In Vivo Relaxation Time Measurements in the Human Placenta Using Echo Planar Imaging at 0.5 T

This paper presents the first in vivo measurements of the nuclear magnetic resonance relaxation times T₁ and T₂ at 0.5 T in the human placenta from 20 weeks gestational age until term, in both normal and compromised pregnancies. T₁ measurements were performed by using both an inversion recovery sequence and the Look-Locher echo planar imaging (EPI) sequence on a total of 41 women with normal pregnancies and 11 women with compromised pregnancies. T₂ measurements were performed by using a spin-echo EPI sequence on 36 women with normal pregnancies and 14 women with compromised pregnancies. In normal pregnancies, both the T₁ values measured with the inversion recovery sequence and the T₂ values were found to decrease with gestational age, the linear regression results gave T₁=−9.1t+1538 r²=0.23 p=0.03 T₂=−4.0t+338 r²=0.47 p=4 10⁻⁶ where t is the gestational age in weeks, and T₁ and T₂ are the relaxation times in milliseconds. T₁ values measured very rapidly with the Look-Locher EPI sequence, but, therefore, with a much lower signal-to-noise ratio, showed no significant trends.The T₁ values measured in the abnormal group were significantly lower than those measured in the normal group. Four out of eight patients with compromised pregnancies had placental T₁ values lying outside the 90% confidence limits for the normal population based about the regression line, significantly more than expected by chance (p = 0.005). Ten out of fourteen of the T₂ measurements in the abnormal group were below the regression line established for the normal group, with 4 lying below the 90% confidence interval, although these trends were only just significant (p = 0.06 and p = 0.03).     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Relaxation effects in two-dimensional zero-field nutation NQR spectroscopy

The relaxation and off-resonance effects on the NQR (nuclear quadrupole resonance) nutation frequency and on the damping constant of the nutation spectrum for spinsI = 3/2 are considered. Using the solution of dynamic equations for nuclear magnetisation in the rotating frame, we obtained a general expression for determination of the asymmetry parameter η, which includes the relaxation time and frequency offset. Specific requirements for the RF (radio frequency) field allowing the presence of nutation and the sufficient resolution of nutation spectra are determined. It is shown that at low RF field it is necessary to take into account theT ₂ relaxation effect on the location of frequency singularities in the nutation spectrum. The values ofH ₁ andT ₂ must be exactly known in nutation NQR spectroscopy. The 2D NQR spin-echo separation technique was used for determination of transverse relaxation of individual spin packets in case of inhomogeneously broadened NQR lines, so that the asymmetry parameter could then be determined by the nutation experiment with consideration of relaxation effects and frequency offset. The theoretical results are confirmed experimentally for the narrow and inhomogeneously broadened 2D-nutation NQR spectra in several molecular compounds containing the³⁵Cl and⁷⁵As nuclei.     

Condition for adiabatic passage in the earth’s-field NMR technique

The equation of motion dM/dt=γ M×B(t) is solved for the case B(t)=jB_p(t)+kB_e. The field B_e is a small static field, typically the earth’s field. The field B_p(t) decays exponentially toward zero with time constant T. This decay is produced by an overdamped switching transient that occurs near the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed that B_p is initially large compared to B_e, and that magnetization M is initially along the resultant field B. Exact solutions are obtained numerically for several decay time constants of B_p, and the motion of M is depicted graphically. It is found that for adiabatic passage, the final cone angle β of the precession in field B_e is related to the decay time constant of B_p by β=2e^{−(π/2)ω_eT}. This is confirmed by measurements of the amplitudes of the ensuing free-precession signals for various decay rates of B_p. Near-perfect adiabatic passage (magnetization aligned within 2° of the earth’s field) can be achieved for time constants T2.6/ω_e. For the case of sudden passage, an approximate analytic solution is developed by linearizing the equation of motion in the laboratory frame of reference. For the adiabatic case, an approximate analytic solution is obtained by linearizing the equation of motion in a rotating frame of reference that follows the resultant field B=B_p+B_e.     

