A comprehensive approach to the analysis and interpretation of the resonances of spins 3/2 from living systems

Abstract

An extensive protocol for the study of tissue resonances of spin 3/2 nuclei is described. The roles of the most relevant multiple pulse experiments are indicated. Their theory is organized in terms of irreducible tensor operators and the pulse and quadrupolar relaxation transfer functions which relate them for a type c spectrum. A systematic approach to the interpretation of the temperature and/or magnetic field dependences of all six of the relaxation rate constants of the resonance of a single population of isolated spins in fast exchange, and giving rise to a type c spectrum, is presented. An experimental calibration and an application of this protocol are presented in an accompanying paper. The comprehensive method we describe has a number of practical benefits in the interpretation of the physiological spectra obtained from conventional one pulse experiments. A consideration of the appropriate transverse relaxation transfer function leads to an analytical expression for the heretofore empirical NMR visibility factor. This includes factors which account for relaxation during the receiver 'dead' time and relaxation during the pulse itself. Also, consideration of realistic transverse relaxation times likely to be observed in tissue leads to a reasonable strategy for the quantitative resolution and integration of in vivo spectra obtained in the presence of hyperfine shift reagents.

Sodium and T1ρ MRI for molecular and diagnostic imaging of articular cartilage

“…The theory of NMR of quadrupolar nuclei (74,75,(77)(78)(79)(80), relaxation-induced sodium single and multiple quantum coherences (MQC) and their applications in the studies of biological systems has been extensively discussed in several original and review articles (81)(82)(83)(84)(85)(86)(87)(88)(89)(90)(91). Here a brief overview of steps involved in the calculation of spin dynamics using the density matrix approach is presented.…”

“…Single and multiple quantum sodium NMR has been used extensively to study various biological tissues such as brain (89,90,104,(116)(117)(118)(119)(120), breast (121) heart (122)(123)(124)(125)(126)(127)(128), muscle (129,130), tumors (131)(132)(133), blood (122) and cartilage (27,93,(134)(135)(136) and reviewed in several articles (86,87,91,108,119,(137)(138)(139)(140)(141). In this review, however, we restrict our discussion to sodium NMR of cartilage.…”

“…Other methods that are promising in detection of ordered sodium ions include quadrupolar filter by nutation (QFN) (115). QFN exploits the dependence of quadrupolar interaction on nutation frequencies to suppress isotropic sodium and detect the central transition of ordered sodium.Single and multiple quantum sodium NMR has been used extensively to study various biological tissues such as brain (89,90,104,(116)(117)(118)(119)(120), breast (121) heart (122-128), muscle (129,130), tumors (131-133), blood (122) and cartilage (27,93,(134)(135)(136) and reviewed in several articles (86,87,91,108,119,(137)(138)(139)(140)(141). In this review, however, we restrict our discussion to sodium NMR of cartilage.…”

Triple-quantum filtered NMR imaging of sodium in the human brain

“…One method is to subtract an image obtained from an initial free induction decay and an image obtained from a subsequent echo [14]. Another method is to fit the acquired free induction decay to a sum of exponentials [23,24]. A third I method is to use an inverse Laplace Transform to estimate a distribution of relaxation times [25,26].…”

“…The pulse sequence used to measure these terms is ,shown in Figure 4.3 [23]. The 57 degree flip angle for the second pulse optimizes the production' of 3Q coherence in the evolution period.…”