Thermal relaxation and coherence dynamics of spin 3/2. I. Static and fluctuating quadrupolar interactions in the multipole basis

Low-rank reconstruction for simultaneous double half-echo 23Na and undersampled 23Na multi-quantum coherences MRI

PURPOSE

To develop a new sequence to simultaneously acquire Cartesian sodium (23Na) MRI and accelerated Cartesian single (SQ) and triple quantum (TQ) sodium MRI of in vivo human brain at 7 T by leveraging two dedicated low-rank reconstruction frameworks.

THEORY AND METHODS

The Double Half-Echo technique enables short echo time Cartesian 23Na MRI and acquires two k-space halves, reconstructed by a low-rank coupling constraint. Additionally, three-dimensional (3D) 23Na Multi-Quantum Coherences (MQC) MRI requires multi-echo sampling paired with phase-cycling, exhibiting a redundant multidimensional space. Simultaneous Autocalibrating and k-Space Estimation (SAKE) were used to reconstruct highly undersampled 23Na MQC MRI. Reconstruction performance was assessed against five-dimensional (5D) CS, evaluating structural similarity index (SSIM), root mean squared error (RMSE), signal-to-noise ratio (SNR), and quantification of tissue sodium concentration and TQ/SQ ratio in silico, in vitro, and in vivo.

RESULTS

The proposed sequence enabled the simultaneous acquisition of fully sampled 23Na MRI while leveraging prospective undersampling for 23Na MQC MRI. SAKE improved TQ image reconstruction regarding SSIM by 6% and reduced RMSE by 35% compared to 5D CS in vivo. Thanks to prospective undersampling, the spatial resolution of 23Na MQC MRI was enhanced from8 × 8 × 15 $$ 8\times 8\times 15 $$ mm3 to8 × 8 × 8 $$ 8\times 8\times 8 $$ mm3 while reducing acquisition time from2 × 31 $$ 2\times 31 $$ min to2 × 23 $$ 2\times 23 $$ min.

CONCLUSION

The proposed sequence, coupled with low-rank reconstructions, provides an efficient framework for comprehensive whole-brain sodium MRI, combining TSC, T2*, and TQ/SQ ratio estimations. Additionally, low-rank matrix completion enables the reconstruction of highly undersampled 23Na MQC MRI, allowing for accelerated acquisition or enhanced spatial resolution.

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.

Mobility of sodium ions in agarose gels probed through combined single- and triple-quantum NMR

Metal ions, including biologically prevalent sodium ions, can modulate electrostatic interactions frequently involved in the stability of condensed compartments in cells. Quantitative characterization of heterogeneous ion dynamics inside biomolecular condensates demands new experimental approaches. Here we develop a 23Na NMR relaxation-based integrative approach to probe dynamics of sodium ions inside agarose gels as a model system. We exploit the electric quadrupole moment of spin-3/2 23Na nuclei and, through combination of single-quantum and triple-quantum-filtered 23Na NMR relaxation methods, disentangle the relaxation contribution of different populations of sodium ions inside gels. Three populations of sodium ions are identified: a population with bi-exponential relaxation representing ions within the slow motion regime and two populations with mono-exponential relaxation but at different rates. Our study demonstrates the dynamical heterogeneity of sodium ions inside agarose gels and presents a new experimental approach for monitoring dynamics of sodium and other spin-3/2 ions (e.g. chloride) in condensed environments.

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.

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.

