Dynamics of 23Na during completely balanced steady-state free precession

The dynamics of 23Na during completely balanced steady-state free precession (SSFP) have been studied in numerical simulations and experiments. Results from both agree well. It is shown that during SSFP multiple quantum coherences are excited and that their excitation affects the observable signal. The signal response to the sequence parameters (flip angle, TR, and RF pulse phase cycle) shows a structure which can not be described by the Bloch equations. Due to excitation of T31 (s,a), the amplitude ratio of the fast and slowly decaying components deviates from 3:2 and is a function of the sequence parameters. The results shown here represent a basis for the implementation and optimization of 23Na-SSFP imaging sequences.     

Effects of RF pulse profile and intra-voxel phase dispersion on MR fingerprinting with balanced SSFP readout

PurposeTo investigate possible errors in T1 and T2 quantification via MR fingerprinting with balanced steady-state free precession readout in the presence of intra-voxel phase dispersion and RF pulse profile imperfections, using computer simulations based on Bloch equations.Materials and methodsA pulse sequence with TR changing in a Perlin noise pattern and a nearly sinusoidal pattern of flip angle following an initial 180-degree inversion pulse was employed. Gaussian distributions of off-resonance frequency were assumed for intra-voxel phase dispersion effects. Slice profiles of sinc-shaped RF pulses were computed to investigate flip angle profile influences. Following identification of the best fit between the acquisition signals and those established in the dictionary based on known parameters, estimation errors were reported. In vivo experiments were performed at 3 T to examine the results.ResultsSlight intra-voxel phase dispersion with standard deviations from 1 to 3 Hz resulted in prominent T2 under-estimations, particularly at large T2 values. T1 and off-resonance frequencies were relatively unaffected. Slice profile imperfections led to under-estimations of T1, which became greater as regional off-resonance frequencies increased, but could be corrected by including slice profile effects in the dictionary. Results from brain imaging experiments in vivo agreed with the simulation results qualitatively.ConclusionMR fingerprinting using balanced SSFP readout in the presence of intra-voxel phase dispersion and imperfect slice profile leads to inaccuracies in quantitative estimations of the relaxation times.     

Effects of RF profile on precision of quantitative T2 mapping using dual-echo steady-state acquisition

The dual echo steady-state (DESS) sequence has been shown successful in achieving fast T2 mapping with good precision. Under-estimation of T2, however, becomes increasingly prominent as the flip angle decreases. In 3D DESS imaging, therefore, the derived T2 values would become a function of the slice location in the presence of non-ideal slice profile of the excitation RF pulse. Furthermore, the pattern of slice-dependent variation in T2 estimates is dependent on the RF pulse waveform. Multi-slice 2D DESS imaging provides better inter-slice consistency, but the signal intensity is subject to integrated effects of within-slice distribution of the actual flip angle. Consequently, T2 measured using 2D DESS is prone to inaccuracy even at the designated flip angle of 90°. In this study, both phantom and human experiments demonstrate the above phenomena in good agreement with model prediction.     

Maximizing MR signal for 2D UTE slice selection in the presence of rapid transverse relaxation

Ultrashort TE (UTE) sequences allow direct visualization of tissues with very short T2 relaxation times, such as tendons, ligaments, menisci, and cortical bone. In this work, theoretical calculations, simulations, and phantom studies, as well as in vivo imaging were performed to maximize signal-to-noise ratio (SNR) for slice selective RF excitation for 2D UTE sequences. The theoretical calculations and simulations were based on the Bloch equations, which lead to analytic expressions for the optimal RF pulse duration and amplitude to maximize magnetic resonance signal in the presence of rapid transverse relaxation. In steady state, it was found that the maximum signal amplitude was not obtained at the classical Ernst angle, but at an either lower or higher flip angle, depending on whether the RF pulse duration or amplitude was varied, respectively.     

RF slice profile effects in magnetic resonance fingerprinting

The radio frequency (RF) slice profile effects on T1 and T2 estimation in magnetic resonance fingerprinting (MRF) are investigated with respect to time-bandwidth product (TBW), flip angle (FA) level and field inhomogeneities. Signal evolutions are generated incorporating the non-ideal slice selective excitation process using Bloch simulation and matched to the original dictionary with and without the non-ideal slice profile taken into account. For validation, phantom and in vivo experiments are performed at 3T. Both simulations and experiments results show that T1 and T2 error from non-ideal slice profile increases with increasing FA level, off-resonance, and low TBW values. Therefore, RF slice profile effects should be compensated for accurate determination of the MR parameters.     

