A model for the dynamics of spins 3/2 in biological media: signal loss during radiofrequency excitation in triple-quantum-filtered sodium MRI

Comparison of triple quantum (TQ) TPPI and inversion recovery TQ TPPI pulse sequences at 9.4 and 21.1 T

PURPOSE

Both sodium T1 triple quantum (TQ) signal and T1 relaxation pathways have a unique sensitivity to the sodium molecular environment. In this study an inversion recovery time proportional phase increment (IRTQTPPI) pulse sequence was investigated for simultaneous and reliable quantification of sodium TQ signal and bi-exponential T1 relaxation times.

METHODS

The IRTQTPPI sequence combines inversion recovery TQ filtering and time proportional phase increment. The reliable and reproducible results were achieved by the pulse sequence optimized in three ways: (1) optimization of the nonlinear fit for the determination of both T1-TQ signal and T1 relaxation times; (2) suppression of unwanted signals by assessment of four different phase cycles; (3) nonlinear sampling during evolution time for optimal scan time without any compromises in fit accuracy. The relaxation times T1 and T2 and the TQ signals from IRTQTPPI and TQTPPI were compared between 9.4 and 21.1 T. The motional environment of the sodium nuclei was evaluated by calculation of correlation times and nuclear quadrupole interaction strengths.

RESULTS

Reliable measurements of the T1-TQ signals and T1 bi-exponential relaxation times were demonstrated. The fit parameters for all four phase cycles were in good agreement with one another, with a negligible influence of unwanted signals. The agar samples yielded normalized T1-TQ signals from 3% to 16% relative to single quantum (SQ) signals at magnetic fields of both 9.4 and 21.1 T. In comparison, the normalized T2-TQ signal was in the range 15%-35%. The TQ/SQ signal ratio was decreased at 21.1 T as compared with 9.4 T for both T1 and T2 relaxation pathways. The bi-exponential T1 relaxation time separation ranged from 15 to 18 ms at 9.4 T and 15 to 21 ms at 21.1 T. The T2 relaxation time separation was larger, ranging from 28 to 35 ms at 9.4 T and 37 to 40 ms at 21.1 T.

CONCLUSION

The IRTQTPPI sequence, while providing a less intensive TQ signal than TQTPPI, allows a simultaneous and reliable quantification of both the T1-TQ signal and T1 relaxation times. The unique sensitivities of the T1 and T2 relaxation pathways to different types of molecular motion provide a deeper understanding of the sodium MR environment.

Sodium Triple Quantum MR Signal Extraction Using a Single-Pulse Sequence with Single Quantum Time Efficiency

PURPOSE

Sodium triple quantum (TQ) signal has been shown to be a valuable biomarker for cell viability. Despite its clinical potential, application of Sodium TQ signal is hindered by complex pulse sequences with long scan times. This study proposes a method to approximate the TQ signal using a single excitation pulse without phase cycling.

METHODS

The proposed method is based on a single excitation pulse and a comparison of the free induction decay (FID) with the integral of the FID combined with a shifting reconstruction window. The TQ signal is calculated from this FID only. As a proof of concept, the method was also combined with a multi-echo UTE imaging sequence on a 9.4 T preclinical MRI scanner for the possibility of fast TQ MRI.

RESULTS

The extracted Sodium TQ signals of single-pulse and spin echo FIDs were in close agreement with theory and TQ measurement by traditional three-pulse sequence (TQ time proportional phase increment [TQTPPI)]. For 2%, 4%, and 6% agar samples, the absolute deviations of the maximum TQ signals between SE and theoretical (time proportional phase increment TQTPPI) TQ signals were less than 1.2% (2.4%), and relative deviations were less than 4.6% (6.8%). The impact of multi-compartment systems and noise on the accuracy of the TQ signal was small for simulated data. The systematic error was <3.4% for a single quantum (SQ) SNR of 5 and at maximum <2.5% for a multi-compartment system. The method also showed the potential of fast in vivo SQ and TQ imaging.

CONCLUSION

Simultaneous SQ and TQ MRI using only a single-pulse sequence and SQ time efficiency has been demonstrated. This may leverage the full potential of the Sodium TQ signal in clinical applications.

Multidimensional compressed sensing to advance 23 Na multi-quantum coherences MRI

PURPOSE

Sodium (23 Na) multi-quantum coherences (MQC) MRI was accelerated using three-dimensional (3D) and a dedicated five-dimensional (5D) compressed sensing (CS) framework for simultaneous Cartesian single (SQ) and triple quantum (TQ) sodium imaging of in vivo human brain at 3.0 and 7.0 T.

