Diffusion measurements with the aid of nutation spin echoes appearing after two inhomogeneous radiofrequency pulses in inhomogeneous magnetic fields

Nutation echoes are generated by radiofrequency (RF) pulses with an inhomogeneous amplitude, B(1) = B(1)(r), in inhomogeneous magnetic fields, B(0) = B(0)(r). The two gradients of strengths G(1) and G(0), respectively, must be aligned in parallel for a maximum echo signal. After two RF pulses, two echoes appear at times tau(a) = 2 tau(1) + tau(2) + (G(1)/G(0))tau(1) and tau(b) = 2 tau(1) + tau(2) + 2(G(1)/G(0))tau(1), where tau(1) is the RF pulse duration and tau(2) the interpulse interval. It is shown that these echoes can favorably be employed for the determination of self-diffusion coefficients even in the poor experimental situation one often faces in low-resolution or low-field NMR. The signal intensity is comparable to that of ordinary Hahn echoes. Diffusion coefficients and spin-lattice relaxation times can be evaluated from the same experimental data set if both nutation echoes are recorded. Test experiments are in good agreement with literature data. Applications of the technique to "inside out" NMR, well logging NMR, surface coil NMR, toroid cavity NMR, etc., are suggested.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

SAR reduced pulse sequences

Three techniques were considered for reducing the RF (radiofrequency) power deposition in the body while maintaining scan time efficiency: reducing the RF peak amplitude while increasing the pulse width, substituting gradient echoes for spin echoes, and reducing the flip angle of the phase reversal pulse. The use of gradient echoes was found to be the most efficient means to reduce the power delivered to the patient and to obtain rapid data acquisition. The effect upon SAR (specific absorption rate) and SNR (signal-to-noise ratio) was demonstrated on a phantom when the phase reversal pulse was reduced from the standard 180 degrees to 90 degrees. Data in the body indicated a fairly constant SNR down to a refocusing flip angle between 110 degrees and 135 degrees. An initial clinical evaluation was performed at three institutions using the method of reducing the flip angle of the phase reversal pulse. The scan with theta = 120 degrees was rated by readers in a blinded study as having acceptable diagnostic image quality while the 135 degrees scan had comparable image quality to a conventional 90 degrees - 180 degrees pulse sequence. The use of reduced phase reversal pulses was seen as an efficient protocol to obtain T1-weighted images at rapid data rates while reducing the power delivered to the body by about 40%.     

A Near-Resonance Solution to the Bloch Equations and Its Application to RF Pulse Design

A near-resonance expansion of the solution to the Bloch equations in the presence of a radiofrequency (RF) pulse is presented in this paper. The first-order approximation explicitly demonstrates the nonlinear nature of the Bloch equations and precisely relates the excitation profile with the RF pulse when the flip angle is less than π/2. As an application of this solution, we present a procedure for designing RF pulses to generate symmetric excitation profiles with arbitrary shapes for new encoding approaches such as wavelet encoding.     

Tailored sinc pulses for uniform excitation and artifact-free radio frequency time-domain EPR imaging

A method to generate shaped radiofrequency pulses for uniform excitation of electron spins in time-domain radio frequency (RF) electron paramagnetic resonance (EPR) imaging is presented. A commercial waveform generator was integrated with the transmit arm of the existing time-domain RF-EPR spectrometer to generate tailored excitation pulses with sub-nano second resolution for excitation with a 90 degrees flip-angle. A truncated sinc [sin(x)/x] pulse, tailored to compensate for the Q-profile (RF frequency response) of the resonator, was shown to yield images from phantom objects as well as in vivo images, with minimal distortion. These studies point to the advantages in using shaped sinc pulses to achieve improved uniform excitation over a relatively wide bandwidth region in time-domain RF-EPR imaging (RF-FT-EPRI).     

Semi-adiabatic Shinnar–Le Roux pulses and their application to diffusion tensor imaging of humans at 7T

The adiabatic Shinnar–Le Roux (SLR) algorithm for radiofrequency (RF) pulse design enables systematic control of pulse parameters such as bandwidth, RF energy distribution and duration. Some applications, such as diffusion-weighted imaging (DWI) at high magnetic fields, would benefit from RF pulses that can provide greater B₁ insensitivity while adhering to echo time and specific absorption rate (SAR) limits. In this study, the adiabatic SLR algorithm was employed to generate 6-ms and 4-ms 180° semi-adiabatic RF pulses which were used to replace the refocusing pulses in a twice-refocused spin echo (TRSE) diffusion-weighted echo planar imaging (DW-EPI) sequence to create two versions of a twice-refocused adiabatic spin echo (TRASE) sequence. The two versions were designed for different trade-offs between adiabaticity and echo time. Since a pair of identical refocusing pulses is applied, the quadratic phase imposed by the first is unwound by the second, preserving the linear phase created by the excitation pulse. In vivo images of the human brain obtained at 7 Testa (7 T) demonstrate that both versions of the TRASE sequence developed in this study achieve more homogeneous signal in the diffusion-weighted images than the conventional TRSE sequence. Semi-adiabatic SLR pulses offer a more B₁-insensitive solution for diffusion preparation at 7 T, while operating within SAR constraints. This method may be coupled with any EPI readout trajectory and parallel imaging scheme to provide more uniform coverage for diffusion tensor imaging at 7 T and 3 T.     

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.     

Single-shot line scan imaging using stimulated echoes

A new high-speed MRI method is described for single-shot line scan imaging (LSI) based on stimulated echoes (STE). To allow for multislice imaging, the technique comprises a series of slice-selective preparation pulses (each corresponding to the first RF pulse of a STE sequence), a slab-selective refocusing pulse (second RF pulse), and multiple line-selective read pulses (third RF pulses). An alternative version employs packages of two slice-selective pulses followed by multiple line-selective read pulses. Experimental applications deal with human brain imaging on a clinical MRI system at 2.0 T. The technique offers user-selectable trade-offs between volume coverage (1-15 sections) and in-plane spatial resolution (1-5 mm linear pixel dimension) within total acquisition times of less than 500 ms. Although LSI yields a lower signal-to-noise ratio than Fourier imaging, single-shot LSI with STEs is free from resonance offset effects (e.g., magnetic field inhomogeneities and susceptibility differences) that are typical for echo-planar imaging. Moreover, the technique exhibits considerable robustness against motion and provides access to arbitrary fields-of-view, i.e., localized imaging of inner volumes without aliasing artifacts due to phase wrapping.     

Improved Broadband Inversion Performance for NMR in Liquids

New NMR broadband inversion pulses that compensate both for resonance offset and radiofrequency (RF) inhomogeneity are described. The approach described is a straightforward computer optimization of an initial digitized waveform generated from either a constant-amplitude frequency sweep or from an existing composite inversion pulse. Problems with convergence to local minima are alleviated by the way the optimization is carried out. For a given duration and maximum allowable RF field strength B₁ (but not necessarily given RMS power deposition), the resultant broadband inversion pulse (BIP) shows superior inversion compared to inversion pulses obtained from previous methods, including adiabatic inversion pulses. Any existing BIP can be systematically elaborated to build up longer inversion pulses that perform over larger and larger bandwidths. The resulting pulse need not be adiabatic throughout its duration or across the entire operational bandwidth.     

Minimisation of slab-selective radiofrequency excitation pulse durations constrained by an acceptable aliasing coefficient

A technical note is presented on the slab-direction aliasing of 3D imaging, introducing a simple methodology for determining the minimised duration of low flip-angle sinc radiofrequency (RF) excitation pulses, with respect to a required slab profile accuracy. The various interdependent factors affected in modifying an RF pulse duration are considered and analysed in the context of a new metric for quantifying the levels of permitted slab-aliasing. A general framework is presented for the selection of standard sinc RF excitation pulses with system-minimised durations, as well as their analysis and validation, and a demonstration of this methodology is performed for an example requirement and scanner. This methodology enables implementation of standard (vendor-generated) RF pulses with minimised duration for a required application, with high confidence in their operational reliability. Parts of such a methodology may also in theory be extended to more advanced RF pulse designs.     

Universal equations for linear adiabatic pulses and characterization of partial adiabaticity

