Radiofrequency Pulse Sequences Research Articles

Linear Bloch-Siegert phase-encoded low-field MRI: RF coils, pulse sequence, and image reconstruction.

Conventional gradient systems have several weaknesses including high cost and bulk. As a step towards addressing these while providing new degrees of freedom for spatial encoding and system design in Magnetic Resonance Imaging (MRI), a radio frequency (RF) gradient encoding system and pulse sequence for phase encoding using the Bloch-Siegert (BS) shift were developed. Optimized BS spatial encoding coils with bucking windings (counter-wound loops) were designed and constructed, along with compatible homogeneous imaging coils for excitation and signal reception. Two coil systems were developed: one for phantom imaging and a second for human wrist imaging. BS phase-encoded imaging and BS RF pulse simulations were performed. Pulse sequences were designed for linear stepping in k-space and implemented on a 47.5-mT scanner to image resolution phantoms in both coil setups. Reconstructions were performed using both the full -based encoding fields for each BS pulse amplitude and using inverse discrete Fourier transforms. A gradient was used for frequency encoding during signal readout, and the third axis was projected. Specific absorption ratio (SAR) calculations were performed for the wrist coil to determine the safety of BS-based RF encoding for fields in the low field MRI regime. The optimized RF spatial encoding coils resulted in higher linearity ( and 0.9921 in the phantom and wrist coils, respectively) than coils used in previous work. The phantom and wrist imaging coils were validated in simulations and experimentally to produce a peak G and 0.8 G with 12-W input power, respectively, in the field-of-view (length = 11 cm) used for imaging. Nominal imaging resolutions of 5.22 and 7.21 mm were, respectively, achieved by the two-coil systems in the RF phase-encoded dimension. Coil systems, pulse sequences, and image reconstructions were developed for linear RF phase encoding using the BS shift and validated using a 47.5-mT open low field scanner, establishing a key component required for gradient-free imaging at low field strengths.

Parahydrogen‐Induced Polarization of 14N Nuclei

AbstractHyperpolarization techniques provide a dramatic increase in sensitivity of nuclear magnetic resonance spectroscopy and imaging. In spite of the outstanding progress in solution‐state hyperpolarization of spin‐1/2 nuclei, hyperpolarization of quadrupolar nuclei remains challenging. Here, hyperpolarization of quadrupolar 14N nuclei with natural isotopic abundance of >99 % is demonstrated. This is achieved via pairwise addition of parahydrogen to tetraalkylammonium salts with vinyl or allyl unsaturated moieties followed by a subsequent polarization transfer from 1H to 14N nuclei at high magnetic field using PH‐INEPT or PH‐INEPT+ radiofrequency pulse sequence. Catalyst screening identified water‐soluble rhodium complex [Rh(P(m‐C6H4SO3Na)3)3Cl] as the most efficient catalyst for hyperpolarization of the substrates under study, providing up to 1.3 % and up to 6.6 % 1H polarization in the cases of vinyl and allyl precursors, respectively. The performance of PH‐INEPT and PH‐INEPT+ pulse sequences was optimized with respect to interpulse delays, and the resultant experimental dependences were in good agreement with simulations. As a result, 14N NMR signal enhancement of up to 760‐fold at 7.05 T (corresponding to 0.15 % 14N polarization) was obtained.

Parahydrogen-Induced Polarization of 14N Nuclei.

Hyperpolarization techniques provide a dramatic increase in sensitivity of nuclear magnetic resonance spectroscopy and imaging. In spite of the outstanding progress in solution-state hyperpolarization of spin-1/2 nuclei, hyperpolarization of quadrupolar nuclei remains challenging. Here, hyperpolarization of quadrupolar 14N nuclei with natural isotopic abundance of >99 % is demonstrated. This is achieved via pairwise addition of parahydrogen to tetraalkylammonium salts with vinyl or allyl unsaturated moieties followed by a subsequent polarization transfer from 1H to 14N nuclei at high magnetic field using PH-INEPT or PH-INEPT+ radiofrequency pulse sequence. Catalyst screening identified water-soluble rhodium complex [Rh(P(m-C6H4SO3Na)3)3Cl] as the most efficient catalyst for hyperpolarization of the substrates under study, providing up to 1.3 % and up to 6.6 % 1H polarization in the cases of vinyl and allyl precursors, respectively. The performance of PH-INEPT and PH-INEPT+ pulse sequences was optimized with respect to interpulse delays, and the resultant experimental dependences were in good agreement with simulations. As a result, 14N NMR signal enhancement of up to 760-fold at 7.05 T (corresponding to 0.15 % 14N polarization) was obtained.

