Multiquantum filters and order in tissues

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.

17O Solid-State NMR Spectroscopy of Lipid Membranes

Despite the limitations posed by poor sensitivity, studies have reported the unique advantages of 17O based NMR spectroscopy to study systems existing in liquid, solid, or semisolid states. 17O NMR studies have exploited the remarkable sensitivity of quadrupole coupling and chemical shift anisotropy tensors to the local environment in the characterization of a variety of intra- and intermolecular interactions and motion. Recent studies have considerably expanded the use of 17O NMR to study dynamic intermolecular interactions associated with some of the challenging biological systems under magic angle spinning (MAS) and aligned conditions. The very fast relaxing nature of 17O has been well utilized in cellular and in vivo MRS (magnetic resonance spectroscopy) and MRI (magnetic resonance imaging) applications. The main focus of this Review is to highlight the new developments in the biological solids with a detailed discussion for a few selected examples including membrane proteins and nanodiscs. In addition to the unique benefits and limitations, the remaining challenges to overcome, and the impacts of higher magnetic fields and sensitivity enhancement techniques are discussed.

Deuterium Magnetic Resonance Imaging Using Deuterated Water-Induced 2H-Tissue Labeling Allows Monitoring Cancer Treatment at Clinical Field Strength

PURPOSE

An accurate and noninvasive assessment of tumor response following treatment other than traditional anatomical imaging techniques is essential. Deuterium magnetic resonance spectroscopic (MRS) imaging has been demonstrated as an alternative for cancer metabolic imaging by high-field MRI using deuterium-labeled molecules. The study aim was to use 2H tissue labeling and deuterium MRI at clinical field strength for tumor visualization and assessment of three anticancer therapies in pancreatic cancer model mice.

EXPERIMENTAL DESIGN

MIA PaCa-2 pancreatic carcinoma and C26 colorectal carcinoma models of BALB/c-nu mice was prepared, and repeated deuterium MRI was performed during the first 10 days of free drinking of 30% D2O to track 2H distribution in tissues. 2H accumulation in the tumor after irradiation, bevacizumab administration, or gemcitabine administration was also measured in MIA PaCa-2-bearing mice. Confirmatory proton MRI, ex vivo metabolic hyperpolarization 13C-MRS, and histopathology were performed.

RESULTS

The mouse's whole-body distribution of 2H was visible 1 day after drinking, and the signal intensity increased daily. Although the tumor size did not change 1 and 3 days after irradiation, the amount of 2H decreased significantly. The 2H image intensity of the tumor also significantly decreased after the administration of bevacizumab or gemcitabine. Metabolic hyperpolarization 13C-MRS, proton MRI, and 2H-NMR spectroscopy confirmed the efficacy of the anticancer treatments.

CONCLUSIONS

Deuterium MRI at 1.5T proved feasible to track 2H distribution throughout mouse tissues during D2O administration and revealed a higher 2H accumulation in the tumor xenografts. This research demonstrated a promising successful method for preliminary assessment of radiotherapy and chemotherapy of cancer.

A molecular-mechanical link in shear-induced self-assembly of a functionalized biopolymeric fluid

23Na multiple quantum filtered (MQF) rheo-NMR methods were applied to probe the molecular foundation for flow induced self-assembly in 0.5% κ-carrageenan fluid. This method is sensitive enough to utilize an endogenous sodium ion concentration of approximately 0.02%. Rheo-NMR experiments were conducted at different temperatures and shear rates to explore varying molecular dynamics of the biopolymer in the fluid under shear. The temperature in the rheo-NMR experiments was changes from 288 K to 313 K to capture transition of κ-carrageenan molecules from helices to coils. At each temperature, the fluid was also tested for flow and oscillatory shear behaviour using bulk rheometry methods. It was found that the 23Na MQF signals were observed for the 0.5% κ-carrageenan solution only under shear and when the fluid demonstrated yielding and/or shear-thinning behaviour. At temperatures of 303 K and above, no 23Na MQF signals were observed independent of the presence or absence of shear as the molecular phase transition to random coils occurs and the fluid becomes Newtonian.