Combined simulated annealing and Shinnar-Le Roux pulse design of slice-multiplexed RF pulses for multi-slice imaging

Slice-multiplexed RF pulses have recently been introduced for simultaneous multi-slice imaging. Their novel aspect is that each slice is given a different linear phase profile, and hence a different slice-rephasing requirement, by the pulse. During readout, extra slice gradients are applied such that when one slice is rephased, the others are dephased to prevent aliasing. In this paper, an improved method of designing slice-multiplexed RF pulses is presented: component pulses which are optimized with simulated annealing for a specific rephasing are combined using Shinnar-Le Roux methods. In this way, non-linearities at higher flip angles are taken into account and more slices can be excited. Bloch simulations show the phase and amplitude profile of component pulses are faithfully preserved in the multiplexed pulse. Three- and four-slice multiplex pulses are demonstrated in gradient- and spin-echo in-vivo imaging.     

Large angle spin-echo imaging

A study was undertaken to assess the use of excitation flip angles greater than 90° for T₁ weighted spin-echo (SE) imaging with a single 180° refocusing pulse and short TR values. Theoretical predictions of signal intensity for SE images with excitation pulse angles of 90–180° were calculated based on the Bloch equations and then measured experimentally from MR images of MnCl₂ phantoms of various concentrations. Liver signal-to-noise ratios (SNR) and liver-spleen contrast-to-noise ratios (CNR) were measured from breathhold MR images of the upper abdomen in 16 patients using 90 and 110° excitation flip angles. The theoretical predictions showed significant improvements in SNR with excitation flip angles >90°, which were more pronounced at small TR values. The phantom studies showed reasonably good agreement with the theoretical predictions in correlating the excitation pulse angle with signal intensity. In the human imaging studies, the 110° excitation pulse angle resulted in a 7.4% (p < .01) increase in liver SNR and an 8.2% (p = .2) increase in liver-spleen CNR compared to the 90° pulse angle at TR = 275 ms. Increased signal intensity resulting from the use of large flip angle excitation pulses with a single echo SE pulse sequence was predicted and confirmed experimentally in phantoms and humans.     

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.     

Partial angle inversion recovery (PAIR) MR imaging: spin-echo and snapshot implementation.

The effects of varying the inversion or excitation RF pulse flip angles on image contrast and imaging time have been investigated in IR imaging theoretically, with phantoms and with normal volunteers. Signal intensity in an IR pulse sequence as a function of excitation, inversion and refocusing pulse flip angles was calculated from the solution to the Bloch equations and was utilized to determine the contrast behavior of a lesion/liver model. Theoretical and experimental results were consistent with each other. With the TI chosen to suppress the fat signal, optimization of the excitation pulse flip angle results in an increase in lesion/liver contrast or allows reduction in imaging time which, in turn, can be traded for an increased number of averages. This, in normal volunteers, improved spleen/liver contrast-to-noise ratio (9.0 vs. 5.7, n = 8, p less than 0.01) and suppressed respiratory ghosts by 33% (p less than 0.01). Reducing or increasing the inversion pulse from 180 degrees results in shorter TI needed to null the signal from the tissue of interest. Although this decreases the contrast-to-noise ratio, it can substantially increase the number of sections which can be imaged per given TR in conventional IR imaging or during breathold in the snapshot IR (turboFLASH) technique. Thus, the optimization of RF pulses is useful in obtaining faster IR images, increasing the contrast and/or increasing the number of imaging planes.     

Truncated sinc slice excitation for 31P spectroscopic imaging

The shortest possible delay (Td) between slice selection and data acquisition is important for producing high quality 31P spectra. In single slice multivoxel spectroscopic imaging, conventional excitation using sinc-shaped rf pulses within typical gradient limitations can have values of Td that lead to significant spectral distortion and loss of signal. Truncated sinc excitation, which ends the excitation close to the center of the main rf lobe has been suggested for MR angiographic applications to produce short values of Td. In this work, the slice profiles, spectral signal-to-noise ratio (SNR) and spectral distortions are compared using the minimum delay achievable on a commercial MRI system for conventional 'sinc' rf excitation and truncated sinc excitation. Slice profiles are calculated using the Bloch equations and measured with a phantom. SNR and spectral distortions are evaluated from whole slice spectra on a human volunteer. On an MRI system with 1 G/cm gradients (0.5 msec risetime), for a 2.5-cm slice at 31P frequencies, conventional excitation can be adjusted to achieve Td = 2.5 msec while truncated sinc excitation yields Td = 1.5 msec. The truncated sinc excitation's shorter value of Td leads to much smaller spectral distortions, but its slice profile has "dispersive tails" which increase as more of the rf is truncated. Slice profile corrected SNR for the beta-ATP peak of 31P on a human volunteer is equivalent for both sequences while, qualitatively, in the PDE region the truncated sinc approach has improved SNR.     

