Chapter 2 - Excitation of the Transverse Magnetization

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In nuclear magnetic resonance (NMR) imaging and spectroscopy it is a common practice to excite repeatedly a macroscopic system of nuclei by a series of r.f. pulses. In the conventional approach used for spatial encoding in magnetic resonance imaging (MRI) a number of excitations are needed to collect all spatially encoded signals required for subsequent image reconstruction. One of the main assumptions of this approach is the existence of a steady state, under which repetitive excitations would produce the same transverse magnetization in a sample. Using the Bloch equations, it is demonstrated that such a steady state can indeed be established as a result of the evolution of the nuclear magnetization subjected to a series of r.f. pulses. An example of spatially selective excitation that creates nonzero transverse magnetization only in a chosen slice of material is also described. The dynamics of nuclear magnetization in an external magnetic field in the presence of a train of identical r.f. pulses are also described. To simplify further derivations, it is assumed that the transverse magnetization in a sample is negligibly small immediately before the beginning of each successive excitation. To avoid signal loss due to magnetic field nonuniformity, 180-degree pulses are frequently included in pulse sequences used in NMR imaging and spectroscopy. Magnetic resonance imaging is typically used to image an object in three dimensions. To achieve spatial localization, it is a common practice to first selectively excite transverse magnetization in a thin slice of material, which is subsequently imaged in the two remaining directions.