Measuring T₂ and T₁, and imaging T₂ without spin echoes

During adiabatic excitation, the nuclear magnetization in the transverse plane is subject to T(2) (spin-spin) relaxation, depending on the pulse length τ. Here, this property is exploited in a method of measuring T(2) using the ratio of NMR signals acquired with short and long-duration self-refocusing adiabatic pulses, without spin-echoes. This Dual-τ method is implemented with B(1)-insensitive rotation (BIR-4) pulses. It is validated theoretically with Bloch equation simulations independent of flip-angle, and experimentally in phantoms. Dual-τT(2) measurements are most accurate at short T(2) where results agree with standard spin-echo measures to within 10% for T(2) ≤ 100 ms. Dual-τ MRI performed with a long 0° BIR-4 pre-pulse provides quantitative T(2) imaging of phantoms and the human foot while preserving desired contrast and functional properties of the rest of the MRI sequence. A single 0° BIR-4 pre-pulse can provide T(2) contrast-weighted MRI and serve as a "T(2)-prep" sequence with a lower B(1) requirement than prior approaches. Finally, a Tri-τ experiment is introduced in which both τ and flip-angle are varied, enabling measurement of T(2), T(1) and signal intensity in just three acquisitions if flip-angles are well-characterized. These new methods can potentially save time and simplify relaxation measurements and/or contrast-weighted NMR and MRI.     

An improved 3-D Look--Locker imaging method for T(1) parameter estimation

The 3-D Look-Locker (LL) imaging method has been shown to be a highly efficient and accurate method for the volumetric mapping of the spin lattice relaxation time T(1). However, conventional 3-D LL imaging schemes are typically limited to small tip angle RF pulses (5 degrees ), thereby improving the SNR and the accuracy of the method. In phantom studies, a mean T(1) measurement accuracy of less than 2% (0.2-3.1%) using a tip angle of 10 degrees was obtained for a range of T(1) from approximately 300 to 1,700 ms with a measurement time increase of only 15%. This accuracy compares favorably with the conventional 3-D LL method that provided an accuracy between 2.2% and 7.3% using a 5 degrees flip angle.     

Two-level systems with relaxation

A method is presented for the coherent control of two-level systems when T2 relaxation is significant. The Bloch equations are rewritten as an equation of motion of the stereographic projection, Gamma, of the spin vector. This allows a Schur-type iteration used for the design of shaped pulses in magnetic resonance and coherent optics to be extended to include the effect of T2. In general, the effect of T2 on Gamma cannot be completely compensated for, although in practice it can be to a high degree. An example is presented of a driving field that produces a coherent superposition (no on-diagonal elements of the density matrix) over a chosen band of frequencies, in the presence of relaxation.     

Fast and simultaneous measurement of longitudinal and transverse NMR relaxation times in a single continuous wave free precession experiment

The purpose of this communication is to describe a method for rapid and simultaneous determination of longitudinal (T1) and transversel (T2) relaxation times, based on a single continuous wave free precession (CWFP) experiment which employs RF pulses with a pi/2 flip angle. We analyze several examples, involving nuclei such as 1H, 31P, and 19F, where good agreement with T1 and T2 measurements obtained by traditional methods is apparent. We also compare with the more time-consuming steady-state free precession (SSFP) method of Kronenbitter and Schwenk where several experiments are needed to determine the optimum flip angle. The role of an inhomogeneous magnetic field on the observed decays and its effect upon the accuracy of relaxation times obtained by these methods is examined by comparing numerical simulations with experimental data. Possible sources of error and conditions to minimize its effects are described.     

