Estimating the apparent transverse relaxation time (R2(*)) from images with different contrasts (ESTATICS) reduces motion artifacts.

Relaxation rates provide important information about tissue microstructure. Multi-parameter mapping (MPM) estimates multiple relaxation parameters from multi-echo FLASH acquisitions with different basic contrasts, i.e., proton density (PD), T1 or magnetization transfer (MT) weighting. Motion can particularly affect maps of the apparent transverse relaxation rate R2(*), which are derived from the signal of PD-weighted images acquired at different echo times. To address the motion artifacts, we introduce ESTATICS, which robustly estimates R2(*) from images even when acquired with different basic contrasts. ESTATICS extends the fitted signal model to account for inherent contrast differences in the PDw, T1w and MTw images. The fit was implemented as a conventional ordinary least squares optimization and as a robust fit with a small or large confidence interval. These three different implementations of ESTATICS were tested on data affected by severe motion artifacts and data with no prominent motion artifacts as determined by visual assessment or fast optical motion tracking. ESTATICS improved the quality of the R2(*) maps and reduced the coefficient of variation for both types of data-with average reductions of 30% when severe motion artifacts were present. ESTATICS can be applied to any protocol comprised of multiple 2D/3D multi-echo FLASH acquisitions as used in the general research and clinical setting.

Relaxation time of processes driven by multiplicative noise

We consider systems described by nonlinear stochastic differential equations with multiplicative noise. We study the relaxation time of the steady-state correlation function as a function of noise parameters. We consider the white- and nonwhite-noise case for a prototype model for which numerical data are available. We discuss the validity of analytical approximation schemes. For the white-noise case we discuss the results of a projector-operator technique. This discussion allows us to give a generalization of the method to the non-white-noise case. Within this generalization, we account for the growth of the relaxation time as a function of the correlation time of the noise. This behavior is traced back to the existence of a non-Markovian term in the equation for the correlation function.

Transient and preparation colored-noise effects: The nonlinear relaxation-time approach

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

The nonlinear relaxation time and quasideterministic-theory approaches to characterize the decay of unestable states

We present the relationship between nonlinear-relaxation-time (NLRT) and quasideterministic approaches to characterize the decay of an unstable state. The universal character of the NLRT is established. The theoretical results are applied to study the dynamical relaxation of the Landau model in one and n variables and also a laser model.

Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

Is it the grain size or the characteristic pore size that controls the induced polarization relaxation time of clean sands and sandstones?

There is a wide range of evidence to suggest that permeability can be constrained through of induced polarization measurements. For clean sands and sandstones, current mechanistic models of induced polarization predict a relationship between the low-frequency time constant inferred from induced polarization measurements and the grain diameter. A number of observations do, however, disagree with this and indicate that the observed relaxation behavior is rather governed by the so-called dynamic pore radius L. To test this hypothesis, we have developed a set of new scaling relationships, which allow the relaxation time to be computed from the pore size and the permeability to be computed from both the Cole-Cole time constant and the formation factor. Moreover, these new scaling relationships can be also used to predict the dependence of the Cole-Cole time constant as a function of the water saturation under unsaturated conditions. Comparative tests of the proposed new relationships with regard to various published experimental results for saturated clean sands and sandstones as well as for partially saturated clean sandstones, do indeed confirm that the dynamic pore radius L is a much more reliable indicator of the observed relaxation behavior than grain-size-based models.

Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.

The role of an insulating surface layer on the relaxation time of the ionic redistribution in an electrolytic cell

We analyze the influence of a surface dielectric layer on the transient phenomena related to the ionic redistribution in an electrolytic cell submitted to a step-like external voltage. The adsorption-desorption phenomenon is taken into account in the famework of the Gouy-Chapman approximation, where the ions are assumed dimensionless. In the limit of small amplitude of the applied voltage, where the equations of the problem can be linearized, we obtain an analytical solution for the surface densities of ions, for the electrical potential and for the relaxation time for the transient phenomena. In the general case, when the linearized analysis is no longer valid, the solution of the problem is obtained numerically. The role of the thickness of the dielectric layer on the relaxation time is also discussed.