Sodium Dynamics in the Cellular Environment

Sodium ions are essential for the functions of biological cells, and they are maintained at the balance between intra- and extracellular environments. The quantitative assessment of intra- and extracellular sodium as well as its dynamics can provide crucial physiological information on a living system. ²³Na nuclear magnetic resonance (NMR) is a powerful and noninvasive technique to probe the local environment and dynamics of sodium ions. However, due to the complex relaxation behavior of the quadrupolar nucleus in the intermediate-motion regime and because of the heterogeneous compartments and diverse molecular interactions in the cellular environment, the understanding of the ²³Na NMR signal in biological systems is still at the early stage. In this work, we characterize the relaxation and diffusion of sodium ions in the solutions of proteins and polysaccharides, as well as in the in vitro samples of living cells. The multi-exponential behavior of ²³Na transverse relaxation has been analyzed according to the relaxation theory to derive the crucial information related to the ionic dynamics and molecular binding in the solutions. The bi-compartment model of transverse relaxation and diffusion measurements can corroborate each other to quantify the fractions of intra- and extracellular sodium. We show that ²³Na relaxation and diffusion can be used to monitor the viability of human cells, which offers versatile NMR metrics for in vivo studies.

Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber

The ¹H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH₂ and CH₃ functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.

Deuterium double quantum-filtered NMR studies of peripheral and optic nerves

OBJECTIVE

Characterization of the nerve components by deuterium double quantum-filtered magnetization transfer (DQF-MT) NMR.

METHODS

Nerves were equilibrated in deuterated saline and ²H single-pulse and ²H DQF-MT NMR spectra were measured, enabling the separation of the different water compartments, according to their quadrupolar splittings.

RESULTS

Rat sciatic and brachial nerves and porcine optic nerve immersed in deuterated saline yielded ²H DQF spectra composed of three pairs of quadrupolar-split signals assigned to the water in the collagenous compartments and the myelin bilayer and one narrow signal assigned to the axonal water. Stretching of the nerves, application of osmotic stress and incubation in collagenase did not affect the quadrupolar splitting of the myelin water. The signals of myelin and axonal water were shown to decay during Wallerian degeneration and to rise during maturation. The chemical exchange between the myelin and the intra-axonal water was measured for optic nerve during maturation. The quadrupolar splitting of the signal of myelin water was not sensitive to its orientation relative to the magnetic field. This resembles liquid crystalline behavior, but leaves its mechanism open for interpretation.

CONCLUSIONS

²H DQF-MT NMR characterizes the different components of nerves, the water exchange between them and their changes during processes such as nerve maturation and Wallerian degeneration.

Sodium in the dermis colocates to glycosaminoglycan scaffold, with diminishment in type 2 diabetes mellitus

BACKGROUND

Dietary sodium intake mismatches urinary sodium excretion over prolonged periods. Our aims were to localize and quantify electrostatically bound sodium within human skin using triple-quantum-filtered (TQF) protocols for MRI and magnetic resonance spectroscopy (MRS) and to explore dermal sodium in type 2 diabetes mellitus (T2D).

METHODS

We recruited adult participants with T2D (n = 9) and euglycemic participants with no history of diabetes mellitus (n = 8). All had undergone lower limb amputations or abdominal skin reduction surgery for clinical purposes. We used 20 μm in-plane resolution 1H MRI to visualize anatomical skin regions ex vivo from skin biopsies taken intraoperatively, 23Na TQF MRI/MRS to explore distribution and quantification of freely dissolved and bound sodium, and inductively coupled plasma mass spectrometry to quantify sodium in selected skin samples.

RESULTS

Human dermis has a preponderance (>90%) of bound sodium that colocalizes with the glycosaminoglycan (GAG) scaffold. Bound and free sodium have similar anatomical locations. T2D associates with a severely reduced dermal bound sodium capacity.

CONCLUSION

We provide the first evidence to our knowledge for high levels of bound sodium within human dermis, colocating to the GAG scaffold, consistent with a dermal "third space repository" for sodium. T2D associates with diminished dermal electrostatic binding capacity for sodium.