Slice profile optimization in arterial spin labeling using presaturation and optimized RF pulses

OBJECTIVE: An important source of error in arterial spin labeling (ASL) is incomplete static tissue subtraction due to imperfect slice profiles. This effect can be reduced by saturating the spins in the imaging area prior to labeling. In this study, the use of optimized presaturation is compared with the use of optimized RF pulses for minimizing this error. MATERIALS AND METHODS: Different methods for optimizing presaturation were simulated by numerical solution of the Bloch equation. Presaturation was optimized by changing the number of presaturation pulses, their position in the pulse sequence and the area of the crusher gradients following each saturation pulse. It was also investigated whether the use of optimized presaturation could reduce the tag gap needed to ensure complete static tissue subtraction. Simulation results were verified using phantom and in vivo studies at 3T. RESULTS: In proximal inversion with control for off-resonance effects, optimized presaturation could reduce the necessary tag gap to 15% of the imaging slab for experiments using standard RF pulses, while c-FOCI RF pulses could reduce it to 11%. In flow-sensitive alternating inversion recovery, a single presaturation pulse could reduce the inversion width to 122% of the imaging slab and neither multiple presaturation pulses nor optimized RF pulses could reduce it further. CONCLUSION: Optimized presaturation can reduce the necessary inversion width to the same level as if using optimized RF pulses and can, therefore, be used to optimize ASL sensitivity. Furthermore, optimized presaturation can reduce the B(1)-dependent sensitivity in static tissue subtraction.     

Low-power MRI by Frank-sequence excitation

Recently, a new NMR method employing an rf excitation scheme with strongly reduced power has been introduced, which is based on modulating rf pulses according to Frank sequences. For many applications, a reduction of rf power is essential, e.g. to eliminate bulky rf pre-amplifiers or in medical high-field MRI to preserve patient safety. Another benefit of the new scheme are very short dead times allowing for measurements of samples with short relaxation times. In this work, Frank-sequence excitation is used for low-power imaging for the first time. Results of one-, two-, and three-dimensional imaging experiments are presented and compared to conventional images.     

Spin-lock techniques and CPMG imaging sequences: a critical appraisal of T1p contrast at 0.15 T

The addition of a spin-lock preparatory sequence to a Carr-Purcell-Meiboom-Gill (CPMG) imaging sequence provides a method which allows an accurate and simple comparison of T1p and T2 contrast. Sagittal and axial brain images, produced with the application of a three pulse preparatory spin-lock sequence prior to a sixteen-echo CPMG imaging sequence, are compared with images acquired without the spin-lock sequence. The CPMG sequence uses non-selective refocusing pulses. Therefore, observed echo signals accurately reflect T2 relaxation. This allows a convenient method for assessing the degree to which T1p and T2 contrast differ. The spin-lock CPMG (SL-CPMG) images were acquired with a spin-locking field amplitude of 0.4 G and resemble heavily T2-weighted images at 0.15 T. Quantitative analyses of signal intensities from edema and normal brain tissue confirm the qualitative observations. This in vivo method should prove useful for determining when the additional RF power deposition associated with spin-locking techniques will provide an alternate form of tissue contrast than that available from additional echo collection.     

Relaxation dispersion in MRI induced by fictitious magnetic fields

A new method entitled Relaxation Along a Fictitious Field (RAFF) was recently introduced for investigating relaxations in rotating frames of rank ≥ 2. RAFF generates a fictitious field (E) by applying frequency-swept pulses with sine and cosine amplitude and frequency modulation operating in a sub-adiabatic regime. In the present work, MRI contrast is created by varying the orientation of E, i.e. the angle ε between E and the z″ axis of the second rotating frame. When ε > 45°, the amplitude of the fictitious field E generated during RAFF is significantly larger than the RF field amplitude used for transmitting the sine/cosine pulses. Relaxation during RAFF was investigated using an invariant-trajectory approach and the Bloch-McConnell formalism. Dipole-dipole interactions between identical (like) spins and anisochronous exchange (e.g., exchange between spins with different chemical shifts) in the fast exchange regime were considered. Experimental verifications were performed in vivo in human and mouse brain. Theoretical and experimental results demonstrated that changes in ε induced a dispersion of the relaxation rate constants. The fastest relaxation was achieved at ε ≈ 56°, where the averaged contributions from transverse components during the pulse are maximal and the contribution from longitudinal components are minimal. RAFF relaxation dispersion was compared with the relaxation dispersion achieved with off-resonance spin lock T(?ρ) experiments. As compared with the off-resonance spin lock T(?ρ) method, a slower rotating frame relaxation rate was observed with RAFF, which under certain experimental conditions is desirable.     