Application of the Wavelet Transform for Detecting Signals of Nuclear Quadrupole Resonance

In the present study, the wavelet transform is used to increase the signal-to-noise ratio of nuclear quadrupole resonance (NQR) signals in the direct pulse method. The efficiency of the wavelet and Fourier transforms used for detecting the NQR signal component is compared. The signal consists of noise, magnetoacoustic and piezoelectric signals, noise from external sources, and NQR signal. Signals from ¹⁴ N nuclei in hexahydro-1,3,5-trinitro-s-triazine C₃H₆N₆O₆ (RDX) are investigated at a temperature of 298 K.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 2005.     

On the pumping of plasma lasers by a high-frequency-modulated electron beam

The possibility of effective pumping of plasma lasers by a high-frequency-modulated electron beam, i.e. an electron beam in the form of a periodic train of electron bunches, is discussed. It is shown that if such parameters of the medium as the relaxation times of the electron temperature ρ_Te and the electron density ρ_Ne are in agreement with the pulse width ρ_p and the interval between pulses, 1/?_m, this will facilitate effective laser pumping and amplitude modulation of the laser radiation. Existing microwave tubes, such as a traveling-wave tube and a klystron, provide the required parameters of a periodic train of current pulses (electron bunches) over a wide range of pulse widths ρ_p and pumping current amplitudes.     

Orbital Divergence and Relaxation in the Gravitational N-Body Problem

One of the fundamental aspects of statistical behaviour in many-body systems is exponential divergence of neighbouring orbits, which is often discussed in terms of Liapounov exponents. Here we study this topic for the classical gravitational N-body problem. The application we have in mind is to old stellar systems such as globular star clusters, where N10⁶, and so we concentrate on spherical, centrally concentrated systems with total energy E<0. Hitherto no connection has been made between the time scale for divergence (denoted here by t _e ) and the time scale on which the energies of the particles evolve because of two-body encounters (i.e., the two-body relaxation time scale, t _r ), even though both may be calculated by similar considerations. In this paper we give a simplified model showing that divergence in phase space is initially roughly exponential, on a timescale proportional to the crossing time (defined as a mean time for a star to cross from one side of the system to another). In this phase t _e <<t _r , if N is not too small (i.e., N30). After several e-folding times, the model shows that the divergence slows down. Thereafter the divergence (measured by the energies of the bodies) varies with time as t ^1/2, on a timescale nearly proportional to the familiar two-body relaxation timescale, i.e., t _e t _r in this phase. These conclusions are illustrated by numerical results.     

Proton NMR relaxation in albumin solutions doped with Mn(II)

The aim of this study is to obtain further information about the source of proton relaxation in the Mn(II)-human serum albumin complex. For this purpose, proton relaxation rates in albumin solutions 1/T ₁ and 1/T ₂ were measured versus increasing amounts of manganese [Mn_t]. The fractions of manganese bound to albumin [Mn_b] and free manganese [Mn_f] were then determined from proton relaxation rate enhancement data. Paramagnetic contributions of bound manganese to the observed relaxation rates (1/T _1p^*)_b and (1/T _2p^*)_b were also determined. Finally, the (1/T _2p^*)_b/(1/T _1p^*)_b ratio was used in a derived equation to estimate an effective correlation time τ. Mean τ value of the complex was found to be in the order of 3 ns, while the hydration number of bound manganese q was estimated to be about 4. The 1/τ was found to be the sum of the inverse values of rotational correlation time 1/τ _r, mean residence time of water in hydration spheres of the complex 1/τ _m, and longitudinal electronic relaxation time of manganese 1/τ _s in the complex. In conclusion, the relaxation mechanism in albumin solutions containing Mn(II) can be interpreted through dipolar and scalar interactions modulated by τ _r, τ _m and τ _s. This analysis enables one to get reasonable figures for the τ _r and q of Mn(II) in albumin solution.     

Electron Temperature Relaxation in Afterglow Plasmas: Diffusion Cooling

We have carried out a thorough theoretical analysis of the cooling and heating processes of the electron gas in Ne, Ar and Kr afterglow plasmas. Thus the rate of relaxation of the electron temperature, T_e, is seen to be in good agreement with the experimental measurements when spatial gradients of T_e in the early afterglow and heating of the electron gas by superelastic collisions between the electrons and metastable atoms are accounted for. At low pressures of the rare gases, p_g, the phenomenon of diffusion cooling occurs in which T_e relaxes to an equilibrium temperature, T_ee, which is less than the gas temperature, T_g. This reduction in T_ee below T_g is mirrored in a reduction in the ambipolar diffusion coefficient, D_a, for the rare gas atomic ions and electrons. Thus the D_a can be calculated as a function of p_g using the values of T_ee, and when this is done, properly accounting for the heating by metastable atoms, the calculated and experimental values of D_a in all three rare gas afterglows are seen to be in agreement.     

