A new approach for simultaneous measurement of ADC and T2 from echoes generated via multiple coherence transfer pathways

The study of rotational and translational diffusion requires the measurement of both T2 and apparent diffusion coefficient (ADC), quantities that are typically measured in separate experiments. The exploitation of echoes generated via multiple coherence transfer pathways offers an opportunity for measuring T2 and ADC values simultaneously in a single experiment. A series of RF pulses can generate multiple echoes via different coherence pathways with each one being uniquely encoded. Here, we demonstrate one pulse sequence that uses an initial theta; RF pulse to generate three coherence orders (C = 0, -1, +1). In the particular version of the method discussed here only two are used (C = 0, +1). Each order is encoded with a different b value from which the ADC is derived. The coherence order echo C = 0 is refocused to quantify T2. The performance of the method--dubbed simultaneous measurement of ADC and relaxation time (SMART)--is demonstrated on a set of samples differing in T2 and ADC achieved by varying the relative volume fractions in mixtures of gadolinium-doped H2O and D2O. The regional SMART derived T2 and ADC agree well with those obtained with conventional double-spin-echo and pulsed gradient spin-echo methods.     

Theory of Spin Echo in Restricted Geometries under a Step-wise Gradient Pulse Sequence

A closed matrix form solution of the Bloch-Torrey equation is presented for the magnetization density of spins diffusing in a bounded region under a steady gradient field and for the Stejskal-Tanner gradient pulse sequence, assuming straightforward generalization to any step-wise gradient profile. The solution is expressed in terms of the eigenmodes of the diffusion propagator in a given geometry with appropriate boundary conditions (perfectly reflecting or relaxing walls). Applications to rectangular, cylindrical, and spherical geometries are discussed. The relationship with the multiple propagator approach is established and an alternative step-wise gradient discretization procedure is suggested to handle arbitrary gradient waveforms.     

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.     

Velocity and diffusion imaging in dynamic NMR microscopy

The imposition of resolution gradients in a pulsed-gradient spin-echo (PGSE) NMR sequence induces motionally dependent phase and amplitude modulation in the image, a technique which we have termed dynamic NMR microscopy. Fourier analysis of this modulation gives a dynamic displacement profile for each pixel which can then be analyzed to obtain velocity and diffusion maps. The application of this method at high spatial resolution is motivated by a desire to measure vascular flow in living plants and variations in molecular self-diffusion under the influence of velocity shear in narrow capillaries. The theory of dynamic NMR microscopy is presented and potential artifacts discussed, including the effect of slice selection gradients, PGSE gradient nonuniformity, and specific problems associated with the measurement of self-diffusion in the presence of velocity gradients. It is demonstrated that a double-echo PGSE pulse sequence can be used to restore coherent phase shifts associated with steady-state flow, and examples of self-diffusion maps and signed velocity maps from sequences of phase-encoded images obtained by projection reconstruction are given. This method has been applied at 20,um transverse resolution in laminar capillary flow.     

Cross-term-compensated pulsed-gradient stimulated echo MR with asymmetric gradient pulse lengths

The magic asymmetric gradient stimulated echo (MAGSTE) sequence developed to compensate background-gradient cross-terms in the preparation and readout interval independently, assumes identical lengths for the two gradient pulses applied in each interval. However, this approach is rather inefficient if some extra delay time is present in one half of an interval, e.g. as required for special RF excitations or spatial encoding prior to the stimulated echo in MR imaging. Therefore, a generalized version of the sequence is presented that considers different gradient pulse lengths within an interval. It is shown theoretically that (i) for any pulse lengths a "magic" amplitude ratio exists which ensures the desired cross-term compensation in each interval and that (ii) prolonging one of the gradients can deliver a considerably higher diffusion weighting efficiency. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3T using an echo-planar trajectory. In the examples shown, typically 10 times higher b values can be achieved or an echo time reduction with a 40% signal gain in brain white matter. Thus, in case of asymmetric timing requirements, the generalized MAGSTE sequence with different gradient pulse lengths may help to overcome signal-to-noise limitations in diffusion weighted MR.     