An approach to evaluation of the point-spread function for 23 Na magnetic resonance imaging

Despite the technical challenges that require lengthy acquisitions to overcome poor signal-to-noise ratio (SNR), sodium (²³ Na) magnetic resonance imaging (MRI) is an intriguing area of research due to its essential role in human metabolism. Low SNR images can impact the measurement of the point-spread function (PSF) by adding uncertainty into the resulting quantities. Here, we present methods to calculate the PSF by using the modulation transfer function (MTF), and a 3D-printed line-pair phantom in the context of ²³ Na MRI. A simulation study investigated the effect of noise on the resulting MTF curves, which were derived by direct modulation (DM) and a method utilizing Fourier harmonics (FHs). Experimental data utilized a line-pair phantom with nine spatial frequencies, filled with different concentrations (15, 30, and 60 mM) of sodium in 3% agar. MTF curves were calculated using both methods from data acquired from density-adapted 3D radial projections (DA-3DRP) and Fermat looped orthogonally encoded trajectories (FLORET). Simulations indicated that the DM method increased variability in the MTF curves at all tested noise levels over the FH method. For the experimental data, the FH method resulted in PSFs with a narrower full width half maximum with reduced variability, although the improvement in variability was not as pronounced as predicted by simulations. The DA-3DRP data indicated an improvement in the PSF over FLORET. It was concluded that a 3D-printed line-pair phantom represents a convenient method to measure the PSF experimentally. The MTFs from the noisy images in ²³ Na MRI have reduced variability from a FH method over DM.

Water and Ion Dynamics in Confined Media: A Multi-Scale Study of the Clay/Water Interface

This review details a large panel of experimental studies (Inelastic Neutron Scattering, Quasi-Elastic Neutron Scattering, Nuclear Magnetic Resonance relaxometry, Pulsed-Gradient Spin-Echo attenuation, Nuclear Magnetic Resonance Imaging, macroscopic diffusion experiments) used recently to probe, over a large distribution of characteristic times (from pico-second up to days), the dynamical properties of water molecules and neutralizing cations diffusing within clay/water interfacial media. The purpose of this review is not to describe these various experimental methods in detail but, rather, to investigate the specific dynamical information obtained by each of them concerning these clay/water interfacial media. In addition, this review also illustrates the various numerical methods (quantum Density Functional Theory, classical Molecular Dynamics, Brownian Dynamics, macroscopic differential equations) used to interpret these various experimental data by analyzing the corresponding multi-scale dynamical processes. The purpose of this multi-scale study is to perform a bottom-up analysis of the dynamical properties of confined ions and water molecules, by using complementary experimental and numerical studies covering a broad range of diffusion times (between pico-seconds up to days) and corresponding diffusion lengths (between Angstroms and centimeters). In the context of such a bottom-up approach, the numerical modeling of the dynamical properties of the diffusing probes is based on experimental or numerical investigations performed on a smaller scale, thus avoiding the use of empirical or fitted parameters.

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.

Efficient 23 Na triple-quantum signal imaging on clinical scanners: Cartesian imaging of single and triple-quantum 23 Na (CRISTINA)

PURPOSE

To capture the multiquantum coherence (MQC) 23 Na signal. Different phase-cycling options and sequences are compared in a unified theoretical layout, and a novel sequence is developed.

METHODS

An open source simulation overview is provided with graphical explanations to facilitate MQC understanding and access to techniques. Biases such as B0 inhomogeneity and stimulated echo signal were simulated for 4 different phase-cycling options previously described. Considerations for efficiency and accuracy lead to the implementation of a 2D Cartesian single and triple quantum imaging of sodium (CRISTINA) sequence employing two 6-step cycles in combination with a multi-echo readout. CRISTINA was compared to simultaneous single-quantum and triple-quantum-filtered MRI of sodium (SISTINA) under strong static magnetic gradient. CRISTINA capabilities were assessed on 8 × 60 mL, 0% to 5% agarose phantom with 50 to 154 mM 23 Na concentration at 7 T. CRISTINA was demonstrated subsequently in vivo in the brain.

RESULTS

Simulation of B0 inhomogeneity showed severe signal dropout, which can lead to erroneous MQC measurement. Stimulated echo signal was highest at the time of triple-quantum coherences signal maximum. However, stimulated echo signal is separated by Fourier Transform as an offset and did not interfere with MQC signals. The multi-echo readout enabled capturing both single-quantum coherences and triple-quantum coherences signal evolution at once. Signal combination of 2 phase-cycles with a corresponding B0 map was found to recover the signal optimally. Experimental results confirm and complement the simulations.