Identification of water compartments in spinal cords by 2 H double quantum filtered NMR

In ² H double quantum filtered (DQF) NMR, the various water compartments are characterized by their different residual quadrupolar interactions. The spectral separation between the different signals enables the measurement of the relaxation of each compartment and the magnetization transfer (MT) between them. In the current study, five water compartments were identified in the ² H DQF spectra of porcine spinal cord. The most prominent signal was the pair of satellites with a quadrupolar splitting of about 550 Hz. ² H DQF MRI optimized for the 550 Hz quadrupolar splitting indicated that this signal originated mainly from the white matter and it was assigned to the myelin water. This splitting does not change upon changing the orientation of the spinal cord relative to the magnetic field, indicating a liquid crystalline nature. Another site exhibiting splitting of about 1500 Hz was assigned to collagenous connective tissue. The narrow central peak was assigned to a combination of intra- and inter-axonal water. The assignment of the other two sites is not certain and requires further study. The rates of MT between the various sites were recorded.

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.

Quantitative 1H and 23Na muscle MRI in Facioscapulohumeral muscular dystrophy patients

Objective

Our aim was to assess the role of quantitative ¹H and ²³Na MRI methods in providing imaging biomarkers of disease activity and severity in patients with Facioscapulohumeral muscular dystrophy (FSHD).

Methods

We imaged the lower leg muscles of 19 FSHD patients and 12 controls with a multimodal MRI protocol to obtain STIR-T₂w images, fat fraction (FF), water T₂ (wT₂), water T₁ (wT₁), tissue sodium concentration (TSC), and intracellular-weighted sodium signal (inversion recovery (IR) and triple quantum filter (TQF) sequence). In addition, the FSHD patients underwent muscle strength testing.

Results

Imaging biomarkers related with water mobility (wT₁ and wT₂) and ion homeostasis (TSC, IR, TQF) were increased in muscles of FSHD patients. Muscle groups with FF > 10% had higher wT₂, wT₁, TSC, IR, and TQF values than muscles with FF < 10%. Muscles with FF < 10% resembled muscles of healthy controls for these MRI disease activity measures. However, wT₁ was increased in few muscles without fat replacement. Furthermore, few STIR-negative muscles (n = 11/76) exhibited increased wT₁, TSC, IR or TQF. Increased wT₁ as well as ²³Na signals were also present in muscles with normal wT₂. Muscle strength was related to the mean FF and all imaging biomarkers of tibialis anterior except wT₂ were correlated with dorsal flexion.

Conclusion

The newly evaluated imaging biomarkers related with water mobility (wT₁) and ion homeostasis (TSC, IR, TQF) showed different patterns compared to the established markers like FF in muscles of FSHD patients. These quantitative biomarkers could thus contain valuable complementary information for the early characterization of disease progression.

Electronic supplementary material

The online version of this article (10.1007/s00415-020-10254-2) contains supplementary material, which is available to authorized users.

NMR techniques in studying water in biotechnological systems

Different NMR methodologies have been considered in studying water as a part of the structure of heterogeneous biosystems. The current work mostly describes NMR techniques to investigate slow translational dynamics of molecules affecting anisotropic properties of polymers and biomaterials. With these approaches, information about organized structures and their stability could be obtained in conditions when external factors affect biomolecules. Such changes might include rearrangement of macromolecular conformations at fabrication of nano-scaffolds for tissue engineering applications. The changes in water-fiber interactions could be mirrored by the magnetic resonance methods in various relaxations, double-quantum filtered (DQF), 1D and 2D translational diffusion experiments. These findings effectively demonstrate the current state of NMR studies in applying these experiments to the various systems with the anisotropic properties. For fibrous materials, it is shown how NMR correlation experiments with two gradients (orthogonal or collinear) encode diffusion coefficients in anisotropic materials and how to estimate the permeability of cell walls. It is considered how the DQF NMR technique discovers anisotropic water in natural polymers with various cross-links. The findings clarify hydration sites, dynamic properties, and binding of macromolecules discovering the role of specific states in improving scaffold characteristics in tissue engineering processes. Showing the results in developing these NMR tools, this review focuses on the ways of extracting information about biophysical properties of biomaterials from the NMR data obtained.