Crossing fibers, diffractions and nonhomogeneous magnetic field: correction of artifacts by bipolar gradient pulses

In recent years, diffusion tensor imaging (DTI) and its variants have been used to describe fiber orientations and q-space diffusion MR was proposed as a means to obtain structural information on a micron scale. Therefore, there is an increasing need for complex phantoms with predictable microcharacteristics to challenge different indices extracted from the different diffusion MR techniques used. The present study examines the effect of diffusion pulse sequence on the signal decay and diffraction patterns observed in q-space diffusion MR performed on micron-scale phantoms of different geometries and homogeneities. We evaluated the effect of the pulse gradient stimulated-echo, the longitudinal eddy current delay (LED) and the bipolar LED (BPLED) pulse sequences. Interestingly, in the less homogeneous samples, the expected diffraction patterns were observed only when diffusion was measured with the BPLED sequence. We demonstrated the correction ability of bipolar diffusion gradients and showed that more accurate physical parameters are obtained when such a diffusion gradient scheme is used. These results suggest that bipolar gradient pulses may result in more accurate data if incorporated into conventional diffusion-weighted imaging and DTI.     

Investigating 3He diffusion NMR in the lungs using finite difference simulations and in vivo PGSE experiments

Finite difference simulations have been used to model (3)He gas diffusion in simulated lung tissue. The technique has the advantage that a wide range of structural models and diffusion-sensitizing gradient waveforms can be investigated, for which analytical methods would otherwise be virtually impossible. Results from simulations and in vivo pulsed-gradient-spin-echo (PGSE) experiments show that the apparent diffusion coefficient (ADC) is a function of diffusion time and gradient strength, and suggests diffusion is locally anisotropic. The simulations have been compared to recent work on an analytical model that characterizes lung tissue as a series of independent cylinders. The results presented may have clinical implications for (3)He ADC measurements in assessing lung diseases such as chronic-obstructive-pulmonary-disease.     

Measuring protein self-diffusion in protein-protein mixtures using a pulsed gradient spin-echo technique with WATERGATE and isotope filtering

Here we report a modified pulsed gradient spin-echo (PGSTE) pulse sequence to measure diffusion coefficients. This approach incorporates WATERGATE combined with isotopic filtering into a standard PGSTE experiment. Doing this eliminates much of the disadvantages from the combination of diffusion encoding and heteronuclear selection intervals and allows for facile modification of the diffusion pulse sequence with flexibility of the time period between RF pulses. The new diffusion pulse sequence is demonstrated using an 15N-labeled peptide and an 15N-labeled protein in a mixture with a protein of similar size.     

The suppression of selected acoustic frequencies in MRI

A study is made of certain dominant frequencies in the acoustic noise spectrum of the magnetic resonance imaging system. Motivated by both spring and string ideas, we investigate whether the contributions to the sound from certain frequencies can be canceled by the appropriate gradient pulse sequence design. From both simulations and experiments, vibrations resulting from an impulsive force associated with a ramping up of a gradient pulse are shown to be cancelled immediately upon the application of another impulsive force coming from the subsequent appropriately timed ramping down of that pulse. A general approach to suppression of multiple-frequency contributions involving a series of gradient pulses with variable timings is given for the cancellations between pairs of impulsive forces. Various examples are confirmed through string simulations, MRI experiments, and linear response theory. This also provides a foundation to explain some results in previous papers on this subject. The method suggests that a variety of pulse profiles and timing combinations can be used to attenuate important contributions to the acoustic spectrum.     

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.     

Generalized MAGSTE with bipolar diffusion-weighting gradient pulses

The generalized magic asymmetric gradient stimulated echo (generalized MAGSTE) sequence compensates background gradient cross-terms and can be adjusted to asymmetric timing boundary conditions which for instance are present in echo-planar MR imaging. However, its efficiency is not optimal because one of the two diffusion-weighting gradients applied in each interval usually must have a reduced amplitude to ensure the desired cross-term compensation. In this work, a modification of generalized MAGSTE is investigated where this gradient pulse is replaced by two gradient pulses with full amplitude but opposite polarities. It is shown that with these bipolar gradients (i) the sequence retains the cross-term compensation capability for an appropriate choice of the gradient pulse durations and (ii) the diffusion-weighting efficiency is improved, i.e. higher k and b values can be achieved without prolonging the echo time. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3 T using spin-echo and echo-planar MR imaging. In the examples shown, the b value could be increased between about 30% and 200% when using the bipolar gradient pulses. Thus, bipolar gradients may help to improve the applicability of the generalized MAGSTE sequence.     

