Theoretical studies of the effect of the dipolar field in multiple spin-echo sequences with refocusing pulses of finite duration

It has been observed recently that the finite duration of refocusing rf pulses in a multiecho acquisition of the signal formed under the influence of the dipolar field leads to significant signal attenuation [S. Kennedy, Z. Chen, C.K. Wong, E.W.-C. Kwok, J. Zhong, Investigation of multiple-echo spin-echo signal acquisition under distant dipole-dipole interactions, Proc. Int. Soc. Magn. Reson. Med. 13 (2005) 2288]. Hereto, we quantify the phenomenon by evaluating analytically the influences of both the distant dipolar field (DDF) and transverse relaxation T2 on the magnetization in a multiecho pulse sequence based on correlation spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED). Analytic expressions for the magnetization were obtained, which demonstrate explicitly the origin of rephased signal in the presence of the finite pi pulses in the multiecho train. The expressions also explain the effects of the DDF and T2 during the refocusing pulses on the signal strength, and show the substantial signal dependence on the phase of the rf pulses. We show that when the DDF effect during the pulse is canceled, the signal rises primarily during the free evolution time in the acquisition period. This elucidates the signal attenuation when the rf pulses cover a significant proportion of time in the sequence. In addition, we performed an optimization on the number of refocusing pulses that maximizes the total acquired signal using parameters for water, brain white matter, and muscle. We found that maximal signal-to-noise ratio is obtained when the pulse duration approximately equals the free evolution time in the samples with a wide range of T2.     

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.     

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.     

The generating functions formalism for the analysis of spin response to the periodic trains of RF pulses. Echo sequences with arbitrary refocusing angles and resonance offsets

The generating functions (GF) formalism was applied for calculation of spin density matrix evolution under the influence of periodic trains of RF pulses. It was shown that in a general case, closed expression for the generating function can be found that allows in many cases to derive analytical expressions for the generating function of spin density matrix (magnetization, coherences). This approach was shown to be particularly efficient for the analysis of multi-echo sequences, where one has to average over various frequency isochromats. The explicit analytical expressions for the generating function for echo amplitudes in a Carr–Purcell–Meiboom–Gill (CPMG) echo sequence, a multiecho sequence with incremental phase of refocusing pulse, a gradient echo sequence including transient period were obtained for an arbitrary flip angle and an arbitrary resonance offset. Comparison of the theory and the spin-echo experiments was done, demonstrating a good agreement.     

Transverse spin relaxation in liquid 129Xe in the presence of large dipolar fields

Using spin-echo NMR techniques we study the transverse spin relaxation of hyperpolarized liquid 129Xe in a spherical cell. We observe an instability of the transverse magnetization due to dipolar fields produced by liquid 129Xe, and find that imperfections in the pi pulses of the spin-echo sequence suppress this instability. A simple perturbative model of this effect is in good agreement with the data. We obtain a transverse spin relaxation time of 1300 sec in liquid 129Xe, and discuss applications of hyperpolarized liquid 129Xe as a sensitive magnetic gradiometer and for a permanent electric dipole moment search.     

Contrast manipulation and artifact assessment of 2D and 3D RARE sequences

The extent of contrast manipulation and the assessment of characteristic artifacts in imaging studies of brain and knee as performed with novel variants of the Rapid Acquisition Relaxation Enhanced (RARE) sequence are reported. Methods of ordering the phase encoding within one or two echo trains are proposed for manipulating T2 contrast. Options for minimizing artifacts associated with the various schemes are discussed. The extent of T1 contrast manipulation in RARE sequences is explored by varying repetition rates in a signal averaging scheme and by applying inversion pulses prior to data acquisition. The results demonstrate that RARE sequences can be utilized for obtaining good quality images with a range of tissue contrast options similar to those associated with slower spin-echo methods. They also suggest that RARE applications need not be confined to highlighting long T2 fluid spaces, an application already well documented.     

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.     

Application of double spin echo spiral chemical shift imaging to rapid metabolic mapping of hyperpolarized [1-¹³C]-pyruvate

Undersampled spiral CSI (spCSI) using a free induction decay (FID) acquisition allows sub-second metabolic imaging of hyperpolarized 13C. Phase correction of the FID acquisition can be difficult, especially with contributions from aliased out-of-phase peaks. This work extends the spCSI sequence by incorporating double spin echo radiofrequency (RF) pulses to eliminate the need for phase correction and obtain high quality spectra in magnitude mode. The sequence also provides an added benefit of attenuating signal from flowing spins, which can otherwise contaminate signal in the organ of interest. The refocusing pulses can potentially lead to a loss of hyperpolarized magnetization in dynamic imaging due to flow of spins through the fringe field of the RF coil, where the refocusing pulses fail to provide complete refocusing. Care must be taken for dynamic imaging to ensure that the spins remain within the B?-homogeneous sensitive volume of the RF coil.     