Artificial Intelligence-Powered Pulse Sequences in Nuclear Magnetic Resonance and Magnetic Resonance Imaging: Historical Trends, Current Innovations and Perspectives

This review article explores the historical background and recent advances in the application of artificial intelligence (AI) in the development of radiofrequency pulses and pulse sequences in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI). The introduction of AI into this field, which traces back to the late 1970s, has recently witnessed remarkable progress, leading to the design of specialized frameworks and software solutions such as DeepRF, MRzero, and GENETICS-AI. Through an analysis of literature and case studies, this review tracks the transformation of AI-driven pulse design from initial proof-of-concept studies to comprehensive scientific programs, shedding light on the potential implications for the broader NMR and MRI communities. The fusion of artificial intelligence and magnetic resonance pulse design stands as a promising frontier in spectroscopy and imaging, offering innovative enhancements in data acquisition, analysis, and interpretation across diverse scientific domains.

From strength to precision: A systematic review exploring the clinical utility of 7-Tesla magnetic resonance imaging in abdominal imaging.

After approval for clinical use in 2017 early investigations of ultra-high-field abdominal magnetic resonance imaging (MRI) have demonstrated the feasibility as well as diagnostic capabilities of liver, kidney, and prostate MRI at 7-Tesla. However, the elevation of the field strength to 7-Tesla not only brought advantages to abdominal MRI but also presented considerable challenges and drawbacks, primarily stemming from heightened artifacts and limitations in Specific Absorption Rate, etc. Furthermore, evidence in the literature is relatively scarce concerning human studies in comparison to phantom/animal studies which necessitates an investigation into the evidence so far in humans and summarizing all relevant evidence. To offer a comprehensive overview of current literature on clinical abdominal 7T MRI that emphasizes current trends, details relevant challenges, and provides a concise set of potential solutions. This systematic review adheres to Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. A PubMed search, utilizing Medical Subject Headings terms such as "7-Tesla" and organ-specific terms, was conducted for articles published between January 1, 1985, and July 25, 2023. Eligibility criteria included studies exploring 7T MRI for imaging human abdominal organs, encompassing various study types (in-vivo/ex-vivo, method development, reviews/meta-analyses). Exclusion criteria involved animal studies and those lacking extractable data. Study selection involved initial identification via title/abstract, followed by a full-text review by two researchers, with discrepancies resolved through discussion. Data extraction covered publication details, study design, population, sample size, 7T MRI protocol, image characteristics, endpoints, and conclusions. The systematic review included a total of 21 studies. The distribution of clinical 7T abdominal imaging studies revealed a predominant focus on the prostate (n = 8), followed by the kidney (n = 6) and the hepatobiliary system (n = 5). Studies on these organs, and in the pancreas, demonstrated clear advantages at 7T. However, small bowel studies showed no significant improvements compared to traditional MRI at 1.5T. The majority of studies evaluated originated from Germany (n = 10), followed by the Netherlands (n = 5), the United States (n = 5), Austria (n = 2), the United Kingdom (n = 1), and Italy (n = 1). Further increase of abdominal clinical MRI field strength to 7T demonstrated high imaging potential, yet also limitations mainly due to the inhomogeneous radiofrequency (RF) excitation field relative to lower field strengths. Hence, further optimization of dedicated RF coil elements and pulse sequences are expected to better optimize clinical imaging at high magnetic field strength.

Clinically Translatable Hyperpolarized 13C Bicarbonate pH Imaging Method for Use in Prostate Cancer.

