MSE-MRI sequence optimisation for measurement of bi- and tri-exponential T2 relaxation in a phantom and fruit

The transverse relaxation signal from vegetal cells can be described by multi-exponential behaviour, reflecting different water compartments. This multi-exponential relaxation is rarely measured by conventional MRI imaging protocols; mono-exponential relaxation times are measured instead, thus limiting information about of the microstructure and water status in vegetal cells. In this study, an optimised multiple spin echo (MSE) MRI sequence was evaluated for assessment of multi-exponential transverse relaxation in fruit tissues. The sequence was designed for the acquisition of a maximum of 512 echoes. Non-selective refocusing RF pulses were used in combination with balanced crusher gradients for elimination of spurious echoes. The study was performed on a bi-compartmental phantom with known T₂ values and on apple and tomato fruit. T₂ decays measured in the phantom and fruit were analysed using bi- and tri-exponential fits, respectively. The MRI results were compared with low field non-spatially resolved NMR measurements performed on the same samples.     

An investigation of the origins of contrast in NMR spin echo images of plant tissue.

The effects that the spatial distribution of water protons and their transverse relaxation times have on the image contrast of spin echo images of courgette was investigated. The T2-weighted image of courgette contains the most anatomical information. The image contrast was explained using a phenomenological theory based on the Bloch equations, which gave an insight into the morphology and microdynamics of water in the plant tissue. The perceived contrast in the spin echo images of courgette, glucose and Sephadex bead solutions can be dramatically altered by keeping all the imaging acquisition parameters constant, such as the recycle and echo time, but reducing the interpulse spacing by introducing a CPMG train of 180 degrees pulses into the middle of the sequence. These changes were interpreted by considering the microenvironment of the water. This work demonstrates that the origin of image contrast in T2-weighted images of plant tissue can be understood using the water proton transverse relaxation theory developed by Hills et al.     

Frequency (250 MHz to 9.2 GHz) and viscosity dependence of electron spin relaxation of triarylmethyl radicals at room temperature

Electron spin relaxation times for four triarylmethyl (trityl) radicals at room temperature were measured by long-pulse saturation recovery, inversion recovery, and electron spin echo at 250 MHz, 1.5, 3.1, and 9.2 GHz in mixtures of water and glycerol. At 250 MHz T(1) is shorter than at X-band and more strongly dependent on viscosity. The enhanced relaxation at 250 MHz is attributed to modulation of electron-proton dipolar coupling by tumbling of the trityl radicals at rates that are comparable to the reciprocal of the resonance frequency. Deuteration of the solvent was used to distinguish relaxation due to solvent protons from the relaxation due to intra-molecular electron-proton interactions at 250 MHz. For trityl-CD(3), which contains no protons, modulation of dipolar interaction with solvent protons dominates T(1). For proton-containing radicals the relative importance of modulation of intra- and inter-molecular proton interactions varies with solution viscosity. The viscosity and frequency dependence of T(1) was modeled based on dipolar interaction with a defined number of protons at specified distances from the unpaired electron. At each of the frequencies examined T(2) decreases with increasing viscosity consistent with contributions from T(1) and from incomplete motional averaging of anisotropic hyperfine interaction.     

Exploiting the chemical shift displacement effect in the detection of glutamate and glutamine (Glx) with PRESS

A PRESS (Point RESolved Spectroscopy) sequence for the improved detection of the C2 protons of Glx (glutamate and glutamine) at approximately 3.75ppm is presented in this work. It is shown that for spins like the C2 protons of Glx which are involved solely in weak coupling interactions, the chemical shift displacement effect can be turned to advantage by exploiting PRESS refocusing pulses with bandwidths less than the chemical shift difference between the target spins and the spins to which they are weakly coupled. The narrow-bandwidth PRESS sequence allows refocusing of the J-coupling evolution of the target protons in the voxel of interest independently of echo time yielding signal equivalent to that which can be obtained with a one-pulse acquire sequence (assuming ideal pulses and ignoring T2 relaxation). The total echo time of PRESS was set long enough for the decay of macromolecule signal and the two echo times were empirically optimized so that the Glx signal at 3.75ppm suffered minimal contamination from myo-inositol. The efficacy of the method was verified on phantom solutions of Glx and on brain in vivo.     