Slice profile effects in 2D slice-selective MRI of hyperpolarized nuclei

This work explores slice profile effects in 2D slice-selective gradient-echo MRI of hyperpolarized nuclei. Two different sequences were investigated: a Spoiled Gradient Echo sequence with variable flip angle (SPGR-VFA) and a balanced Steady-State Free Precession (SSFP) sequence. It is shown that in SPGR-VFA the distribution of flip angles across the slice present in any realistically shaped radiofrequency (RF) pulse leads to large excess signal from the slice edges in later RF views, which results in an undesired non-constant total transverse magnetization, potentially exceeding the initial value by almost 300% for the last RF pulse. A method to reduce this unwanted effect is demonstrated, based on dynamic scaling of the slice selection gradient. SSFP sequences with small to moderate flip angles (<40°) are also shown to preserve the slice profile better than the most commonly used SPGR sequence with constant flip angle (SPGR-CFA). For higher flip angles, the slice profile in SSFP evolves in a manner similar to SPGR-CFA, with depletion of polarization in the center of the slice.     

Slice-selective excitation with B₁⁺-insensitive composite pulses

Spatially selective excitation pulses have been designed to produce uniform flip angles in the presence of the RF and static field inhomogeneities typically encountered in MRI studies of the human brain at 7 T. Pulse designs are based upon non-selective, composite pulses numerically optimized for the desired performance over prescribed ranges of field inhomogeneities. The non-selective pulses are subsequently transformed into spatially selective pulses with the same field-insensitive properties through modification of the spectral composition of the individual sub-pulses which are then executed in conjunction with an oscillating gradient waveform. An in-depth analysis of the performance of these RF pulses is presented in terms of total pulse durations, slice profiles, linearity of in-slice magnetization phase, sensitivity to RF and static field variations, and signal loss due to T(2) effects. Both simulations and measurements in phantoms and in the human brain are used to evaluate pulses with nominal flip angles of 45° and 90°. Target slice thickness in all cases is 2mm. Results indicate that the described class of field-insensitive RF pulses is capable of improving flip-angle uniformity in 7 T human brain imaging. There appears to be a subset of pulses with durations ?10 ms for which non-linearities in the magnetization phase are minimal and signal loss due to T(2) decay is not prohibitive. Such pulses represent practical solutions for achieving uniform flip angles in the presence of the large field inhomogeneities common to high-field human imaging and help to better establish the performance limits of high-field imaging systems with single-channel transmission.     

Selective excitation in Fourier transform nuclear magnetic resonance. 1978

The applications of frequency-selective excitation methods in Fourier transform NMR are discussed, and a simple technique is described for selective excitation of a narrow frequency region of a high-resolution NMR spectrum in a Fourier transform spectrometer. A regular sequence of identical radiofrequency pulses of small flip angle exerts a strong cumulative effect on magnetizations close to resonance with the transmitter frequency or one of a set of equally spaced sidebands separated by the pulse repetition rate. All other magnetizations precess through an incomplete number of full rotations between pulses, and are caught by successive pulses at an ever changing phase of their precession, which destroys the cumulative effect. The motion of the various nuclear magnetization vectors may be described pictorially according to the Bloch equations, neglecting relaxation during the pulse sequence. A general theory is presented for selective or “tailored” excitation by an arbitrary modulation of the radiofrequency transmitter signal. It confirms earlier conclusions that the frequency-domain excitation spectrum corresponds to the Fourier transform of the transmitter modulation pattern, provided that the NMR response remains linear. The excitation spectra calculated for the selective pulse sequence by these two alternative approaches show good agreement within their respective limitations. A number of practical applications of selective excitation are explored, including solvent peak suppression, the detection of partial spectra from individual chemical sites, selective studies of relaxation and slow chemical exchange, and holeburning or localized saturation.     

Excitation of photon echo by pulses modulated with Barker codes

The excitation of the primary and stimulated photon echoes by pulses modulated in phase with Barker codes is modeled. The shape of the complex envelopes of the primary and stimulated echoes is found by solving the optical Bloch equations. Linear and nonlinear excitation modes are considered. In linear modes, it is possible to realize a time delay and form the correlation function of modulated pulses. The results obtained can be used in modeling and analyzing the corresponding algorithms of the photon echo excitation and in calculating the characteristics of signal processors based on the phenomena of photon and spin echoes.     

Signal intensities in FLASH-EPI-hybrid sequences.