Solid tumors such as prostate cancer (PCa) commonly develop an acidic microenvironment with pH 6.5-7.2, owing to heterogeneous perfusion, high metabolic activity, and rapid cell proliferation. In preclinical prostate cancer models, disease progression is associated with a decrease in tumor extracellular pH, suggesting that pH imaging may reflect an imaging biomarker to detect aggressive and high-risk disease. Therefore, we developed a hyperpolarized carbon-13 MRI method to image the tumor extracellular pH (pHe) and prepared it for clinical translation for detection and risk stratification of PCa. This method relies on the rapid breakdown of hyperpolarized (HP) 1,2-glycerol carbonate (carbonyl-13C) via base-catalyzed hydrolysis to produce HP 13CO32-, which is neutralized and converted to HP H13CO3-. After injection, HP H13CO3- equilibrates with HP 13CO2 in vivo and enables the imaging of pHe. Using insights gleaned from mechanistic studies performed in the hyperpolarized state, we solved issues of polarization loss during preparation in a clinical polarizer system. We successfully customized a reaction apparatus suitable for clinical application, developed clinical standard operating procedures, and validated the radiofrequency pulse sequence and imaging data acquisition with a wide range of animal models. The results demonstrated that we can routinely produce a highly polarized and safe HP H13CO3- contrast agent suitable for human injection. Preclinical imaging studies validated the reliability and accuracy of measuring acidification in healthy kidney and prostate tumor tissue. These methods were used to support an Investigational New Drug application to the U.S. Food and Drug Administration. This methodology is now ready to be implemented in human trials, with the ultimate goal of improving the management of PCa.

Compact multi-channel radio frequency pulse-sequence generator with fast-switching capability for cold-atom interferometers.

Cold-atom interferometers have matured into a powerful tool for fundamental physics research, and they are currently moving from realizations in the laboratory to applications in the field. A radio frequency (RF) generator is an indispensable component of these devices for controlling lasers and manipulating atoms. In this work, we developed a compact RF generator for fast switching and sweeping the frequencies and amplitudes of atomic-interference pulse sequences. In this generator, multi-channel RF signals are generated using a field-programmable gate array (FPGA) to control eight direct digital synthesizers (DDSs). We further propose and demonstrate a method for pre-loading the parameters of all the RF pulse sequences to the DDS registers before their execution, which eliminates the need for data transfer between the FPGA and DDSs to change RF signals. This sharply decreases the frequency-switching time when the pulse sequences are running. Performance characterization showed that the generated RF signals achieve a 100ns frequency-switching time and a 40 dB harmonic-rejection ratio. The generated RF pulse sequences were applied to a cold-atom-interferometer gyroscope, and the contrast of atomic interference fringes was found to reach 38%. This compact multi-channel generator with fast frequency/amplitude switching and/or sweeping capability will be beneficial for applications in field-portable atom interferometers.

Updates on Compositional MRI Mapping of the Cartilage: Emerging Techniques and Applications.

Osteoarthritis (OA) is a widely occurring degenerative joint disease that is severely debilitating and causes significant socioeconomic burdens to society. Magnetic resonance imaging (MRI) is the preferred imaging modality for the morphological evaluation of cartilage due to its excellent soft tissue contrast and high spatial resolution. However, its utilization typically involves subjective qualitative assessment of cartilage. Compositional MRI, which refers to the quantitative characterization of cartilage using a variety of MRI methods, can provide important information regarding underlying compositional and ultrastructural changes that occur during early OA. Cartilage compositional MRI could serve as early imaging biomarkers for the objective evaluation of cartilage and help drive diagnostics, disease characterization, and response to novel therapies. This review will summarize current and ongoing state-of-the-art cartilage compositional MRI techniques and highlight emerging methods for cartilage compositional MRI including MR fingerprinting, compressed sensing, multiexponential relaxometry, improved and robust radio-frequency pulse sequences, and deep learning-based acquisition, reconstruction, and segmentation. The review will also briefly discuss the current challenges and future directions for adopting these emerging cartilage compositional MRI techniques for use in clinical practice and translational OA research studies. EVIDENCE LEVEL: 2 TECHNICAL EFFICACY: Stage 2.

Better neural images by combining ultrahigh field strength MRI with innovative MRI sequences