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.

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.

Acute changes in extracellular volume fraction in skeletal muscle monitored by 23Na NMR spectroscopy

In this article, we induced acute changes in extracellular volume fraction in skeletal muscle tissue and compared the sensitivity of a standard ¹H T₂ imaging method with different ²³Na‐NMR spectroscopy parameters within acquisition times compatible with clinical investigations. First, we analyzed the effect of a short ischemia on the sodium distribution in the skeletal muscle. Then, the lower leg of 21 healthy volunteers was scanned under different vascular filling conditions (vascular draining, filling, and normal condition) expected to modify exclusively the extracellular volume. The first experiment showed no change in the total sodium content during a 15 min ischemia, but the intracellular weighted ²³Na signal slowly decreased. For the second part, significant variations of total sodium content, sodium distribution, and T₁ and T2∗ of ²³Na signal were observed between different vascular filling conditions. The measured sodium distribution correlates significantly with sodium T₁ and with the short and long T2∗ fractions. In contrast, significant changes in the proton T₂w signal were observed only in three muscles. Altogether, the mean T₂w signal intensity of all muscles as well as their mean T₂ did not vary significantly with the extracellular volume changes. In conclusion, at the expense of giving up spatial resolution, the proposed ²³Na spectroscopic method proved to be more sensitive than standard ¹H T₂ approach to monitor acute extracellular compartment changes within muscle tissue.

Orientation-dependent proton double-quantum NMR build-up function for soft materials with anisotropic mobility

In recent years, the analysis of proton double-quantum NMR build-up curves has become an important tool to quantify anisotropic mobility in different kinds of soft materials such as polymer networks or liquid crystals. In the former case, such data provides a measure of orientation-dependent residual (time-averaged) dipolar couplings arising from anisotropic segmental motions, informing about the length and the state of local stretching of the network chains. Previous studies of macroscopically ordered, i.e. stretched, networks were subject to the limitation that a detailed build-up curve analysis on the basis of a universal "Abragam-like" (A-l) build-up function valid for a proton multi-spin system was only possible for an isotropic orientation-averaged response. This situation is here remedied by introducing a generic orientation-dependent build-up function for an anisotropically mobile protonated molecular segment. We discuss an application to the modeling of data for a stretched network measured at different orientations with respect to the magnetic field, and present a validation by fitting data of different liquid-crystal molecules oriented in the magnetic field.

Quantitative sodium magnetic resonance imaging of cartilage, muscle, and tendon

Sodium magnetic resonance imaging (MRI), or imaging of the 23Na nucleus, has been under exploration for several decades, and holds promise for potentially revealing additional biochemical information about the health of tissues that cannot currently be obtained from conventional hydrogen (or proton) MRI. This additional information could serve as an important complement to conventional MRI for many applications. However, despite these exciting possibilities, sodium MRI is not yet used routinely in clinical practice, and will likely remain strictly in the domain of exploratory research for the coming decade. This paper begins with a technical overview of sodium MRI, including the nuclear magnetic resonance (NMR) signal characteristics of the sodium nucleus, the challenges associated with sodium MRI, and the specialized pulse sequences, hardware, and reconstruction techniques required. Various applications of sodium MRI for quantitative analysis of the musculoskeletal system are then reviewed, including the non-invasive assessment of cartilage degeneration in vivo, imaging of tendinopathy, applications in the assessment of various muscular pathologies, and assessment of muscle response to exercise.

