A simplified formula for T1 contrast optimization for short-TR steady-state incoherent (spoiled) gradient echo sequences

There are certain instances in practical magnetic resonance imaging where T₁ changes by a small amount relative to a neighboring pixel or between scans for a given pixel. The source of these small changes in T₁ can be caused either by changes in tissue water content or by the uptake of a contrast agent. For short repetition time (TR) spoiled gradient echo imaging, we show that a robust and a simple, easy to use back-of-the-envelope expression for the flip angle that optimizes contrast under these conditions is given by √3θ_E in radians or (180/π)√6TR/T₁ in degrees. We show that for a TR/T₁ ratio of up to 0.3 and for a T₁ change of up to ±50%, this approximation to the optimal flip angle produces a contrast to within 6% of the theoretical maximum value and that these predictions are in good agreement with experiment.     

MRI measurements of the dependence on T1 of the echo amplitudes using a multiple spin-echo scheme

Analytical calculations using the Bloch formalism were performed to assess the dependence on T₁ of the echo amplitudes for the Phase-Alternating Phase-Shift (PHAPS) multiple spin-echo protocol. Measurements in a 0.5 T MR imaging unit were performed to ratify the analytical results. especially for low T₂ values, the echo amplitudes were erroneous, with an increasing contribution from stimulated echo components with increasing T₁. Apart from affecting T₂ estimates, stimulated echoes generated a non-monoexponential signal decay of the echo trains. The results confirmed previous simulation studies as regards the dependence on T₁ of T₂ estimates from PHAPS.     

In vivo quantification of citrate concentration and water T2 relaxation time of the pathologic prostate gland using H MRS and MRI

We have previously reported a striking correlation between water T₂ relaxation time and citrate concentration in the normal prostate (Liney G.P.; Lowry M.; Turnbull L.W.; Manton D.J.; Knowles A.J.; Blackband S.J.; Horsman A. Proton MR T₂ maps correlate with the citrate concentration in the prostate. NMR Biomed. 9:59–64; 1996). In this study we present data from similar studies of the pathologic gland. The findings support the hypothesis that measurement of both citrate concentration and water T₂ relaxation time in vivo may aid the differentiation of prostatic carcinoma from benign disease and normal tissue.     

Establishing norms for age-related changes in proton T1 of human brain tissue in vivo

The goal of this study was to determine the expected normal range of variation in spin-lattice relaxation time (T₁) of brain tissue in vivo, as a function of age. A previously validated precise and accurate inversion recovery method was used to map T₁ transversely, at the level of the basal ganglia, in a study population of 115 healthy subjects (ages 4 to 72; 57 male and 58 female). Least-squares regression analysis shows that T₁ varied as a function of age in pulvinar nucleus (R² = 56%), anterior thalamus (R² = 51%), caudate (R² = 50%), frontal white matter (R² = 47%), optic radiation (R² = 39%), putamen (R² = 36%), genu (R² = 22%), occipital white matter (R² = 20%) (all p < 0.0001), and cortical gray matter (R² = 53%) (p < 0.001). There were no significant differences in T₁ between men and women. T₁ declines throughout adolescence and early adulthood, to achieve a minimum value in the fourth to sixth decade of life, then T₁ begins to increase. Quantitative magnetic resonance imaging provides evidence that brain tissue continues to change throughout the lifespan among healthy subjects with no neurologic deficits. Age-related changes follow a strikingly different schedule in different brain tissues; white matter tracts tend to reach a minimum T₁ value, and to increase again, sooner than do gray matter tracts. Such normative data may prove useful for the early detection of brain pathology in patients.     

Measurement of Hartmann-Hahn cross-polarization dynamics with quenching of proton T1ρ relaxation dependence

A simple modification of the standard cross-polarization method designed for quenching the proton T_1ρ dependence when studying polarization transfer is presented. It is demonstrated that by using this simple procedure, new and subtle details of cross-polarization dynamics, previously hidden by the T_1ρ(¹H) effect, can be observed in dipolar-coupled spin systems.     

Phase-alternated compositeπ/2 pulses for solid state quadrupole echo NMR spectroscopy

Phase-alternated compositeπ/2 pulses have been constructed for spinI=1 to overcome quadrupole interaction effects in solid state nuclear magnetic resonance (NMR) spectroscopy. Magnus expansion approach is used to design these sequences in a manner similar to the NMR coherent averaging theory. It is inferred that the symmetric phase-alternated compositeπ/2 pulses reported here are quite successful in producing quadrupole echo free from phase distortions. This effectiveness of the present composite pulses is due to the fact that most of them are of shorter durations as compared to the ones reported in literature. In this theoretical procedure, irreducible spherical tensor operator formalism is employed to simplify the complexity involved in the evaluation of Magnus expansion terms. It has been argued in this paper that compositeπ/2 pulse sequences for this purpose can also be derived from the broadband inversionπ pulses which are designed to compensate electric field gradient (efg) inhomogeneity in spinI=1 nuclear quadrupole resonance (NQR) spectroscopy.     