THEORY AND METHODS

3D 23 Na MQC MRI requires multi-echo paired with phase-cycling and exhibits thus a multidimensional space. A joint reconstruction framework to exploit the sparsity in all imaging dimensions by extending the conventional 3D CS framework to 5D was developed. 3D MQC images of simulated brain, phantom and healthy brain volunteers obtained from 3.0 T and 7.0 T were retrospectively and prospectively undersampled. Performance of the CS models were analyzed by means of structural similarity index (SSIM), root mean squared error (RMSE), signal-to-noise ratio (SNR) and signal quantification of tissue sodium concentration and TQ/SQ ratio.

RESULTS

It was shown that an acceleration of three-fold, leading to less than2 × 10 $$ 2\times 10 $$ min of scan time with a resolution of8 × 8 × 20   mm 3 $$ 8\times 8\times 20\;{\mathrm{mm}}^3 $$ at 3.0 T, are possible. 5D CS improved SSIM by 3%, 5%, 1% and reduced RMSE by 50%, 30%, 8% for in vivo SQ, TQ, and TQ/SQ ratio maps, respectively. Furthermore, for the first time prospective undersampling enabled unprecedented high resolution from8 × 8 × 20   mm 3 $$ 8\times 8\times 20\;{\mathrm{mm}}^3 $$ to6 × 6 × 10   mm 3 $$ 6\times 6\times 10\;{\mathrm{mm}}^3 $$ MQC images of in vivo human brain at 7.0 T without extending acquisition time.

CONCLUSION

5D CS proved to allow up to three-fold acceleration retrospectively on 3.0 T data. 2-fold acceleration was demonstrated prospectively at 7.0 T to reach higher spatial resolution of 23 Na MQC MRI.

Recent technical developments and clinical research applications of sodium (23Na) MRI

Sodium is an essential ion that plays a central role in many physiological processes including the transmembrane electrochemical gradient and the maintenance of the body's homeostasis. Due to the crucial role of sodium in the human body, the sodium nucleus is a promising candidate for non-invasively assessing (patho-)physiological changes. Almost 10 years ago, Madelin et al. provided a comprehensive review of methods and applications of sodium (23Na) MRI (Madelin et al., 2014) [1]. More recent review articles have focused mainly on specific applications of 23Na MRI. For example, several articles covered 23Na MRI applications for diseases such as osteoarthritis (Zbyn et al., 2016, Zaric et al., 2020) [2,3], multiple sclerosis (Petracca et al., 2016, Huhn et al., 2019) [4,5] and brain tumors (Schepkin, 2016) [6], or for imaging certain organs such as the kidneys (Zollner et al., 2016) [7], the brain (Shah et al., 2016, Thulborn et al., 2018) [8,9], and the heart (Bottomley, 2016) [10]. Other articles have reviewed technical developments such as radiofrequency (RF) coils for 23Na MRI (Wiggins et al., 2016, Bangerter et al., 2016) [11,12], pulse sequences (Konstandin et al., 2014) [13], image reconstruction methods (Chen et al., 2021) [14], and interleaved/simultaneous imaging techniques (Lopez Kolkovsky et al., 2022) [15]. In addition, 23Na MRI topics have been covered in review articles with broader topics such as multinuclear MRI or ultra-high-field MRI (Niesporek et al., 2019, Hu et al., 2019, Ladd et al., 2018) [16-18]. During the past decade, various research groups have continued working on technical improvements to sodium MRI and have investigated its potential to serve as a diagnostic and prognostic tool. Clinical research applications of 23Na MRI have covered a broad spectrum of diseases, mainly focusing on the brain, cartilage, and skeletal muscle (see Fig. 1). In this article, we aim to provide a comprehensive summary of methodological and hardware developments, as well as a review of various clinical research applications of sodium (23Na) MRI in the last decade (i.e., published from the beginning of 2013 to the end of 2022).

Influence of Residual Quadrupolar Interaction on Quantitative Sodium Brain Magnetic Resonance Imaging of Patients With Multiple Sclerosis

OBJECTIVES

The purpose of this work was to evaluate the influence of residual quadrupolar interaction on the determination of human brain apparent tissue sodium concentrations (aTSCs) using quantitative sodium magnetic resonance imaging ( 23 Na MRI) in healthy controls (HCs) and patients with multiple sclerosis (MS). Especially, it was investigated if the more detailed examination of residual quadrupolar interaction effects enables further analysis of the observed 23 Na MRI signal increase in MS patients.