Carr-Purcell sequences with composite pulses

We present novel Carr-Purcell-like sequences using composite pulses that exhibit improved performance in strongly inhomogeneous fields. The sequences are designed to retain the intrinsic error correction of the standard Carr-Purcell-Meiboom-Gill (CPMG) sequence. This is achieved by matching the excitation pulse with the refocusing cycle such that the initial transverse magnetization lies along the axis n(Beta) characterizing the overall rotation of the refocusing cycle. Such sequences are suitable for relaxation measurements. It is shown that in sufficiently inhomogeneous fields, the echo amplitudes have an initial transient modulation that is limited to the first few echoes and then decay with the intrinsic relaxation time of the sample. We show different examples of such sequences that are constructed from simple composite pulses. Sequences of the form 90 degrees (0)-(90 degrees (90-theta/2)-theta(180-theta/2)-90 degrees (90-theta/2))(n) with theta approximately 90 degrees and 270 degrees generate signal over a bandwidth larger than that of the conventional CPMG sequence, resulting in an improved signal-to-noise ratio in inhomogeneous fields. The new sequence 127 degrees (x,y)-(127 degrees (x)-127 degrees (-x))(n) only excites signal off-resonance with a spectrum that is bimodal, peaking at Delta omega(0)=+/-omega(1). Depending on the phase and exact timing of the first pulse, symmetric or antisymmetric excitation is obtained. We also demonstrate several new sequences with improved dependence on the RF field strength. The sequence (22.5 degrees (67.5)-90 degrees (-22.5))-(90 degrees (67.5)-45 degrees (157.5)-90 degrees (67.5))(n) has the property that the phase of the signal depends on B(1), allowing coarse B(1) imaging in a one-dimensional experiment.     

Steady-state free precession with hyperpolarized 3He: experiments and theory

The magnetization response of hyperpolarized 3He gas to a steady-state free precession (SSFP) sequence was simulated using matrix product operators. The simulations included the effects of flip angle (alpha), sequence timings, resonant frequency, gas diffusion coefficient, imaging gradients, T1 and T2. Experiments performed at 1.5 T, on gas phantoms and with healthy human subjects, confirm the predicted theory, and indicate increased SNR with SSFP through use of higher flip angles when compared to optimized spoiled gradient echo (SPGR). Simulations and experiments show some compromise to the SNR and some point spread function broadening at high alpha due to the incomplete refocusing of transverse magnetization, caused by diffusion dephasing from the readout gradient. Mixing of gas polarization levels by diffusion between slices is also identified as a source of signal loss in SSFP at higher alpha through incomplete refocusing. Nevertheless, in the sample experiments, a SSFP sequence with an optimized flip angle of alpha=20 degrees, and 128 sequential phase encoding views, showed a higher SNR when compared to SPGR (alpha=7.2 degrees) with the same bandwidth. Some of the gas sample experiments demonstrated a transient signal response that deviates from theory in the initial phase. This was identified as being caused by radiation damping interactions between the large initial transverse magnetization and the high quality factor (Q=250) birdcage resonator. In 3He NMR experiments, performed without imaging gradients, diffusion dephasing can be mitigated, and the effective T2 is relatively long (1 s). Under these circumstances the SSFP sequence behaves like a CPMG sequence with sinalpha/2 weighting of SNR. Experiments and simulations were also performed to characterize the off-resonance behaviour of the SSFP HP 3He signal. Characteristic banding artifacts due to off-resonance harmonic beating were observed in some of the in vivo SSFP images, for instance in axial slices close to the diaphragm where B0 inhomogeneity is highest. Despite these artifacts, a higher SNR was observed with SSFP in vivo when compared to the SPGR sequence. The trends predicted by theory of increasing SSFP SNR with increasing flip angle were observed in the range alpha=10-20 degrees without compromise to image quality through blurring caused by excessive k-space filtering.     

