T1 and T2 effects during radio-frequency pulses in spoiled gradient echo sequences

Finite pulse durations in diverse pulse schemes lead to the reduction of the magnitude of the magnetization vector due to T₁ and T₂ effects during the radio-frequency pulses. This paper presents an analysis of the steady state signal in the presence of relaxation effects during radio-frequency pulses in MRI spoiled gradient echo sequences. It is shown that minor attenuations of the magnetization vector can have dramatic consequences on the measured signal, and may thus entail a loss in SNR benefits at high static magnetic fields if a careful analysis is not performed. It is emphasized that it is the time-integrated magnetization vector trajectory that matters for these effects and not only the pulse duration. Some experimental results obtained on a phantom at 3 T verify this analysis.     

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.     

Expanding the Frequency Range of the Solid-State T1 ρ Experiment for Heteronuclear Dipolar Relaxation

Solid-state spin–lattice relaxation in the rotating frame permits the investigation of dynamic processes with correlation times in the range of microseconds. The relaxation process in organic solids is driven by the fluctuation of the local magnetic field due to the dipole–dipole interaction of the probe nuclei (¹³C,¹⁵N) with ¹H in close proximity. However, its effect is often hidden by a competing relaxation process due to the contact between the rotating frame ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. In most cases the latter process becomes superior for the commonly applied low and moderate spin-lock fields and practically does not provide information about the molecular dynamics. To suppress this undesired process and to expand the dynamic range of T_{1 ρ} experiments, we present two approaches. The first one uses a resonance offset of the frequency of the spin-lock irradiation, which leads to a significant enhancement of the effective spin-lock frequency without the application of destructive high transmitter powers. We derive the theory and demonstrate the applicability of the method on various model compounds. The second approach utilizes heteronuclear ¹H decoupling during the ¹³C/¹⁵N spin-lock irradiation which disrupts the contact between the ¹³C/¹⁵N Zeeman and ¹H dipolar reservoirs. We demonstrate the method and discuss the results qualitatively.     

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.     

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”.     

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.     

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.     

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.     

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.     

Relaxation Behavior of Laser-Polarized Xe Gas: Size Dependency and Wall Effect of the T1 Relaxation Time in Glass and Gelatin Bulbs

Size dependency of the relaxation time T₁ was measured for laser-polarized ¹²⁹Xe gas encapsulated in different sized cavities made by glass bulbs or gelatin capsules. The use of laser-polarized gas enhances the sensitivity a great deal, making it possible to measure the longer ¹²⁹Xe relaxation time in quite a short time. The size dependency is analyzed on the basis of the kinetic theory of gases and a relationship is derived in which the relaxation rate is connected with the square inverse of the diameter of the cavity. Such an analysis provides a novel parameter which denotes the wall effect on the relaxation rate when a gas molecule collides with the surface once in a second. The relaxation time of ¹²⁹Xe gas is also dependent on the material which forms the cavity. This dependency is large and the relaxation study using polarized ¹²⁹Xe gas is expected to offer important information about the state of the matter of the cavity wall.     

Uniform-Penalty Inversion of Multiexponential Decay Data: II. Data Spacing, T2 Data, Systematic Data Errors, and Diagnostics

The basic method of UPEN (uniform penalty inversion of multiexponential decay data) is given in an earlier publication (Borgia et al., J. Magn. Reson. 132, 65–77 (1998)), which also discusses the effects of noise, constraints, and smoothing on the resolution or apparent resolution of features of a computed distribution of relaxation times. UPEN applies negative feedback to a regularization penalty, allowing stronger smoothing for a broad feature than for a sharp line. This avoids unnecessarily broadening the sharp line and/or breaking the wide peak or tail into several peaks that the relaxation data do not demand to be separate. The experimental and artificial data presented earlier were T₁ data, and all had fixed data spacings, uniform in log-time. However, for T₂ data, usually spaced uniformly in linear time, or for data spaced in any manner, we have found that the data spacing does not enter explicitly into the computation. The present work shows the extension of UPEN to T₂ data, including the averaging of data in windows and the use of the corresponding weighting factors in the computation. Measures are implemented to control portions of computed distributions extending beyond the data range. The input smoothing parameters in UPEN are normally fixed, rather than data dependent. A major problem arises, especially at high signal-to-noise ratios, when UPEN is applied to data sets with systematic errors due to instrumental nonidealities or adjustment problems. For instance, a relaxation curve for a wide line can be narrowed by an artificial downward bending of the relaxation curve. Diagnostic parameters are generated to help identify data problems, and the diagnostics are applied in several examples, with particular attention to the meaningful resolution of two closely spaced peaks in a distribution of relaxation times. Where feasible, processing with UPEN in nearly real time should help identify data problems while further instrument adjustments can still be made. The need for the nonnegative constraint is greatly reduced in UPEN, and preliminary processing without this constraint helps identify data sets for which application of the nonnegative constraint is too expensive in terms of error of fit for the data set to represent sums of decaying positive exponentials plus random noise.     

In vivo NMR T2 relaxation of experimental brain tumors in the cat: A multiparameter tissue characterization

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time t = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.     

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.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

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.     

1H spin–lattice relaxation in water solution of 209Bi counterparts of Gd3+contrast agents

ABSTRACT

¹H spin–lattice relaxation studies of water solutions of Bismuth-ethylenediamine-tetraacetic acid (Bi-EDTA), Bismuth-ethylenediamine-tetrakis(methylenephosphonic) acid (Bi-EDTP), Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (Bi-DOTA), Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrakis(methylenephosphonic acid) (Bi-DOTP) and Bismuth-1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid (Bi-DO3A) have been performed in order to compare Quadrupole Relaxation Enhancement (QRE) effects with Paramagnetic Relaxation Enhancement (PRE) from the perspective of exploiting the first one as a novel contrast mechanism for Magnetic Resonance Imaging (MRI). The selected compounds can be considered as ²⁰⁹Bi counterparts of Gd³⁺ complexes. The relaxation experiments have been performed in a broad frequency range of 5?kHz–30?MHz. The relaxation contribution associated with QRE has been extracted from the data and compared with PRE. Similarities and differences between the two effects have been discussed.     

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}     

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.     

A ProtonT1,T2, and NOE Study of Relative Motion of the Indole Ring of Tryptophans in Gramicidin Analogs Incorporated into SDS Micelles

The proton spin–lattice relaxation time, spin–spin relaxation time, and NOE of the indole ring NH proton of tryptophan residues have been determined for seven analogs of gramicidin A incorporated into SDS micelles. The data obtained indicate that the motion of the indole rings systematically decreases, proceeding from the aqueous interface to the interior of the micelle.     

T1-weighting of Hahn echo-trains in the stray-field for deuterium: prospects for imaging using long echo-train summation

Hahn-echoes have been observed in stray-field gradients of 37.5 T/m and 74.5 T/m for deuterium in heavy water in a number of forms: liquid, ice, and coordinated in solid copper sulfate and silica gel. In the diamagnetic samples, the application of many pulses (>1000 or more) in long pulse-trains produced many sustained echoes. This lengthening of T_echo is caused by T₁-weighting of the components of the Hahn echo (even in the absence of spin-locking). In contrast, for the paramagnetic complex, the shortening of T₁ greatly reduces T_echo and only few echoes are obtained. A new protocol for stray field imaging is suggested when T₁ is long: long echo-train summation (LETS). The observed magnetisation is much greater for heavy ice than for heavy water because the line-width, and hence the thickness of the excited slice, is greater.