Another approach to protons with constricted mobility in white matter: pilot studies using wideline and high-resolution NMR spectroscopy

We report a new approach for the identification of an independent method of studying the semi-solid pool of protons, i.e., protons with constrained motion as a result of being bound to lipid and protein matrices. These protons cannot be observed using conventional imaging techniques since their transverse relaxation times are much shorter than the minimum echo times that are currently available on clinical scanners. In this pilot study, in vitro multicomponent transverse relaxation experiments were made on human white matter slices, fixed in formalin (7 normal and 5 with multiple sclerosis). The transverse relaxation decay curves were multiexponential and were decomposed to yield three primary components. The shortest T(2) component that we obtained (a component too short to be seen by in vivo methods) was of the order of microseconds. We hypothesize that this might correspond to the macromolecular pool of lipid protons trapped within the myelin sheaths. To our knowledge, this is the first attempt at extracting this ultra short T(2) component from human white matter. Subsequently, an attempt was made to directly detect the lipid protons in a proton NMR spectrum and, if possible, measure their concentration in some of the tissues, using the technique of magic angle spinning.     

The Use of the Levenberg–Marquardt and Variable Projection Curve-Fitting Algorithm in Intravoxel Incoherent Motion Method for DW-MRI Data Analysis

The objective of this study was to evaluate the performances of different algorithms for diffusion parameters estimation in intravoxel incoherent motion method for diffusion-weighted magnetic resonance imaging (DW-MRI) data analysis. Traditionally, the method of non-linear least squares analysis by means of Levenberg–Marquardt algorithms has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the Variable Projection curve-fitting algorithm and the performance of two non-linear regression methods when single and multiple starting points were used. Analysis was done on simulation data to which different amounts of Gaussian noise had been added. The performance of two non-linear regression methods was compared using the residual sum of squares and the number of failures in data fitting. We conclude that the VarPro algorithm is superior to the LM algorithm for curve fitting in intravoxel incoherent motion method for DW-MRI data analysis.     

A Robust Method for Estimating Cross-Relaxation Rates from Simultaneous Fits to Build-Up and Decay Curves

This paper introduces a novel computational method for estimating relaxation rates among pairs of spin orders. This method simultaneously estimates all the auto- and cross-relaxation rates from the same measurements, and avoids the ill-conditioning problems associated with multiexponential fits. The method models the relaxation dynamics by a system of linear differential equations, and assumes that measurements of the spin orders have been made at an equally spaced sequence of time points. It computes a nonlinear least-squares fit of the exponential of the rate matrix at the shortest time point to these measurements. Preliminary estimates of the exponential matrix and initial spin orders from which to start the computations are obtained by solving simpler linear-least-squares problems. The performance of the method on simulated 2 × 2 test problems indicates that when measurements at eight or more equally spaced times spanning the maximum and inflection points of the build-up curves are available, the relative errors in the rates are usually less than the relative errors in the measurements. The method is further demonstrated by applying it to the problem of determining the cross correlation-induced cross-relaxation rates between the in-phase and antiphase coherence of the amide groups in the¹⁵N-labeled protein oxidized flavodoxin. Finally, the possibility of extending the method to other kinds of relaxation measurements and larger spin systems is discussed.     

Influence of molecular motions on NQR echoes

The influence of thermal molecular motions on spin echo decay in pure nuclear quadrupole resonance (NQR) is considered. Our calculations show that the Hahn echo decay is caused by dipole-dipole interaction of the nuclear spins and is strongly affected by molecular mobility that can lead to the shortening of the echo decay with increased temperature. Slow molecular motion yields an exponential τ₃ time dependence, while fast motion yields an exponential decay. The outlined theory allows us to explain an unusual shortening of the³⁵Cl NQR echo decay on heating in thiourea-C₂Cl₆ inclusion compound.     

Characterization of ZnO and Zn0.95Co0.05O prepared by sol-gel method using PAC spectroscopy

We report on the first NMR study of ⁷³Ge nuclear spin decoherence in germanium single crystals with different abundance of the ⁷³Ge isotope. Hahn echo decays are well fit by a superposition of two exponentials. The deviation from the single exponential is more pronounced in the more spin-diluted sample, causing long-lived echoes. We show that the decay of these echoes becomes slower with the reduction of ⁷³Ge abundance and is therefore caused by dipole–dipole interaction, reflecting the fundamental decoherence process in the spin system. The fast decay at the beginning of the relaxation process is shown to be mainly caused by the quadrupole interaction. Our experimental findings are supported by the calculations of Hahn echo decays in the germanium crystals under study. Quite good agreement between the theory and experiment is demonstrated.     

Echo-spacing optimization for the simultaneous measurement of reversible (R2') and irreversible (R2) transverse relaxation rates

Accurate measurement of reversible (R2') and irreversible (R2) transverse relaxation rates plays a key role in various magnetic resonance imaging research and applications. Although optimization of echo spacing for a multiecho pulse sequence measuring a single exponential decay has been investigated, optimization in sequences such as Gradient-Echo Sampling of Free Induction Decay and Echo (GESFIDE), in which two echo trains are simultaneously measured to obtain both R2 and R2', has not been reported. In this work, optimum echo spacings for the GESFIDE sequence are determined to improve the accuracy of measured relaxation parameters. Various relaxation rates and the number of acquired echoes are considered, as well as whether the receiver bandwidth is kept fixed or is varied with echo spacing. In the case of constant receiver bandwidth, results show that the echo train length approximately equal to T2* should be used for each echo train in GESFIDE to minimize uncertainty in R2 or R2'. If the receiver bandwidth is allowed to change with echo spacing in order to maximize the image signal-to-noise ratio, the optimum echo train length will vary, generally increasing with the number of echoes.     