Better MRI scanning technologies and protocols can provide insights into neurological disorders. In this review, we describe the basic concepts of MRI and, in the process, we convey to the reader the relevance of MRI as a high-resolution imaging modality of tissue structure and metabolism. We outline the main parameters for improving MRI resolution and sensitivity for the ultimate goal of optimizing the diagnosis of neurological diseases. A key to obtaining high-resolution images by MRI is the strength of the magnet’s external field strength (Bo). The higher the field strength, the better the signal-to-noise (SNR) of acquired signals. Hence, this results in improved sensitivity and resolution of the reconstructed images. This article recapitulates the advancement of MRI technology towards Ultra-High-Field Strength (UHF) apparatus and the consequent benefits in SNR. Other keys towards improving MRI images include deftly modifying the parameters of longitudinal magnetization relaxation time (T1), transverse magnetization relaxation time (T2), repetition times between radiofrequency (RF) pulses (TR), and the time of reading post-pulse (TE). Such parameters can be controlled through acquisition software associated with the MRI machines. The review profiles the cumulative efforts by researchers to complement UHF-MRI hardware with innovative RF pulse sequences protocols such as Diffusion Weighted Imaging (DWI), Pulse Gradient Spin Echo (PGSE), Oscillating Gradient Spin Echo (OGSE), Blood Oxygen Level Dependent (BOLD)-MRI and Arterial Spin Label (ASL)-MRI. Collectively, these advances in both MRI hardware and software have pushed the field to attain a mesoscopic level of resolution. Further enhancements in analyzing MRI images through Artificial Intelligence (AI) algorithms may advance resolutions beyond the mesoscopic stage and perhaps even toward the microscopic resolution of living tissue.

Antibiotic depot system with radiofrequency controlled drug release

Drug depot systems have traditionally relied on the spontaneous dissolution and diffusion of drugs or prodrugs from a reservoir with constant exposure to the surrounding physiological fluids. While this is appropriate for clinical scenarios that require constant plasma concentration of the drug over time, there are also situations where multiple bursts of the drug at well-defined time intervals are preferred. This work presents a drug depot system that enables repeated on-demand release of antibiotics in precise doses, controlled by an external radiofrequency magnetic field. The remotely controlled depot system consists of composite microcapsules with a core-shell structure. The core contains micronized drug particles embedded in a low-melting hydrophobic matrix. The shell is formed by a hydrogel with immobilised magnetic nanoparticles that facilitate local heat dissipation after exposure to a radiofrequency magnetic field. When the melting point of the core material is locally exceeded, the embedded drug particles are mobilised and their surface is exposed to the external aqueous phase. It is shown that drug release can be controlled in an on/off manner by a chosen sequence and duration of radiofrequency pulses. The capacity of the depot system is shown to be significantly higher than that of purely diffusion-controlled systems containing a pre-dissolved drug. The functionality of the depot system is demonstrated in vitro for the specific case of norfloxacin acting on E. coli.

Optimization of a quantum control sequence for initializing a nitrogen-vacancy spin register

Implementation of many quantum information protocols requires an efficient initialization of the quantum register. In the present paper, we optimize a population trapping protocol for initializing a hybrid spin register associated with a single nitrogen-vacancy (NV) center in diamond. We initialize the quantum register by polarizing the electronic and nuclear spins of the NV with a sequence of microwave, radio-frequency, and optical pulses. We use a rate equation model to explain the distribution of population under the effect of the optical pulses. The model is compared to the experimental data obtained by performing partial quantum state tomography. To further increase the spin polarization, we propose a recursive protocol with optimized optical pulses. We also discuss the role of the relative values of the nuclear- and electronic-spin pumping rate in achieving the maximum degree of spin polarization.

Direct Production of a Hyperpolarized Metabolite on a Microfluidic Chip.

Microfluidic systems hold great potential for the study of live microscopic cultures of cells, tissue samples, and small organisms. Integration of hyperpolarization would enable quantitative studies of metabolism in such volume limited systems by high-resolution NMR spectroscopy. We demonstrate, for the first time, the integrated generation and detection of a hyperpolarized metabolite on a microfluidic chip. The metabolite [1-13C]fumarate is produced in a nuclear hyperpolarized form by (i) introducing para-enriched hydrogen into the solution by diffusion through a polymer membrane, (ii) reaction with a substrate in the presence of a ruthenium-based catalyst, and (iii) conversion of the singlet-polarized reaction product into a magnetized form by the application of a radiofrequency pulse sequence, all on the same microfluidic chip. The microfluidic device delivers a continuous flow of hyperpolarized material at the 2.5 μL/min scale, with a polarization level of 4%. We demonstrate two methods for mitigating singlet–triplet mixing effects which otherwise reduce the achieved polarization level.