A rotational approach to localized SPAMM 1-1 tagging

Magnetic resonance tagging usually relies on controlling the phase dispersion of the transverse magnetization component. Phase dispersion is, however, affected by the inherent phase of selective excitation pulses, thus limiting their combination with tagging sequences to the application of refocusable pulses, as in the localized spatial modulation of magnetization (L-SPAMM) technique. In this study, we examine the effect of selective excitation pulses on a L-SPAMM 1-1 sequence, showing that in the case of two identical pulses the phase component is canceled out, and thus preemphasis and refocus gradients are not needed, allowing us to take advantage of a constant gradient throughout the tagging sequence, and also that one might choose nonrefocusable maximum and minimum phase pulses.     

Encoding to the longitudinal magnetization for MR imaging and flow velocity mapping

Phase-encoding to the longitudinal magnetization is implemented by adding encoding gradient pulses in the evolution period tau of the NMR pulse sequence 90 degrees+x-tau-90 degrees-x. This work focuses on the effect of the spin-lattice relaxation and its removal and on the constraint that the 90 degrees-x pulse can only transform the phase of the transverse magnetization partially to the longitudinal magnetization. Theoretical analysis shows that the encoded phase information and the spin-lattice relaxation effect are separable and the latter is identical in each repetition in collecting phase-encoding data. Thus the relaxation effect can be eliminated by subtracting a second data set whose phase information is inverted or by alternating the polarity of the relaxation contribution. From data with partial phase information, Fourier-transform image reconstruction results in mirror aliasing in which the two halves of the Fourier spectrum of positive and negative coordinates overlap. Removal of mirror aliasing requires imaging data of the orthogonal component. Nevertheless mirror aliasing is not necessarily a problem, depending on the subject of study. Phase-encoding to the longitudinal magnetization for spatial MRI and flow velocity mapping are demonstrated using the rotating ultra-fast imaging sequence (RUFIS).     

Current density imaging sequences with separation of mobile-ion current from immobile-ion current

Three sequences for electric current density imaging (CDI) are studied by testing their ability to selectively detect the electric current of different types of charge carriers. Two of the methods are standard DC-CDI and AC-CDI sequences, and a new AC-DC-CDI sequence is also introduced. The methods rely on the application of square voltage pulses in combination with refocusing RF pulses that can, depending on their position with respect to the voltage pulses, eliminate resistive, capacitive or neither of the current components from the detection pathway. It is demonstrated by experiments on a model system that the DC-CDI sequence detects only the resistive current of mobile ions, the AC-DC-CDI sequence detects only the capacitive current of fixed ions, while the AC-CDI sequence detects both current components. The three sequences introduce a new MRI contrast mechanism that depends on the ion mobility of the sample. As such, the methods may play an important role in the study of electric conductivity phenomena in biological systems.     

Acquisition time reduction in magnetic resonance spectroscopic imaging using discrete wavelet encoding

This paper describes a new magnetic resonance spectroscopic imaging (MRSI) technique based upon the discrete wavelet transform to reduce acquisition time and cross voxel contamination. Prototype functions called wavelets are used in wavelet encoding to localize defined regions in localized space by dilations and translations. Wavelet encoding in MRSI is achieved by matching the slice selective RF pulse profiles to a set of dilated and translated wavelets. Single and dual band slice selective excitation and refocusing pulses, with profiles resembling Haar wavelets, are used in a spin-echo sequence to acquire 2D-MRSI wavelet encoding data. The 2D space region is spanned up to the desired resolution by a proportional number of dilations (increases in the localization gradients) and translations (frequency shift) of the Haar wavelets (RF pulses). Acquisition time is reduced by acquiring successive MR signals from regions of space with variable size and different locations with no requirement for a TR waiting time between acquisitions. An inverse wavelet transform is performed on the data to produce the correct spatial MR signal distribution.     

Optimization of the ultrafast look-locker echo-planar imaging T1 mapping sequence

The Look–Locker echo-planar imaging (LL-EPI) sequence has been numerically optimized in terms of the signal-to-noise ratio in the measured value of T₁, for both single-shot (repetition time (T_R) = ∞), and dynamically repeated T₁ measurements. The sequence is optimized for the normal biologic range of T₁ (0.2 s to 2.0 s) and for a range of sequence parameters found on most magnetic resonance (MR) scanners. Both linearly and geometrically spaced magnetization sample pulse intervals were considered. For single-shot measurements, the sequence with 24 linearly spaced sample pulses, an inversion time of 0.01 s, an inter-sample pulse delay of 0.10 s, and a sample radiofrequency (RF) pulse flip angle of 25^o was found to be optimum. When the number of sample pulses was limited due to hardware limitations, different pulse sequence parameters were indicated. The optimization procedures used are appropriate for any single-shot T₁ mapping sequence variant and for any rapid T₁ mapping application. The use of an optimized Look–Locker echo-planar imaging sequence is demonstrated by an example of dynamic contrast-enhanced scanning in the brain using fast T₁ mapping.     