White matter shifts in MRI: Rehabilitating the Lorentz sphere in magnetic resonance

A thorough exposition and analysis of the role of the Lorentz sphere in magnetic resonance is presented from the fundamental standpoint of macroscopic magnetostatics. The analysis will be useful to those interested in understanding susceptibility and chemical shift contributions to frequency shifts in magnetic resonance. Though the topic is mature, recent research on white matter shifts in the brain promotes the notion of replacing the Lorentz sphere with a generalized Lorentzian cylinder, and has put into question the long standing spherical approach when elongated structures are present. The cavity shape issue can be resolved by applying Helmholtz's theorem, which can be expressed in a differential and an integral formulation. The general validity of the Lorentz sphere for any situation is confirmed. Furthermore, a clear exposition of the "generalized approach" is offered, using the language of Lorentz's theory. With the rehabilitation of the Lorentz sphere settled, one must consider alternative contributions to white matter shifts and a likely candidate is the effect of molecular environment on chemical shifts.

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.

In vivo observation of quadrupolar splitting in (39)K magnetic resonance spectroscopy of human muscle tissue

The purpose of this work was to explore the origin of oscillations of the T(*)2 decay curve of (39)K observed in studies of (39)K magnetic resonance imaging of the human thigh. In addition to their magnetic dipole moment, spin-3/2 nuclei possess an electric quadrupole moment. Its interaction with non-vanishing electrical field gradients leads to oscillations in the free induction decay and to splitting of the resonance. All measurements were performed on a 7T whole-body MRI scanner (MAGNETOM 7T, Siemens AG, Erlangen, Germany) with customer-built coils. According to the theory of quadrupolar splitting, a model with three Lorentzian-shaped peaks is appropriate for (39)K NMR spectra of the thigh and calf. The frequency shifts of the satellites depend on the angle between the calf and the static magnetic field. When the leg is oriented parallel to the static magnetic field, the satellites are shifted by about 200 Hz. In the thigh, rank-2 double quantum coherences arising from anisotropic quadrupolar interaction are observed by double-quantum filtration with magic-angle excitation. In addition to the spectra, an image of the thigh with a nominal resolution of (16 × 16 × 32) mm(3) was acquired with this filtering technique in 1:17 h. From the line width of the resonances, (39)K transverse relaxation time constants T(*)2, fast  = (0.51 ± 0.01) ms and T(*)2, slow  = (6.21 ± 0.05) ms for the head were determined. In the thigh, the left and right satellite, both corresponding to the short component of the transverse relaxation time constant, take the following values: T(*)2, fast  = (1.56 ± 0.03) ms and T(*)2, fast  = (1.42 ± 0.03) ms. The centre line, which corresponds to the slow component, is T(*)2, slow  = (9.67 ± 0.04) ms. The acquisition time of the spectra was approximately 10 min. Our results agree well with a non-vanishing electrical field gradient interacting with (39)K nuclei in the intracellular space of muscle tissue.

Sodium NMR/MRI for anisotropic systems

Sodium ((23)Na) plays a central role in many physiological processes, and its high NMR sensitivity makes it an attractive nucleus for biomedical NMR and MRI research. Many biological tissues contain structures such as fibers and membranes that impose anisotropic translational and rotational motions on the sodium ions. Translational motion can be studied by diffusion measurements. Anisotropic rotational motion results in non-vanishing quadrupolar interaction that it is best studied by exploiting multiple quantum coherences for (23)Na NMR spectroscopy and MRI. The current review covers the application of the various NMR techniques to the study of (23)Na in anisotropic compartments in cartilage, tendon, intervertebral discs, red blood cells, nervous system and muscles.

Sodium inversion recovery MRI on the knee joint at 7 T with an optimal control pulse

In the field of sodium magnetic resonance imaging (MRI), inversion recovery (IR) is a convenient and popular method to select sodium in different environments. For the knee joint, IR has been used to suppress the signal from synovial fluids, which improves the correlation between the sodium signal and the concentration of glycosaminoglycans (GAGs) in cartilage tissues. For the better inversion of the magnetization vector under the spatial variations of the B0 and B1 fields, the IR sequence usually employ adiabatic pulses as the inversion pulse. On the other hand, it has been shown that RF shapes robust against the variations of the B0 and B1 fields can be generated by numerical optimization based on optimal control theory. In this work, we compare the performance of fluid-suppressed sodium MRI on the knee joint in vivo, between one implemented with an adiabatic pulse in the IR sequence and the other with the adiabatic pulse replaced by an optimal-control shaped pulse. While the optimal-control pulse reduces the RF power deposited to the body by 58%, the quality of fluid suppression and the signal level of sodium within cartilage are similar between two implementations.

