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A method to measure arbitrary k-space trajectories for rapid MR imaging.

A method to measure arbitrary k-space trajectories was developed to compensate for nonideal gradient performance during rapid magnetic resonance (MR) imaging with actively or nonactively shielded gradients at a magnetic field strength of 4.1 T. Accurate MR image reconstruction requires knowledge of the k-trajectory produced by the gradient waveforms during k-space sampling. Even with shielded gradients, residual eddy currents and imperfections in gradient amplifier performance can cause the true k-space trajectory to deviate from the ideal trajectory. The k-space determination was used for spiral gradient-echo imaging fo the human brain. While individual calibrations are needed for new pulse sequences, the method of k-space determination can be used for any sequence of preparation pulses and readout gradient waveforms and should prove useful for other trajectories, including the rastered lines of echo-planar imaging.

Artifacts↗

Fast three-dimensional k-space trajectory design using missile guidance ideas.

Three-dimensional (3D) k-space trajectories are needed to acquire volumetric images in MRI. While scan time is determined by the trajectory efficiency, image quality and distortions depend on the shape of the trajectories. There are several 3D trajectory strategies for sampling the k-space using rectilinear or curve schemes. Since there is no evidence about their optimality in terms of image quality and acquisition time, a new design method based on missile guidance ideas is explored. Since air-to-air missile guidance shares similar goals and constraints with the problem of k-space trajectory design, a control approach for missiles is used to design a 3D trajectory. The k-space is divided into small cubes, and each one is treated as a target to be sampled. The main goal is to cover the entire space as quickly and efficiently as possible, with good performance under different conditions. This novel design method is compared to other trajectories using simulated and real data. As an example, a trajectory that requires 0.11 times the number of shots needed by the cylindrical 3DFT acquisition was designed. This trajectory requires more shots (1.66 times) than the stack of spirals, but behaves better under nonideal conditions, such as off-resonance and motion.

Algorithms↗

Processing of radial fast spin-echo data for obtaining T2 estimates from a single k-space data set.

Radially acquired fast spin-echo data can be processed to obtain T2-weighted images and a T2 map from a single k-space data set. The general approach is to use data at a specific TE (or narrow TE range) in the center of k-space and data at other TE values in the outer part of k-space. With this method high-resolution T2-weighted images and T2 maps are obtained in a time efficient manner. The mixing of TE data, however, introduces errors in the T2-weighted images and T2 maps that affect the accuracy of the T2 estimates. In this work, various k-space data processing methods for reconstructing T2-weighted images and T2 maps from a single radial fast spin-echo k-space data set are analyzed in terms of the accuracy of T2 estimates. The analysis is focused on the effect of image artifacts, object dependency, and noise on the T2 estimates. Results are presented in computer-generated phantoms and in vivo.

Algorithms↗

k-t GRAPPA: a k-space implementation for dynamic MRI with high reduction factor.

A novel technique called "k-t GRAPPA" is introduced for the acceleration of dynamic magnetic resonance imaging. Dynamic magnetic resonance images have significant signal correlations in k-space and time dimension. Hence, it is feasible to acquire only a reduced amount of data and recover the missing portion afterward. Generalized autocalibrating partially parallel acquisitions (GRAPPA), as an important parallel imaging technique, linearly interpolates the missing data in k-space. In this work, it is shown that the idea of GRAPPA can also be applied in k-t space to take advantage of the correlations and interpolate the missing data in k-t space. For this method, no training data, filters, additional parameters, or sensitivity maps are necessary, and it is applicable for either single or multiple receiver coils. The signal correlation is locally derived from the acquired data. In this work, the k-t GRAPPA technique is compared with our implementation of GRAPPA, TGRAPPA, and sliding window reconstructions, as described in Methods. The experimental results manifest that k-t GRAPPA generates high spatial resolution reconstruction without significant loss of temporal resolution when the reduction factor is as high as 4. When the reduction factor becomes higher, there might be a noticeable loss of temporal resolution since k-t GRAPPA uses temporal interpolation. Images reconstructed using k-t GRAPPA have less residue/folding artifacts than those reconstructed by sliding window, much less noise than those reconstructed by GRAPPA, and wider temporal bandwidth than those reconstructed by GRAPPA with residual k-space. k-t GRAPPA is applicable to a wide range of dynamic imaging applications and is not limited to imaging parts with quasi-periodic motion. Since only local information is used for reconstruction, k-t GRAPPA is also preferred for applications requiring real time reconstruction, such as monitoring interventional MRI.