Water phases in rat striated muscles as determined by T2 proton NMR relaxation times

The spin echo decay curve of NMR protons in in-vitro rat muscle is two or three exponential as Hazlewood demonstrated in 1974. This author hypothesized that the longer T2 component is extracellular water and that the medium T2 is intracellular water. Our purpose was to test the histological significance of these two T2. Variations of water contents in two types of rat muscles were induced by electrical stimulation and osmotic diuresis and their incidence on the decomposition of the proton spin echo signal analysed. Decomposition of signal in resting muscles revealed two phases with T2 values similar to the Hazlewood's: a short phase, S, with T2 of 40 ms (20 MHz, 276 degrees K) representing 90-97% of the total signal and a long one, L, with T2 of 100-120 ms representing 3-10% of the signal. Increasing vascular volume appeared to increase the percentage of phase (L) in the total signal. Osmotic diuresis decreased the volume of the phase (S) and increased the volume of the phase (L). The use of Gd-DTPA allowed to differentiate the vascular compartment: Gd DTPA decreased in a great extent the T2 values of phase (L) and in low extent the T2 values of phases (S). From these results, it appears that phase (L) could correspond to vascular volume and that phase (S) would be interstitial and intracellular water. Elements of comparison with classical methods for determination of water compartmentation in tissues are given.     

Comparative analysis of pulsed electron spin resonance spectrometers at X-band and S-band

Comparative analysis of pulsed electron spin resonance spectroscopy at X-band and at S-band indicates that despite the lower sensitivity at the lower frequency, electron spin echo spectroscopy at S-band provides valuable information on the electron-nuclear interactions in systems where the electron spin echo modulation is too small to study well at X-band. It is shown that independent experimental data on electron spin echo modulation and decay at both X-band and S-band put additional constraints on the structural parameters obtained by comparison of experimental and simulated nuclear modulation patterns, and can also help to elucidate the electron spin relaxation mechanism.     

Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

The dependence of nuclear magnetic resonance (NMR) image contrast on intrinsic and pulse sequence timing parameters

In Nuclear Magnetic Resonance (NMR) the image pixel value is governed by at least three major intrinsic parameters: the spin density N (H), the spin-lattice relaxation time T1, and the spin-spin relaxation time T2. The extent to which the signal is weighted toward one or several parameters is related to the history of the spin system preceding detection. On the simplifying, though not generally warranted assumption that the spin density does not vary significantly in soft tissues, relative tissue contrast can be predicted quantitatively provided the relaxation times are known. Signal intensities and contrast were computed on the basis of the Bloch equations and experimentally determined relaxation times as a function of pulse timing parameters and the data compared with those in images recorded at 0.5T field strength. Significant deviations from the equal density hypothesis were found for gray and white substance. Notably partial saturation but also spin echo and inversion-recovery images are not in full accordance with predictions made on the basis of relaxation times alone.     

Dephasing of a superconducting flux qubit

In order to gain a better understanding of the origin of decoherence in superconducting flux qubits, we have measured the magnetic field dependence of the characteristic energy relaxation time (T(1)) and echo phase relaxation time (T(2)(echo)) near the optimal operating point of a flux qubit. We have measured T(2)(echo) by means of the phase cycling method. At the optimal point, we found the relation T(2)(echo) approximately 2T(1). This means that the echo decay time is limited by the energy relaxation (T(1) process). Moving away from the optimal point, we observe a linear increase of the phase relaxation rate (1/T(2)(echo)) with the applied external magnetic flux. This behavior can be well explained by the influence of magnetic flux noise with a 1/f spectrum on the qubit.     

What Are the Conditions for Exponential Time-Cubed Echo Decays?

Diffusion of precessing spins through a constant field gradient is well-known to produce two distinctive features: an exp(-bt(3)) decay of the echo amplitude in response to two pulses and a much slower decay of the Carr-Purcell echo train. These features will appear whenever the spin frequency is described by a continuous random-walk. The present work shows that this may also occur in the presence of motions with long correlation times tau(c)-continuous Gaussian frequency noise with an exponential autocorrelation has the correct properties over time durations smaller than tau(c). Thus, time-cubed echo decays will occur in situations other than physical diffusion. The decay rate of the Carr-Purcell echo train is shown to vary with the pulse spacing tau whenever the correlation time tau(c) is long; the slower Carr-Purcell decay compared to the two-pulse echo decay is not unique to diffusion. Simulations are presented that display time-cubed decays. The simulations confirm two important criteria: the echo time must be less than tau(c) and the frequency noise must consist of nearly continuous variations, as opposed to step-like changes. These criteria define the range of physical parameters for which time-cubed decays will be observable.     