Double and zero quantum filtered (2)H NMR analysis of D2O in intervertebral disc tissue

The analysis of double and zero quantum filtered (2)H NMR spectra obtained from D2O perfused in the nucleus pulposus of human intervertebral disc tissue samples is reported. Fitting the spectra with a three-site model allows for residual quadrupolar couplings and T2 relaxation times to be measured. The analysis reveals changes in both the couplings and relaxation times as the tissue begins to show signs of degradation. The full analysis demonstrates that information about tissue hydration, water collagen interactions, and sample heterogeneity can be obtained and used to better understand the biochemical differences between healthy and degraded tissue.

Effect of partial H2O-D2O replacement on the anisotropy of transverse proton spin relaxation in bovine articular cartilage

Anisotropy of transverse proton spin relaxation in collagen-rich tissues like cartilage and tendon is a well-known phenomenon that manifests itself as the "magic-angle" effect in magnetic resonance images of these tissues. It is usually attributed to the non-zero averaging of intra-molecular dipolar interactions in water molecules bound to oriented collagen fibers. One way to manipulate the contributions of these interactions to spin relaxation is by partially replacing the water in the cartilage sample with deuterium oxide. It is known that dipolar interactions in deuterated solutions are weaker, resulting in a decrease in proton relaxation rates. In this work, we investigate the effects of deuteration on the longitudinal and the isotropic and anisotropic contributions to transverse relaxation of water protons in bovine articular cartilage. We demonstrate that the anisotropy of transverse proton spin relaxation in articular cartilage is independent of the degree of deuteration, bringing into question some of the assumptions currently held over the origins of relaxation anisotropy in oriented tissues.

Spatial Mapping of Flow-Induced Molecular Alignment in a Noncrystalline Biopolymer Fluid Using Double Quantum Filtered (DQF) (23)Na MRI

Flow-induced molecular alignment was observed experimentally in a non-liquid-crystalline bioplymeric fluid during developed tubular flow. The fluid was comprised of rigid rods of the polysaccharide xanthan and exhibited shear-thinning behavior. Without a requirement for optical transparency or the need for an added tracer, (23)Na magic angle (MA) double quantum filtered (DQF) magnetic resonance imaging (MRI) enabled the mapping of the anisotropic molecular arrangement under flow conditions. A regional net molecular alignment was found in areas of high shear values in the vicinity of the tube wall. Furthermore, the xanthan molecules resumed random orientations after the cessation of flow. The observed flow-induced molecular alignment was correlated with the rheological properties of the fluid. The work demonstrates the ability of (23)Na MA DQF magnetic resonance to provide a valuable molecular-mechanical link.

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.

Monitoring cartilage tissue engineering using magnetic resonance spectroscopy, imaging, and elastography

A key technical challenge in cartilage tissue engineering is the development of a noninvasive method for monitoring the composition, structure, and function of the tissue at different growth stages. Due to its noninvasive, three-dimensional imaging capabilities and the breadth of available contrast mechanisms, magnetic resonance imaging (MRI) techniques can be expected to play a leading role in assessing engineered cartilage. In this review, we describe the new MR-based tools (spectroscopy, imaging, and elastography) that can provide quantitative biomarkers for cartilage tissue development both in vitro and in vivo. Magnetic resonance spectroscopy can identify the changing molecular structure and alternations in the conformation of major macromolecules (collagen and proteoglycans) using parameters such as chemical shift, relaxation rates, and magnetic spin couplings. MRI provides high-resolution images whose contrast reflects developing tissue microstructure and porosity through changes in local relaxation times and the apparent diffusion coefficient. Magnetic resonance elastography uses low-frequency mechanical vibrations in conjunction with MRI to measure soft tissue mechanical properties (shear modulus and viscosity). When combined, these three techniques provide a noninvasive, multiscale window for characterizing cartilage tissue growth at all stages of tissue development, from the initial cell seeding of scaffolds to the development of the extracellular matrix during construct incubation, and finally, to the postimplantation assessment of tissue integration in animals and patients.

