Relaxation times and NMR signals

The strength of signals in magnetic resonance imaging (and the resulting image contrast) depends not just on the number density of the nuclei being detected, but also on the relaxation times, T1 and T2. The relationship of signal strength to relaxation time depends on the particular choice of pulse sequences used to produce the signals. The effects of the T1 relaxation time on signal strength are discussed for the commonly used imaging techniques "partial saturation" and "inversion recovery." Production of spin echos and the effect of the T2 relaxation time on spin-echo signal strength are also discussed.     

Oxygen-sensitive 19F NMR imaging of the vascular system in vivo

The fluorine nuclear magnetic resonance spin-lattice relaxation rate (1/T1) of the perfluorochemical blood substitute perfluorotripropylamine (FTPA) is very sensitive to oxygen tension. This presents the possibility of measuring blood oxygen tension by 19F MR imaging. We obtained oxygen-sensitive 19F NMR images of the circulatory system of rats infused with emulsified FTPA. Blood oxygenation was assessed under conditions of both air- and 100% O2-breathing. T1 relaxation times were derived from MR images using a partial saturation pulse sequence. The T1 times were compared with a phantom calibration curve to calculate average blood pO2 values in the lung, liver, and spleen. The results showed marked, organ-specific increases in blood oxygen tension when the rat breathed 100% O2 instead of air.     

TriTone: a radiofrequency field (B1)-insensitive T1 estimator for MRI at high magnetic fields

Fast, high-resolution, longitudinal relaxation time (T1) mapping is invaluable in clinical and research applications. It has been shown that two spoiled gradient recalled echo (SPGR) images acquired in steady state with variable flip angles is an attractive alternative to the multi-image sets previously acquired with inversion or saturation recovery. The known sensitivity of the two-point method to transmit radiofrequency field (B1) inhomogeneity exacerbated at 3 T and above, however, mandates its combination with an additional, time-consuming and possibly specific-absorption-rate-intensive B1 measurement, preventing direct migration of the method to these fields. To address this, we introduce a method designed to be free of systematic errors caused by B1 inhomogeneity in which the value of T1 is extracted from three SPGR images acquired with echo planar imaging (EPI) readout. The precision of the T1 maps produced is found to be comparable to the two-point method, while the accuracy is greatly improved in the same time and spatial resolution. A welcome byproduct of the method is a map of B1 that can be used to correct other acquisitions in the same session. Tables of the optimal acquisition protocols are provided for several total imaging times.     

Correction of intensity nonuniformity in spin-echo T(1)-weighted images

This paper presents a method to correct intensity nonuniformity in spin-echo T(1)-weighted images and particularly the inhomogeneities due to RF transmission imperfections which have tissue-dependent effects through the T(1) relaxation times. This method is based on the use of a uniform phantom, first for classic normalization by division by the phantom images, and second for T(1)-correction using the RF transmitted cartography. We present experimental results from a bi-phasic (oil/water) phantom and from a salmon with a 0.2 T imager. The results demonstrate the efficiency of the method in the two cases and its ability to cope with partial volume effect.     

The effect of relaxation on the epitope mapping by saturation transfer difference NMR

The effect of longitudinal relaxation of ligand protons on saturation transfer difference (STD) was investigated by using a known binding system, dihydrofolate reductase and trimethoprim. The results indicate that T1 relaxation of ligand protons has a severe interference on the epitope map derived from a STD measurement. When the T1s of individual ligand protons are distinctly different, STD experiments may not give an accurate epitope map for the ligand-target interactions. Measuring the relaxation times prior to mapping is strongly advised. A saturation time shorter than T1s is suggested for improving the potential epitope map. Reduction in temperature was seen to enhance the saturation efficiency in small to medium size targets.     

Artifacts in T(1rho)-weighted imaging: correction with a self-compensating spin-locking pulse

Significant artifacts arise in T(1rho)-weighted imaging when nutation angles suffer small deviations from their expected values. These artifacts vary with spin-locking time and amplitude, severely limiting attempts to perform quantitative imaging or measurement of T(1rho) relaxation times. A theoretical model explaining the origin of these artifacts is presented in the context of a T(1rho)-prepared fast spin-echo imaging sequence. Experimentally obtained artifacts are compared to those predicted by theory and related to B(1) inhomogeneity. Finally, a "self-compensating" spin-locking preparatory pulse cluster is presented, in which the second half of the spin-locking pulse is phase-shifted by 180 degrees. Use of this pulse sequence maintains relatively uniform signal intensity despite large variations in flip angle, greatly reducing artifacts in T(1rho)-weighted imaging.     