Selective imaging of biofilms in porous media by NMR relaxation.

Nuclear magnetic resonance imaging (NMRI) techniques were employed to identify and selectively image biological films (biofilm) growing in aqueous systems. Biofilms are shown to affect both the longitudinal (T1) and transverse (T2) NMR relaxation time values of proximal water hydrogens. Results are shown for biofilm growth experiments performed in a transparent parallel-plate reactor. A comparison of biofilm distributions by both NMR and optical imaging yielded general agreement for both an open-flow system and an idealized porous system (the reactor without and with packed glass beads, respectively). The selective imaging of biofilm by relaxation NMRI is dependent upon the resolution of relaxation times for the fluid phases, dynamic range, and signal-to-noise ratio. For open-flow systems, the use of a rapid and quantitative T2-sorted NMRI technique was preferred. For porous systems where T2 values are generally more similar, a T1-weighted technique was preferred.     

Generalized equation for describing the magnetization in spoiled gradient-echo imaging

The purpose of this study was to demonstrate a generalized equation for describing the magnetization in spoiled gradient-echo (SPGR) imaging in which the in-pulse relaxation and magnetization transfer (MT) effects are taken into account. First, the time-dependent Bloch equations for the two-pool exchange model with MT effect were reduced to an inhomogeneous linear differential equation, and then a simple equation was derived to solve it using a matrix operation. Second, the equations describing the magnetization before and after the radiofrequency (RF) pulse were derived based on the above solution for the RF-pulse excitation and evolution phases. Finally, a generalized equation describing the steady-state magnetization was derived. The validity of this equation was investigated by comparing with the transverse magnetization obtained by the regular Ernst equation and analytical solution in which the in-pulse transverse relaxation is considered. When the same assumption was made in our method, there were good agreements between them, indicating the validity of our method. The in-pulse transverse and longitudinal relaxations decreased the transverse magnetization compared to the case in which these effects were neglected, whereas MT increased it. In conclusion, we derived a generalized equation for describing the magnetization in SPGR imaging. This equation will provide a suitable basis for understanding the signal intensity in SPGR imaging and/or T₁ measurement using an SPGR sequence in cases in which the effect of in-pulse relaxation and/or MT cannot be neglected.     

Construction of phase cycles of minimum cycle length: MakeCycle

A magnetic resonance imaging method is presented for imaging of heterogeneous broad linewidth materials. This method allows for distortionless relaxation weighted imaging by obtaining multiple phase encoded k-space data points with each RF excitation pulse train. The use of this method, turbo spin echo single-point imaging-(turboSPI), leads to decreased imaging times compared to traditional constant-time imaging techniques, as well as the ability to introduce spin-spin relaxation contrast through the use of longer effective echo times. Imaging times in turboSPI are further decreased through the use of low flip angle steady-state excitation. Two-dimensional images of paramagnetic doped agarose phantoms were obtained, demonstrating the contrast and resolution characteristics of the sequence, and a method for both amplitude and phase deconvolution was demonstrated for use in high-resolution turboSPI imaging. Three-dimensional images of a partially water-saturated porous volcanic aggregate (T(2L) approximately 200 ms, Deltanu(1/2) approximately 2500 Hz) contained in a hardened white Portland cement matrix (T(2L) approximately 0.5 ms, Deltanu(1/2) approximately 2500 Hz) and a water-saturated quartz sand (T(2) approximately 300 ms, T(2)(*) approximately 800 microseconds) are shown.     