Nuclear magnetic resonance water relaxation time changes in bananas during ripening: a new mechanism

BACKGROUND: Nuclear magnetic resonance studies of banana fragments during ripening show an increase on the water transverse relaxation time (T(2)) and a decrease in water self-diffusion coefficient (D). As T(2) and D are normally directly correlated, we studied these two properties in intact bananas during ripening, in an attempt to rule out the effect of injury on the apparent discrepancies in the behavior of T(2) and D. RESULTS: The results show that injury in bananas causes a decrease in T(2) of the water in vacuoles (T(2vac)). They also show that T(2vac) increased and D decreased during ripening, ruling out the injury effect. To explain the apparent discrepancies, we propose a new hypothesis for the increase in T(2) values, based on the reduction of Fe(3+) ions to Fe(2+) by galacturonic acid, produced by the hydrolysis of pectin and a decrease in internal oxygen concentration during ripening. CONCLUSION: As injury alters T(2) values it is necessary to use intact bananas to study relaxation times during ripening. The novel interpretation for the increase in T(2vac) based on reduction of Fe(+3) and O(2) concentration is an alternative mechanism to that based on the hydrolysis of starch in amyloplasts. (C) 2010 Society of Chemical Industry

Feasibility of texture analysis for the assessment of biochemical changes in meniscal tissue on T1 maps calculated from delayed gadolinium-enhanced magnetic resonance imaging of cartilage data: comparison with conventional relaxation time measurements

To (1) establish the feasibility of texture analysis for the in vivo assessment of biochemical changes in meniscal tissue on delayed gadolinium-enhanced magnetic resonance imaging of cartilage (dGEMRIC), and (2) compare textural with conventional T1 relaxation time measurements calculated from dGEMRIC data ("T1(Gd) relaxation times").

High-field 1H T1 and T2 NMR Relaxation Time Measurements of H2O in Homeopathic Preparations of Quartz, Sulfur and Copper Sulfate

Quantitative meta-analyses of randomized clinical trials investigating the specific therapeutic efficacy of homeopathic remedies yielded statistically significant differences compared to placebo. Since the remedies used contained mostly only very low concentrations of pharmacologically active compounds, these effects cannot be accounted for within the framework of current pharmacology. Theories to explain clinical effects of homeopathic remedies are partially based upon changes in diluent structure. To investigate the latter, we measured for the first time high-field (600/500 MHz) 1H T1 and T2 nuclear magnetic resonance relaxation times of H2O in homeopathic preparations with concurrent contamination control by inductively coupled plasma mass spectrometry (ICP-MS). Homeopathic preparations of quartz (10c–30c, n = 21, corresponding to iterative dilutions of 100−10–100−30), sulfur (13x–30x, n = 18, 10−13–10−30), and copper sulfate (11c–30c, n = 20, 100−11–100−30) were compared to n = 10 independent controls each (analogously agitated dilution medium) in randomized and blinded experiments. In none of the samples, the concentration of any element analyzed by ICP-MS exceeded 10 ppb. In the first measurement series (600 MHz), there was a significant increase in T1 for all samples as a function of time, and there were no significant differences between homeopathic potencies and controls. In the second measurement series (500 MHz) 1 year after preparation, we observed statistically significant increased T1 relaxation times for homeopathic sulfur preparations compared to controls. Fifteen out of 18 correlations between sample triplicates were higher for controls than for homeopathic preparations. No conclusive explanation for these phenomena can be given at present. Possible hypotheses involve differential leaching from the measurement vessel walls or a change in water molecule dynamics, i.e., in rotational correlation time and/or diffusion. Homeopathic preparations thus may exhibit specific physicochemical properties that need to be determined in detail in future investigations.

Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time

We perform numerical simulations on a model describing a Brillouin-based temperature and strain sensor, testing its response when it is probed with relatively short pulses. Experimental results were recently published [e.g., Opt. Lett. 24, 510 (1999)] that showed a broadening of the Brillouin loss curve when the probe pulse duration is reduced, followed by a sudden and rather surprising reduction of the linewidth when the pulse duration gets shorter than the acoustic relaxation time. Our study reveals the processes responsible for this behavior. We give a clear physical insight into the problem, allowing us to define the best experimental conditions required for one to take the advantage of this effect.

Transient response in high-resolution Brillouin-based distributed sensing using probe pulses shorter than the acoustic relaxation time

We perform numerical simulations on a model describing a Brillouin-based temperature and strain sensor, testing its response when it is probed with relatively short pulses. Experimental results were recently published [e.g., Opt. Lett. 24, 510 (1999)] that showed a broadening of the Brillouin loss curve when the probe pulse duration is reduced, followed by a sudden and rather surprising reduction of the linewidth when the pulse duration gets shorter than the acoustic relaxation time. Our study reveals the processes responsible for this behavior. We give a clear physical insight into the problem, allowing us to define the best experimental conditions required for one to take the advantage of this effect.

Quantitative MRI of Vastus Medialis, Vastus Lateralis and Gluteus Medius Muscle Workload after Squat Exercise: Comparison Between Squatting with Hip Adduction and Hip Abduction

The aim of the present study was to evaluate the use MRI to quantify the workload of gluteus medius (GM), vastus medialis (VM) and vastus lateralis (VL) muscles in different types of squat exercises. Fourteen female volunteers were evaluated, average age of 22 +/- 2 years, sedentary, without clinical symptoms, and without history of previous lower limb injuries. Quantitative MRI was used to analyze VM, VL and GM muscles before and after squat exercise, squat associated with isometric hip adduction and squat associated with isometric hip abduction. Multi echo images were acquired to calculate the transversal relaxation times (T2) before and after exercise. Mixed Effects Model statistical analysis was used to compare images before and after the exercise (Delta T2) to normalize the variability between subjects. Imaging post processing was performed in Matlab software. GM muscle was the least active during the squat associated with isometric hip adduction and VM the least active during the squat associated with isometric hip abduction, while VL was the most active during squat associated with isometric hip adduction. Our data suggests that isometric hip adduction during the squat does not increase the workload of VM, but decreases the GM muscle workload. Squat associated with isometric hip abduction does not increase VL workload.

Proton T1 relaxation times of metabolites in human occipital white and gray matter at 7 T.

Proton T1 relaxation times of metabolites in the human brain have not previously been published at 7 T. In this study, T1 values of CH3 and CH2 group of N-acetylaspartate and total creatine as well as nine other brain metabolites were measured in occipital white matter and gray matter at 7 T using an inversion-recovery technique combined with a newly implemented semi-adiabatic spin-echo full-intensity acquired localized spectroscopy sequence (echo time = 12 ms). The mean T1 values of metabolites in occipital white matter and gray matter ranged from 0.9 to 2.2 s. Among them, the T1 of glutathione, scyllo-inositol, taurine, phosphorylethanolamine, and N-acetylaspartylglutamate were determined for the first time in the human brain. Significant differences in T1 between white matter and gray matter were found for water (-28%), total choline (-14%), N-acetylaspartylglutamate (-29%), N-acetylaspartate (+4%), and glutamate (+8%). An increasing trend in T1 was observed when compared with previously reported values of N-acetylaspartate (CH3 ), total creatine (CH3 ), and total choline at 3 T. However, for N-acetylaspartate (CH3 ), total creatine, and total choline, no substantial differences compared to previously reported values at 9.4 T were discernible. The T1 values reported here will be useful for the quantification of metabolites and signal-to-noise optimization in human brain at 7 T. Magn Reson Med 69:931-936, 2013. © 2012 Wiley Periodicals, Inc.