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.     

Quantitative evaluation of porous media wettability using NMR relaxometry

We propose a new method to determine wettability indices from NMR relaxometry. The new method uses the sensitivity of low field NMR relaxometry to the fluid distribution in oil-water saturated porous media. The model is based on the existence of a surface relaxivity for both oil and water, allowing the determination of the amount of surface wetted either by oil or by water. The proposed NMR wettability index requires the measurement of relaxation time distribution at four different saturation states. At the irreducible water saturation, we determine the dominant relaxation time of oil in the presence of a small amount of water, and at the oil residual saturation, we determine the dominant relaxation time of water in the presence of a small amount of oil. At 100% water and 100% oil saturation, we determine the surface relaxivity ratio. The interaction of oil with the surface is also evidenced by the comparison of the spin-lattice (T1) and spin-locking (T1rho) relaxation times. The new NMR index agrees with standard wettability measurements based on drainage-imbibition capillary pressure curves (USBM test) in the range [-0.3-1].     

In vivo evaluation of the reproducibility of T1 and T2 measured in the brain of patients with multiple sclerosis.

The precision (reproducibility) of relaxation times derived from magnetic resonance images of patients with multiple sclerosis (MS) were investigated. Measurements of 10 MS patients were performed at 1.5 T on two occasions within 1 wk. T1 and T2 was measured using a partial saturation inversion recovery sequence (6 points) and a Carr-Purcell-Meiboom-Gill phase alternating-phase shift multiple spin-echo sequence with 32 echoes. Regions of interest (ROI) were placed both in apparently normal white matter and plaques. The precision (+/- 1.96 SD) and the confidence intervals for T1 and T2 for white matter and plaques were calculated. The precision of T1 for white matter and plaques was respectively +/- 94 msec and +/- 208 msec. The precision of T2 for white matter and plaques was respectively +/- 18 msec and +/- 26 msec. For all measurements the coefficient of variation was about 9%. Judging from our own study and others as well, a precision better than 10% for T1 and T2 would seem unrealistic at present.     

A fast T1 algorithm.

Multispectral tissue classification using magnetic resonance T1, T2, and rho images may be useful in diagnosing and locating certain pathology. Techniques for generating the T1 images necessary for this classification scheme often require longer data collection and post processing times than are practical. As a consequence, further development of this classification scheme may be limited. This paper addresses an improvement in the post processing time required to generate T1 images. A nonlinear least-squares algorithm is described for rapidly generating spin-lattice relaxation time images from variable repetition time magnetic resonance images. The algorithm generates a 256 x 256 pixel T1 image from nine variable repetition time images in approximately 60 sec on a VAX-6510 computer.     

Two-exponential analysis of spin-spin proton relaxation times in MR imaging using surface coils

Proton relaxation time measurements were performed on a standard whole body MR imager operating at 1.5 T using a conventional surface coil of the manufacturer. A combined CP/CPMG multiecho, multislice sequence was used for the T1 and T2 relaxation time measurements. Two repetition times of 2000 ms (30 echoes) and 600 ms (2 echoes) with 180 degrees-pulse intervals of 2 tau = 22 ms were interleaved in this sequence. A two-exponential T2 analysis of each pixel of the spin-echo images was computed in a case of an acoustic neurinoma. The two-exponential images show a "short" component (T2S) due to white and gray matter and a "long" component (T2S) due to the cerebrospinal fluid. In the fatty tissue two components with T2S = 35 +/- 3 ms and T2L = 164 +/- 7 ms were measured. Comparing with Gd-DTPA imaging the relaxation time images show a clear differentiation of vital tumor tissue and cerebrospinal fluid.     