Optic nerve: separating compartments based on 23Na TQF spectra and TQF-diffusion anisotropy

We present a triple quantum filtered (TQF) sodium spectroscopy study of an excised bovine optic nerve. By choosing proper experimental parameters, this technique allowed us to independently observe the satellite transitions originating from the various compartments in the tissue. TQF-based diffusion experiments provided further characterization of the compartments in terms of their geometry. As a result, the peak that exhibited the smallest residual quadrupolar splitting, and the largest diffusion anisotropy was assigned to axons. Two other pairs of satellite peaks were assigned to extra-cellular compartments on the basis of either the size of their quadrupolar splitting or the diffusion properties.

Application of sodium triple-quantum coherence NMR spectroscopy for the study of growth dynamics in cartilage tissue engineering

We studied the tissue growth dynamics of tissue-engineered cartilage at an early growth stage after cell seeding for four weeks using sodium triple-quantum coherence NMR spectroscopy. The following tissue-engineering constructs were studied: 1) bovine chondrocytes cultured in alginate beads; 2) bovine chondrocytes cultured as pellets (scaffold-free chondrocyte pellets); and 3) human marrow stromal cells (HMSCs) seeded in collagen/chitosan based biomimetic scaffolds. We found that the sodium triple-quantum coherence spectroscopy could differentiate between different tissue-engineered constructs and native tissues based on the fast and slow components of relaxation rate as well as on the average quadrupolar coupling. Both fast (Tf ) and slow (Ts ) relaxation times were found to be longer in chondrocyte pellets and biomimetic scaffolds compared to chondrocytes suspended in alginate beads and human articular cartilage tissues. In all cases, it was found that relaxation rates and motion of sodium ions measured from correlation times were dependent on the amount of macromolecules, high cell density and anisotropy of the cartilage tissue-engineered constructs. Average quadrupolar couplings were found to be lower in the engineered tissue compared to native tissue, presumably due to the lack of order in collagen accumulated in the engineered tissue. These results support the use of sodium triple-quantum coherence spectroscopy as a tool to investigate anisotropy and growth dynamics of cartilage tissue-engineered constructs in a simple and reliable way.

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.

Sodium imaging as a marker of tissue injury in patients with multiple sclerosis

Recent studies have suggested that intra-axonal sodium accumulation contribute to axonal degeneration in patients with MS. Advances in MRI hardware and software allow acquisition of brain sodium signal in vivo. This review begins with a summary of the experimental evidence for impairment of sodium homeostasis in MS. Then, MRI methods for sodium acquisition are reviewed and the application of the techniques in patients with MS is discussed. Sodium imaging and ultra-high field MRI have the potential to provide tissue-specific markers of neurodegeneration in MS.

B0 insensitive multiple-quantum resolved sodium imaging using a phase-rotation scheme

Triple-quantum filtering has been suggested as a mechanism to differentiate signals from different physiological compartments. However, the filtering method is sensitive to static field inhomogeneities because different coherence pathways may interfere destructively. Previously suggested methods employed additional phase-cycles to separately acquire pathways. Whilst this removes the signal dropouts, it reduces the signal-to-noise per unit time. In this work we suggest the use of a phase-rotation scheme to simultaneously acquire all coherence pathways and then separate them via Fourier transform. Hence the method yields single-, double- and triple-quantum filtered images. The phase-rotation requires a minimum of 36 instead of six cycling steps. However, destructive interference is circumvented whilst maintaining full signal-to-noise efficiency for all coherences.