Theoretical considerations on the signal-to-noise ratio (SNR) in FLASH-EPI-Hybrid imaging were published previously. The purpose of this work was to investigate in vivo the signal intensities in Hybrid images as a function of sequence specific parameters. In detail, the SNR as a function of the number of echoes m per RF excitation, the excitation flip angle alpha, and the dependence on the tissue relaxation times T1 and T2* were studied. In eight healthy subjects brain and abdominal Hybrid images were acquired where m and alpha were changed independently. Signal intensities in human brain, liver, and kidney were evaluated for each Hybrid experiment. Additionally, T1 and T2* values of these tissue types were quantified to allow for a comparison with the theory. An excellent agreement between calculated and measured signal behavior was found. The theory was therefore validated in vivo and can thus be used to optimize the signal-to-noise in Hybrid experiments.     

Cyclic variation of T1 in the myocardium at 3 T

Standard methods of longitudinal relaxation (T1) measurements in the heart produce only one T1 map of the myocardium, usually at the end diastole (ED). In this article, we investigated the feasibility of using a dual flip angle fast gradient echo technique in the steady state to generate a movie of T1 maps in the myocardium during the cardiac cycle. The effects of nonideal slice profile and transient steady state on the T1 measurements were evaluated by Bloch simulations. Based on these results, we introduce a linear correction to the measured T1 values, which was validated by phantom experiments. In vivo T1 cine maps in healthy volunteers show 70+/-7% drop in T1 from the ED to the end systole in the septum and a 43+/-13% drop in the left ventricular lateral wall. With further improvements, this technique could be used to assess the myocardial blood volume changes during the cardiac cycle.     

Experimental and computational analyses of the effects of slice distortion from a metallic sphere in an MRI phantom

Susceptibility artifacts due to metallic prostheses are a major problem in clinical magnetic resonance imaging. We theoretically and experimentally analyze slice distortion arising from susceptibility differences in a phantom consisting of a stainless steel ball bearing embedded in agarose gel. To relate the observed image artifacts to slice distortion, we simulate images produced by 2D and 3D spin-echo (SE) and a view angle tilting (VAT) sequence. Two-dimensional SE sequences suffer from extreme slice distortion when a metal prosthesis is present, unlike 3D SE sequences for which--since slices are phase-encoded--distortion of the slice profile is minimized, provided the selected slab is larger than the region of interest. In a VAT sequence, artifacts are reduced by the application of a gradient along the slice direction during readout. However, VAT does not correct for the excitation slice profile, which results in the excitation of spins outside the desired slice location and can lead to incorrect anatomical information in MR images. We propose that the best sequences for imaging in the presence of a metal prosthesis utilize 3D acquisition, with phase encoding replacing slice selection to minimize slice distortion, combined with excitation and readout gradient strengths at their maximum values.     

Linear response equilibrium

A new periodic pulse sequence employing weak excitation is presented. This type of sequence drives the system into a steady-state with periodic time evolution from which the data can be reconstructed to a spectrum. It is demonstrated that the frequency response of such a sequence can be analyzed using perturbation methods and linear system analysis. A mathematical framework is proposed allowing the frequency response to be tailored by weighting a periodic flip function. The weak excitation level used implies very low specific absorption rates while generating a highly frequency selective signal in the order of 1/T2 with signal strengths comparable to those obtainable with conventional large flip angle balanced steady-state free precession techniques. The concept is illustrated with phantom experiments and in vivo feasibility of water fat separation is shown on human knee images.     

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.     

Consideration of slice profiles in inversion recovery Look–Locker relaxation parameter mapping

Purpose

To include the flip angle distribution caused by the slice profile into the model used for describing the relaxation curves observed in inversion recovery Look–Locker FLASH T₁ mapping for a more accurate determination of the relaxation parameters.

Materials and methods

For each inversion time, the flip angle dependent signal of the mono-exponential relaxation model is integrated across the slice profile. The resulting Consideration of Slice Profiles (CSP) relaxation curves are compared to the mono-exponential signal model in numerical simulations as well as in phantom and in-vivo experiments.

Results

All measured relaxation curves showed systematic deviations from a mono-exponential curve increasing with flip angle and T₁ but decreasing with repetition time. Additionally, the accuracy of T₁ was found to be largely dependent on the temporal coverage of the relaxation curve. All these systematic errors were largely reduced by the CSP model.

Conclusion

The proposed CSP model represents a useful extension of the conventionally used mono-exponential relaxation model. Despite inherent model inaccuracies, the mono-exponential model was found to be sufficient for many T₁ mapping situations. However, if only a poor temporal coverage of the relaxation process is achievable or a very precise modeling of the relaxation course is needed as in model-based techniques, the mono-exponential model leads to systematic errors and the CSP model should be used instead.