Continuous-Wave Magnetic Resonance Imaging of Short T2 Materials

There is growing interest in the use of magnetic resonance imaging (MRI) to examine solid materials where the restricted motion of the probed spins leads to broad lines and short T₂ values, rendering many interesting systems invisible to conventional 2DFT pulsed imaging methods. In EPR T₂ seldom exceeds 0.1 μs and continuous-wave methods are adopted for spectroscopy and imaging. In this paper we demonstrate the use of continuous-wave MRI to obtain 2-dimensional images of short T₂ samples. The prototype system can image samples up to 50 mm in diameter by 60 mm long and has been used to image polymers and water penetration in porous media. Typical acquisition times range between 10 and 40 min. Resolution of 1 to 2 mm has been achieved for samples with T₂ values ranging from 38 to 750 μs. There is the possibility of producing image contrast that is determined by the material properties of the sample.     

Optimal echo spacing for multi-echo imaging measurements of Bi-exponential T2 relaxation

Calculations, analytical solutions, and simulations were used to investigate the trade-off of echo spacing and receiver bandwidth for the characterization of bi-exponential transverse relaxation using a multi-echo imaging pulse sequence. The Cramer–Rao lower bound of the standard deviation of the four parameters of a two-pool model was computed for a wide range of component T₂ values and echo spacing. The results demonstrate that optimal echo spacing (TE_opt) is not generally the minimal available given other pulse sequence constraints. The TE_opt increases with increasing value of the short T₂ time constant and decreases as the ratio of the long and short time constant decreases. A simple model of TE_opt as a function of the two T₂ time constants and four empirically derived scalars is presented.     

T1–T2 Correlation Spectra Obtained Using a Fast Two-Dimensional Laplace Inversion

Spin relaxation is a sensitive probe of molecular structure and dynamics. Correlation of relaxation time constants, such as T₁ and T₂, conceptually similar to the conventional multidimensional spectroscopy, have been difficult to determine primarily due to the absense of an efficient multidimensional Laplace inversion program. We demonstrate the use of a novel computer algorithm for fast two-dimensional inverse Laplace transformation to obtain T₁–T₂ correlation functions. The algorithm efficiently performs a least-squares fit on two-dimensional data with a nonnegativity constraint. We use a regularization method to find a balance between the residual fitting errors and the known noise amplitude, thus producing a result that is found to be stable in the presence of noise. This algorithm can be extended to include functional forms other than exponential kernels. We demonstrate the performance of the algorithm at different signal-to-noise ratios and with different T₁–T₂ spectral characteristics using several brine-saturated rock samples.     

Radiation-induced changes in phosphorus T1values in human melanoma xenografts studied by P-MRS

³¹P-magnetic resonance spectroscopy (MRS) has been shown to be a promising method for monitoring tumor response to radiation therapy. The purpose of the work reported here was to investigate whether the usefulness of ³¹P-MRS might be enhanced by measurement of spin-lattice relaxation times (T₁s) in addition to resonance ratios. The work was based on the hypothesis that tumors having a high probability of being controlled locally would show shortened T₁s during the treatment course due to reoxygenation and development of necrosis. BEX-t human melanoma xenografts, which show efficient reoxygenation and development of necrosis following single dose irradiation, were used as tumor models. Tumors were treated with single doses of 5.0 or 15.0 Gy and the T₁s of the inorganic phosphate and nucleoside triphosphate β resonances were measured as a function of time after irradiation by using the superfast inversion recovery method. Fractional tumor water content was determined by drying excised tumors at 50°C until a constant weight was reached. The T₁s in irradiated tumors were either longer than or not significantly different from those in unirradiated control tumors. The increase in the T₁s following irradiation coincided in time with a radiation-induced increase in tumor water content, suggesting a causal relationship. The effects of reoxygenation and development of necrosis on T₁s were probably overshadowed by the effects of tumor water content. Consequently, the usefulness of ³¹P-MRS in monitoring tumor response to radiation therapy might not be significantly enhanced by measurement of T₁s.     