CONCLUSION

Considerations for efficient MQC measurements, most importantly avoiding B0 signal loss, led to the design of CRISTINA. CRISTINA captures triple-quantum coherences and single-quantum coherences signal evolution to provide complete sodium signal characterization including T 2 ∗ fast, T 2 ∗ slow, MQC amplitudes, and sodium concentration.

Intracellular Sodium Changes in Cancer Cells Using a Microcavity Array-Based Bioreactor System and Sodium Triple-Quantum MR Signal

The sodium triple-quantum (TQ) magnetic resonance (MR) signal created by interactions of sodium ions with macromolecules has been demonstrated to be a valuable biomarker for cell viability. The aim of this study was to monitor a cellular response using the sodium TQ signal during inhibition of Na/K-ATPase in living cancer cells (HepG2). The cells were dynamically investigated after exposure to 1 mM ouabain or K+-free medium for 60 min using an MR-compatible bioreactor system. An improved TQ time proportional phase incrementation (TQTPPI) pulse sequence with almost four times TQ signal-to-noise ratio (SNR) gain allowed for conducting experiments with 12–14 × 106 cells using a 9.4 T MR scanner. During cell intervention experiments, the sodium TQ signal increased to 138.9 ± 4.1% and 183.4 ± 8.9% for 1 mM ouabain (n = 3) and K+-free medium (n = 3), respectively. During reperfusion with normal medium, the sodium TQ signal further increased to 169.2 ± 5.3% for the ouabain experiment, while it recovered to 128.5 ± 6.8% for the K+-free experiment. These sodium TQ signal increases agree with an influx of sodium ions during Na/K-ATPase inhibition and hence a reduced cell viability. The improved TQ signal detection combined with this MR-compatible bioreactor system provides a capability to investigate the cellular response of a variety of cells using the sodium TQ MR signal.

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.

Protein conformational changes affect the sodium triple-quantum MR signal

The aim of this study was to investigate possible sodium triple-quantum (TQ) signal dependence on pH variation and protein unfolding which may happen in vivo. The model system, composed of bovine serum albumin (BSA), was investigated over a wide pH range of 0.70 to 13.05 and during urea-induced unfolding. In both experimental series, the sodium and BSA concentration were kept constant so that TQ signal changes solely arose from an environmental change. The experiments were performed using unique potential to detect weak TQ signals by implementing a TQ time proportional phase increment pulse sequence. At a pH of 0.70, in which case the effect of the negatively charged groups was minimized, the minimum TQ percentage relative to single-quantum of 1.34% ± 0.05% was found. An increase of the pH up to 13.05 resulted in an increase of the sodium TQ signal by 225%. Urea-induced unfolding of BSA, without changes in pH, led to a smaller increase in the sodium TQ signal of up to 40%. The state of BSA unfolding was verified by fluorescence microscopy. Results of both experiments were well fitted by sigmoid functions. Both TQ signal increases were in agreement with an increase of the availability of negatively charged groups. The results point to vital contributions of the biochemical environment to the TQ MR signals. The sodium TQ signal in vivo could be a valuable biomarker of cell viability, and therefore possible effects of pH and protein unfolding need to be considered for a proper interpretation of changes in sodium TQ signals.