MATERIALS AND METHODS

23 Na MRI with a 7 T MR system was performed on 21 HC and 50 MS patients covering all MS subtypes (25 patients with relapsing-remitting MS, 14 patients with secondary progressive MS, and 11 patients with primary progressive MS) using 2 different 23 Na pulse sequences for quantification: a commonly used standard sequence (aTSC Std ) as well as a sequence with shorter excitation pulse length and lower flip angle for minimizing signal loss resulting from residual quadrupolar interactions (aTSC SP ). Apparent tissue sodium concentration was determined using the same postprocessing pipeline including correction of the receive profile of the radiofrequency coil, partial volume correction, and relaxation correction. Spin dynamic simulations of spin-3/2 nuclei were performed to aid in the understanding of the measurement results and to get deeper insight in the underlying mechanisms.

RESULTS

In normal-appearing white matter (NAWM) of HC and all MS subtypes, the aTSC SP values were approximately 20% higher than the aTSC Std values ( P < 0.001). In addition, the ratio aTSC SP /aTSC Std was significantly higher in NAWM than in normal-appearing gray matter (NAGM) for all subject cohorts ( P < 0.002). In NAWM, aTSC Std values were significantly higher in primary progressive MS compared with HC ( P = 0.01) as well as relapsing-remitting MS ( P = 0.03). However, in contrast, no significant differences between the subject cohorts were found for aTSC SP . Spin simulations assuming the occurrence of residual quadrupolar interaction in NAWM were in good accordance with the measurement results, in particular, the ratio aTSC SP /aTSC Std in NAWM and NAGM.

CONCLUSIONS

Our results showed that residual quadrupolar interactions in white matter regions of the human brain have an influence on aTSC quantification and therefore must be considered, especially in pathologies with expected microstructural changes such as loss of myelin in MS. Furthermore, the more detailed examination of residual quadrupolar interactions may lead to a better understanding of the pathologies themselves.

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.

3D sodium (23 Na) magnetic resonance fingerprinting for time-efficient relaxometric mapping

PURPOSE

To develop a framework for 3D sodium (²³ Na) MR fingerprinting (MRF), based on irreducible spherical tensor operators with tailored flip angle (FA) pattern and time-efficient data acquisition for simultaneous quantification of T₁ , T 2 l ∗ , T 2 s ∗ , and T 2 ∗ in addition to ΔB₀ .

METHODS

²³ Na-MRF was implemented in a 3D sequence and irreducible spherical tensor operators were exploited in the simulations. Furthermore, the Cramér Rao lower bound was used to optimize the flip angle pattern. A combination of single and double echo readouts was implemented to increase the readout efficiency. A study was conducted to compare results in a multicompartment phantom acquired with MRF and reference methods. Finally, the relaxation times in the human brain were measured in four healthy volunteers.

RESULTS

Phantom experiments revealed a mean difference of 1.0% between relaxation times acquired with MRF and results determined with the reference methods. Simultaneous quantification of the longitudinal and transverse relaxation times in the human brain was possible within 32 min using 3D ²³ Na-MRF with a nominal resolution of (5 mm)³ . In vivo measurements in four volunteers yielded average relaxation times of: T_1,brain = (35.0 ± 3.2) ms, T 2 l , brain ∗ = (29.3 ± 3.8) ms and T 2 s , brain ∗ = (5.5 ± 1.3) ms in brain tissue, whereas T_1,CSF = (61.9 ± 2.8) ms and T 2 , CSF ∗ = (46.3 ± 4.5) ms was found in cerebrospinal fluid.

CONCLUSION

The feasibility of in vivo 3D relaxometric sodium mapping within roughly ½ h is demonstrated using MRF in the human brain, moving sodium relaxometric mapping toward clinically relevant measurement times.

Relaxometry and quantification in sodium MRI of cerebral gliomas: A FET-PET and MRI small-scale study

Sodium MRI is a promising method for assessing the metabolic properties of brain tumours. In a recent study, a strong relationship between semi-quantitative abnormalities in sodium MRI and the mutational status of the isocitrate dehydrogenase enzyme (IDH) with untreated cerebral gliomas was observed. Here, sodium relaxometry in brain tumour tissue was investigated in relation to molecular markers in order to reveal quantitative sodium tissue parameters and the differences between healthy tissue and brain tumour. The previous semi-quantitative approach is extended by use of suitable relaxometry methods accompanied by numerical simulation to achieve detailed quantitative analysis of intra- and extracellular sodium concentration using an enhanced SISTINA sequence at 4 T. Using optimised techniques, biexponential sodium relaxation times in tumour (T*_2f , T*_2s ) and in healthy contralateral brain tissue (T*_2f,CL , T*_2s,CL ) were estimated in 10 patients, along with intracellular sodium molar fractions (χ, χ_CL ), volume fractions (η, η_CL ) and concentrations (ρ_in , ρ_in,CL ). The total sodium tissue concentrations (ρ_T , ρ_T,CL ) were also estimated. The ratios T*_2f /T*_2f,CL (P = .05), η/η_CL (P = .02) and χ/χ_CL (P = .02) were significantly lower in IDH mutated than in IDH wildtype gliomas (n = 4 and n = 5 patients, respectively). The Wilcoxon rank-sum test was used to compare sodium MRI parameters in patients with and without IDH mutation. Thus, quantitative analysis of relaxation rates, intra- and extracellular sodium concentrations, intracellular molar and volume fractions based on enhanced SISTINA confirmed a relationship between abnormalities in sodium parameters and the IDH mutational status in cerebral gliomas, hence catering for the potential to provide further insights into the status of the disease.