Measurement of hyperpolarized gas diffusion at very short time scales

We present a new pulse sequence for measuring very-short-time-scale restricted diffusion of hyperpolarized noble gases. The pulse sequence is based on concatenating a large number of bipolar diffusion-sensitizing gradients to increase the diffusion attenuation of the MR signal while maintaining a fundamentally short diffusion time. However, it differs in several respects from existing methods that use oscillating diffusion gradients for this purpose. First, a wait time is inserted between neighboring pairs of gradient pulses; second, consecutive pulse pairs may be applied along orthogonal axes; and finally, the diffusion-attenuated signal is not simply read out at the end of the gradient train but is periodically sampled during the wait times between neighboring pulse pairs. The first two features minimize systematic differences between the measured (apparent) diffusion coefficient and the actual time-dependent diffusivity, while the third feature optimizes the use of the available MR signal to improve the precision of the diffusivity measurement in the face of noise. The benefits of this technique are demonstrated using theoretical calculations, Monte-Carlo simulations of gas diffusion in simple geometries, and experimental phantom measurements in a glass sphere containing hyperpolarized (3)He gas. The advantages over the conventional single-bipolar approach were found to increase with decreasing diffusion time, and thus represent a significant step toward making accurate surface-to-volume measurements in the lung airspaces.     

Combined relaxation and displacement experiment: a fast method to acquire T2, diffusion and velocity maps

A fast method for quantitative imaging of T2 and displacement (flow and diffusion) is presented. The pulse sequence combines multi-PGSE NMR with multi-echo acquisition and compensates for flow effects in the read gradient and diffusion during multi-echo trains. The impact of the gradient pulses in a multi-echo train on the signal phase and amplitude is discussed. It is shown that separate T2 and displacement images with microscopic resolution can be obtained within minutes. The capability for 3D flow imaging is demonstrated. The sequence is then used to investigate forced detachment of a biofilm in a tube.     

Diffusion-weighted imaging in the prostate: an apparent diffusion coefficient comparison of half-Fourier acquisition single-shot turbo spin-echo and echo planar imaging

Prostate cancer detection using diffusion-weighted imaging is highly affected by the accuracy of the apparent diffusion coefficient (ADC) values in an image. Echo planar imaging (EPI) is a fast sequence commonly used for diffusion imaging but has inherent magnetic susceptibility and chemical shift artefacts associated. A diffusion sequence that is less affected by these artefacts is therefore advantageous. The half-Fourier acquisition single-shot turbo spin-echo (HASTE) sequence was chosen. The diffusion sequences were compared in image quality, repeatability of the ADC value and the effect on the ADC value with varied b values. Eight volunteers underwent three scans of each sequence, on a 1.5-T Siemens system, using b values of 0, 150, 300, 450, 600, 750, 900 and 1000 s/mm(2). ADC maps were created to address the reproducibility of the ADC value when using two b values compared to eight b values. The ADC value using all b values with the HASTE sequence gave the best performance in all tested categories. Both sequences gave significantly different ADC mean values for two b values compared to when using eight b values (P<.05) suggesting larger error is present when using two b values. HASTE was shown to be an improvement over EPI in terms of repeatability, signal variation within a region of interest and standard deviation over the volunteer set. The improved accuracy of the ADC value in the HASTE sequence makes it potentially a more sensitive tumor detection technique.     

Improved Spin-Echo-Edited NMR Diffusion Measurements

The need for simple and robust schemes for the analysis of ligand-protein binding has resulted in the development of diffusion-based NMR techniques that can be used to assay binding in protein solutions containing a mixture of several ligands. As a means of gaining spectral selectivity in NMR diffusion measurements, a simple experiment, the gradient modified spin-echo (GOSE), has been developed to reject the resonances of coupled spins and detect only the singlets in the (1)H NMR spectrum. This is accomplished by first using a spin echo to null the resonances of the coupled spins. Following the spin echo, the singlet magnetization is flipped out of the transverse plane and a dephasing gradient is applied to reduce the spectral artifacts resulting from incomplete cancellation of the J-coupled resonances. The resulting modular sequence is combined here with the BPPSTE pulse sequence; however, it could be easily incorporated into any pulse sequence where additional spectral selectivity is desired. Results obtained with the GOSE-BPPSTE pulse sequence are compared with those obtained with the BPPSTE and CPMG-BPPSTE experiments for a mixture containing the ligands resorcinol and tryptophan in a solution of human serum albumin.     