Transient NMR/ON of56CoFe

Adiabatic Fast Passage NMR/ON measurements on single crystal⁵⁶CoFe indicate a unique electric field gradient when the applied field is parallel to the 100 direction.A well defined spin echo has been observed with pulsed NMR/ON using the 847 keV gamma and the echo amplitude decay followed for pulse separations out to 75 ms. The decay of the echo is non exponential, being essentially constant for pulse separations of 75 s, 750 s and 7.5 ms. The echo is significantly attenuated at 75 ms. This may be contrasted with an effective nuclear spin lattice relaxation time of T ₁ 30 s.     

Magnetic field- and concentration-dependent photon echo relaxation in ruby with simple exponential decay

Magnetic field- and concentration-dependent, simple exponential photon echo decay in ruby is observed in apparent disagreement with previous work. Similar results are obtained with electron spin echoes.     

Single-slice mapping of ultrashort T(2)

In this communication we present a method for single-slice mapping of ultrashort transverse relaxation times T(2). The RF pulse sequence consists of a spin echo preparation of the magnetization followed by slice-selective ultrashort echo time (UTE) imaging with radial k-space sampling. In order to keep the minimum echo time as small as possible, avoid out-of-slice contamination and signal contamination due to unwanted echoes, the implemented pulse sequence employs a slice-selective 180° RF refocusing pulse and a 4-step phase cycle. The slice overlap of the two slice-selective RF pulses was investigated. An acceptable Gaussian slice profile could be achieved by adjusting the strength of the two slice-selection gradients. The method was tested on a short T(2) phantom consisting of an arrangement of a roll of adhesive tape, an eraser, a piece of modeling dough made of Plasticine?, and a 10% w/w agar gel. The T(2) measurements on the phantom revealed exponential signal decays for all samples with T(2)(adhesive tape)=(0.5 ± 0.1)ms, T(2)(eraser)=(2.33 ± 0.07)ms, T(2)(Plasticine?)=(2.8 ± 0.06)ms, and T(2)(10%agar)=(9.5 ± 0.83)ms. The T(2) values obtained by the mapping method show good agreement with the T(2) values obtained by a non-selective T(2) measurement. For all samples, except the adhesive tape, the effective transverse relaxation time T(2)(?) was significantly shorter than T(2). Depending on the scanner hardware the presented method allows mapping of T(2) down to a few hundreds of microseconds. Besides investigating material samples, the presented method can be used to study the rapidly decaying MR-signal from biological tissue (e.g.: bone, cartilage, and tendon) and quadrupolar nuclei (e.g.: (23)Na, (35)Cl, and (17)O).     

Constrained modeling for spectroscopic measurement of bi-exponential spin-lattice relaxation of water in vivo

The (1)H NMR water signal from spectroscopic voxels localized in gray matter contains contributions from tissue and cerebral spinal fluid (CSF). A typically weak CSF signal at short echo times makes separating the tissue and CSF spin-lattice relaxation times (T(1)) difficult, often yielding poor precision in a bi-exponential relaxation model. Simulations show that reducing the variables in the T(1) model by using known signal intensity values significantly improves the precision of the T(1) measurement. The method was validated on studies on eight healthy subjects (four males and four females, mean age 21 +/- 2 years) through a total of twenty-four spectroscopic relaxation studies. Each study included both T(1) and spin-spin relaxation (T(2)) experiments. All volumes were localized along the Sylvian fissure using a stimulated echo localization technique with a mixing time of 10 ms. The T(2) experiment consisted of 16 stimulated echo acquisitions ranging from a minimum echo time (TE) of 20 ms to a maximum of 1000 ms, with a repetition time of 12 s. All T(1) experiments consisted of 16 stimulated echo acquisition, using a homospoil saturation recovery technique with a minimum recovery time of 50 ms and a maximum 12 s. The results of the T(2) measurements provided the signal intensity values used in the bi-exponential T(1) model. The mean T(1) values when the signal intensities were constrained by the T(2) results were 1055.4 ms +/- 7.4% for tissue and 5393.5 ms +/- 59% for CSF. When the signal intensities remained free variables in the model, the mean T(1) values were 1085 ms +/- 19.4% and 5038.8 ms +/- 113.0% for tissue and CSF, respectively. The resulting improvement in precision allows the water tissue T(1) value to be included in the spectroscopic characterization of brain tissue.