23 Na-MRI as a Noninvasive Biomarker for Cancer Diagnosis and Prognosis

The influx of sodium (Na⁺) ions into a resting cell is regulated by Na⁺ channels and by Na⁺/H⁺ and Na⁺/Ca²⁺ exchangers, whereas Na⁺ ion efflux is mediated by the activity of Na⁺/K⁺‐ATPase to maintain a high transmembrane Na⁺ ion gradient. Dysfunction of this system leads to changes in the intracellular sodium concentration that promotes cancer metastasis by mediating invasion and migration. In addition, the accumulation of extracellular Na⁺ ions in cancer due to inflammation contributes to tumor immunogenicity. Thus, alterations in the Na⁺ ion concentration may potentially be used as a biomarker for malignant tumor diagnosis and prognosis. However, current limitations in detection technology and a complex tumor microenvironment present significant challenges for the in vivo assessment of Na⁺ concentration in tumor. ²³Na‐magnetic resonance imaging (²³Na‐MRI) offers a unique opportunity to study the effects of Na⁺ ion concentration changes in cancer. Although challenged by a low signal‐to‐noise ratio, the development of ultrahigh magnetic field scanners and specialized sodium acquisition sequences has significantly advanced ²³Na‐MRI. ²³Na‐MRI provides biochemical information that reflects cell viability, structural integrity, and energy metabolism, and has been shown to reveal rapid treatment response at the molecular level before morphological changes occur. Here we review the basis of ²³Na‐MRI technology and discuss its potential as a direct noninvasive in vivo diagnostic and prognostic biomarker for cancer therapy, particularly in cancer immunotherapy. We propose that ²³Na‐MRI is a promising method with a wide range of applications in the tumor immuno‐microenvironment research field and in cancer immunotherapy monitoring.

Level of Evidence

2

Technical Efficacy

Stage 2

23Na MRI of human skeletal muscle using long inversion recovery pulses

²³Na inversion recovery (IR) imaging allows for a weighting toward intracellular sodium in the human calf muscle and thus enables an improved analysis of pathophysiological changes of the muscular ion homeostasis. However, sodium signal-to-noise ratio (SNR) is low, especially when using IR sequences. ²³Na has a nuclear spin of 3/2 and therefore experiences a strong electrical quadrupolar interaction. This results in very short relaxation times as well as in possible residual quadrupolar splitting. Consequently, relaxation effects during a radiofrequency pulse can no longer be neglected and even allow for increasing SNR as has previously been shown for human brain and knee. The aim of this work was to increase the SNR in ²³Na IR imaging of the human calf muscle by using long inversion pulses instead of the usually applied short pulses. First, the influence of the inversion pulse length (1 to 20 ms) on the SNR as well as on image contrast was simulated for different model environments and verified by phantom measurements. Depending on the model environment (agarose 4% and 8%, xanthan 2% and 3%), SNR values increased by a factor of 1.15 up to 1.35, while NaCl solution was successfully suppressed. Thus, image contrast between the non-suppressed model compartments changes with IR pulse length. Finally, in vivo measurements of the human calf muscle of ten healthy volunteers were conducted at 3 Tesla. On average, a 1.4-fold increase in SNR could be achieved by increasing the inversion pulse length from 1 ms to 20 ms, leaving all other parameters - including the scan time - constant. This enables ²³Na IR MRI with improved spatial resolution or reduced acquisition time.

Statistical tensor analysis of the MQ MR signals generated by weak quadrupole interactions

Multiple quantum NMR signals that appear in the presence of weak quadrupole interactions were formulated using statistical tensors (Fano, 1957). The approach aimed to present a concise and a computer-based tool for a detailed analysis and modification of the MQ pulse sequences. The calculation avoids a lengthy procedure of utilizing exponential operators and, moreover, the same formulae are applicable for any interval in the TQ pulse sequence, as well as any spin value. The quantum operator algebra was implemented using "Mathematica" software (Wolfram Inc.). The results of tensor's evolutions in the TQ pulse sequence were graphically illustrated using corresponding spherical harmonics. The visualization takes into consideration the parity properties of irreducible tensors and the corresponding spherical harmonics.