A Multi-Scale Study of Water Dynamics under Confinement, Exploiting Numerical Simulations in Relation to NMR Relaxometry, PGSE and NMR Micro-Imaging Experiments: An Application to the Clay/Water Interface

Water mobility within the porous network of dense clay sediments was investigated over a broad dynamical range by using 2H nuclear magnetic resonance spectroscopy. Multi-quanta 2H NMR spectroscopy and relaxation measurements were first performed to identify the contributions of the various relaxation mechanisms monitoring the time evolution of the nuclear magnetisation of the confined heavy water. Secondly, multi-quanta spin-locking NMR relaxation measurements were then performed over a broad frequency domain, probing the mobility of the confined water molecules on a time-scale varying between microseconds and milliseconds. Thirdly, 1H NMR pulsed-gradient spin-echo attenuation experiments were performed to quantify water mobility on a time-scale limited by the NMR transverse relaxation time of the confined NMR probe, typically a few milliseconds. Fourthly, the long living quantum state of the magnetisation of quadrupolar nuclei was exploited to probe a two-time correlation function at a time-scale reaching one second. Finally, magnetic resonance imaging measurements allow probing the same dynamical process on time-scales varying between seconds and several hours. In that context, multi-scale modelling is required to interpret these NMR measurements and extract information on the influences of the structural properties of the porous network on the apparent mobility of the diffusing water molecules. That dual experimental and numerical approach appears generalizable to a large variety of porous networks, including zeolites, micelles and synthetic or biological membranes.

Coexistence of three types of sodium motion in double molybdate Na9Sc(MoO4)6: 23Na and 45Sc NMR data and ab initio calculations

The rechargeable Na-ion batteries attract much attention as an alternative to the widely used but expensive Li-ion batteries. The search for materials with high sodium diffusion is important for the development of solid state electrolytes. We present the results of experimental and ab initio studies of the Na-ion diffusion mechanism in Na9Sc(MoO4)6. The ion conductivity reaches the value of 3.6 × 10-2 S cm-1 at T ∼ 850 K. The 23Na and 45Sc NMR data reveal the coexistence of three different types of Na-ion motion in the temperature range from 300 to 750 K. They are activated at different temperatures and are characterized by substantially different dynamics parameters. These features are confirmed by ab initio calculations of activation barriers for sodium diffusion along various paths.

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.

Experimental evidence for the relaxation coupling of all longitudinal 7Li magnetization orders in the superionic conductor Li10GeP2S12

This contribution addresses the experimental proof of the relaxation coupling of the ⁷Li (I = 3/2) longitudinal magnetization orders in the solid-state electrolyte Li₁₀GeP₂S₁₂ (LGPS). This effect was theoretically described by Korb and Petit in 1988 but has not yet been shown experimentally. In a 2D-T₁/spin-alignment echo (SAE) experiment, the inverse Laplace transformation of the spectral component over two time dimensions revealed the asymmetric course of the spin-lattice relaxation following from the coupling of all longitudinal orders. These observations were supported by Multi-quantum-filter experiments and by simulations of the 2D-T₁/SAE experiment with a lithium spin system. Since the asymmetric relaxation effects are directly dependent on the velocities and degrees of freedom of ion motion they could be used especially in fast Li-ion conductors as a separation tool for environments with different mobility processes.

Multinuclear MRI at Ultrahigh Fields

In this article, an overview of the current developments and research applications for non-proton magnetic resonance imaging (MRI) at ultrahigh magnetic fields (UHFs) is given. Due to technical and methodical advances, efficient MRI of physiologically relevant nuclei, such as Na, Cl, Cl, K, O, or P has become feasible and is of interest to obtain spatially and temporally resolved information that can be used for biomedical and diagnostic applications. Sodium (Na) MRI is the most widespread multinuclear imaging method with applications ranging over all regions of the human body. Na MRI yields the second largest in vivo NMR signal after the clinically used proton signal (H). However, other nuclei such as O and P (energy metabolism) or Cl and K (cell viability) are used in an increasing number of MRI studies at UHF. One major advancement has been the increased availability of whole-body MR scanners with UHFs (B0 ≥7T) expanding the range of detectable nuclei. Nevertheless, efforts in terms of pulse sequence and post-processing developments as well as hardware designs must be made to obtain valuable information in clinically feasible measurement times. This review summarizes the available methods in the field of non-proton UHF MRI, especially for Na MRI, as well as introduces potential applications in clinical research.