A numerical analysis of the sech/tanh (or hyperbolic secant) and tanh/tan adiabatic inversion pulses provides a set of master equations for each type of pulse that guarantee their optimal implementation over a wide range of practical conditions without needing to further simulate the inversion profiles of the pulses. These simple equations determine the necessary maximum RF amplitude (RF(max)) required for a preselected degree of inversion across a chosen effective bandwidth (bw(eff)) and for a chosen pulse length (T(p)). The two types of pulse function differently: The sech/tanh pulse provides a rectangular inversion profile with bw(eff) being a large fraction of the adiabatic frequency sweep (bwdth), whereas for tanh/tan bw(eff) is < or =bwdth/20. If the quality of inversion is defined as the minimum allowable extent of inversion, iota(bw), at the boundaries of bw(eff), two basic linear equations are found for both types of pulse and these are of the form (RF(max)T(p))(2)=m(1)T(p)bwdth+c(1) and T(p)bwdth=m(3)T(p)bw(eff)+c(3). The different behavior of the two pulses is expressed as different dependencies of the slopes m(n) and intercepts c(n) on iota(bw) and allowances are made for second order effects within these equations. The availability of these master relationships enables a direct comparison of the two types of adiabatic pulse and it is found that tanh/tan requires about half the pulse length of an equivalent sech/tanh pulse and also has the advantage of being less sensitive to the effects of scalar coupling. In contrast sech/tanh delivers about half the total RF power of an equivalent tanh/tan pulse. It is expected that the forms of these two basic linear equations are generally applicable to adiabatic inversion pulses and thus define the concept of "linear adiabaticity." At low values of T(p)bwdth or T(p)bw(eff) the linear equations no longer apply, defining a region of "partial adiabaticity." Normal adiabatic pulses in the middle of this partial region are more efficient in terms of RF(max) or T(p) but are moderately less tolerant to RF inhomogeneity. A class of numerically optimized pulses has recently been developed that specifically trades adiabaticity in an attempt to gain RF(max) or T(p) efficiency. In comparison to normal adiabatic pulses implemented under optimal conditions, these new partially adiabatic pulses show only marginal improvements; they are restricted to single values of T(p)bw(eff), and they are vastly less tolerant to RF inhomogeneity. These comparisons, and direct comparisons between any types of inversion pulse, adiabatic or otherwise, can be made using plots of (RF(max)T(p))(2) or (Total Power) T(p) versus T(p)bw(eff).     

Study of radiofrequency radiation by means of optical effect of electromagnetically induced transparency

We propose a method of all-optical investigation of radiofrequency (RF) radiation based on the coherent effect of electromagnetically induced transparency (EIT). It is shown that if the atomic coherence is perturbed by an RF field, the shape of probe pulse propagating in a three-level ??-type atomic medium under EIT conditions is modified correspondingly to the temporal structure of the RF pulse. The effect is sensitive to the parameters of the pulse which enables measuring the intensity and the spectrum of the RF pulse. The method can be used for storage and lossless transfer of RF information over long distances using optical pulses.     

Generation of 320 fs pulses with a distributed feedback dye laser

A new achromatic distributed feedback dye laser (DFDL) arrangement is described. The experimental conditions for subpicosecond pulse generation with the new device were investigated. For the first time, stable generation of subpicosecond pulses (350 fs) at 616 nm was achieved with a DFDL. The simultaneous spectral and autocorrelation measurements showed that the amplified DFDL pulses are nearly transform limited, having a pulse form close to the sech² shape.     

Multiple echoes, multiple quantum coherence, and the dipolar field: demonstrating the significance of higher order terms in the equilibrium density matrix.

It is well known that dipolar field effects lead to multiple spin echoes in a simple two-RF pulse experiment (the MSE experiment). We show here that coherence transfer echoes (which identify the existence of multiple quantum coherences in liquid NMR) and multiple spin echoes have a common origin. Using density matrix theory we have calculated the phase and timing of multiple spin echoes from all quadrature phase combinations of RF pulses. We show for the MSE experiment that there is a one-to-one correspondence between the time domain echo order and the multiple quantum coherence order. The experimental confirmation of these phase predictions shows that multiple spin echoes provide independent evidence for the breakdown of the high temperature approximation as proposed by Warren et al. (Science 262, 2005 (1993)).     

Optimization schemes for selective excitations: application to the DIGGER pulses.

In this work, two distinct approaches to the tailoring of selective radiofrequency (RF) pulses were applied to a cos-sinc pulse of the DIGGER sequence used in localized spectroscopy. Ideally, three such pulses combined with a gradient in each direction destroy the Mz component of the magnetization everywhere but in the volume of interest. In the first approach, the optimal RF amplitude modulation is found by minimizing the difference between the ideal and the computed Mz profiles. In the second strategy, the RF pulse envelope is adjusted by optimization of the tip angle profile. Computed slice profiles optimized by each of these methods have been compared to experimental results. Simulations as well as experiments show that the second approach, which optimizes tip angles, is the most efficient.     