Algorithms↗

The effect of growth rate on tissue-diet isotopic spacing in rapidly growing animals. An experimental study with Atlantic salmon (Salmo salar).

The difference in isotopic composition between a consumer's tissues and that of its diet is a critical aspect of the use of stable isotope analyses in ecological and palaeoecological studies. In a controlled feeding experiment with the Atlantic salmon, Salmo salar, we demonstrate for the first time that the value of tissue-diet isotope spacing in nitrogen in a growing animal is not constant, but varies inversely with growth rate. The value of tissue-diet isotopic spacing in N reflects N use efficiency. Thus, in salmon, growth rate is accompanied by, or requires, increased N use efficiency. The total range in tissue-diet isotopic spacing in N seen in the experimental population of 25 fish was 1 per thousand, approximately 50% of the total trophic shift. Mean equilibrium tissue-diet isotopic spacing (+/-standard deviation) in salmon averaged 2.3 per thousand (+/-0.3 per thousand) and 0.0 per thousand (+/-0.3 per thousand) for N in muscle and liver, respectively, and 2.1 per thousand (+/-0.1 per thousand) and 1.6 per thousand (+/-0.3 per thousand) for C in muscle and liver, respectively. Feeding with a mixed dietary source (wheat and fish-meal origin) resulted in tissue-diet isotopic fractionation in both C and N due to the differential digestibility of food components with distinct isotopic composition. The rate of change in isotopic composition of S. salar tissues was dominated by growth, but the estimated contribution of metabolic turnover to change in tissue N was relatively high for an ectothermic animal at ca. 20-40%. The estimated half-life for metabolic turnover of the tissue N pool was ca. 4 months in both muscle and liver tissue. This is the first study to demonstrate a direct relationship between tissue-diet isotopic spacing in N and growth rate and adds to the growing list of factors known to influence the level of isotopic separation between a consumer's tissue and that of its diet.

Animal Feed↗

Submillisecond changes in myosin lattice spacing resulting from rapid length changes.

The speed of the myofilament lattice spacing response to rapid changes in load or length of single, intact muscle fibres of the frog, was investigated during isometric tetani. During ramp releases at close to Vmax and during step length changes (completed within 250 microseconds), lattice spacing was calculated from the equatorial X-ray diffraction pattern (sampled at 250 microseconds time resolution using synchrotron radiation). Ramp releases (total shortening=1.39 %) caused a spacing increase, described with an exponential function (alpha=271 s-1, amplitude=1.15 nm) plus an elastic component having the time course of discharge of axial tension (amplitude 0.28 nm). For a step release (amplitude=0.87%), lattice expansion could be described with an exponential (alpha =1005 s-1, amplitude=0.56 nm) plus an elastic component of 0.25 nm amplitude. Lattice compression was associated with a step stretch (amplitude=0.62 %), and was also quasi-exponential (alpha=367 s-1, amplitude=0.74 nm), with an elastic component of 0.28 nm. The spacing change time course for length steps resembled that of the accompanying quick recovery of axial tension and the associated change in the meridional 14.5 nm reflection intensity, which are both believed to be determined by the kinetics of the molecular power stroke. Therefore, this shows that lattice spacing changes, arising from radial forces exerted by attached crossbridges, are fast enough to occur during the power stroke event.

Animals↗

A novel feature of DNA recognition: a mutant Gcn4p bZip peptide with dual DNA binding specificities dependent of half-site spacing.

Homodimeric DNA-binding proteins with relaxed half-site spacing requirements for their DNA targets have been described. As an example, the yeast transcriptional activator Gcn4p binds in vitro equally well to the AP1 site (5'A4T3G2A1C0T1'C2'A3'T4'3') and the ATF/CREB site (5'A4T3G2A1C0G0'T1'C2'A3'T4'3'), which have identical but differently spaced half-site blocks. We describe a novel feature for the bZip class of DNA-binding proteins. The N-14 mutant of a Gcn4p-derived bZip peptide shows a diametrically opposed base-pair recognition specificity depending on the half-site spacing of its DNA target: on pseudo-palindromic, AP1 site-like binding sites, guanine is required in position 2 for proper binding; in contrast, on palindromic, ATF/CREB site-like targets, position 2 must be cytosine to prevent a loss of binding. Modeling studies suggest that the different base-pair requirements on differently spaced DNA targets are due to minimal alterations of the distances between the relevant atoms of the N-14 side-chain and the corresponding target groups on the DNA. Although the N-14 peptide does not have a natural counterpart, its behavior hints at the possibility that dual binding modi dependent on half-site spacing may occur also for natural homodimeric DNA-binding proteins.