Simple and cost-effective cross-polarization experiments under dissolution-dynamic nuclear polarization conditions with a 3D-printed 1H-13C background-free radiofrequency coil

The low sensitivity of conventional nuclear magnetic resonance experiments can be overcome, in suitable cases, by employing hyperpolarization methodologies. One such technique, dissolution-dynamic nuclear polarization, provides a robust means of strongly polarizing a variety of small molecules. A drawback of the dissolution-dynamic nuclear polarization approach, the excessively long polarization timescales for insensitive nuclei, has been circumvented by using cross-polarization radiofrequency pulse sequences, which in general yield quick and substantial 13C polarizations. However, the capacity to effectively perform efficient cross-polarization experiments under dissolution-dynamic nuclear polarization conditions remains challenging, and polarization quantification can be plagued by additional complications including spurious background signals from the probe. Here we propose a background-free1H-13C radiofrequency coil specifically designed for use in cross-polarization experiments on samples of up to 500 μL in volume at liquid helium temperatures. We additionally introduce simple guidelines for the optimization and implementation of cross-polarization radiofrequency pulse sequences. Experimental demonstrations of 13C polarizations reaching ∼60% are presented for the case of [1-13C]sodium acetate.

Frozen water NMR lineshape analysis enables absolute polarization quantification.

Typical magnetic resonance experiments are routinely limited by weak signal responses. In some cases, the low intrinsic sensitivity can be alleviated by the implementation of hyperpolarization technologies. Dissolution-dynamic nuclear polarization offers a means of hyperpolarizing small molecules. Hyperpolarized water is employed in several dynamic nuclear polarization studies, and hence accurate and rapid quantification of the 1H polarization level is of utmost importance. The solid-state nuclear magnetic resonance spectrum of water acquired under dissolution-dynamic nuclear polarization conditions has revealed lineshapes which become asymmetric at high levels of 1H polarization, which is an interesting fundamental problem in itself, but also complicates data interpretation and can prevent correct estimations of polarization levels achieved. In previous studies, attempts to simulate the 1H spectral lineshape of water as a function of the 1H polarization led to significant disagreement with the experimental results. Here we propose and demonstrate that such simulations, and therefore polarization quantification, can be implemented accurately, in particular by taking into account the detector dead time during 1H signal acquisition that can lead to severe spectral distortions. Based on these findings, we employed an echo-based radiofrequency pulse sequence to achieve distortion-free 1H spectra of hyperpolarized water, and adequate simulations of these echo-based spectra were implemented to extract the absolute 1H polarization level from the hyperpolarized water signal only, thus alleviating the need for lengthy and insensitive measurements of thermal equilibrium signals.

Ultrahigh field brain magnetic resonance imaging using semiadiabatic radiofrequency pulses.

Great attention is being paid to solving, or mitigating, the technical problems associated with MRI at ultrahigh field strengths of 7 T and higher. This paper explores the use of the semiadiabatic spin-echo (SA-SE) pulse sequence, which uses semiadiabatic radiofrequency (RF) pulses to remove and/or mitigate the effects of the nonuniform B1 excitation field and B0 inhomogeneity associated with the electromagnetic properties of the human brain. A semiadiabatic RF pulse version of the recently published serial transmit excitation pulse (STEP) RF pulse sequence is also presented that now incorporates semiadiabatic pulses, henceforth is called SA-STEP. As demonstrated by computer simulation, and confirmed using head imaging, both techniques can produce multislice SE MR imaging at 7 T. These new methods use relatively low RF power and achieve good coverage of the human brain in a single scan.

Boosting dissolution-dynamic nuclear polarization by multiple-step dipolar order mediated 1H→13C cross-polarization

Dissolution-dynamic nuclear polarization can be boosted by employing multiple-contact cross-polarization techniques to transfer polarization from 1H to 13C spins. The method is efficient and significantly reduces polarization build-up times, however, it involves high-power radiofrequency pulses in a superfluid helium environment which limit its implementation and applicability and prevent a significant scaling-up of the sample size. We propose to overcome this limitation by a stepwise transfer of polarization using a low-energy and low-peak power radiofrequency pulse sequence where the 1H→13C polarization transfer is mediated by a dipolar spin order reservoir. An experimental demonstration is presented for [1-13C]sodium acetate. A solid-state 13C polarization of ∼43.5% was achieved using this method with a build-up time constant of ∼5.1 minutes, leading to a ∼27.5% 13C polarization in the liquid-state after sample dissolution. The low-power multiple-step polarization transfer efficiency achieved with respect to the most advanced and highest-power multiple-contact cross-polarization approach was found to be ∼0.69.