On neglecting chemical exchange effects when correcting in vivo (31)P MRS data for partial saturation

Signal acquisition in most MRS experiments requires a correction for partial saturation that is commonly based on a single exponential model for T(1) that ignores effects of chemical exchange. We evaluated the errors in (31)P MRS measurements introduced by this approximation in two-, three-, and four-site chemical exchange models under a range of flip-angles and pulse sequence repetition times (T(R)) that provide near-optimum signal-to-noise ratio (SNR). In two-site exchange, such as the creatine-kinase reaction involving phosphocreatine (PCr) and gamma-ATP in human skeletal and cardiac muscle, errors in saturation factors were determined for the progressive saturation method and the dual-angle method of measuring T(1). The analysis shows that these errors are negligible for the progressive saturation method if the observed T(1) is derived from a three-parameter fit of the data. When T(1) is measured with the dual-angle method, errors in saturation factors are less than 5% for all conceivable values of the chemical exchange rate and flip-angles that deliver useful SNR per unit time over the range T(1)/5 < or = T(R) < or = 2T(1). Errors are also less than 5% for three- and four-site exchange when T(R) > or = T(1)(*)/2, the so-called "intrinsic" T(1)'s of the metabolites. The effect of changing metabolite concentrations and chemical exchange rates on observed T(1)'s and saturation corrections was also examined with a three-site chemical exchange model involving ATP, PCr, and inorganic phosphate in skeletal muscle undergoing up to 95% PCr depletion. Although the observed T(1)'s were dependent on metabolite concentrations, errors in saturation corrections for T(R) = 2 s could be kept within 5% for all exchanging metabolites using a simple interpolation of two dual-angle T(1) measurements performed at the start and end of the experiment. Thus, the single-exponential model appears to be reasonably accurate for correcting (31)P MRS data for partial saturation in the presence of chemical exchange. Even in systems where metabolite concentrations change, accurate saturation corrections are possible without much loss in SNR.     

An MR imaging method for simultaneous measurement of gaseous diffusion constant and longitudinal relaxation time

A magnetic resonance imaging method for simultaneous and accurate determination of gaseous diffusion constant and longitudinal relaxation time is presented. The method is based on direct observation of diffusive motion. Initially, a slice-selective saturation of helium-3 (3He) spins was performed on a 3He/O2 phantom (9 atm/2 atm). A time-delay interval was introduced after saturation, allowing spins to diffuse in and out of the labeled slice. Following the delay interval a one-dimensional (1-D) projection image of the phantom was acquired. A series of 21 images was collected, each subsequent image having been acquired with an increased delay interval. Gradual spreading of the slice boundaries due to diffusion was thus observed. The projection profiles were fit to a solution of the Bloch equation corrected for diffusive motion. The fitting procedure yielded a value of D3He = 0.1562+/-0.0013 cm2/s, in good agreement with a measurement obtained with a modified version of the standard pulsed-field gradient technique. The method also enabled us to accurately measure the longitudinal relaxation of 3He spins by fitting the change of the total area under the projection profiles to an exponential. A value of T1 = 1.67 s (2 T field) was recorded, in excellent agreement with an inversion recovery measurement.     

Transient nutation of dressed spin states of <Emphasis Type="Italic">E</Emphasis>′<Subscript>1</Subscript> centers in a quartz crystal

The transient nutation of states dressed by a microwave field in a two-level system (E′₁ centers in a quartz crystal) is observed in pulsed electron paramagnetic resonance (EPR) in the course of an additional pulse of a linearly polarized radio-frequency (rf) field that has an amplitude 2B₂ and is applied parallel to the static magnetic field. It is shown that, when the frequency of the rf field coincides with the frequency of nutation of the bare spin system, the signal of this nutation is modulated by the nutation of dressed states at the frequency ω₂=γB₂, where γ is the electron gyromagnetic ratio. The decay time of nutation of dressed states is considerably (no less than four times) longer than that of bare states of E′₁ centers due to spin-spin relaxation and correlates with the spin-lattice relaxation time in the rotating coordinate system.     

Precision in calculated rho, T1 and T2 images as a function of data analysis method

In NMR imaging rho, T1 and T2 images are usually calculated from a set of partial saturation, saturation recovery or inversion recovery experiments with multiple echoes and multiple repetition times. Several methods can be envisaged to extract parameter images from such a set of source images. These methods to a greater or lesser extent take advantage of the fact that a multiple echo/multiple repetition time experiment provides a set of largely independent T1 and T2 measurements. In this study several data analysis methods, including weighted and non-weighted averaging of results of independent T1 and T2 measurements, weighted and non-weighted averaging of source images prior to data reduction and simultaneous three-parameter fitting, were compared against another in terms of precision, computational efficiency and robustness. The predicted performance of the examined methods was verified by stochastic simulation experiments.     

