A spin echo method adapted to the measurement of long nuclear relaxation times (T2) in liquids is described. The pulse sequence is identical to the one proposed by Carr and Purcell, but the rf of the successive pulses is coherent, and a phase shift of 90° is introduced in the first pulse. Very long T2 values can be measured without appreciable effect of diffusion.

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Modified Spin‐Echo Method for Measuring Nuclear Relaxation Times

Molecular diffusion and microcirculation in the capillary network result in a distribution of phases in a single voxel in the presence of magnetic field gradients. This distribution produces a spin-echo attenuation. The authors have developed a magnetic resonance (MR) method to image such intravoxel incoherent motions (IVIMs) by using appropriate gradient pulses. Images were generated at 0.5 T in a high-resolution, multisection mode. Diffusion coefficients measured on images of water and acetone phantoms were consistent with published values. Images obtained in the neurologic area from healthy subjects and patients were analyzed in terms of an apparent diffusion coefficient (ADC) incorporating the effect of all IVIMs. Differences were found between various normal and pathologic tissues. The ADC of in vivo water differed from the diffusion coefficient of pure water. Results were assessed in relation to water compartmentation in biologic tissues (restricted diffusion) and tissue perfusion. Nonuniform slow flow of cerebrospinal fluid appeared as a useful feature on IVIM images. Observation of these motions may significantly extend the diagnostic capabilities of MR imaging.

MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders.

Intravoxel incoherent motion (IVIM) imaging is a method the authors developed to visualize microscopic motions of water. In biologic tissues, these motions include molecular diffusion and microcirculation of blood in the capillary network. IVIM images are quantified by an apparent diffusion coefficient (ADC), which integrates the effects of both diffusion and perfusion. The aim of this work was to demonstrate how much perfusion contributes to the ADC and to present a method for obtaining separate images of diffusion and perfusion. Images were obtained at 0.5 T with high-resolution multisection sequences and without the use of contrast material. Results in a phantom made of resin microspheres demonstrated the ability of the method to separately evaluate diffusion and perfusion. The method was then applied in patients with brain and bone tumors and brain ischemia. Clinical results showed significant promise of the method for tissue characterization by perfusion patterns and for functional studies in the eva...

Separation of diffusion and perfusion in intravoxel incoherent motion MR imaging.

Diffusion of ions in sea water and in deep-sea sediments

The biochemistry and medical significance of the flavonoids.

Nuclear resonance techniques involving free precession are examined, and, in particular, a convenient variation of Hahn's spin-echo method is described. This variation employs a combination of pulses of different intensity or duration ("90-degree" and "180-degree" pulses). Measurements of the transverse relaxation time ${T}_{2}$ in fluids are often severely compromised by molecular diffusion. Hahn's analysis of the effect of diffusion is reformulated and extended, and a new scheme for measuring ${T}_{2}$ is described which, as predicted by the extended theory, largely circumvents the diffusion effect. On the other hand, the free precession technique, applied in a different way, permits a direct measurement of the molecular self-diffusion constant in suitable fluids. A measurement of the self-diffusion constant of water at 25\ifmmode^\circ\else\textdegree\fi{}C is described which yields $D=2.5(\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ ${\mathrm{cm}}^{2}$/sec, in good agreement with previous determinations. An analysis of the effect of convection on free precession is also given. A null method for measuring the longitudinal relaxation time ${T}_{1}$, based on the unequal-pulse technique, is described.

Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments

A steady-state free precession technique for observing nuclear magnetic resonance is described. A mathematical analysis is presented for certain special conditions, and initial experiments verifying the results of this analysis are reported. This technique provides two opportunities for improving the signal-to- noise ratio. First, it provides a mechanism, similar to that of the "spin echo," for eliminating the effect of the inhomogeneity of the magnetic field on signal strength. This permits the effective use of larger samples. In the second place it provides a steady-state signal which can be observed with a narrow-band detector. Under certain conditions the technique has a broad response as a function of frequency or field. The upper limit to the width of this response is determined by the electronic apparatus supplying the rf pulse; rather than the magnet or the nuclear sample. (auth)

Steady-state free precession in nuclear magnetic resonance

The diffusion coefficient and the spin lattice relaxation time of protons in ordinary water have been measured in the temperature range 0-100\ifmmode^\circ\else\textdegree\fi{}C using nuclear magnetic resonance free precession techniques. Unlike previous diffusion measurements, the present values describe the diffusion of protons rather than foreign isotopes introduced as tracers. To within the experimental error the Stokes-Einstein relation adequately describes the relative temperature dependence of viscosity and diffusion, but above the vicinity of 40\ifmmode^\circ\else\textdegree\fi{}C the spin lattice relaxation does not follow the viscosity in the predicted manner.

Diffusion and nuclear spin relaxation in water

The spin-lattice relaxation time ${T}_{1}$ of ${\mathrm{Xe}}^{129}$ has been measured as a function of temperature in the liquid and as a function of pressure in the gas. A strong shift $\ensuremath{\Delta}H$ in the external field required for resonance at constant frequency but varying sample density $\ensuremath{\rho}$ has been discovered. As the sample density increases in the region above 48 atm, $\ensuremath{\Delta}H$ decreases linearly at the rate of 3.45 milligauss per amagat (density at standard conditions) in a field of 8060 gauss. In the liquid the temperature dependence of the product of ${T}_{1}$ and $\ensuremath{\rho}$ can be described by an activation energy of 0.7\ifmmode\pm\else\textpm\fi{}0.1 kcal/mole. In the gas at room temperature between 48 and 73 atm, ${T}_{1}$ varies as ${\ensuremath{\rho}}^{\ensuremath{-}2.1\ifmmode\pm\else\textpm\fi{}0.4}$. The largest value of ${T}_{1}$ observed was 2600\ifmmode\pm\else\textpm\fi{}600 sec for a gas sample at 48 atm, and the shortest value was 57\ifmmode\pm\else\textpm\fi{}2 sec in the liquid at -101\ifmmode^\circ\else\textdegree\fi{}C. The experimental values of ${T}_{1}$ have been compared with theoretical predictions in two limiting cases, the rare gas and the dense liquid. In both cases the experimental values, although larger than previously reported values, are still two to three orders of magnitude smaller than predicted from an intermolecular nuclear magnetic dipole interaction. The relaxation time was found to be independent of field. Implications of our data for determining the relaxation mechanism are discussed. It is suggested that the relaxation may be caused by a fluctuating magnetic field at the nucleus resulting from the motion of nonsymmetrical electronic charge distributions during collisions.

H. Y. Carr

Papers

Effects of Diffusion on Free Precession in Nuclear Magnetic Resonance Experiments

Steady-state free precession in nuclear magnetic resonance

Diffusion and nuclear spin relaxation in water

Nuclear Magnetic Resonance of Xe 129 in Natural Xenon