基于差分进化算法的核磁共振T2谱多指数反演

提出了一种基于差分进化(DE)算法的核磁共振弛豫信号多指数反演新方法. 将核磁共振T₂谱反演问题转化为带非负约束的非线性优化问题,不需要预先给定横向弛豫时间T_{2分布,直接利用差分进化算法进行反演计算. 在测量信号低信噪比的情况下,计算机模拟和实验数据反演都表明了该方法在分析处理NMR弛豫信号中的有效性. 关键词： 核磁共振 多指数反演 差分进化 岩心分析}     

Linewidth-Resolved N HSQC, a Simple 3D Method to Measure N Relaxation Times from T1 and T2 Linewidths

A three-dimensional approach for measuring ¹⁵N relaxation times is described. Instead of selecting particular values for the relaxation period, in the proposed method the relaxation period is incremented periodically in order to create a 3D spectrum. This additional frequency domain of the transformed spectrum contains the relaxation time information in the T₁ and T₂ linewidths, and thus the longitudinal and transverse ¹⁵N relaxation times can be measured without determination of 2D cross peak volumes/intensities and subsequent curve fitting procedures.     

H NMR Measurements of Wet/Dry Ratio andT1,T2Distributions in Lung

Proton-magnetic-resonance measurements have been carried out on juvenile porcine peripheral lung parenchyma. The free-induction-decay signal contained a motionally restricted component which decayed in a few tens of microseconds and a mobile component with aT₂time greater than 1 ms. The average second moment,M₂, for the motionally restricted signal was found to be 3.42 ± (0.25) × 10⁹s⁻². TheT₂distribution for the mobile signal consistently showed four resolvable components ofT₂range: 2–6, 10–40, 80–110, and 190–400 ms. The 2–6 ms component was present in a fully dehydrated preparation and was therefore assigned to a nonaqueous lung constituent. The motionally restricted FID component had aT₁= 0.772 ± 0.11 s and the mobile component had aT₁= 0.967 ± 0.02 s. The hydrogen content per unit mass for lung parenchyma and water were estimated in two ways: (1) on the basis of chemical content and (2) on the basis of comparison of restricted and mobile signals to the gravimetric (G) water content for a lung sample studied at a wide range of water contents. Lung wet/dry weight ratios were estimated from the free-induction decays and compared with gravimetric measurement. The ratio of (wet/dry)_NMR/(wet/dry)_Gwas 1.00 ± 0.08 and 1.00 ± 0.05 for the two methods of estimation.     

T1ρ-weighted MRI using a surface coil to transmit spin-lock pulses

T1rho-weighted MRI is a novel basis for generating tissue contrast. However, it suffers from sensitivity to B1 inhomogeneity. First, excitation with a spatially varying B1 causes flip-angle artifacts and second, spin locking with an inhomogeneous B1 results in non-uniform T1rho contrast. In this study, we overcome the former complication with a specially designed spin-locking pulse sequence and we successfully obtain T1rho-weighted images with a surface coil. In this pulse sequence, the spin-lock pulse was divided into segments of equal duration and alternating phase. This "self-compensating" T1rho-preparatory pulse sequence was analyzed and the effect of an inhomogeneous B1 field was simulated using the Bloch equations. T1rho-weighted MR images of a phantom and a human knee joint in vivo were obtained on a clinical scanner with a surface coil to demonstrate the utility of the pulse sequence. The self-compensating T1rho-prepared pulses sequence resulted in substantially reduced image artifacts compared to the conventional, single-phase spin-lock pulse.     

Short, shaped pulses in a large magnetic field gradient

A number of materials MR developments require that measurements be made in a large magnetic field gradient, including unilateral (single-sided) magnet designs for portability and open access. In such cases, all radiofrequency (RF) pulses are slice selective. Typically, little effort is made to tailor the shape of the selected slice, because shaped RF excitations are viewed as too lengthy in duration to be useful in materials MRI, where signal lifetimes are mostly less than 1 ms. We compare measured magnetization responses to various standard shaped pulses under extreme conditions of application (30 μs duration, offset frequencies up to 0.3 MHz, and in the presence of a 13 T/m permanent magnetic field gradient). We discuss the feasibility of their implementation for materials MRI in a large gradient, including the difficulty of choosing optimized pulse area, and propose viable solutions.     

Anisotropy and relaxation processes of uniaxially oriented CoFe2O4 nanoparticles dispersed in PDMS

When a uniaxial magnetic field is applied to a non-magnetic dispersive medium filled with magnetic nanoparticles, they auto-assemble into thin needles parallel to the field direction, due to the strong dipolar interaction among them. We have prepared in this way magnetically oriented nanocomposites of nanometer-size CoFe₂O₄ particles in a polydimethylsiloxane polymer matrix, with 10% w/w of magnetic particles. We present the characteristic magnetic relaxation curves measured after the application of a magnetic field forming an angle α with respect to the needle direction. We show that the magnetic viscosity (calculated from the logarithmic relaxation curves) as a function of α presents a minimum at α=0, indicating slower relaxation processes associated with this configuration of fields. The results seems to point out that the local magnetic anisotropy of the nanoparticles is oriented along the needles, resulting in the macroscopic magnetic anisotropy observed in our measurements.     