Low-power suppression of fast-motion spin 3/2 signals

Triple Quantum Filters (TQFs) are frequently used for the selection of bi-exponentially relaxing spin 3/2 nuclei (in particular ²³Na) in ordered environments, such as biological tissues. These methods provide an excellent selection of slow-motion spins, but their sensitivity is generally low, and coherence selection requirements may lead to long experiments when applied in vivo. Alternative methods, such as 2P DIM, have demonstrated that the sensitivities of the signals from bi-exponentially relaxing sodium can be significantly increased using strategies other than TQFs. A shortcoming of the 2P DIM method is its strong dependence on B₀ inhomogeneities. We describe here a method, which is sensitive to the slow-motion regime, while the signal from spins in the fast-motion regime is suppressed. This method is shown to be more effective than TQFs, requires minimal phase cycling for the suppression of the influence of rf inhomogeneity, and has less dependence on resonance offsets and B₀-inhomogeneity than 2P DIM.

Effects of instrumental artifacts on triple quantum filtered NMR spectra for spin I=3/2

In this work, the effects of various instrumental artifacts on the triple quantum filtered NMR spectra for spin I=3/2 nuclei are investigated. The studied artifacts include finite pulse widths, phase errors, radio frequency field inhomogeneity and pulse transients, which are commonly encountered in practice. The triple quantum filtered spectra are numerically simulated, based on the evolution of the spin density operator under the Hamiltonian for the artifacts. The results show that the presence of the artifacts introduces a shape distortion in the spectrum as well as a variation in the peak intensity, compared with the spectrum without any artifacts. This work indicates that the existence of the instrumental artifacts may cause a misunderstanding of the triple quantum filtered NMR spectra in experiments. The results suggest that one be aware of the instrumental artifacts when performing the triple quantum filtered NMR experiments.

Residual quadrupole interaction in brain and its effect on quantitative sodium imaging

Sodium MRI is particularly interesting given the key role that sodium ions play in cellular metabolism. To measure concentration, images must be free from contrast unrelated to sodium density. However, spin 3/2 NMR is complicated by more than rapid biexponential signal decay. Residual quadrupole interactions (described by frequency ωQ) can reduce Mxy development during RF excitation. Three experiments, each performed on the same four healthy volunteers, demonstrate that residual quadrupole interactions are of concern in quantitative sodium imaging of the brain. The first experiment shows a reliable increase in the rate of excitation 'flipping' (1%-6%), particularly in white matter with tracts running superior-inferior (i.e. parallel to B0). Increased flip-rates imply an associated signal loss and are to be expected when ωQ ~ ω1. The second experiment shows that a prescribed flip-angle decrease from 90° to 20°, with concomitant decrease in TE from 0.25 ms to 0.10 ms and no T1 weighting, results in a 14%-26% saline calibration phantom normalized signal (SN) increase in the white matter regions. The third experiment shows that this (SN) increase is primarily due to a residual quadrupole effect, with a small contribution from T2 weighting. There is an observed deviation from the spin 3/2 biexponential curve, also suggesting ωQ dephasing. Using simulation to explain the results of all three experiments, a model of brain tissue is hypothesized. It includes one pool (50%) with ωQ = 0, and another (50%) in which ωQ has a Gaussian distribution with a standard deviation of 625 Hz. Given the result of the second experiment, it is suggested that the use of reduced flip-angles with large ω1 will provide more accurate measures of sodium concentration than 'standard' methods using 90° pulses. Alternatively, further study of sodium ωQmay provide a means to explore tissue structure and organization.

Triple-quantum-filtered sodium imaging at 9.4 Tesla

PURPOSE

Efficient acquisition of triple-quantum-filtered (TQF) sodium images at ultra-high field (UHF) strength.

METHODS

A three-pulse preparation and a stack of double-spirals were used for the acquisition of TQF images at 9.4 Tesla. The flip angles of the TQ preparation were smoothly reduced toward the edge of k-space along the partition-encoding direction. In doing so, the specific absorption rate could be reduced while preserving the maximal signal intensity for the partitions most relevant for image contrast in the center of k-space. Simulations, phantom and in vivo measurements were used to demonstrate the usefulness of the proposed method.