Velocity sensitivity of slice-selective excitation

The purpose of this study was to investigate how flow affects slice-selective excitation, particularly for radiofrequency (rf) pulses optimized for slice-selective excitation of stationary material. Simulation methods were used to calculate the slice profiles for material flowing at different velocities, using optimal flow compensation when appropriate. Four rf pulses of very different shapes were used in the simulation study: a 90° linear-phase Shinnar-LeRoux pulse; a 90° self-refocusing pulse; a minimum-phase Shinnar-LeRoux inversion pulse; and a SPINCALC inversion pulse. Slice profiles from simulations with a laminar flow model were compared with experimental studies for two different rf pulses using a clinical magnetic resonance imaging (MRI) system. We found that, for a given rf pulse, the effect of flow on slice-selective excitation depends on the product of the selection gradient amplitude, the component of velocity in the slice selection direction, and the square of the rf pulse duration. The shapes of the slice profiles from the Shinnar-LeRoux pulses were relatively insensitive to velocity. However, the slice profiles from the self-refocusing pulse and the SPINCALC pulse were significantly degraded by velocity. Experimental slice profiles showed excellent agreement with simulation. In conclusion, our study demonstrates that slice-selective excitation can be significantly degraded by flow depending on the velocity, the gradient amplitude, and characteristics of the rf excitation pulse used. The results can aid in the design of rf pulses for slice-selective excitation of flowing material.     

Dependence of temporal diffusion spectra on microstructural properties of biological tissues

The apparent diffusion coefficient (ADC) measured using magnetic resonance imaging methods provides information on microstructural properties of biological tissues, and thus has found applications as a useful biomarker for assessing changes such as those that occur in ischemic stroke and cancer. Conventional pulsed gradient spin echo methods are in widespread use and provide information on, for example, variations in cell density. The oscillating gradient spin echo (OGSE) method has the additional ability to probe diffusion behaviors more readily at short diffusion times, and the temporal diffusion spectrum obtained by the OGSE method provides a unique tool for characterizing tissues over different length scales, including structural features of intracellular spaces. It has previously been reported that several tissue properties can affect ADC measurements significantly, and the precise biophysical mechanisms that account for ADC changes in different situations are still unclear. Those factors may vary in importance depending on the time and length scale over which measurements are made. In the present work, a comprehensive numerical simulation is used to investigate the dependence of the temporal diffusion spectra measured by OGSE methods on different microstructural properties of biological tissues, including cell size, cell membrane permeability, intracellular volume fraction, intranucleus and intracytoplasm diffusion coefficients, nuclear size and T₂ relaxation times. Some unique characteristics of the OGSE method at relatively high frequencies are revealed. The results presented in the paper offer a framework for better understanding possible causes of diffusion changes and may be useful to assist the interpretation of diffusion data from OGSE measurements.     

Displacement power spectrum measurement by CPMG in constant gradient

The modulation of spin phase produced by Carr-Purcell-Meiboom-Gill (CPMG) sequence in combination with constant magnetic field gradient is appropriate to probe the displacement power spectrum (DPS). The spin-echo attenuation is directly proportional to the DPS value at the applied modulation frequency. Relaxation and selective excitation effects can be factored out while probing the DPS. The modulation frequency is adjusted by varying the pulse separation time while the gradient strength and the time of acquisition are kept constant. In designing the experiment gradient strength limitations, imposed by off-resonance effects, as well as limitations arising from using Gaussian phase approximation must be considered. An effective experimental strategy is presented, supported by experimental results for free and restricted diffusion.     

Modified oscillating gradient pulses for direct sampling of the diffusion spectrum suitable for imaging sequences

A variation of the oscillating gradient spin echo method had been developed, which isolates temporal frequencies of the dephasing spectrum. This allows sampling of the diffusion spectrum, the Fourier transform of the velocity correlation function (VCF). It has been shown that restriction and flow alter this function in ways that can be mathematically characterized, yielding quantitative information on restriction geometry and flow parameters. It is demonstrated that in many systems of interest, dispersion of velocity will produce a peak in the VCF spectrum near omega=0, while restricted diffusion will manifest itself in the spectrum at higher frequencies. The method, therefore, may be useful for decoupling their effects on the apparent diffusion coefficient (ADC), as well as in revealing the physics of both phenomena. This method has been implemented in model systems of packed beads, yielding data consistent with theoretical models of restricted diffusion spectra and data from one previous study. The method may have significant application to biology and medicine, as well as the study of transport phenomena in porous media and complex flow.