Exchange-Correlation Contribution for the Thermodynamic Functions of a Hydrogen Plasma

For a hydrogen model the exchange-correlation energy is calculated at any degree of degeneracy. The numerical data run into the T=O — RPA values, which were evaluated independently. An equation of state for hydrogen without bound states is compared with HNC-calculations in the nondegenerate limit. The influence of increasing y=m_iw/m_e — values for the agreement with limiting results derived analytically is given in detail.     

Ageing exploration of the energy landscape of a glass by the TSDC technique

Different thermal treatments were used in order to follow the structural relaxation of m-toluidine by thermally stimulated depolarization currents (TSDC) in the sub-T _g temperature region. In some of these thermal treatments, the ageing time, t _a, and the probing (or polarization) time, t _P, are varied independently in order to allow a clear understanding of the exploration of the energy landscape which occurs as a consequence of the structural relaxation. The TSDC results show that ageing induces a shift to higher temperatures of the TSDC peaks, in a way similar to that observed in the calorimetric heat capacity overshoot. More importantly, TSDC results show that ageing induces a decrease of the activation energies with regard to the window defined by the probing time and a sharpening of the energy distribution of the modes of motion that are present in the glass, in the studied sub-T _g temperature region.     

Transitions and Spin Dynamics at Very Low Temperature in the Pyrochlores Yb2Ti2O7 and Gd2Sn2O7

An orientational disorder of the cation in [(PyO)D][AuCl₄] crystal was investigated by the ³⁵Cl NQR and ¹H NMR measurements. A structural phase transition was found at ca. 70 K from the temperature dependence of the NQR frequencies both in [(PyO)D][AuCl₄] and [(PyO)H][AuCl₄]. Temperature dependence of the spin-lattice relaxation time T ₁ of the NQR of [AuCl₄]⁻ could be interpreted by an electric field gradient modulation due to the motion of the cation. Characteristics of T ₁ of ³⁵Cl NQR as well as that of ¹H NMR suggest a dynamic orientational disorder of the cation.     

Molecular Diffusion in NMR Microscopy

The signal-to-noise ratio and the T₂ contrast in ¹H NMR microscopy are strongly affected by self-diffusion effects. Here, we investigate the free diffusion of water within imaging gradients. As a result we obtain an apparent relaxation time T₂ which in NMR microscopy is at least one order of magnitude smaller than the true T₂ value of water in the object. This apparent T₂ relaxation is considerably reduced by improving spatial resolution. We conclude that quantitative true T₂ values cannot be calculated from series of images with increasing echo time. Furthermore, from the knowledge of the apparent T₂, an optimum short echo time can be found in order to maximize signal-to-noise ratio. Our theoretical findings are confirmed by phantom experiments at 11.75 T field strength.     

Dimensional Crossover of Magnetic Transition in Diluted Ising Spin Nets Probed by Muon Spin Relaxation

The magnetic ordering process of Ising spins on diluted square lattice was studied by muon spin relaxation using model compounds Rb₂Co _c Mg_1−c F₄. Muon relaxation shows an anomaly at a remarkably higher temperature T _N ^μSR than the transition temperature determined by neutron Bragg scattering T _N ^ND near the percolation threshold for square lattice (c _p=0.593). The difference between the two temperatures amounts to 50% of T _N ^ND just above c _p. The field cooling effect of DC magnetic susceptibility is appreciable below T _N ^ND while the temperature of the anomaly in AC susceptibility approaches to T _N ^μSR as the frequency is increased. It was concluded that there is a crossover from two-dimensional ordering at T _N ^μSR to three-dimensional ordering at T _N ^ND but the two-dimensional order between T _N ^μSR and T _N ^ND has slow fluctuations due to the fractal structure with a plenty of weak links. This revised version was published online in September 2006 with corrections to the Cover Date.     