New experimental observations of the behavior of sodium ions in saturated rock samples

¹H NMR relaxometry of saturated rock samples has become a useful tool for the characterization of porosity and transport phenomena of enclosed fluids. The pore size can be measured using the difference between inverse relaxation values of protons absorbed by the saturated rock and that present in the bulk fluids. These experiments are usually performed at low magnetic fields to reduce the influence of the diffusion on the relaxation values in the presence of Internal Gradient Fields. Recently, sodium ions have become objects of investigation. The main advantage of sodium ions over protons as measured spins in the Petrophysic NMR experiments is their presence in water and not other phases like oil and gas. However unlike protons, sodium ions can have slow motion properties like appearance of the bi-exponential relaxation and residual quadrupolar distribution, which can lead to complex behavior of spins inside the pores. Here, we describe eight ²³Na NMR experiments at 9.39 T external magnetic field, in which we have investigated the behavior of sodium ions in 4 saturated rock samples: Berea 500, Fontainebleau 1, Bentheimer sandstones, and Austin chalk. We show that the reduction of spin-spin relaxation is caused by anisotropic motion and not diffusion in the presence of Internal Gradient Fields. There can be a link between free diffusional and motional averaging regimes regardless of the size of environment in which the measured spin ions are. Using different NMR sequences, we reveal and quantitatively describe bi-exponentially relaxing spins and spins with residual quadrupolar coupling. This work demonstrates unique model for the behavior of ions inside porous media, which is different than known models (Brownstein-Tarr model and "agarose gel model").

Double quantum filtered 23 Na MRI with magic angle excitation of human skeletal muscle in the presence of B0 and B1 inhomogeneities

Double quantum filtered ²³ Na MRI with magic angle excitation (DQF-MA) can be used to selectively detect sodium ions located within anisotropic structures such as muscle fibers. It might therefore be a promising tool to analyze the microscopic environment of sodium ions, for example in the context of osmotically neutral sodium retention. However, DQF-MA imaging is challenging due to various signal dependences, on both measurement parameters and external influences. The aim of this work was to examine how B₀ in combination with B₁ inhomogeneities alter the DQF-MA signal intensity. We showed that, in the presence of B₀ inhomogeneities, flip angle schemes with only one 54.7° pulse can be favorable compared with the classical 90°-54.7°-54.7° scheme. DQF-MA images of the human lower leg were acquired at B₀  = 3 T with a nominal spatial resolution of 12 × 12 × 36 mm³ within an acquisition time of T_Acq  < 10 min, and compared with spin density weighted (DW), as well as triple quantum filtration (TQF) ²³ Na images. We found mean normalized signal-to-noise ratios of TQF/DW = 13.7 ± 2.3% (tibialis anterior), 11.9 ± 2.3% (soleus) and 11.4 ± 2.2% (gastrocnemius medialis), as well as DQF-MA/DW = 4.7 ± 1.1% (tibialis anterior), 3.3 ± 0.73% (soleus) and 3.4 ± 0.6% (gastrocnemius medialis). These ratios might serve as additional measures in future clinical studies of sodium retention within human skeletal muscle. However, the influence of B₀ and B₁ inhomogeneities should be considered when interpreting DQF-MA images.