Superparamagnetic iron oxide particles and positive enhancement for myocardial perfusion studies assessed by subsecond T1-weighted MRI

Superparamagnetic iron oxide particles (SPIOs) are usually referred to as T₂ MR contrast agents, reducing signal intensity (SI) on T₂-weighted MR images (negative enhancement). This study reports the original use of SPIOs as T₁-enhancing contrast agents, primarily assessed in vitro, and then applied to an in vivo investigation of a myocardial perfusion defect. Using a strongly T₁-weighted subsecond MR sequence with SPIOs intravenous (IV) bolus injection, MR imaging of myocardial vascularization after reperfusion was performed, on a dog model of coronary occlusion followed by reperfusion. Immediately after the intravenous bolus injection of 20 μmol/kg of SPIOs, a positive signal intensity enhancement was observed respectively, in the right and left ventricular cavity and in the nonischemic left myocardium. Moreover, compared to normal myocardium, the remaining ischemic myocardial region (anterior wall of the left ventricle) appeared as a lower and delayed SI enhancing area (cold spot). Mean peak SIE in the nonischemic myocardium (posterior wall) was significantly higher than in the ischemic myocardium (anterior wall) (110 ± 23% vs. 74 ± 22%, Mann-Whitney test < 1%, n₁ = 6, n₂ − n₁ = 0, U > 2). In conclusion, the T₁ effect of SPIOs at low dose, during their first intravascular distribution, suggests their potential use as positive markers to investigate the regional myocardial blood flow and some perfusion defects such as the “no-reflow phenomenon”.     

Line strength measurements of carbonyl sulfide (OCS) in the 2v3, v1+2v2+v3, and 4v2+v3 bands

To support planetary studies of the Venus atmosphere, we measured line strengths of the 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ bands of the primary isotopologue of carbonyl sulfide (¹⁶O¹²C³²S), whose band centers are located at 4101.387, 3937.427, and 4141.212 cm⁻¹, respectively. For this, infrared absorption spectra in normal carbonyl sulfide (OCS) sample gas were recorded at an unapodized resolution of 0.0033 cm⁻¹ at ambient room temperatures using a Bruker Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory. The FTS instrumental line shape (ILS) function was investigated, which revealed no significant instrumental line broadening or distortions. Various custom-made short cells and a multi-pass White cell were employed to achieve optical densities sufficient to observe the strong 2v₃ and the weaker bands in the region. Gas sample impurities and the isotopic abundances were determined from mass spectrum analysis. Line strengths were retrieved spectrum by spectrum using a non-linear curve fitting algorithm adopting a standard Voigt line profile, from which Herman–Wallis factors were derived for the three bands. The band strengths of 2v₃, v₁+2v₂+v₃, and 4v₂+v₃ of ¹⁶O¹²C³²S (normalized at 100% of isotopologue) are observed to be 6.315(13)×10⁻¹⁹, 1.570(2)×10⁻²⁰, and 7.949(20)×10⁻²¹ cm⁻¹/molecule cm⁻², respectively, at 296 K. These results are compared with earlier measurements and the HITRAN 2004 database.     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Multi-components of T2 relaxation in ex vivo cartilage and tendon

The multi-components of T₂ relaxation in cartilage and tendon were investigated by microscopic MRI (μMRI) at 13 and 26 μm transverse resolutions. Two imaging protocols were used to quantify T₂ relaxation in the specimens, a 5-point sampling and a 60-point sampling. Both multi-exponential and non-negative-least-square (NNLS) fitting methods were used to analyze the μMRI signal. When the imaging voxel size was 6.76 × 10⁻⁴ mm³ and within the limit of practical signal-to-noise ratio (SNR) in microscopic imaging experiments, we found that (1) canine tendon has multiple T₂ components; (2) bovine nasal cartilage has a single T₂ component; and (3) canine articular cartilage has a single T₂ component. The T₂ profiles from both 5-point and 60-point methods were found to be consistent in articular cartilage. In addition, the depletion of the glycosaminoglycan component in cartilage by the trypsin digestion method was found to result in a 9.81–20.52% increase in T₂ relaxation in articular cartilage, depending upon the angle at which the tissue specimen was oriented in the magnetic field.