Sodium relaxometry using 23 Na MR fingerprinting: A proof of concept

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.

Accelerated multiple-quantum-filtered sodium magnetic resonance imaging using compressed sensing at 7 T

PURPOSE

Multiple-quantum-filtered (MQF) sodium magnetic resonance imaging (MRI), such as enhanced single-quantum and triple-quantum-filtered imaging of 23Na (eSISTINA), enables images to be weighted towards restricted sodium, a promising biomarker in clinical practice, but often suffers from clinically infeasible acquisition times and low image quality. This study aims to mitigate the above limitation by implementing a novel eSISTINA sequence at 7 T with the application of compressed sensing (CS) to accelerate eSISTINA acquisitions without a noticeable loss of information.

METHODS

A novel eSISTINA sequence with a 3D spiral-based sampling scheme was implemented at 7 T for the application of CS. Fully sampled datasets were obtained from one phantom and ten healthy subjects, and were then retrospectively undersampled by various undersampling factors. CS undersampled reconstructions were compared to fully sampled and undersampled nonuniform fast Fourier transform (NUFFT) reconstructions. Reconstruction performance was evaluated based on structural similarity (SSIM), signal-to-noise ratio (SNR), weightings towards total and compartmental sodium, and in vivo quantitative estimates.

RESULTS

CS-based phantom and in vivo images have less noise and better structural delineation while maintaining the weightings towards total, non-restricted (predominantly extracellular), and restricted (primarily intracellular) sodium. CS generally outperforms NUFFT with a higher SNR and a better SSIM, except for the SSIM in TQ brain images, which is likely due to substantial noise contamination. CS enables in vivo quantitative estimates with <15% errors at an undersampling factor of up to two.

CONCLUSIONS

Successful implementation of an eSISTINA sequence with an incoherent sampling scheme at 7 T was demonstrated. CS can accelerate eSISTINA by up to twofold at 7 T with reduced noise levels compared to NUFFT, while maintaining major structural information, reasonable weightings towards total and compartmental sodium, and relatively reliable in vivo quantification. The associated reduction in acquisition time has the potential to facilitate the clinical applicability of MQF sodium 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).

MR-Nucleomics: The study of pathological cellular processes with multinuclear magnetic resonance spectroscopy and imaging in vivo

Clinical medicine has experienced a rapid development in recent decades, during which therapies targeting specific cellular signaling pathways, or specific cell surface receptors, have been increasingly adopted. While these developments in clinical medicine call for improved precision in diagnosis and treatment monitoring, modern medical imaging methods are restricted mainly to anatomical imaging, lagging behind the requirements of precision medicine. Although positron emission tomography and single photon emission computed tomography have been used clinically for studies of metabolism, their applications have been limited by the exposure risk to ionizing radiation, the subsequent limitation in repeated and longitudinal studies, and the incapability in assessing downstream metabolism. Magnetic resonance spectroscopy (MRS) or spectroscopic imaging (MRSI) are, in theory, capable of assessing molecular activities in vivo, although they are often limited by sensitivity. Here, we review some recent developments in MRS and MRSI of multiple nuclei that have potential as molecular imaging tools in the clinic.

Repeatability assessment of sodium (23Na) MRI at 7.0 T in healthy human calf muscle and preliminary results on tissue sodium concentrations in subjects with Addison's disease

OBJECTIVES

To determine the relaxation times of the sodium nucleus, and to investigate the repeatability of quantitative, in vivo TSC measurements using sodium magnetic resonance imaging (23Na-MRI) in human skeletal muscle and explore the discriminatory value of the method by comparing TSCs between healthy subjects and patients with Addison's disease.

MATERIALS AND METHODS

In this prospective study, ten healthy subjects and five patients with Addison's disease were involved. 23Na-MRI data sets were acquired using a density-adapted, three-dimensional radial projection reconstruction pulse sequence (DA-3DPR) with a modification for the relaxation times measurements. Differences in TSC between muscle groups and between healthy participants were analysed using a nonparametric Friedman ANOVA test. An interclass correlation coefficient (ICC) was used as the repeatability index. Wilcoxon rank sum test was used for evaluation of differences in TSC between study participants.

