Free Precession Signal Research Articles

Getting the phase consistent: The importance of phase description in balanced steady-state free precession MRI of multi-compartment systems.

Determine the correct mathematical phase description for balanced steady-state free precession (bSSFP) signals in multi-compartment systems. Based on published bSSFP signal models, different phase descriptions can be formulated: one predicting the presence and the other predicting the absence of destructive interference effects in multi-compartment systems. Numerical simulations of bSSFP signals of water and acetone were performed to evaluate the predictions of these different phase descriptions. For experimental validation, bSSFP profiles were measured at 3T using phase-cycled bSSFP acquisitions performed in a phantom containing mixtures of water and acetone, which replicates a system with two signal components. Localized single voxel MRS was performed at 7T to determine the relative chemical shift of the acetone-water mixtures. Based on the choice of phase description, the simulated bSSFP profiles of water-acetone mixtures varied significantly, either displaying or lacking destructive interference effects, as predicted theoretically. In phantom experiments, destructive interference was consistently observed in the measured bSSFP profiles of water-acetone mixtures, supporting the theoretical description that predicts such interference effects. The connection between the choice of phase description and predicted observation enables unambiguous experimental identification of the correct phase description for multi-compartment bSSFP profiles, which is consistent with the Bloch equations. The study emphasizes that consistent phase descriptions are crucial for accurately describing multi-compartment bSSFP signals, as incorrect phase descriptions result in erroneous predictions.

Stand-Off Magnetometry with Directional Emission from Sodium Vapors.

Stand-off magnetometry allows measuring magnetic field at a distance, and can be employed in geophysical research, hazardous environment monitoring, and security applications. Stand-off magnetometry based on resonant scattering from atoms or molecules is often limited by the scarce amounts of detected light. The situation would be dramatically improved if the light emitted by excited atoms were to propagate towards the excitation light source in a directional manner. Here, we demonstrate that this is possible by means of mirrorless lasing. In a tabletop experiment, we detect free-precession signals of ground-state sodium spins under the influence of an external magnetic field by measuring backward-directed light. This method enables scalar magnetometry in the Earth field range, that can be extended to long-range remote sensing.

Lineshape of Magnetic Resonance and its Effects on Free Induction Decay and Steady-State Free Precession Signal Formation

Magnetic resonance imaging based on steady-state free precision (SSFP) sequences is a fast method to acquire T1, T2, and T2∗-weighted images. In inhomogeneous tissues such as lung tissue or blood vessel networks, however, microscopic field inhomogeneities cause a nonexponential free induction decay and a non-Lorentzian lineshape. In this work, the SSFP signal is analyzed for different prominent tissue models. Neglecting the effect of non-Lorentzian lineshapes can easily result in large errors of the determined relaxation times. Moreover, sequence parameters of SSFP measurements can be optimized for the nonexponential signal decay in many tissue structures.

Prospective GIRF-based RF phase cycling to reduce eddy current-induced steady-state disruption in bSSFP imaging.

PurposeTo propose an explicit Balanced steady‐state free precession (bSSFP) signal model that predicts eddy current‐induced steady‐state disruptions and to provide a prospective, practical, and general eddy current compensation method.Theory and MethodsGradient impulse response functions (GIRF) were used to simulate trajectory‐specific eddy current‐induced phase errors at the end of a repetition block. These phase errors were included in bloch simulations to establish a bSSFP signal model to predict steady‐state disruptions and their corresponding image artifacts. The signal model was embedded in the MR system and used to compensate the phase errors by prospectively modifying the phase cycling scheme of the RF pulse. The signal model and eddy current compensation method were validated in phantom and in vivo experiments. In addition, the signal model was used to analyze pre‐existing eddy current mitigation methods, such as 2D tiny golden angle radial and 3D paired phase encoded Cartesian acquisitions.ResultsThe signal model predicted eddy current‐induced image artifacts, with the zeroth‐order GIRF being the primary factor to predict the steady‐state disruption. Prospective RF phase cycling schemes were automatically computed online and considerably reduced eddy current‐induced image artifacts. The signal model provides a direct relationship for the smoothness of k‐space trajectories, which explains the effectiveness of phase encode pairing and tiny golden angle trajectory.ConclusionsThe proposed signal model can accurately predict eddy current‐induced steady‐state disruptions for bSSFP imaging. The signal model can be used to derive the eddy current‐induced phase errors required for trajectory‐specific RF phase cycling schemes, which considerably reduce eddy current‐induced image artifacts.

Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters.

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T1 ) signals, acquired with very low flip angles that contain six times more noise than the Carr-Purcell-Meiboom-Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky-Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T1 signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T1 , as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T1 method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.

Three-dimensional localization spectroscopy of individual nuclear spins with sub-Angstrom resolution

Nuclear magnetic resonance (NMR) spectroscopy is a powerful method for analyzing the chemical composition and molecular structure of materials. At the nanometer scale, NMR has the prospect of mapping the atomic-scale structure of individual molecules, provided a method that can sensitively detect single nuclei and measure inter-atomic distances. Here, we report on precise localization spectroscopy experiments of individual 13C nuclear spins near the central electronic sensor spin of a nitrogen-vacancy (NV) center in a diamond chip. By detecting the nuclear free precession signals in rapidly switchable external magnetic fields, we retrieve the three-dimensional spatial coordinates of the nuclear spins with sub-Angstrom resolution and for distances beyond 10 Å. We further show that the Fermi contact contribution can be constrained by measuring the nuclear g-factor enhancement. The presented method will be useful for mapping atomic positions in single molecules, an ambitious yet important goal of nanoscale nuclear magnetic resonance spectroscopy.

Sensitive and stable vector magnetometer for operation in zero and finite fields.

We report on an optically pumped magnetometer that uses multiple laser beams to pump and probe spin-polarized Cs atoms. The selected sensor geometry allows for operation in finite magnetic fields as well as close to zero field. In finite fields the magnetometer employs free spin precession signals to determine the field modulus and direction as described in a separate publication. This publication focuses on the magnetometer operation close to zero field, which is based on a ground state Hanle resonance. The four laser beams permit the simultaneous measurement of two orthogonal magnetic field components in a differential detection scheme that greatly suppresses technical laser power noise. Sensitivities better than 54 fT/Hz1/2 could be demonstrated simultaneously for both measurement channels in a well shielded environment. A minimum Allan deviation, limited by residual field fluctuations, of better than 40 fT was observed for integration times of 2s. The magnetometer achieves high sensitivity and stability in offset fields as well as close to zero field and is, thus, a universal tool for low frequency magnetic field measurements.

Precise measurement of magnetic field gradients from free spin precession signals of 3He and 129Xe magnetometers

We report on precise measurements of magnetic field gradients extracted from transverse relaxation rates of precessing spin samples. The experimental approach is based on the free precession of gaseous, nuclear spin polarized $^3$He and $^{129}$Xe atoms in a spherical cell inside a magnetic guiding field of about 400 nT using LT$_C$ SQUIDs as low-noise magnetic flux detectors. The transverse relaxation rates of both spin species are simultaneously monitored as magnetic field gradients are varied. For transverse relaxation times reaching 100 h, the residual longitudinal field gradient across the spin sample could be deduced to be$|\vec{\nabla}B_z|=(5.6 \pm 0.4)$ pT/cm. The method takes advantage of the high signal-to-noise ratio with which the decaying spin precession signal can be monitored that finally leads to the exceptional accuracy to determine magnetic field gradients at the sub pT/cm scale.

Steady‐state free precession signals of arbitrary dephasing order and their sensitivity to T2∗

AbstractA simple approach how to calculate analytical expressions for unbalanced steady‐state free precession (ubSSFP) signals of arbitrary dephasing order is presented. Dephasing order is the number of effective gradient dephasing cycles that magnetization immediately after an RF‐pulse has experienced during the ubSSFP sequence. Based on the obtained equations, which are in accordance with existing literature, the sensitivity of ubSSFP signals to T2∗ is derived under the assumption of a Lorentzian frequency distribution resulting from static field inhomogeneities. Further, the phases of all ubSSFP signals are calculated and a general expression of how to use them for B0‐fieldmapping is given. The derivation is supported by the extended phase graph (EPG) model, and as such the work also acts as a comprehensive introduction to the formal description of SSFP. In addition, the balanced SSFP (bSSFP) sequence is explored. The connection of bSSFP to ubSSFP is shown, and potential T2∗‐sensitivity of bSSFP is examined based on numerical simulations. It is shown that ubSSFP signals with negative dephasing order have a refocusing character and behave similar to spin‐echo signals. Conversely, ubSSFP signals with zero or positive dephasing order can be regarded as T2∗‐weighted. The behavior of bSSFP depends largely on the exact distribution of frequencies. For instance, for a narrow spherical distribution, bSSFP acts like a spin‐echo sequence, while for a Lorentzian distribution a refocusing behavior does not occur.