Investigation of the Li-ion conduction behavior in the Li10GeP2S12 solid electrolyte by two-dimensional T1-spin alignment echo correlation NMR

Li₁₀GeP₂S₁₂ (LGPS) is the fastest known Li-ion conductor to date due to the formation of one-dimensional channels with a very high Li mobility. A knowledge-based optimization of such materials for use, for example, as solid electrolyte in all-solid-state batteries requires, however, a more comprehensive understanding of Li ion conduction that considers mobility in all three dimensions, mobility between crystallites and different phases, as well as their distributions within the material. The spin alignment echo (SAE) nuclear magnetic resonance (NMR) technique is suitable to directly probe slow Li ion hops with correlation times down to about 10^-5 s, but distinction between hopping time constants and relaxation processes may be ambiguous. This contribution presents the correlation of the ⁷Li spin lattice relaxation (SLR) time constants (T₁) with the SAE decay time constant τ_c to distinguish between hopping time constants and signal decay limited by relaxation in the τ_c distribution. A pulse sequence was employed with two independently varied mixing times. The obtained multidimensional time domain data was processed with an algorithm for discrete Laplace inversion that does not use a non-negativity constraint to deliver 2D SLR-SAE correlation maps. Using the full echo transient, it was also possible to estimate the NMR spectrum of the Li ions responsible for each point in the correlation map. The signal components were assigned to different environments in the LGPS structure.

Tracking protein function with sodium multi quantum spectroscopy in a 3D-tissue culture based on microcavity arrays

The aim of this study was to observe the effects of strophanthin induced inhibition of the Na-/K-ATPase in liver cells using a magnetic resonance (MR) compatible bioreactor. A microcavity array with a high density three-dimensional cell culture served as a functional magnetic resonance imaging (MRI) phantom for sodium multi quantum (MQ) spectroscopy. Direct contrast enhanced (DCE) MRI revealed the homogenous distribution of biochemical substances inside the bioreactor. NMR experiments using advanced bioreactors have advantages with respect to having full control over a variety of physiological parameters such as temperature, gas composition and fluid flow. Simultaneous detection of single quantum (SQ) and triple quantum (TQ) MR signals improves accuracy and was achieved by application of a pulse sequence with a time proportional phase increment (TQTPPI). The time course of the Na-/K-ATPase inhibition in the cell culture was demonstrated by the corresponding alterations of sodium TQ/SQ MR signals.

Comparison of potassium and sodium binding in vivo and in agarose samples using TQTPPI pulse sequence

Potassium and sodium specific binding in vivo were explored at 21.1T by triple quantum (TQ) magnetic resonance (MR) signals without filtration to achieve high sensitivities and precise quantifications. The pulse sequence used time proportional phase increments (TPPI). During simultaneous phase-time increments, it provided total single quantum (SQ) and TQ MR signals in the second dimension at single and triple quantum frequencies, respectively. The detection of both TQ and SQ signals was performed at identical experimental conditions and the resulting TQ signal equals 60±3% of the SQ signal when all ions experience sufficient time for binding. In a rat head in vivo the TQ percentage relative to SQ for potassium is 41.5±3% and for sodium is 16.1±1%. These percentages were compared to the matching values in an agarose tissue model with MR relaxation times similar to those of mammalian brain tissue. The sodium TQ signal in agarose samples decreased in the presence of potassium, suggesting a competitive binding of potassium relative to sodium ions for the same binding sites. The TQTPPI signals correspond to almost two times more effective binding of potassium than sodium. In vivo, up to ∼69% of total potassium and ∼27% of total sodium can be regarded as bound or experiencing an association time in the range of several milliseconds. Experimental data analyses show that more than half of the in vivo total sodium TQ signal could be from extracellular space, which is an important factor for quantification of intracellular MR signals.

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.

Quantitative sodium MRI of kidney

One of the main tasks of the human kidneys is to maintain the homeostasis of the body's fluid and electrolyte balance by filtration of the plasma and excretion of the end products. Herein, the regulation of extracellular sodium in the kidney is of particular importance. Sodium MRI ((23)Na MRI) allows for the absolute quantification of the tissue sodium concentration (TSC) and thereby provides a direct link between TSC and tissue viability. Renal (23)Na MRI can provide new insights into physiological tissue function and viability thought to differ from the information obtained by standard (1)H MRI. Sodium imaging has the potential to become an independent surrogate biomarker not only for renal imaging, but also for oncology indications. However, this technique is now on the threshold of clinical implementation. Numerous, initial pre-clinical and clinical studies have already outlined the potential of this technique; however, future studies need to be extended to larger patient groups to show the diagnostic outcome. In conclusion, (23)Na MRI is seen as a powerful technique with the option to establish a non-invasive renal biomarker for tissue viability, but is still a long way from real clinical implementation.