RESULTS

A higher sensitivity (∼ 20%) was achieved compared to the standard acquisition without flip angle apodization. Signals from free sodium ions were successfully suppressed irrespective of the amount of apodization used. B0 corrected TQF images with a nominal resolution of 5 × 5 × 5 mm(3) and an acceptable signal-to-noise ratio could be acquired in vivo within 21 min.

CONCLUSION

Conventional TQF in combination with flip angle apodization permits to exploit more efficiently the increased sensitivity available at 9.4T.

Second-order quadrupole interaction based detection of ultra-slow motions: Tensor operator framework for central-transition spectroscopy and the dynamics in hexagonal ice as an experimental example

The second-order quadrupolar broadening of the central transition of nuclear probes with half-integer spins I is demonstrated to be useful to detect ultraslow molecular motions. On the basis of density matrix calculations explicit expressions are derived for quadrupolarly modulated sin-sin and cos-cos signals of selectively excited nuclei with I=3/2, 5/2, 7/2, and 9/2. These correlation functions are suitable for implementation in two-dimensional exchange spectroscopy as well as for stimulated-echo experiments. As an application, ¹⁷O measurements of the reorientational correlation function of water molecules in hexagonal ice are presented.

Sodium MRI: methods and applications

Sodium NMR spectroscopy and MRI have become popular in recent years through the increased availability of high-field MRI scanners, advanced scanner hardware and improved methodology. Sodium MRI is being evaluated for stroke and tumor detection, for breast cancer studies, and for the assessment of osteoarthritis and muscle and kidney functions, to name just a few. In this article, we aim to present an up-to-date review of the theoretical background, the methodology, the challenges, limitations, and current and potential new applications of sodium MRI.

Sodium imaging of the human knee using soft inversion recovery fluid attenuation

Sodium signal strength in MRI is low when compared with (1)H. Thus, image voxel volumes must be relatively large in order to produce a sufficient signal-to-noise ratio (SNR). The measurement of sodium in cartilage is hindered by conflation with signal from the adjacent fluid spaces. Inversion recovery can be used to null signal from fluid, but reduces SNR. The purpose of this work was to optimize inversion recovery sodium MRI to enhance cartilage SNR while nulling fluid. Sodium relaxation was first measured for knee cartilage (T1=21±1 ms, T(2 fast)(∗)=0.8±0.2 ms, T(2 slow)(∗)=19.7±0.5 ms) and fluid (T1=48±3 ms, T2(∗)=47±4 ms) in nine healthy subjects at 4.7 T. The rapid relaxation of cartilage in relation to fluid permits the use of a lengthened inversion pulse to preferentially invert the fluid components. Simulations of inversion pulse length were performed to yield a cartilage SNR enhancing combination of parameters that nulled fluid. The simulations were validated in a phantom and then in vivo. B0 inhomogeneity was measured and the effect of off-resonance during the soft inversion pulse was assessed with simulation. Soft inversion recovery yielded twice the SNR and much improved sodium images of cartilage in human knee with little confounding signal from fluid.

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.

Evaluation of B0-inhomogeneity correction for triple-quantum-filtered sodium MRI of the human brain at 4.7 T

Off-resonance can result in signal loss on triple-quantum-filtered (TQF) sodium images. Three correction methods have been proposed to mitigate this problem, but their effectiveness and necessity has not yet been evaluated for human brain. This evaluation is warranted given the doubling or quadrupling of scan length without the expected signal-to-noise ratio (SNR) benefit. First, simulations and agar gel experiments showed that the off-resonance effects on signal loss were asymmetric about on-resonance. Second, the two scan length doubling correction methods were tested for two sets of TQF acquisition parameters in 10 healthy volunteers at 4.7 Tesla. Using only manual shimming on the sodium signal and a 3-pulse TQF sequence with an optimal preparation time value of 6 ms, the majority of brain tissue voxels (87-94% depending on sequence parameters) experienced B0 inhomogeneity amounting to less than 10% signal losses. Relative signal intensities of 0.96 ± 0.04 and 0.98 ± 0.02 were measured in these voxels relative to on-resonant voxels for SNR-optimized and standard TQF parameters. The remaining brain voxels in regions with known susceptibility problems suffered more substantial signal losses, which were partially recovered with the correction methods. At field strengths below 4.7T, at similar ranges of offset frequencies at higher fields and in typical volunteers, B0 correction appears unnecessary for TQF analysis in most of the brain. In many cases where regions with known susceptibility issues are not of concern, a doubling of scan time may be better spent to either improve SNR or spatial resolution in the TQF sodium images.