Effect of the structure of solid compounds on the shape of their NMR spectra and manifestations of dynamic chaos in paramagnetic spin systems

The shape of NMR absorption line for typical ionic crystals, molecular crystals, and glasses is studied. The proposed theory and available experimental results suggest that the shape of NMR spectra of conventional dielectric crystals (and even molecular) is the convolution of a frequency-truncated nearly-rectangle-shaped function (characteristic oscillations in free precession signals) and a Gaussian-like function. A Gaussian-like shape of the spectra of glasses with a rigid structure (no oscillations in the free precession signal) is probably associated with a random scatter of interatomic distances. The results are interpreted within the framework of the proposed theory. It is demonstrated that, at least for solids the lattice of which contains no isolated groups of nuclei and are not quasi-one-dimensional, the structure only weakly affects the shape of the spectrum, which in turn is associated with the onset of dynamic chaos in the spin system.

Rapid High-resolution, Self-registered, Dual Lumen-contrast MRI Method for Vessel-wall Assessment in Peripheral Artery Disease:: A Preliminary Investigation

Contrast-enhanced angiographic evaluation by magnetic resonance imaging (MRI) and computed tomography (CT) is the reference standard for assessing peripheral artery disease (PAD). However, because PAD and diabetes often coexist, the prevalence of renal insufficiency is a major challenge to contrast-based angiography. The objective of this work is to describe and demonstrate a new application of three-dimensional double-echo steady-state (3D DESS) as a noncontrast vascular MRI method for evaluating peripheral atherosclerosis at 3 Tesla (3T). A water-selective 3D DESS pulse sequence was designed to simultaneously collect two steady-state free-precession signals (free induction decay and Echo) yielding "black blood" (BB) and "gray blood" (GB) images. For completeness Bloch equation, simulations were performed to characterize DESS signals of various tissues including blood at different velocities and to assess two healthy subjects for the purpose of pulse sequence optimization. Exploratory studies were performed as an add-on protocol to an existing study involving patients with PAD. To evaluate the method's specificity for detecting calcification, images from select patients were compared against CT angiography. Simulations agreed qualitatively with in vivo images supporting DESS' potential for generating distinct lumen contrast (GB vs BB). Lesions representing calcium were easily identifiable on the basis of signal void occurring on both image types and were confirmed by CT angiography. Further, BB allowed visualization of stent restenosis, and data suggest its ability to visualize acute thrombus by virtue of T2 weighting. Preliminary investigation and results suggest noncontrast 3D DESS to have the potential to improve diagnosis of PAD patients by providing detailed structural assessment of vessel-wall architecture.

Utilization of a balanced steady state free precession signal model for improved fat/water decomposition.

Chemical shift based fat/water decomposition methods such as IDEAL are frequently used in challenging imaging environments with large B0 inhomogeneity. However, they do not account for the signal modulations introduced by a balanced steady state free precession (bSSFP) acquisition. Here we demonstrate improved performance when the bSSFP frequency response is properly incorporated into the multipeak spectral fat model used in the decomposition process. Balanced SSFP allows for rapid imaging but also introduces a characteristic frequency response featuring periodic nulls and pass bands. Fat spectral components in adjacent pass bands will experience bulk phase offsets and magnitude modulations that change the expected constructive and destructive interference between the fat spectral components. A bSSFP signal model was incorporated into the fat/water decomposition process and used to generate images of a fat phantom, and bilateral breast and knee images in four normal volunteers at 1.5 Tesla. Incorporation of the bSSFP signal model into the decomposition process improved the performance of the fat/water decomposition. Incorporation of this model allows rapid bSSFP imaging sequences to use robust fat/water decomposition methods such as IDEAL. While only one set of imaging parameters were presented, the method is compatible with any field strength or repetition time.

Fast 3D T2 -weighted imaging using variable flip angle transition into driven equilibrium (3D T2 -TIDE) balanced SSFP for prostate imaging at 3T.