Thomson Scattering Applied to a Noisy Radiative Plasma

Thomson scattering with a 1.5 ms long pulse mode 20 J ruby laser has been applied to a radiative argon plasma with electron densities n_e from 2.5 10¹⁹ m^?3 to 1.5 10²⁰ m^?3 and an electron temperature T_e of about 3 eV. Photon counting techniques have been used. The accuracy of n_e and T_e to be reached is about 5% after 10 shots. The signal to noise ratio S/N has been optimized by the use of optical filters and a special purpose grating. The effects of these elements on S/N have been calculated. The entrance angle, transmission and quantum efficiency have also been optimized. A comparison between 5 possible laser systems, including a normal mode and a Q-switched mode ruby laser, has been carried out.     

Atomic Model Calculations of Gain Saturation in the 46.9 nm Line of Ne‐like Ar

The gain saturation in the 46.9 nm line of the Ar⁺⁸ laser is analyzed using an atomic kinetics code. The dependence of the gain (G) on the electron kinetic temperature (T_e) in the region (50 ‐150 eV) is calculated in the quasi steady‐state approximation for the different values of the electron density (N_e) and the plasma radius (r_pl). The influence of radiat on trapping, ion random and mean velocities, Stark line broadening and refraction losses on the gain saturation is taken into consideration. For r_pl = 150‐600 μm, the amplplication (G > 0 cm^‐1) exists in the large temperature/density domain (T_e = 60‐150 eV, N_e = 0.5‐10 × 10¹⁸ cm^‐3). However, the value G_s ∼ 1.4 cm^‐1 required for the gain saturation at the typical plasma length L_pl ∼ 15 cm is reached in the extremely narrow density regions at the high temperatures. The saturation is reached for r_pl = 600 μm at T^s_e = 150 eV in the region N^s_e = 1.8‐2 × 10¹⁸ cm ^‐3, for r_pl = 300 μm at T^s_e = 125 eV and N^s_e = 2.5‐3 × 10¹⁸ cm^‐3, and for r_pl = 150 μm at T^s_e = 110 eV and N^s_e = 3‐4 × 10¹⁸ cm^‐3. The broadest density region (N^s_e = 2 ‐8 × 10¹⁸ cm^‐3) is predicted for the narrowest column (r_pl = 150 μm) at the highest temperature (T^s_e = 150 eV). The operation in the broadest density region N^s_e, should make easier achievement of the gain saturation in the experiments.     

Utilization of rotational and vibrational temperatures for plasma diagnostics of high-pressure discharges

In the spectra of high-pressure discharges excited in molecular gases, very intensive molecular spectral bands may usually be observed. We may determine the rotational and vibrational temperatures without difficulty, however, the rotational and vibrational temperatures (T _r, T_v) do not offen equal to the temperature of neutral gas (T ₀) or to that of electrons (T _e). If the collision cross sections of electronic, atomic, and molecular excitation (deexcitation) are known, we may then calculate the dependence of the rotational and vibrational temperatures onT _e,T ₀,N _e and the pressure of the gas. The calculations have been performed for pure N₂ and for an Ar-N₂ mixture at atmospheric pressure. The computed graphs make it possible to determine some of the values 4T _e,T ₀,N _e if the temperaturesT _r andT _v are known.The author wishes to extend his thanks to Prof. V. Truneek for valuable comments and to Mr. A. Struka for the preparation of the diagrams.     

A comparative study at 3 T of sequence dependence of T2 quantitation in the knee

Objective

T₂ mapping has been used widely in detecting cartilage degeneration in osteoarthritis. Several scanning sequences have been developed in the determination of T₂ relaxation times of tissues. However, the derivation of these times may vary from sequence to sequence. This study seeks to evaluate the sequence-dependent differences in T₂ quantitation of cartilage, muscle, fat and bone marrow in the knee joint at 3 T.

Methods

Three commercial phantoms and 10 healthy volunteers were studied using 3 T MR. T₂ relaxation times of the phantoms, cartilage, muscle, subcutaneous fat and marrow were derived using spin echo (SE), multiecho SE (MESE), fast SE (FSE) with varying echo train length (ETL), spiral and spoiler gradient (SPGR) sequences. The differences between these times were then evaluated using Student's t test. In addition, the signal-to-noise ratio (SNR) efficiency and coefficient of variation of T₂ from each sequence were calculated.