Base Sequence↗

Sarcomere length versus interfilament spacing as determinants of cardiac myofilament Ca2+ sensitivity and Ca2+ binding.

The Ca2+ sensitivity of skinned cardiac muscle can be increased by either an increase in sarcomere length or osmotic compression of the myofilament lattice. The length-dependent change in Ca2+ sensitivity is considered to be an important component of the steep force-length relation along the ascending limb of the force-length curve (Frank-Starling relation). Since an increase in sarcomere length is accompanied by a reduction in the spacing between myosin and actin filaments it is not clear whether length-dependent changes in Ca2+ sensitivity are related to changes in sarcomere length, interfilament spacing or some combination of both. To obtain quantitative information on the relative contributions of these two parameters to the determination of Ca2+ sensitivity skinned bovine cardiac muscle bundles of varying sarcomere lengths (1.7-2.3 microns) were exposed to varying concentrations (0-5%) of Dextran T-500. Measurements were made of changes in muscle width in response to Dextran T-500 addition and both force-pCa curves and bound Ca(2+)-pCa curves were obtained as a function of sarcomere length and lattice compression. From the data obtained it was possible to compare Ca2+ sensitivity and Ca(2+)-troponin C affinity at different sarcomere lengths under conditions of changing interfilament spacing and constant interfilament spacing. Both Ca2+ sensitivity and Ca2+ binding correlated more closely with change in interfilament spacing than with change in sarcomere length. These results suggest that length-dependent force generation in cardiac muscle is based primarily on length-dependent changes in the separation between myosin and actin filaments.

Actin Cytoskeleton↗

Uniform-penalty inversion of multiexponential decay data. II. Data spacing, T(2) data, systemic data errors, and diagnostics.

The basic method of UPEN (uniform penalty inversion of multiexponential decay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65-77 (1998)), which also discusses the effects of noise, constraints, and smoothing on the resolution or apparent resolution of features of a computed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxation data do not demand to be separate. The experimental and artificial data presented earlier were T(1) data, and all had fixed data spacings, uniform in log-time. However, for T(2) data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the extension of UPEN to T(2) data, including the averaging of data in windows and the use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending beyond the data range. The input smoothing parameters in UPEN are normally fixed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic errors due to instrumental nonidealities or adjustment problems. For instance, a relaxation curve for a wide line can be narrowed by an artificial downward bending of the relaxation curve. Diagnostic parameters are generated to help identify data problems, and the diagnostics are applied in several examples, with particular attention to the meaningful resolution of two closely spaced peaks in a distribution of relaxation times. Where feasible, processing with UPEN in nearly real time should help identify data problems while further instrument adjustments can still be made. The need for the nonnegative constraint is greatly reduced in UPEN, and preliminary processing without this constraint helps identify data sets for which application of the nonnegative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random noise.

Geologic Sediments↗

Biology of the inner space: voids in biopolymers

Dynamic states of biopolymers are associated with appearance and disappearance of spaces, or voids, to an extent larger than what is hitherto recognized. Current awareness of the existence of free space in biopolymers is by and large restricted in terms of (i) essentially small pores obeying Boltzman distribution of sizes and energy and (ii) rigid structures dictated by structural constraints, whose volume merely exhibits fluctuations within the thermal limits. Interconnectivity of these spaces within biopolymers such as membranes give rises to new possibilities in addressing some of the long standing problems in understanding catalysis, transport and the derived biological phenomena. Given the a priori recognition that other kinds of space can exist in biopolymers, which are dynamic, predominantly inducible and possibly larger, a new kind of experimentation becomes possible as also a new set of constraints for the acceptability of molecular models of interactions in the explanation of biological phenomena. The theory of adsorption of liquids and presence of structural cavities as exemplified by zeolites competently accounts for much of the current thinking in our understanding of cavities in biopolymers. Induction of (larger) voids requires approaches that are significantly different. We suggest that it is necessary to consider a reservoir of inner space as a specific contribution to the energetics of polymer dynamics. We outline a methodological approach that helps identify these voids as well as biological phenomena in which the notion of dynamics of voids would bring novel insights. Copyright 1998 Academic Press

Journal Article↗

Red blood cell spacing in rat coronary capillaries during the cardiac cycle.