Solid-state NMR spectroscopy.

Solid-state nuclear magnetic resonance (NMR) spectroscopy is an atomic-level method used to determine the chemical structure, three-dimensional structure, and dynamics of solids and semi-solids. This Primer summarizes the basic principles of NMR as applied to the wide range of solid systems. The fundamental nuclear spin interactions and the effects of magnetic fields and radiofrequency pulses on nuclear spins are the same as in liquid-state NMR. However, because of the anisotropy of the interactions in the solid state, the majority of high-resolution solid-state NMR spectra is measured under magic-angle spinning (MAS), which has profound effects on the types of radiofrequency pulse sequences required to extract structural and dynamical information. We describe the most common MAS NMR experiments and data analysis approaches for investigating biological macromolecules, organic materials, and inorganic solids. Continuing development of sensitivity-enhancement approaches, including 1H-detected fast MAS experiments, dynamic nuclear polarization, and experiments tailored to ultrahigh magnetic fields, is described. We highlight recent applications of solid-state NMR to biological and materials chemistry. The Primer ends with a discussion of current limitations of NMR to study solids, and points to future avenues of development to further enhance the capabilities of this sophisticated spectroscopy for new applications.

Reservoir engineering for maximally efficient quantum engines

Abstract Reservoir engineering is an important tool for quantum information science and quantum thermodynamics since it allows for preparing and/or protecting special quantum states of single or multipartite systems or to investigate fundamental questions of the thermodynamics as quantum thermal machines and their efficiencies. Here we employ this technique to engineer reservoirs with arbitrary (effective) negative and positive temperatures for a single spin system. To this end, we firstly engineer an appropriate interaction between a qubit system, a carbon nuclear spin, to a fermionic reservoir, in our case a large number of hydrogen nuclear spins that acts as the spins bath. This carbon-hydrogen structure is present in a polycrystalline adamantane, which was used in our experimental setup. The required interaction engineering is achieved by applying a specific sequence of radio-frequency pulses using Nuclear Magnetic Resonance (NMR), while the temperature of the bath can be controlled by appropriate preparation of the initial hydrogen nuclear spin state, being the predicted results in very good agreement with the experimental data. As an application we implemented a single qubit quantum thermal machine which operates at a single reservoir at effective negative temperature whose efficiency is always 100%, independent of the unitary transformation performed on the qubit system, as long as it changes the qubit state.

Location and characteristics of osseous spine tumors on MRI

The non-invasiveness of MRI and lack of known biologic hazards at current magnetic field strengths and radio frequency pulse sequences, ensure high patient tolerance. MRI can be performed on out patient basis, thus lowering the overall costs. In the case of a patient with clinical suspicion of osseous spine tumor, a complete clinical history with special reference to neurological symptoms was taken, followed by general physical examination and detailed central nervous system examination. Other systems were also examined and findings were noted. Next, the procedure for MRI was explained to the patient and consent was taken. A detailed history pertaining to the contraindications to MRI was taken. Ear plugs were provided to the patient to minimise noise within the gantry. The patient was then placed in supine position with head first inside the gantry. Proper positioning and immobilisation was done. 11 tumors of osseous spine were located in thoracic region, 8 in lumbar region, 6 in sacrococcygeal region and 2 in cervical region. Thoracic spine was the favoured site for tumors of osseous spine in this study.

A Theoretical Study on a Novel Cartesian Product Operator Formalism Applicable to Strongly-Coupled Two-Spin 1/2 Systems in Solution-State and Solid-State MAS NMR Spectroscopy

Abstract In solution-state and solid-state MAS (Magic Angle Spinning) NMR (Nuclear Magnetic Resonance) spectroscopy, a comprehensive product operator formalism applicable to general two-spin 1/2 systems, including strongly-coupled systems, is proposed. The formalism employs standard product operators, based on the orthogonal coordinate system, easily evaluating the effects of RF (Radio Frequency) pulse sequences. Solid-state anisotropic interactions modulated by MAS are treated in the perturbation theory, yielding striking solid-state effects, whereas the absence of those interactions leads to solution-state cases with strong couplings. Solid-state MAS INADEQUATE spectra are found to give rise to auto-correlation signals even for the spin pairs possessing an identical isotropic chemical shift.