Electron spin-lattice relaxation time and spectral diffusion in γ-irradiated l-alanine

We performed continuous (CW) wave and pulsed ESR experiments to obtain information on the relaxation behavior of the l-alanine radical in an irradiated single crystal. The analysis of the CW saturation behavior gives a relaxation time of 2.8 μs. The echo detected saturation recovery was obtained for a number of different experimental conditions. In any case only a portion of the 120 G wide ESR spectrum can be affected by the microwave (MW) pulses, spectral diffusion is active and a multi-exponential decay is therefore obtained. We measured characteristic spectral diffusion times of 1–10 and 20–50 μs. We found that a long time of about 200 μs can be measured only by using a train of long selective saturating pulses and short detecting pulses. The stimulated echo decay is bi-exponential, and the characteristic times are very short. A variable temperature investigation in the range 200 to 290 K showed that the decay is governed by the spectral diffusion and by the transverse nuclear spin relaxation timeT _2n of the methyl protons.     

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.     

In vivo determination of multiexponential T2 relaxation in the brain of patients with multiple sclerosis

In vivo measurement of T2 relaxation times in multiple sclerosis (MS) lesions by magnetic resonance imaging (MRI) is potentially useful for the evaluation of the disease activity. Seven patients with definite MS were investigated over a period of three years (19 examinations), using a whole-body MRI scanner operating at 0.15 T with a specially designed high-power radio-frequency head coil. A modified CPMG sequence with a 180 degree pulse interval of TE = 6 msec and 128 echoes was used for the T2 relaxation measurement of the areas of increased signal (AIS) and white matter (WM). A biexponential T2 analysis of each pixel of the spin-echo images was computed. The T2 relaxation processes were found to be a monoexponential function in WM. The T2 relaxation times of apparently normal white matter in MS patients was significantly longer than in control subjects. The T2 relaxation curves of the AIS were found in most cases to fit a biexponential function characterized by a short and a long T2. T2 long relaxation times of AIS were spread out over a wide range (150-560 msec). The study of T2 long histograms shows that some AIS can be divided into two or three parts depending on the T2 long values. Each of these parts may correspond to a pathological process such as edema, demyelination and gliosis. Evolution of T2 relaxation times over a period of time cannot as yet be correlated with modifications in the clinical state.     

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.     

Flow and oxygenation dependent (FLOOD) contrast MR imaging to monitor the response of rat tumors to carbogen breathing

Gradient recalled echo (GRE) images are sensitive to both paramagnetic deoxyhaemoglobin concentration (via T2*) and flow (via T1*). Large GRE signal intensity increases have been observed in subcutaneous tumors during carbogen (5% carbon dioxide, 95% oxygen) breathing. We term this combined effect flow and oxygenation-dependent (FLOOD) contrast. We have now used both spin echo (SE) and GRE images to evaluate how changes in relaxation times and flow contribute to image intensity contrast changes. T1-weighted images, with and without outer slice suppression, and calculated T2, T2* and "flow" maps, were obtained for subcutaneous GH3 prolactinomas in rats during air and carbogen breathing. T1-weighted images showed bright features that increased in size, intensity and number with carbogen breathing. H&E stained histological sections confirmed them to be large blood vessels. Apparent T1 and T2 images were fairly homogeneous with average relaxation times of 850 ms and 37 ms, respectively, during air breathing, with increases of 2% for T1 and 11% for T2 during carbogen breathing. The apparent T2* over all tumors was very heterogeneous, with values between 9 and 23 ms and localized increases of up to 75% during carbogen breathing. Synthesised "flow" maps also showed heterogeneity, and regions of maximum increase in flow did not always coincide with maximum increases in T2*. Carbogen breathing caused a threefold increase in arterial rat blood PaO2, and typically a 50% increase in tumor blood volume as measured by 51Cr-labelled RBC uptake. The T2* increase is therefore due to a decrease in blood deoxyhaemoglobin concentration with the magnitude of the FLOOD response being determined by the vascular density and responsiveness to blood flow modifiers. FLOOD contrast may therefore be of value in assessing the magnitude and heterogeneity of response of individual tumors to blood flow modifiers for both chemotherapy, antiangiogenesis therapy in particular, and radiotherapy.