Results

The average T₂ relaxation time was 36.38±5.76 ms in cartilage and 34.08±6.55 ms in muscle, ranging from 27 to 45 ms in both tissues. The times for subcutaneous fat and marrow were longer and more varying, ranging from 41 to 143 ms and from 42 to 160 ms, respectively. In FSE acquisition, relaxation time significantly increases as ETL increases (P<.05). In cartilage, the SE acquisition yields the lowest T₂ values (27.52±3.10 ms), which is significantly lower than those obtained from other sequences (P<.002). T₂ values obtained from spiral acquisition (38.27±6.45 ms) were higher than those obtained from MESE (34.35±5.62 ms) and SPGR acquisition (31.64±4.53 ms). These differences, however, were not significant (P>.05).

Conclusion

T₂ quantification can be a valuable tool for the diagnosis of degenerative disease. Several different sequences exist to quantify the relaxation times of tissues. Sequences range in scan time, SNR efficiency, reproducibility and two- or three-dimensional mapping. However, when choosing a sequence for quantitation, it is important to realize that several factors affect the measured T₂ relaxation time.     

Energy relaxation of electrons in the (100) n-channel of a Si-MOSFET: II. Surface phonon treatment

The electron energy relaxation is investigated as a function of the “electron temperature” T_e in the n-channel of a (100) surface silicon MOSFET device by inspecting the phenomenological energy relaxation time τ_ε(T_e). τ_ε is determined theoretically and compared to experimental results in order to identify the energy relaxation mechanism(s) present at the interface. Two dimensional electron transport is assumed. Single activation temperature (θ) Rayleigh wave scattering and acoustic Rayleigh wave scattering are studied as possible energy loss processes. The effects of electric subbanding near the surface are included. τ_ε is calculated for T_e ? 15 K in the electric quantum limit. We find that a single θ = 12.0 K Rayleigh phonon fits theory to experiment for a single electron inversion density (N_inv) case, but can not provide a fit simultaneously for more than one N_inv value. Theory and experiment disagree when Rayleigh wave acoustic scattering is assumed.     

Cosmology with time-varyingG

It is shown that a Universe with a time-varying gravitational constantG necessarily implies creation if the rest mass of matter particlesm _p is constant. In this case, from Einstein's field equations, the conditions for energy-momentum propagation are ·(GT ^v ) from which matter and photon propagation equations are derived. Free matter particle propagation is not affected by creation that is given byGN _pm_p=const, whereN _p is the number of matter particles within a proper volume. This relation introduces explicitly the rest mass of the Universe into the field equations. Free photon propagation is affected by creation that is given byGT v R=const, whereN is the number of photons within a proper volume, which is the cosmic red shift law. Conservation of the cosmic background photon distribution determines photon creation asG ³ N ⁴ . The results are applied to the caseG t ^–1 equivalent toN _p ÷ t.It is found that at an aget=1, 0^–40 t _o, of the order light takes to travel a proton size, Planck's units become of the order of the proton's massm _p, sizer _p, and timer _p/c. Hence, matter particles at this age are quantum black holes. Evaporation of these quantum black holes at this age gives a background blackbody radiation that, red shifted to present timet ₀, gives the present cosmic microwave background.A cosmological model of the Friedmann type is constructed. The red shift versus distance relation is derived taking into account creation. Using a Hubble's constantH _obs=50 km sec^–1 Mpc^–1 and a deceleration parameterq _obs=1.0 the model is of the typek=1 and gives a present aget ₀=6.81×10⁹ yr, consistent with Uranium model ages. Thus, the three results for the age of the Universe, i.e., radioactive decay, Hubble's constant, and stellar evolution are brought together in this creation model. The matter-dominated era occurs fort>7.6×10^–3 t ₀, while the radiation-dominated era occurs for 7.6×10^–3 t _o>t>10^–40 t _o. The origin of the Universe is placed at this last limit, which is Planck's time at the corresponding G, consisting of quantum black holes at a temperature T_i=3×10¹¹K.