Three-dimensional (3D) T2 -weighted fast spin echo (FSE) imaging of the prostate currently requires long acquisition times. Our objective was to develop a fast 3D T2 -weighted sequence for prostate imaging at 3T using a variable flip angle transition into driven equilibrium (T2 -TIDE) scheme. 3D T2 -TIDE uses interleaved spiral-out phase encode ordering to efficiently sample the ky -kz phase encodes and also uses the transient balanced steady-state free precession signal to acquire the center of k-space for T2 -weighted imaging. Bloch simulations and images from 10 healthy subjects were acquired to evaluate the performance of 3D T2 -TIDE compared to 3D FSE. 3D T2 -TIDE images were acquired in 2:54 minutes compared to 7:02 minutes for 3D FSE with identical imaging parameters. The signal-to-noise ratio (SNR) efficiency was significantly higher for 3D T2 -TIDE compared to 3D FSE in nearly all tissues, including periprostatic fat (45 ± 12 vs. 31 ± 7, P < 0.01), gluteal fat (48 ± 8 vs. 41 ± 10, P = 0.12), right peripheral zone (20 ± 4 vs. 16 ± 8, P = 0.12), left peripheral zone (17 ± 2 vs. 12 ± 3, P < 0.01), and anterior fibromuscular stroma (12 ± 4 vs. 4 ± 2, P < 0.01). 3D T2 -TIDE images of the prostate can be acquired quickly with SNR efficiency that exceeds that of 3D FSE.

Analytical approximations to inhomogeneously broadened, radiation damped free precession and echo signals

The Dirac–Frenkel–Maclachlan (DFM) variation of parameters approach to approximately solving the time dependent Schrödinger equation is used to generate free precession and echo signals from the Bloch equations corrected for the effects of radiation damping and inhomogeneous broadening. Following a brief description of how the DFM method can be applied to the non-linear Bloch equations, two figures of merit designed to evaluate how a DFM optimized approximation compares with the exact solution is provided. This framework is used to optimize and evaluate the performance of six trial functions describing inhomogeneously broadened, radiation damped free precession and echo signals. The trial functions are then used to analyze the resolution enhancement and signal attenuation produced by pulse sequences that suppress radiation damping.

‐mapping with the transient phase of unbalanced steady‐state free precession

A novel B1+-mapping technique (B1-TRAP) is presented, which derives the actual flip angle from the frequency of signal oscillations, observed in the transient phase of unbalanced steady-state free precession sequences. For short repetition times (TR), the angular frequency of distinct oscillations in the transient phase of steady-state free precession sequences is proven to be approximately proportional to the actual flip angle: ω⋅TR≈α. The result is not influenced by off-resonance and it can be shown that deviations are only of second order in the small parameter TR/T2. B1-TRAP makes use of this effect through a frequency analysis of the transient phase of a train of steady-state free precession signals. In terms of reliability and time efficiency, a two-dimensional multislice implementation was found to be optimal. Unlike many steady-state B1+-mapping methods, the accuracy of B1-TRAP was not impaired by imperfect slice profiles. Simulations, phantom, and in vivo measurements showed that B1-TRAP offers a good compromise with respect to speed, robustness, and accuracy.

Incorporating reversible and irreversible transverse relaxation effects into Steady State Free Precession (SSFP) signal intensity expressions for fMRI considerations

Among the multiple sequences available for functional magnetic resonance imaging (fMRI), the Steady State Free Precession (SSFP) sequence offers the highest signal-to-noise ratio (SNR) per unit time as well as distortion free images not feasible with the more commonly employed single-shot echo planar imaging (EPI) approaches. Signal changes occurring with activation in SSFP sequences reflect underlying changes in both irreversible and reversible transverse relaxation processes. The latter are characterized by changes in the central frequencies and widths of the inherent frequency distribution present within a voxel. In this work, the well-known frequency response of the SSFP signal intensity is generalized to include the widths and central frequencies of some common frequency distributions on SSFP signal intensities. The approach, using a previously unnoted series expansion, allows for a separation of reversible from irreversible transverse relaxation effects on SSFP signal intensity changes. The formalism described here should prove useful for identifying and modeling mechanisms associated with SSFP signal changes accompanying neural activation.

