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

The "Spin-3/2 Bloch Equation": System matrix formalism of excitation, relaxation, and off-resonance effects in biological tissue

PURPOSE

This work proposes "Spin-3/2 Bloch Equation" (SBE), a consolidated formalism for spin-3/2 dynamics in biological environments. The formalism encapsulates excitation, relaxation, and off-resonance with accessible matrix representation for a straightforward implementation with high computational efficiency.

THEORY

The SBE is derived using spherical tensor operators to encapsulate the spin-3/2 dynamics in biological systems in a single system matrix, a formalism akin to the well-known Bloch Equations (BE).

METHODS

Using the proposed SBE, simulations of three classical ²³ Na pulse sequences were performed to demonstrate the versatility and applicability of the model, returning the evolution of the ²³ Na spin system during these experiments: soft rectangular and adiabatic inversion recovery (IR) and triple-quantum filtering. IR simulations were compared with two existing spin-3/2 simulators and the adaptive BE as a first-order approximation.

RESULTS

The proposed SBE is straightforward to implement and facilitates accurate and fast simulations of the underlying higher order coherence in sodium experiments of biological tissues. SBE simulations and comparison spin-3/2 simulators outperform the BE simulations as expected, with the SBE offering superior computational efficiency achieved by the single system matrix formalism.

CONCLUSION

The proposed SBE enables comprehensive and accurate simulations for spin-3/2 systems in biological tissue. With a one-line call to an ordinary differential equation solver, it offers a computationally efficient and accessible method for use in ²³ Na pulse sequence design.

Measurement techniques for magnetic resonance imaging of fast relaxing nuclei

In this review article, techniques for sodium ((23)Na) magnetic resonance imaging (MRI) are presented. These techniques can also be used to image other nuclei with short relaxation times (e.g., (39)K, (35)Cl, (17)O). Twisted projection imaging, density-adapted 3D projection reconstruction, and 3D cones are preferred because of uniform k-space sampling and ultra-short echo times. Sampling density weighted apodization can be applied if intrinsic filtering is desired. This approach leads to an increased signal-to-noise ratio compared to postfiltered acquisition in cases of short readout durations relative to T 2 (*) relaxation time. Different MR approaches for anisotropic resolution are presented, which are important for imaging of thin structures such as myocardium, cartilage, and skin. The third part of this review article describes different methods to put more weighting either on the intracellular or the extracellular sodium signal by means of contrast agents, relaxation-weighted imaging, or multiple-quantum filtering.

Exploring and enhancing relaxation-based sodium MRI contrast

OBJECT

Sodium MRI is typically concerned with measuring tissue sodium concentration. This requires the minimization of relaxation weighting. However, (23)Na relaxation may itself be interesting to explore, given an underlying mechanism (i.e. the electric-quadrupole-moment-electric-field-gradient interaction) that differs from (1)H. A new sodium sequence was developed to enhance (23)Na relaxation contrast without decreasing signal-to-noise ratio.

MATERIALS AND METHODS

The new sequence, labeled Projection Acquisition in the steady-state with Coherent MAgNetization (PACMAN), uses gradient refocusing of transverse magnetization following readout, a short repetition time, and a long radiofrequency excitation pulse. It was developed using simulation, verified in model environments (saline and agar), and evaluated in the brain of three healthy adult volunteers.

RESULTS

Projection Acquisition in the steady-state with Coherent MAgNetization generates a large positive contrast-to-noise ratio (CNR) between saline and agar, matching simulation-based design. In addition to enhanced CNR between cerebral spinal fluid and brain tissue in vivo, PACMAN develops substantial contrast between gray and white matter. Further simulation shows that PACMAN has a ln(T 2f/T 1) contrast dependence (where T 2f is the fast component of (23)Na T 2), as well as residual quadrupole interaction dependence.

CONCLUSION

The relaxation dependence of PACMAN sodium MRI may provide contrast related to macromolecular tissue structure.

Simultaneous single-quantum and triple-quantum-filtered MRI of 23Na (SISTINA)

The low MR sensitivity of the sodium nucleus and its low concentration in the human body constrain acquisition time. The use of both single-quantum and triple-quantum sodium imaging is, therefore, restricted. In this work, we present a novel MRI sequence that interleaves an ultra-short echo time radial projection readout into the three-pulse triple-quantum preparation. This allows for simultaneous acquisition of tissue sodium concentration weighted as well as triple-quantum filtered images. Performance of the sequence is shown on phantoms. The method is demonstrated on six healthy informed volunteers and is applied to three cases of brain tumors. A comparison with images from tumor specific O-(2-[18F]fluoroethyl)-L-tyrosine positron emission tomography and standard MR images is presented. The combined information of the triple-quantum-filtered images with single-quantum images may enable a better understanding of tissue viability. Future studies can benefit from the evaluation of both contrasts with shortened acquisition times.

Sodium MRI and the assessment of irreversible tissue damage during hyper-acute stroke

Sodium MRI (sMRI) has undergone a tremendous amount of technical development during the last two decades that makes it a suitable tool for the study of human pathology in the acute setting within the constraints of a clinical environment. The salient role of the sodium ion during impaired ATP production during the course of brain ischemia makes sMRI an ideal tool for the study of ischemic tissue viability during stroke. In this paper, the current limitations of conventional MRI for the determination of tissue viability during evolving brain ischemia are discussed. This discussion is followed by a summary of the known findings about the dynamics of tissue sodium changes during brain ischemia. A mechanistic model for the explanation of these findings is presented together with the technical requirements for its investigation using clinical MRI scanners. An illustration of the salient features of the technique is also presented using a nonhuman primate model of reversible middle cerebral artery occlusion.

Triple-quantum-filtered sodium imaging of the human brain at 4.7 T

The limited signal-to-noise ratio of triple-quantum-filtered MRI of sodium is a major hurdle for its application clinically. Although it has been shown that short 90° radiofrequency pulses in combination with sufficiently long repetition time for full T(1) recovery (labelled "standard" parameters) produce the maximum signal through the triple-quantum-filter, and in this work, simulation and images of agar phantoms and human brain demonstrate that the use of longer radiofrequency pulses and reduced repetition time (optimized parameters to accommodate more averages for a constant specific absorption rate, reducing noise variance for a given scan length) results in signal-to-noise ratio improvement (22 ± 5% in brain tissue of five healthy volunteers--images created in 11 min with nominal resolution of 8.4 mm isotropic). However, residual intensity was observed in the ventricular space on triple-quantum-filtered images acquired with either optimized or standard parameters, contrary to the expectation of complete single-quantum signal suppression. Further simulation and experimentation suggest that this is likely due to the combination of triple-quantum-passed signal from surrounding brain tissue being spatially smeared into the ventricular space and single-quantum-signal breakthrough from sodium nuclei in the fluid space. It is shown that the latter can be eliminated with judicious first flip angle selection.