Theoretical studies have demonstrated a pronounced effect of red blood cell (RBC) spacing on tissue oxygen supply. Our objective was to collect data regarding RBC spacing and related linear capillary hematocrit (Hct) in rat coronary capillaries, from two distinct locations within the capillary bed (proximal and distal portions), in the subendo- and midmyocardium, during systole and diastole. Hearts were rapidly frozen in situ, and tissue sections were stained in order to distinguish capillaries in proximal and distal portions of the capillary bed, as well as the RBCs within them. Morphometric data were compared according to capillary type, cardiac region, and cardiac phase. Distal portions of the capillary bed had a significantly greater capillary Hct (p < 0.001) and significantly lower RBC spacing values (P < 0.01), compared to proximal portions, irrespective of cardiac phase or region. There was a greater frequency of RBC spacing values equal to O microns in systole compared to diastole (P < 0.001) and a greater frequency of RBC spacing values greater than 40 microns in proximal portions of the capillary bed compared to distal portions (P < 0.001). These results suggest that intracapillary resistance to O2 transport is reduced, and O2 carrying capacity of the blood increased, in distal portions of the capillary bed, where PO2 in the blood is lower.

Animals↗

Spatial and space-time correlations in systems of subpopulations with stochastic migration.

The great majority of models of the population genetics of subdivided populations have made the simplifying assumption that the gene frequencies in migrant groups are deterministic. The present paper examines models which more closely mimic natural conditions, in which the gene frequencies in migrant groups are subject to stochastic effects. It is shown that some types of stochastic migration can cause dramatic changes in spatial correlations and variance. These changes depend on how the stochastic migration effects in the gene frequency recursion equations are shared among nearby subpopulations during the same generation. Only for cases where the effects are completely unshared are the equilibrium spatial and space-time correlations among adult subpopulations unaffected, but the variance is always inflated. The analyses here use novel methods, by recasting population genetic migration-drift models as space-time autoregressive moving average (STARMA) processes. Recent theorems for STARMA processes are employed for finding the spatial correlations, and for the first time in population genetics theory the complete set of space-time correlations, for systems with general patterns of migration rates and numbers of spatial dimensions. The space-time correlations provide a uniquely detailed description of a system, and thus form a link between observed spatial autocorrelation statistics and the underlying space-time population genetic process. STARMA theoretical processes have direct statistical analogues that can be applied for process identification, parameter estimation, model fitting, and forecasting in real systems.

Animals↗

Effects of chronically administered d-amphetamine on spaced responding maintained under multiple and single-component schedules.

Key pressing by rats was maintained under spaced-responding and random-ratio schedules of food delivery, and rates of responding were reliably different for each schedule. When responding was maintained under a multiple schedule, appropriate doses of d-amphetamine (1.0 and 1.7 mg/kg) markedly increased low rates of spaced responding while markedly decreasing high rates of ratio responding. These drug-produced changes in response rate resulted in decreased food presentation during both schedule components. When 1.0 mg/kg d-amphetamine was given daily, tolerance developed to initially decreased ratio responding in six to nine sessions, but did not develop to initially increased spaced responding. However, when the ratio schedule was removed, tolerance developed very quickly to increases under the spaced-responding schedule, and associated food frequency returned to control levels. When the ratio schedule was reinstated, spaced responding was once again increased, and its associated frequency of food delivery was again decreased. The development of tolerance to the behavioral effects of d-amphetamine was influenced more by global changes in response consequences during entire experimental sessions than by local changes in response consequences in single components of those sessions. Whenever the concept of "response cost" is used, it should be understood in terms of total "cost".

Animals↗

Responses to simulated echoes by neurons in the barn owl's auditory space map.

The natural acoustical environment contains many reflective surfaces that give rise to echoes, complicating the task of sound localization and identification. The barn owl (Tyto alba), as a nocturnal predator, relies heavily on its auditory system for tracking and capturing prey in this highly echoic environment. The external nucleus of the owl's inferior colliculus (ICx) contains a retina-like map of space composed of "space-specific" auditory neurons that have spatially limited receptive fields. We recorded extracellularly from individual space-specific neurons in an attempt to understand the pattern of activity across the ICx in response to a brief direct sound and a simulated echo. Space-specific neurons responded strongly to the direct sound, but their response to a simulated echo was suppressed, typically, if the echo arrived within 5 ms or less of the direct sound. Thus we expect there to be little or no representation within the ICx of echoes arriving within such short delays. Behavioral tests using the owl's natural tendency to turn their head toward a sound source suggested that owls, like their space-specific neurons, similarly localize only the first of two brief sounds. Naive, untrained owls were presented with a pair of sounds in rapid succession from two horizontally-separated speakers. With interstimulus delays of less than 10 ms, the owl consistently turned its head toward the leading speaker. Longer delays elicited head turns to either speaker with approximately equal frequency and in some cases to both speakers sequentially.