Magnetization-recovery experiments for static and MAS-NMR of I=3/2 nuclei

Multifrequency pulsed NMR experiments on quadrupole-perturbed I=3/2 spins in single crystals are shown to be useful for measuring spin-lattice relaxation parameters even for a mixture of quadrupolar plus magnetic relaxation mechanisms. Such measurements can then be related to other MAS-NMR experiments on powders. This strategy is demonstrated by studies of (71)Ga and (69)Ga (both I=3/2) spin-lattice relaxation behavior in a single-crystal (film) sample of gallium nitride, GaN, at various orientations of the axially symmetric nuclear quadrupole coupling tensor. Observation of apparent single-exponential relaxation behavior in I=3/2 saturation-recovery experiments can be misleading when individual contributing rate processes are neglected in the interpretation. The quadrupolar mechanism (dominant in this study) has both a single-quantum process (T(1Q1)) and a double-quantum process (T(1Q2)), whose time constants are not necessarily equal. Magnetic relaxation (in this study most likely arising from hyperfine couplings to unpaired delocalized electron spins in the conduction band) also contributes to a single-quantum process (T(1M)). A strategy of multifrequency irradiation with observation of satellite and/or central transitions, incorporating different initial conditions for the level populations, provides a means of obtaining these three relaxation time constants from single-crystal (71)Ga data alone. The (69)Ga results provide a further check of internal consistency, since magnetic and quadrupolar contributions to its relaxation scale in opposite directions compared to (71)Ga. For both perpendicular and parallel quadrupole coupling tensor symmetry axis orientations small but significant differences between T(1Q1) and T(1Q2) were measured, whereas for a tensor symmetry axis oriented at the magic-angle (54.74 degrees ) the values were essentially equal. Magic-angle spinning introduces a number of complications into the measurement and interpretation of the spin-lattice relaxation. Comparison of (71)Ga and (69)Ga MAS-NMR saturation-recovery curves with both central and satellite transitions completely saturated by a train of 90 degrees pulses incommensurate with the rotor period provides the simplest means of assessing the contribution from magnetic relaxation, and yields results for the quadrupolar mechanism contribution that are consistent with those obtained from the film sample.     

通过高斯加权的1H CPMG弛豫曲线测定橡胶交联密度

CPMG（Carr-Purcell-Meiboom-Gill）回波法是测量橡胶交联密度[常用交联点之间的分子量（M_c）表示]的一种常用核磁共振（NMR）技术,但实验发现通过该技术获得的M_c对于CPMG序列中脉冲间隔时间具有较强的依赖性,导致交联密度NMR测量值与橡胶材料硬度的相关性低.为了克服这一缺点,本文对不同脉冲间隔时间下CPMG实验测得的质子横向驰豫曲线进行高斯加权.通过对高斯加权求和后的质子横向驰豫曲线进行处理分析,实现了对橡胶交联密度更加准确地测量,大幅提升了天然橡胶交联密度NMR测量值与材料硬度的相关性.本文方案测量能获得与¹H DQ NMR方法相当,或比之更佳的交联密度-硬度相关性.同时,本文方案比¹H DQ NMR方法更为高效,整体测量时间缩短为¹H DQ NMR实验时间的1/10.     

Measurement of the order-parameter relaxation in superconducting Al-strips

The voltage response of superconducting aluminium strips to short current pulses above the critical current is measured. Our measurements can quantitatively be interpreted by order-parameter relaxation described by a TDGL equation. Heat dissipation does not affect these experiments.     

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Semi-adiabatic Shinnar–Le Roux pulses and their application to diffusion tensor imaging of humans at 7T