RESULTS

The mean T1 in the gastrocnemius medialis (GM), the tibialis anterior (TA), and the soleus (S) was 25.9 ± 2.0 ms, 27.6 ± 2.0 ms, and 28.2 ± 2.0 ms, respectively. The mean short component of T2*, T2*short were GM: 3.6 ± 2.0 ms; TA: 3.2 ± 0.5 ms; and S: 3.0 ± 1.0 ms, and the mean long component of T2*, T2*long, were GM: 12.9 ± 0.9 ms; TA: 12.8 ± 0.7 ms; and S: 12.9 ± 2.0 ms, respectively. In healthy volunteers, TSC values in the GM were 19.9 ±0.1  mmol/L, 13.8 ±0.2 mmol/L in TA, and 12.6 ± 0.2 mmol/L in S, and were significantly different (p = 0.0005). The ICCs for GM, TA and S were 0.784, 0.818, 0.807, respectively. In patients with Addison's disease, TSC in GC, TA, and S were 10.2 ± 1.0 mmol/L, 8.4 ± 0.6 mmol/L, and 7.2 ± 0.1 mmol/L, respectively.

CONCLUSIONS

TSC quantification in a healthy subject's calf at 7.0 T is reliable; the technique is able to distinguish sodium level differences between muscles and between healthy subjects and Addison's disease patients.

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.

Compressed Sensing in Sodium Magnetic Resonance Imaging: Techniques, Applications, and Future Prospects

Sodium (²³ Na) yields the second strongest nuclear magnetic resonance (NMR) signal in biological tissues and plays a vital role in cell physiology. Sodium magnetic resonance imaging (MRI) can provide insights into cell integrity and tissue viability relative to pathologies without significant anatomical alternations, and thus it is considered to be a potential surrogate biomarker that provides complementary information for standard hydrogen (¹ H) MRI in a noninvasive and quantitative manner. However, sodium MRI suffers from a relatively low signal-to-noise ratio and long acquisition times due to its relatively low NMR sensitivity. Compressed sensing-based (CS-based) methods have been shown to accelerate sodium imaging and/or improve sodium image quality significantly. In this manuscript, the basic concepts of CS and how CS might be applied to improve sodium MRI are described, and the historical milestones of CS-based sodium MRI are briefly presented. Representative advanced techniques and evaluation methods are discussed in detail, followed by an expose of clinical applications in multiple anatomical regions and diseases as well as thoughts and suggestions on potential future research prospects of CS in sodium MRI. EVIDENCE LEVEL: 5 TECHNICAL EFFICACY: Stage 1.

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.

Fast in vivo 23 Na imaging and T 2 ∗ mapping using accelerated 2D-FID UTE magnetic resonance spectroscopic imaging at 3 T: Proof of concept and reliability study

PURPOSE

To implement an accelerated MR-acquisition method allowing to map T 2 ∗ relaxation and absolute concentration of sodium within skeletal muscles at 3T.

METHODS

A fast-UTE-2D density-weighted concentric-ring-trajectory ²³ Na-MRSI technique was used to acquire 64 time points of FID with a spectral bandwidth of 312.5 Hz with an in-plane resolution of 2.5 × 2.5 mm² in ~15 min. The fast-relaxing ²³ Na signal was localized with a single-shot, inversion-recovery-based, non-echo (SIRENE) outer volume suppression (OVS) method. The sequence was verified using simulation and phantom studies before implementing it in human calf muscles. To evaluate the 2D-SIRENE-MRSI (UTE = 0.55 ms) imaging performance, it was compared to a 3D-MRI (UTE = 0.3 ms) sequence. Both data sets were acquired within 2 same-day sessions to assess repeatability. The T 2 ∗ values were fitted voxel-by-voxel using a biexponential model for the 2D-MRSI data. Finally, intra-subject coefficients of variation (CV) were estimated.

RESULTS

The MRSI-FID data allowed us to map the fast and slow components of T 2 ∗ in the calf muscles. The spatial distributions of ²³ Na concentration for both MRSI and 3D-MRI acquisitions were significantly correlated (P < .001). The test-retest analysis rendered high repeatability for MRSI with a CV of 5%. The mean T 2 Fast ∗ in muscles was 0.7 ± 0.1 ms (contribution fraction = 37%), whereas T 2 Slow ∗ was 13.2 ± 0.2 ms (63%). The mean absolute muscle ²³ Na concentration calculated from the T 2 ∗ -corrected data was 28.6 ± 3.3 mM.

CONCLUSION

The proposed MRSI technique is a reliable technique to map sodium's absolute concentration and T 2 ∗ within a clinically acceptable scan time at 3T.