Exchange-induced relaxation in the presence of a fictitious field

In the present study we derive a solution for two site fast exchange-induced relaxation in the presence of a fictitious magnetic field as generated by amplitude and frequency modulated RF pulses. This solution provides a means to analyze data obtained from relaxation experiments with the method called RAFFn (Relaxation Along a Fictitious Field of rank n), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (rank n). The RAFF2 technique is relevant to MRI relaxation methods that provide good contrast enhancement for tumor detection. The relaxation equations for n=2 are derived for the fast exchange regime using density matrix formalism. The method of derivation can be further extended to obtain solutions for n>2.

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.

Two-pulse biexponential-weighted 23Na imaging

A new method is proposed for acquiring 3D biexponential-weighted sodium images with two instead of three RF pulses to allow for shorter repetition time at high magnetic fields (B0≥7 T) and reduced SAR. The second pulse converts single- into triple-quantum coherences in regions containing sodium ions which are restricted in mobility. Since only single-quantum coherences can be detected, an image acquired after the second pulse is intrinsically single-quantum-filtered and can be used to generate a biexponential-weighted sodium image by a weighted subtraction with the spin-density-weighted image acquired between the pulses. The proposed sequence generates biexponential-weighted sodium images of in vivo human brain with 140% higher SNR than triple-quantum-filtered sodium images and 4% higher SNR than a biexponential-weighted sequence with three RF pulses at equal acquisition time and with 1/3 lower SAR. As SAR is reduced, accordingly repetition time can be spared to obtain even higher SNR-time efficiency. In comparison to a difference image generated from two images of a double-readout sequence, the proposed two-pulse sequence yields about 14% higher SNR. Our new two-pulse biexponential-weighted sequence allows for acquisition of full 3D data sets of the human brain in vivo with a nominal resolution of (5 mm)(3) in about 10 min.

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.

Biomedical applications of sodium MRI in vivo

In this article we present an up-to-date overview of the potential biomedical applications of sodium magnetic resonance imaging (MRI) in vivo. Sodium MRI is a subject of increasing interest in translational imaging research as it can give some direct and quantitative biochemical information on the tissue viability, cell integrity and function, and therefore not only help the diagnosis but also the prognosis of diseases and treatment outcomes. It has already been applied in vivo in most human tissues, such as brain for stroke or tumor detection and therapeutic response, in breast cancer, in articular cartilage, in muscle, and in kidney, and it was shown in some studies that it could provide very useful new information not available through standard proton MRI. However, this technique is still very challenging due to the low detectable sodium signal in biological tissue with MRI and hardware/software limitations of the clinical scanners. The article is divided in three parts: 1) the role of sodium in biological tissues, 2) a short review on sodium magnetic resonance, and 3) a review of some studies on sodium MRI on different organs/diseases to date.

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.

Reduction of B(0) inhomogeneity effects in triple-quantum-filtered sodium imaging

Triple-quantum (TQ) filtered sodium MR imaging has been proposed for separation of sodium signal arising from different physiological compartments. In a three-pulse sequence without refocussing pulse, the TQ signal is strongly sensitive to inhomogeneities of the B(0) field. We examine the dependence of the TQ signal intensity on the sequence parameters and propose a modified phase-cycling scheme to improve image quality. A new method for correction of B(0) inhomogeneity artefacts in TQ filtered sodium imaging is presented which requires only two acquisitions to obtain a correction as far as the B(0) inhomogeneity and the pulse widths are not too large. The method was verified in phantom experiments.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation.