Abstract
Two magnetic resonance imaging studies based on relaxometry are presented. Firstly, various methods of measuring T1, T2, and flip angle are reviewed, along with various applications of relaxometry. After a study of the relevant background and theory, a method of measuring T1, T2, and the flip angle simultaneously using echo planar imaging is described, followed by a study of diffusion in a biological system employing T2 measurements. A series of echo planar images acquired with a repetition time that is short compared with the relaxation times T1 and T2 shows fluctuations in image intensity, which are dependent on these relaxation times and the flip angle. These fluctuations are best modelled using the Kaiser theory of isochromats. The Levenberg-Marquardt non-linear least squares algorithm can then be used to estimate the parameters from the data. This has been shown to work consistently in zero and one dimensions, but inconsistently in two dimensions when high gradient amplitudes affect coherence. Bacterial polysaccharides are known to exhibit a property known as anion exclusion, where the diffusion of cations is permitted, but the diffusion of anions is prevented. According to the theory of permselectivity, negatively-charged functional groups on the surfaces of pores not only block anions, but assist the diffusion of cations. The relationship between T2 and the concentration of paramagnetic species is used to follow the diffusion of Mn2+ ions through several polysaccharides. It is shown that the diffusion coefficients of Mn2+ ions are higher in neutral than in positively-charged polysaccharides, and greater still in negatively charged polysaccharides.