Noninvasive quantification of intracellular sodium in human brain using ultrahigh-field MRI

In vivo sodium magnetic resonance imaging (MRI) measures tissue sodium content in living human brain but current methods do not allow noninvasive quantitative assessment of intracellular sodium concentration (ISC) - the most useful marker of tissue viability. In this study, we report the first noninvasive quantitative in vivo measurement of ISC and intracellular sodium volume fraction (ISVF) in healthy human brain, made possible by measuring tissue sodium concentration (TSC) and intracellular sodium molar fraction (ISMF) at ultra-high field MRI. The method uses single-quantum (SQ) and triple-quantum filtered (TQF) imaging at 7 Tesla to separate intra- and extracellular sodium signals and provide quantification of ISMF, ISC and ISVF. This novel method allows noninvasive quantitative measurement of ISC and ISVF, opening many possibilities for structural and functional metabolic studies in healthy and diseased brains.

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.

MR imaging of articular cartilage physiology

The newer magnetic resonance (MR) imaging methods can give insights into the initiation, progression, and eventual treatment of osteoarthritis. Sodium imaging is specific for changes in proteoglycan (PG) content without the need for an exogenous contrast agent. T1ρ imaging is sensitive to early PG depletion. Delayed gadolinium-enhanced MR imaging has high resolution and sensitivity. T2 mapping is straightforward and is sensitive to changes in collagen and water content. Ultrashort echo time MR imaging examines the osteochondral junction. Magnetization transfer provides improved contrast between cartilage and fluid. Diffusion-weighted imaging may be a valuable tool in postoperative imaging.

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.

Signal-to-noise optimization for sodium MRI of the human knee at 4.7 Tesla using steady state

Sodium magnetic resonance imaging of knee cartilage is a possible diagnostic method for osteoarthritis, but low signal-to-noise ratio yields low spatial resolution images and long scan times. For a given scan time, a steady-state approach with reduced repetition time and increased averaging may improve signal-to-noise ratio and hence attainable resolution. However, repetition time reduction results in increased power deposition, which must be offset with increased radiofrequency pulse length and/or reduced flip angle to maintain an acceptable specific absorption rate. Simulations varying flip angle, repetition time, and radiofrequency pulse length were performed for constant power deposition corresponding to ∼6 W/kg over the human knee at 4.7 T. For 10% agar, simulation closely matched experiment. For healthy human knee cartilage, a 37% increase in signal-to-noise ratio was predicted for steady-state over "fully relaxed" parameters while a 29% ± 4% increase was determined experimentally (n=10). Partial volume of cartilage with synovial fluid, inaccurate relaxation parameters used in simulation, and/or quadrupolar splitting may be responsible for this disagreement. Excellent quality sodium images of the human knee were produced in 9 mins at 4.7 T using the signal-to-noise ratio enhancing steady-state technique.

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.

In vivo sodium magnetic resonance imaging of the human brain using soft inversion recovery fluid attenuation

Sodium imaging with soft inversion recovery fluid attenuation, which may be advantageous for intracellular weighting, was demonstrated with cerebrospinal fluid (CSF) suppression in five healthy volunteers at 4.7 T. Long rectangular inversion pulses reduce the average power deposition in an inversion recovery sequence, allowing repetition time to be shortened and more averages acquired for a given scan length. Longer pulses also significantly reduce the "depth" of Mz inversion in environments with rapid T1 and T2 relaxation (i.e., brain relative to CSF). Phantom experiments and simulation show a marked SNR increase when using a 10-ms, rather than a 1-ms, rectangular inversion pulse. Images were acquired in 11.1 min with a voxel size of 0.25 cm3 and the SNR in CSF, which is typically approximately 3 times larger than in brain, was reduced to 23% of that in the brain tissue, which had an average SNR of 17.

Serial triple quantum sodium MRI during non-human primate focal brain ischemia

Triple quantum (TQ) sodium MRI techniques with clinically acceptable 18-min data acquisition times were demonstrated in vivo in a nonhuman primate model of focal brain ischemia. Focal brain ischemia was induced in four animals using embolization coils to occlude the posterior cerebral artery, and a balloon catheter to occlude the middle cerebral artery. A statistically significant increase (P < 0.001) in the TQ sodium MRI signal intensity in the ischemic hemisphere relative to the contralateral hemisphere was seen at all time points in all four animals. This increased TQ sodium MRI signal intensity was demonstrated as early as 0.6 hr after the onset of ischemia. The TQ sodium MRI hyperintensity corresponded to the anatomical location of the ischemic cortex, as indicated by the registration of the TQ imaging data with anatomical proton MRI data. The results demonstrate that early after the onset of ischemia, there was an increase in the TQ signal intensity in the ischemic hemisphere, and a negligible change in the single quantum (SQ) signal intensity.

Analysis of the Degree of Nematic Ordering within Dense Aqueous Dispersions of Charged Anisotropic Colloids by 23Na NMR Spectroscopy

Aqueous dispersions of Laponite, a synthetic clay neutralized by sodium counterions, are used as a model of charged anisotropic colloids to probe the influence of the shape of the particle on their organization within a macroscopic nematic phase. Because of the large fraction of condensed sodium counterions in the vicinity of the clay particle, (23)Na NMR is a sensitive probe of the nematic ordering of the clay dispersions. We used line shape analysis of the (23)Na NMR spectra and measurements of the Hahn echo attenuation to quantify the degree of alignment of the individual clay particles along a single nematic director. As justified by simple dynamical simulations of the interplay between the sodium quadrupolar relaxation and its diffusion through the porous network limited by the surface of the clay particles, we probe the degree of ordering within these clay nematic dispersions by measuring the variation of the apparent (23)Na NMR relaxation rates as a function of the macroscopic orientation of the clay dispersion within the magnetic field.

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.

A new method for suppressing the central transition in I=3/2 NMR spectra with a demonstration for 23Na in bovine articular cartilage

The splitting and the lineshape of the satellite transitions of 23Na are measures of the residual quadrupolar interaction and its distribution, which are related to the degrees of order and binding of sodium in biological tissues. However, these transitions are often masked by the stronger signals of the central transition and the isotropic sodium ions. A way to suppress the central signals, while preserving the lineshape and the intensity of the satellites, is suggested and tested on a liquid crystal and on bovine articular cartilage.

Detection of sodium ions in anisotropic environments through spin-lock NMR

A new method for selectively detecting sodium ions in anisotropic environments is presented. A spin-lock (SL) sequence, followed by a coherence transfer pulse, generates rank-two zero-quantum coherences, and converts them into observable transverse magnetization. The quadrupolar polarization is only generated when there are residual quadrupolar couplings in the sample, and provided the SL field strength is comparable to these couplings. This filter has proved to be more efficient than a double-quantum magic-angle (DQ-MA) filter in generating observable signal from ions in anisotropic media in both a nasal bovine cartilage sample and a liquid crystalline DNA sample. Finally, the SL filtering technique does not rely on a flip angle effect for the selection of the desired signal component, as does a DQ-MA filter, and may therefore prove desirable in an imaging experiment, due to its better tolerance to phase and flip angle imperfections.

Dynamics of spin I=3/2 under spin-locking conditions in an ordered environment

We have derived approximate analytic solutions to the master equation describing the evolution of the spin I=3/2 density operator in the presence of a radio-frequency (RF) field and both static and fluctuating quadrupolar interactions. Spectra resulting from Fourier transformation of the evolutions of the on-resonance spin-locked magnetization into the various coherences display two satellite pairs and, in some cases, a central line. The central line is generally trimodal, consisting of a narrow component related to a slowly relaxing mode and two broad components pertaining to two faster relaxing modes. The rates of the fast modes are sensitive to slow molecular motion. Neither the amplitude nor the width of the narrow component is affected by the magnitude of the static coupling, whereas the corresponding features of the broad components depend in a rather complicated manner on the spin-lock field strength and static quadrupolar interaction. Under certain experimental conditions, the dependencies of the amplitudes on the dynamics are seen to vanish and the relaxation rates reduce to relatively simple expressions. One of the promising emerging features is the fact that the evolutions into the selectively detected quadrupolar spin polarization order and the rank-two double-quantum coherence do not exhibit a slowly relaxing mode and are particularly sensitive to slow molecular motion. Furthermore, these coherences can only be excited in the presence of a static coupling and this makes it possible to discern nuclei in anisotropic from those in isotropic environment. The feasibility of the spin-lock pulse sequences with limited RF power and a nonvanishing average electric field gradient has been demonstrated through experiments on sodium in a dense lyotropic DNA liquid crystal.

Current awareness

In order to keep subscribers up-to-date with the latest developments in their field, John Wiley & Sons are providing a current awareness service in each issue of the journal. The bibliography contains newly published material in the field of NMR in biomedicine. Each bibliography is divided into 9 sections: 1 Books, Reviews ' Symposia; 2 General; 3 Technology; 4 Brain and Nerves; 5 Neuropathology; 6 Cancer; 7 Cardiac, Vascular and Respiratory Systems; 8 Liver, Kidney and Other Organs; 9 Muscle and Orthopaedic. Within each section, articles are listed in alphabetical order with respect to author. If, in the preceding period, no publications are located relevant to any one of these headings, that section will be omitted.