Molecular dynamics parameter maps by 1H Hahn echo and mixed-echo phase-encoding MRI

Residual dipolar couplings and averaged correlation time maps in soft matter were obtained by mixed echo phase-encoding solid imaging (MIPSI). Use of the mixed echo in soft matter NMR imaging experiments has two crucial advantages: the signal intensity is recovered with a weak incoherence losses, and second, the intervals during which the phase-encoding evolution due to the magnetic field gradients takes place can be chosen to be much larger than with all other spin echo experiments and hence, a higher special resolution can be achieved. The parameter maps are compared to those obtained by the Hahn-echo phase-frequency encoding method. For both MRI methods the density operator formalism is applied in the average Hamiltonian approximation to describe the encoding of the spin echoes by the molecular motions. The results of preliminary experiments are presented.

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.

Magnetic alignment and quadrupolar/paramagnetic cross-correlation in complexes of Na with LnDOTP5-

The observation of a double-quantum filtered signal of quadrupolar nuclei (e.g. (23)Na) in solution has been traditionally interpreted as a sign for anisotropic reorientational motion. Ling and Jerschow (2007) have found that a (23)Na double-quantum signal is observed also in solutions of TmDOTPNa(5). Interference effects between the quadrupolar and the paramagnetic interactions have been reported to lead to the appearance of double-quantum coherences even in the absence of a residual quadrupolar interaction. In addition, such processes lead to differential linebroadening effects between the satellite transitions, akin to effects that are well known for dipolar-CSA cross-correlation. Here, we report experiments on sodium in the presence of LnDOTP compounds, where it is shown that these cross-correlation effects correlate well with the pseudo-contact shift. In addition, anisotropic g-values of the lanthanide compounds in question, can also lead to alignment within the magnetic field, and consequently to the appearance of line splitting and double-quantum coherences. The two competing effects are demonstrated and it is concluded that both cross-correlated relaxation and alignment in the magnetic field must be at work in the systems described here.

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.

2H double- and zero-quantum filtered NMR spectroscopy for probing the environments of water in Nafion

Multiple quantum 2H NMR spectroscopy is used to study the structure and dynamics of D2O in Nafion membranes as a function of membrane hydration. By employing both double- and zero-quantum filtered experiments, residual quadrupolar coupling constants and T2 relaxation values are obtained. The residual couplings vary from 240 to 20 Hz and the T2 values range from 20 to 180 ms, with the high hydration values having smaller couplings and longer T2 values. Analysis of the data using a water-exchange model suggests that the changes in parameters arise from a change in the fraction of time water spends in the anisotropic environments and not from changes in the order parameters that characterize the anisotropic sites. It has been found that a two-site model is needed to accurately fit the spectra above a hydration level of 10 D2O per sulfonate, with the second site having a negligible residual quadrupolar coupling. The data supports a model with two different hydration layers at high hydration and can be understood in terms of the recently proposed parallel-channel model for Nafion hydration.

23Na and 2H magnetic resonance studies of osteoarthritic and osteoporotic articular cartilage

In this study, the short component of the (23)Na T(2) (T(2f)) and the (23)Na and (2)H quadrupolar interactions (nu(Q)) were measured in bone-cartilage samples of osteoarthritic (OA) and osteoporotic (OP) patients. (23)Na nu(Q) was found to increase in osteoarthritic articular cartilage relative to controls. Similar results were found in bovine cartilage following proteoglycan (PG) depletion, a condition that prevails in osteoarthritis. (23)Na nu(Q) and 1/T(2f) for articular cartilage obtained from osteoporotic patients were significantly larger than for control and osteoarthritic cartilage. Decalcification of both human and bovine articular cartilage resulted in an increase of (23)Na nu(Q) and 1/T(2f), showing the same trend as the osteoporotic samples. Differences in the ratio of the intensity of the large (2)H splitting to that of the small one in the calcified zone were also observed. In osteoporosis, this ratio was twice as large as that obtained for both control and osteoarthritic samples. The (2)H and (23)Na results can be interpreted as due to sodium ions and water molecules filling the void created by the calcium depletion and to calcium ions being located in close association with the collagen fibers. To the best of our knowledge, this is the first study reporting differences of NMR parameters in cartilage of osteoporotic patients.