Optimization of spoiler gradients in flash MRI

The FLASH technique for fast magnetic resonance (MR) imaging often employs strong magnetic field gradients, called spoiler gradients, to dephase the transverse magnetization after it has been measured. Otherwise, image artifacts can develop. The effectiveness of spoiler gradients at suppressing these artifacts was evaluated experimentally on two-dimensional MR images of a uniform phantom and patients. It was informative to compare the magnetization immediately before the RF excitation in each phase encoding step. Only spoiler gradients in the slice selection direction were effective. Spoiler gradients that decreased steadily from a large amplitude in the first phase encoding step to zero in the last minimized the transverse magnetization and suppressed the image artifact, without changing the image contrast.     

Evaluation of non-selective refocusing pulses for 7 T MRI

There is a continuing need for improved RF pulses that achieve proper refocusing in the context of ultra-high field (≥ 7 T) human MRI. Simple block or sinc pulses are highly susceptible to RF field inhomogeneities, and adiabatic pulses are generally considered too SAR intensive for practical use at 7 T. The performance of the array of pulses falling between these extremes, however, has not been systematically evaluated. The aim of this work was to compare the performances of 21 non-selective refocusing pulses spanning a range of durations and SAR levels. The evaluation was based upon simulations and both phantom and in vivo human brain experiments conducted at 7 T. Tested refocusing designs included block, composite block, BIR-4, hyperbolic secant, and numerically optimized composite waveforms. These pulses were divided into three SAR classes and two duration categories, and, based on signal gain in a 3-D spin echo sequence, practical recommendations on usage are made within each category. All evaluated pulses were found to produce greater volume-averaged signals relative to a 180° block pulse. Although signal gains often come with the price of increased SAR or duration, some pulses were found to result in significant signal enhancement while also adhering to practical constraints. This work demonstrates the signal gains and losses realizable with single-channel refocusing pulse designs and should assist in the selection of suitable refocusing pulses for practical 3-D spin-echo imaging at 7 T. It further establishes a reference against which future pulses and multi-channel designs can be compared.     

Application of optimal control to CPMG refocusing pulse design

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.     

Magnetic resonance imaging of alternating electric currents

Electric Current Density Imaging (CDI) is a new modality of magnetic resonance imaging that enables electric current distribution imaging in conductive samples containing water. So far, two CDI techniques have been in use: DC-CDI operating at zero frequency and RF-CDI operating at the RF Larmor frequency. In this paper we present a new CDI technique, which extends the CDI frequency range to alternating electric currents (AC-CDI). First, a theoretical model for the electric current response to the alternating voltage is presented. Later, this model is used for the frequency analysis of the AC-CDI sequence. Additionally, the effect of off-resonance spins and imperfect refocusing RF pulses on the stability of the AC-CDI sequence and the echo formation is studied. The new theory is verified by experiments on a model system and compared to the other two methods: DC-CDI and RF-CDI. Finally, an application of the AC-CDI sequence to biological systems is demonstrated by an experiment on a wood twig in which an increase of approximately 30% was obtained at AC as compared to DC electric current.     

Selective refocusing pulses in magic-angle spinning NMR: characterization and applications to multi-dimensional protein spectroscopy

Band-selective pulses are frequently used in multi-dimensional NMR in solution, but have been used relatively less often in solid-state NMR applications because of the complications imposed by magic-angle spinning. In this work, we examine the frequency profiles and the refocusing efficiency of several commonly employed selective general rotation pi pulses through experiments and numerical simulations. We demonstrate that highly efficient refocusing of transverse magnetization can be achieved, with experiments that agree well with numerical simulations. We also show that the rotational echo is shifted by a half rotor period if a selective pulse is applied over an integer number of rotor periods. Appropriately synchronizing indirect evolution periods with selective pulses ensures proper phasing of cross peaks in 2D spectra. The improved performance of selective pulses in multi-dimensional protein spectroscopy is demonstrated on the 56-residue beta1 immunoglobulin binding domain of protein G (GB1).