development. It can be used to test whether and how major genetic effects are expressed differently under altered environmental agents. In a well-designed case-control study, our model has been employed to detect cocaine-dependent genes that affect growth trajectories for head circumference during childhood. The detected gene triggers significant effects on growth curves in both cocaine-exposed (case) and unexposed groups (control), but with different extents. Significant genotype-environment interactions due to this so-called environment-sensitive gene are promising for further studies toward its genomic mapping using polymorphic molecular markers.

Adult↗

Using trajectories from a bivariate growth curve as predictors in a Cox regression model.

An important research objective in most psychiatric clinical trials of maintenance treatment is to find predictors of recurrence of illness. In those trials, patients are first admitted into an open treatment period also called acute treatment. If they respond to the treatment and are considered to have stable remission from the illness, they enter the second phase of the trial where they are randomized into different arms of the 'maintenance treatments'. Often, more than one response variable is measured longitudinally in the acute treatment phase to monitor treatment responses. Trajectories of these response measures are believed to have predictive ability for recurrences in the maintenance phase of the trial. By using a bivariate growth curve from two such longitudinal measures, we developed a method to use the estimated trajectories of each subject in a Cox regression model to predict recurrence in the maintenance phase. To adjust for the parameter estimation errors, we applied a full likelihood approach based on the conditional expectations of the predictors. Simulation studies indicate that the estimation error corrected estimators for the Cox model parameters are less biased when compared to the naive regression estimators without accounting for these errors. The uniqueness of this method lies in estimating trajectories from bivariate unequally spaced longitudinal response measures. An illustrative example is provided with data from a maintenance treatment trial for major depression in an elderly population. Visual Fortran 90 programs were developed to implement the algorithm.

Aged↗

On the Formulation of Lagrangian Stochastic Models for Heavy-Particle Trajectories.

The modeling approach of B. L. Sawford and F. H. Guest ("8th Symposium of Turbulence and Diffusion; San Diego, CA," pp. 96-99. Am. Meteorol. Soc., Boston, MA, 1990) is extended to encompass the formulation of Lagrangian stochastic models for fluid velocities along heavy-particle trajectories in inhomogeneous turbulent flows. The approach ensures consistency with prescribed Eulerian fluid velocity statistics. Models are formulated and then used in conjuction with the equations of motion for heavy particles to simulate the trajectories of heavy particles in vertical turbulent pipe flow. Model predictions for particle-velocity statistics, particle deposition velocities, and mean particle concentrations are shown to be in good agreement with experimental results. In contrast with "eddy-interaction" models but in accord with the results of direct numerical simulations, the models predict a buildup of mean particle concentration within the viscous sublayer at y(+) approximately 0.2. It is suggested that Lagrangian stochastic models for fluid-particle motions provide a good description of fluid velocities along the trajectories of heavy particles, when Lagrangian timescales are appropriately modified. Copyright 2000 Academic Press.

Journal Article↗

Evaluation of permeability of microporous media, using the modified random-trajectory approach.

The random trajectory approach derived recently for the purpose of evaluation of the percolation threshold is modified and applied to the modeling of permeability. The main modification consists in probabilistic accounting of possible trajectories, the total permeability being evaluated as a sum over all available percolation trajectories, without any preferences in orientation. Results of calculations of permeability vs porosity, sample thickness, and other structural factors are presented. It is concluded that the qualitative tendencies regarding permeability do not significantly differ from those found before for percolation.

Journal Article↗

Influence of internal dynamics on accuracy of protein NMR structures: derivation of realistic model distance data from a long molecular dynamics trajectory.

In order to study the effect of internal dynamics on the accuracy of NMR structures in detail, we generated NOE distance data from a long molecular dynamics trajectory of BPTI. Cross-relaxation rates were calculated from the trajectory by analysis of the appropriate proton-proton vector autocorrelation functions. A criterion for the convergence of correlation functions was developed, and the analysis was restricted to those correlation functions that had converged within the simulation time. Effective distances were determined from the calculated cross-relaxation rates. Internal dynamics affected the derived distances in a realistic way, since they were subject both to radial averaging (which increases the cross-relaxation rate) and angular averaging (which decreases the cross-relaxation rate). The comparison of the effective distances with average distance between the protons during the trajectory showed that for most the effects of angular and distance averaging essentially cancel out. For these distances, the effective distance derived from an NOE is therefore a very good estimate of the average distance, or the distance in the average structure. However, for about 10% of the distances, the effective distance was more than 10% larger than the average distance, while for about 5%, it was more than 10% smaller, in some cases by more than 2 A. Little correlation is observed between the effects on cross-relaxation rates to different protons of the same residue. The results of this analysis have implications for the way structures are calculated from NOE distance data. For many distances, the assumption of a rigid structure is valid, and large error bounds would result in the loss of too much information content. On the other hand, the error bounds very often employed are not wide enough for some of the effects seen in our study.