The adiabatic Shinnar–Le Roux (SLR) algorithm for radiofrequency (RF) pulse design enables systematic control of pulse parameters such as bandwidth, RF energy distribution and duration. Some applications, such as diffusion-weighted imaging (DWI) at high magnetic fields, would benefit from RF pulses that can provide greater B₁ insensitivity while adhering to echo time and specific absorption rate (SAR) limits. In this study, the adiabatic SLR algorithm was employed to generate 6-ms and 4-ms 180° semi-adiabatic RF pulses which were used to replace the refocusing pulses in a twice-refocused spin echo (TRSE) diffusion-weighted echo planar imaging (DW-EPI) sequence to create two versions of a twice-refocused adiabatic spin echo (TRASE) sequence. The two versions were designed for different trade-offs between adiabaticity and echo time. Since a pair of identical refocusing pulses is applied, the quadratic phase imposed by the first is unwound by the second, preserving the linear phase created by the excitation pulse. In vivo images of the human brain obtained at 7 Testa (7 T) demonstrate that both versions of the TRASE sequence developed in this study achieve more homogeneous signal in the diffusion-weighted images than the conventional TRSE sequence. Semi-adiabatic SLR pulses offer a more B₁-insensitive solution for diffusion preparation at 7 T, while operating within SAR constraints. This method may be coupled with any EPI readout trajectory and parallel imaging scheme to provide more uniform coverage for diffusion tensor imaging at 7 T and 3 T.     

Analysis of longitudinal relaxation rate constants from magnetization transfer MR images of human tissues at 0.1 T.

The human calf muscle was examined by using the magnetization transfer MR imaging technique. The time-dependent saturation transfer (TDST) method was applied at low magnetic field 0.1 T in order to measure the mobile water relaxation time T1w, the magnetization transfer rate Rwm from water to solid macromolecules, and the magnetization transfer contrast (MTC) of the human tissue. The magnetization transfer contrast of 0.67 was attained. The transfer rate Rwm was 4.5 sec-1 (+/- 0.3 sec-1) for the anterior tibial muscle and 5.0 sec-1 (+/- 0.4 sec-1) for the gastrocnemius muscles. The values of Rwm are considerably larger than the values of corresponding relaxation rates measured at high fields. The relaxation rate measurements of human tissues in vivo was shown to be possible at 0.1 T even within the framework of normal routine MR imaging. Magnetization transfer MR imaging is a very promising and practical method in order to assess the relaxation processes in heterogeneous human tissues in vivo, and it can improve the tissue characterization possibilities of MR imaging techniques.     

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).     

Relaxation of hyperpolarized 129Xe in a deflating polymer bag

In magnetic resonance imaging with hyperpolarized (HP) noble gases, data is often acquired during prolonged gas delivery from a storage reservoir. However, little is known about the extent to which relaxation within the reservoir will limit the useful acquisition time. For quantitative characterization, 129Xe relaxation was studied in a bag made of polyvinyl fluoride (Tedlar). Particular emphasis was on wall relaxation, as this mechanism is expected to dominate. The HP 129Xe magnetization dynamics in the deflating bag were accurately described by a model assuming dissolution of Xe in the polymer matrix and dipolar relaxation with neighboring nuclear spins. In particular, the wall relaxation rate changed linearly with the surface-to-volume ratio and exhibited a relaxivity of κ=0.392±0.008 cm/h, which is in reasonable agreement with κ=0.331±0.051 cm/h measured in a static Tedlar bag. Estimates for the bulk gas-phase 129Xe relaxation yielded T1bulk=2.55±0.22 h, which is dominated by intrinsic Xe-Xe relaxation, with small additional contributions from magnetic field inhomogeneities and oxygen-induced relaxation. Calculations based on these findings indicate that relaxation may limit HP 129Xe experiments when slow gas delivery rates are employed as, for example, in mouse imaging or vascular infusion experiments.     

Fat-water selective excitation in balanced steady-state free precession using short spatial-spectral RF pulses

Fat suppression is important but challenging in balanced steady-state free precession (bSSFP) acquisitions, for a number of clinical applications. In the present work, the practicality of performing fat-water selective excitations using spatial-spectral (SPSP) RF pulses in bSSFP sequence is examined. With careful pulse design, the overall duration of these SPSP pulses was kept short to minimize detrimental effects on TR, scan time and banding artifact content. Fat-water selective excitation using SPSP pulses was demonstrated in both phantom and human bSSFP imaging at 3T, and compared to results obtained using a two-point Dixon method. The sequence with SPSP pulses performed better than the two-point Dixon method, in terms of scan time and suppression performance. Overall, it is concluded here that SPSP RF pulses do represent a viable option for fat-suppressed bSSFP imaging.