T‐one insensitive steady state imaging: A framework for purely T2‐weighted TrueFISP

A new conceptual framework called T-one insensitive steady state imaging is proposed for fast generation of MR images with pure T(2) contrast. This is accomplished by imaging between nonequally spaced inversion pulses, with the magnetization vector alternatively residing in states parallel and antiparallel to B(0) for durations TP(i) and TA(i), respectively. With TP(i) and TA(i) adequately chosen, identical signal time evolution can be obtained for different T(1) values, i.e., T(1) contrast can efficiently be removed from resultant images. As a specific realization of this principle, T-one insensitive steady state imaging sequences are presented which use True free induction steady precession readout blocks between the inversion pulses. While the conventional True free induction steady precession signal time course would be determined by both T(2) and T(1), a pure T(2) dependence is realized with successfully suppressed influence of longitudinal relaxation, and images with essentially T(2) contrast alone are obtained. Analytical expressions are provided for the description of the ideal signal behavior, which help in creating pathways for sequence parameter optimization. The performance of the technique is analyzed with Bloch equation simulations. In vivo results obtained in healthy volunteers and brain tumor patients are presented.

Superbalanced steady state free precession

Steady state free precession (SSFP) signal theory is commonly derived in the limit of quasi-instantaneous radiofrequency (RF) excitation. SSFP imaging protocols, however, are frequently set up with minimal pulse repetition times and RF pulses can thus constitute a considerable amount to the actual pulse repetition time. As a result, finite RF pulse effects can lead to 10-20% signal deviation from common SSFP theory in the transient and in the steady state which may impair the accuracy of SSFP-based quantitative imaging techniques. In this article, a new and generic approach for intrinsic compensation of finite RF pulse effects is introduced. Compensation is based on balancing relaxation effects during finite RF excitation, similar to flow or motion compensation of gradient moments. RF pulse balancing, in addition to the refocusing of gradient moments with balanced SSFP, results in a superbalanced SSFP sequence free of finite RF pulse effects in the transient and in the steady state; irrespective of the RF pulse duration, flip angles, relaxation times, or off-resonances. Superbalancing of SSFP sequences can be used with all quantitative SSFP techniques where finite RF pulse effects are expected or where elongated RF pulses are used.

T2-weighted 3D fMRI usingS2-SSFP at 7 tesla

In this study, the sensitivity of the S(2)-steady-state free precession (SSFP) signal for functional MRI at 7 T was investigated. In order to achieve the necessary temporal resolution, a three-dimensional acquisition scheme with acceleration along two spatial axes was employed. Activation maps based on S(2)-steady-state free precession data showed similar spatial localization of activation and sensitivity as spin-echo echo-planar imaging (SE-EPI), but data can be acquired with substantially lower power deposition. The functional sensitivity estimated by the average z-values was not significantly different for SE-EPI compared to the S(2)-signal but was slightly lower for the S(2)-signal (6.74 +/- 0.32 for the TR = 15 ms protocol and 7.51 +/- 0.78 for the TR = 27 ms protocol) compared to SE-EPI (7.49 +/- 1.44 and 8.05 +/- 1.67) using the same activated voxels, respectively. The relative signal changes in these voxels upon activation were slightly lower for SE-EPI (2.37% +/- 0.18%) compared to the TR = 15 ms S(2)-SSFP protocol (2.75% +/- 0.53%) and significantly lower than the TR = 27 ms protocol (5.38% +/- 1.28%), in line with simulations results. The large relative signal change for the long TR SSFP protocol can be explained by contributions from multiple coherence pathways and the low intrinsic intensity of the S(2) signal. In conclusion, whole-brain T(2)-weighted functional MRI with negligible image distortion at 7 T is feasible using the S(2)-SSFP sequence and partially parallel imaging.

Qualitative agreement of aortic regurgitation assessed by steady state free precession signal void as compared to doppler echocardiography

Introduction Previous studies demonstrated correlation in assessment of severity of AR between spoiled gradient-echo CMR and phase contrast color Doppler echocardiography in AR patients as well as normal subjects (Pflugfelder, et al. Am J Roentgenol 1989; 152:729-35). SSFP gradient-echo sequence is now a mainstay in evaluating cardiac function, as well as valvular structures. Aortic regurgitation creates flow disturbances that manifests as signal void from signal dephasing. This study compares the qualitative assessment of AR using SSFP CMR versus Doppler echocardiography.