Acoustic Stimulation↗

Non-neuronal cells in the spinal cord of nude and heterozygous mice. II. Agranular leukocytes in the subarachnoid and perivascular space.

The lumbar spinal cord of the athymic nude mouse and its heterozygous control were examined at the light and electron microscopic levels for differences in the cellular constituents of the subarachnoid and perivascular spaces. Both macrophages and lymphocytes were found in these spaces associated with the adventitial and leptomeningeal cells. Occasionally, fixed-cells were associated with extensions of the basal lamina and subjacent astrocytic processes. The appearance of the basal lamina of the external glia limitans and perivascular space was enhanced by tannic acid treatment. There were twice as many macrophages as lymphocytes, but no significant strain differences. Comparison was made between cells in the lumina of incompletely perfused vessels and neuroglial cells in the spinal cord. The cellular morphology is distinct in each of these compartments and no cell migrations were observed between the blood, cerebrospinal fluid and C.N.S. interstitial space. The normal presence of both macrophages and lymphocytes in the subarachnoid and perivascular space suggests that these cells could penetrate the basal lamina and gain access to the C.N.S.

Animals↗

Renal function and intra/extravascular distribution spaces in the rat after supralethal whole-body x-irradiation.

Renal function and distribution of 51Cr-EDTA in intra/extravascular space has been studied in rats suffering from the gastro-intestinal syndrome after supralethal doses of X-irradiation. Urine excretion and glomerular filtration were found to decrease until 50 hr p.i. Urine excretion and, in a less degree, glomerular filtration rate increase then to a peak at 67 hrs before falling off to zero values before death. The extravascular space was found to be expanded in several organs from 60 hrs on (kidney, liver, stomach, intestine). Only in kidney where weight follows changes in extravascular space, a return to normal values is seen before death. An expansion in extravascular space due to a reduced re-extraction into intravascular space and diminished excretion constant can also be discerned beginning early after exposure on the basis of compartmental analysis of the blood activity-time curves. It is postulated that the changes observed reflect a state of shock developing slowly after irradiation and entering its irreversible stage 60 to 65 hrs after exposure.

Animals↗

Volume estimation of the preepiglottic and paraglottic space using spiral computed tomography.

The purpose of this study was to estimate the volume variability of the preepiglottic and paraglottic space in the normal larynx. In 23 adult patients (12 women, 11 men), a spiral CT acquisition through the larynx was obtained. No laryngeal pathology was observed. The area of the this submucosal fat space was estimated on each slice by semi-automatic segmentation; the volume was calculated by the summation-of-areas technique. The obtained volumes were correlated with body area, body mass index and gender. The mean estimated volume of the preepiglottic and paraglottic space was 2.8 ml (SD 1.7 ml, range 0.7-5.9). No correlation with body mass index (p = 0.6), but a significant correlation with body area (p < 0.001) was found. A significant volume difference was present between men (mean 4.5 ml, SD 1.0 ml, range 2.8-5.9) and women (mean 1.4 ml, SD 0.5 ml, range 0.7-2.4)(p < 0.0001). Multiple regression analysis showed gender (p < 0.0001) to be a more important variable than body area (p = 0.17) in predicting the volume of the preepiglottic and paraglottic space. In conclusion, the volume of the preepiglottic and paraglottic space appears to be very variable, and should only be analysed with consideration of the gender of the examined subjects.

Adult↗

Behaviour space of a stretch reflex model and its implications for the neural control of voluntary movement.

A nonlinear model for the stretch reflex has recently been used to study the interactions between voluntary and reflex controls during fast, targeted movements. The present study explores the topography of a 'behaviour space' generated by computer simulations of this model under various combinations of values for the gain parameters and time constants in the model's feedback loops. In general, we define a behaviour space to be any set of behavioural characteristics of the simulated movement, such as movement time, peak acceleration or peak velocity. The mathematical model can therefore be viewed as an M x N dimensional map from its parameter space N to a behaviour space M. Here, a one-dimensional behaviour space is explored. This provides a method for quantitatively comparing the different control strategies that might be employed by the nervous system for integrating reflex and descending signals during fast, voluntary movements. The results indicate that an optimal strategy will employ proprioceptive feedback as a means of fine-tuning the braking and clamping activities of fast, goal-directed movements and that descending signals are primarily important for initiating the movement and for controlling reciprocal patterns of muscle activity during the end phase of the movement.

Feedback↗