Solomon echoes for spin 7/2 by soft pulse excitation

Solomon echoes are calculated for spin 7/2 in solids taking into account the first-order quadrupolar interaction while the pulses are on. The computation is performed using the algebraic computer program ‘MAPLE’. Fifteen echoes are predicted and the amplitude of each echo is calculated. Each satellite transition produces five echoes whereas no echo is detected for the central transition. Among these echoes, six are ‘forbidden’ which are a result of the refocusing of exclusively multiple quantum coherences which are developed during the first pulse. These echoes cannot be predicted by a calculation based upon ‘hard’ pulse excitation. The results are valid for any ratio of the quadrupolar coupling to the frequency of the RF field (ω_Q/ω₁).     

Spin-lattice relaxation and a fast T1-map acquisition method in MRI with transient-state magnetization

The magnetization under the spin-lattice relaxation and the nuclear magnetic resonance radiofrequency (RF) pulses is calculated for a signal RF pulse train and for a sequence of multiple RF pulse-trains. It is assumed that the transverse magnetization is zero when each RF pulse is applied. The result expressions can be grouped into two terms: a decay term, which is proportional to the initial magnetization M0, and a recovery term, which has no M0 dependence but strongly depends on the spin-lattice relaxation and the equilibrium magnetization Meq. In magnetic resonance pulse sequences using magnetization in transient state, the recovery term produces artifacts and can seriously degrade the function of the preparation sequence for slice selection, contrast weighting, phase encoding, etc. This work shows that the detrimental effect can be removed by signal averaging in an eliminative fashion. A novel fast data acquisition method for constructing the spin-lattice relaxation (T1) map is introduced. The method has two features: (i) By using eliminative averaging, the curve to fit the T1 value is a decay exponential function rather than a recovery one as in conventional techniques; therefore, the measurement of Meq is not required and the result is less susceptible to the accuracy of the inversion RF pulse. (ii) The decay exponential curve is sampled by using a sequence of multiple pulse-trains. An image is reconstructed from each train and represents a sample point of the curve. Hence a single imaging sequence can yield multiple sample points needed for fitting the T1 value in contrast to conventional techniques that require repeating the imaging sequence for various delay values but obtain only one sample point from each repetition.     

Use of composite refocusing pulses to form spin echoes

The radiofrequency pulses used in NMR are subject to a number of imperfections such as those caused by inhomogeneity of the radiofrequency (B(1)) field and an offset of the transmitter frequency from precise resonance. The effect of these pulse imperfections upon a refocusing pulse in a spin-echo experiment can be severe. Many of the worst effects, those that distort the phase of the spin echo, can be removed completely by selecting the echo coherence pathway using either the "Exorcycle" phase cycle or magnetic field gradients. It is then tempting to go further and try to improve the amplitude of the spin-echo signal by replacing the simple refocusing pulse with a broadband composite 180° pulse that compensates for the relevant pulse imperfection. We show here that all composite pulses with a symmetric or asymmetric phase shift scheme will reintroduce phase distortions into the spin echo, despite the selection of the echo coherence pathway. In contrast, all antisymmetric composite pulses yield no phase distortion whatsoever, both on and off resonance, and are therefore the correct symmetry of composite refocusing pulse to use. These conclusions are verified using simulations and (31)P MAS NMR spin-echo experiments performed on a microporous aluminophosphate.     

Demonstration of partial erasing of picosecond temporal optical data by use of accumulated photon echoes

We demonstrated partial erasing of temporal optical data on a picosecond time scale by use of accumulated photon echoes. In a photon-echo memory the temporal data at time tau are stored as a frequency grating of period 1/tau in the absorption spectrum of a material. Partial erasing of the temporal data is achieved by irradiation of the material with a pulse pair at time separation tau , but the phase of one of the pulses is shifted 180 degrees . This process does not produce a frequency grating, and no echo is emitted. The experiment was performed with a dye-doped polymer film. The 180 degrees phase shift was obtained by use of a half-wave plate.     

Multiple echo diffusion tensor acquisition technique

The standard method of diffusion tensor imaging (DTI) involves one diffusion-sensitizing gradient direction per acquired signal. This paper describes an alternative method in which the entire direction set required for calculating the diffusion tensor is captured in a few scans. In this method, a series of radiofrequency (RF) pulses are applied, resulting in a train of spin echoes. A pattern of applied magnetic field gradients between the RF pulses generates a different diffusion weighting in both magnitude and direction for each echo, resulting in a dataset sufficient to determine the tensor. This significantly reduces the time required for a full DTI scan and potentially allows a tradeoff of this time for image quality. In the present work, this method is demonstrated in an anisotropic diffusion phantom (asparagus).