Animals↗

Analysis methods for comparison of multiple molecular dynamics trajectories: applications to protein unfolding pathways and denatured ensembles.

In molecular dynamics simulations of protein unfolding, the pathway of one protein molecule is studied at a time. In contrast, experimental denaturation studies sample from large ensembles of molecules passing from the native to unfolded state. If reasonable comparisons with experiment are to be made, then the generality of the simulations needs to be confirmed by performing multiple unfolding simulations. Given that protein unfolding trajectories are very complicated functions of the proteins and the environment, comparing different trajectories, even under the same conditions, is not straightforward. Several methods are presented here that attempt to accomplish this task at different levels of complexity. The simpler methods are geometry based and make use of the root-mean-squared deviations between structures, while the more complicated methods are based on the time variation of the various properties of the system during the unfolding process. These methods are applied to multiple simulations of three different proteins, bovine pancreatic trypsin inhibitor, chymotrypsin inhibitor 2, and barnase. In general, for these three proteins protein unfolding proceeded via expansion of the core and fraying of secondary structure to yield the major transition state. Once past the transition state, the trajectories for a given protein diverged as the protein lost further secondary and tertiary structure by a variety of mechanisms. Although the unfolding pathways diverged, similar conformations were populated in the denatured state even when the unfolding occurred via different pathways. The multitude of different pathways leading to the denatured state agrees with the funnel description of protein folding. Although the pathways differed in conformational space, the physical properties of the conformations were often similar, highlighting the danger of assuming that similar observed properties imply similar conformations. In fact, there may be many different "conformational pathways" of unfolding that fit within a preferred "property space pathway".

Aprotinin↗

Coordination dynamics of trajectory formation.

The present study aims to understand the neurally based coordination dynamics (multistability, loss of stability, transitions, etc.) of trajectory formation in a simple task. Six subjects produced two spatial patterns of coordination in the xy plane by alternating the abduction-adduction and flexion-extension motions of their right index finger. Each pattern was characterized by a unique temporal ratio between the x and y directions of motion: (1) a figure zero, a 1:1 temporal pattern; and (2) a figure eight, a 2:1 temporal pattern. The patterns were produced rhythmically and movement frequency was scaled across ten frequency plateaus, with ten cycles of motion per step. As movement frequency increased, switching from a figure eight to a figure zero was observed at critical cycling frequencies. The switch from pattern (2) to pattern (1) was identified in the spatial trajectory and power spectra of x(t) and y(t). En route to the transition, enhancement of fluctuations was observed in the Fourier amplitudes of x(t) and y(t), specifically at f0 (the metronome frequency) and 2f0 (the first harmonic of f0). Interestingly, there was no difference in the spatial variability of the two patterns. Overall, the data demonstrate that spatial patterns of coordination can be characterized in terms of the temporal relationship between the spatial components of the trajectory itself. We discuss the experimental findings in relation to other end-point planning and multijoint control strategies, as well as the much more general problem of temporal synchronization in many interlimb and intralimb coordination tasks.

Adult↗

Estimation of dynamic joint torques and trajectory formation from surface electromyography signals using a neural network model.

In this study, human arm movement was reconstructed from electromyography (EMG) signals using a forward dynamics model acquired by an artificial neural network within a modular architecture. Dynamic joint torques at the elbow and shoulder were estimated for movements in the horizontal plane from the surface EMG signals of 10 flexor and extensor muscles. Using only the initial conditions of the arm and the EMG time course as input, the network reliably reconstructed a variety of movement trajectories. The results demonstrate that posture maintenance and multijoint movements, entailing complex via-point specification and co-contraction of muscles, can be accurately computed from multiple surface EMG signals. In addition to the model's empirical uses, such as calculation of arm stiffness during motion, it allows evaluation of hypothesized computational mechanisms of the central nervous system such as virtual trajectory control and optimal trajectory planning.

Arm↗