Triple quantum imaging of sodium in inhomogeneous fields
Abstract
Triple quantum filtered sodium MRI techniques have been recently demonstrated in vivo. These techniques have been previously advocated as a means to separate the sodium NMR signal from different physiological compartments based on the differences between their relaxation rates. Among the different triple quantum coherence transfer filters, the three-pulse coherence transfer filter has been demonstrated to be better suited for human imaging than the traditional four-pulse implementation. While the three-pulse structure has distinct advantages in terms of the radiofrequency power efficiency, it is characterized, also, by an increased dependence on the main magnetic field inhomogeneities. In this thesis, we characterize these dependences and introduce a method for their compensation through the acquisition of a field map and the use of a modified phase cycling scheme.We analyze the dynamics of spin 3/2 systems using the density matrix theory of relaxation. We show that by using the superoperator formalism, we can obtain an algebraic formulation of the density matrix's evolution, in which the contributions from relaxation and radio frequency application are factored out. To achieve this goal, we derive an exact form for the propagator of the density matrix, in the presence of both static quadrupolar couplings and magnetic field inhomogeneities.Using the algebraic formulation, we derive exact expressions for the behavior of the density matrix in the classical one-, two- and…
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