Unlike its x-ray counterparts, magnetic resonance imaging (also known as nuclear magnetic resonance (NMR) imaging) is not a transmission technique. Rather, the material imaged is itself the signal source (i.e., the macroscopic spin magnetization M from polarized water protons or other nuclei, such as 23Na or 31P). The motion of the magnetization vector of uncoupled spins, such as those for protons in water, is conveniently described in terms of the phenomenological Bloch equations:
where - is the gyromagnetic ratio, H the effective field, M0 the equilibrium magnetization, and T 1 and T 2 the relaxation times. T 1 is the characteristic relaxation time for longitudinal magnetization to align with the magnetic field: following a perturbation such as a 90° RF pulse, the longitudinal magnetization typically returns to its equilibrium value, M0, with a time constant T 1. Likewise, T 2 is the characteristic time for decay of coherent magnetization in the transverse plane: the transverse magnetization decays exponentially with time constant T 2 to its equilibrium value, M° xy = 0. Both relaxation times are determined by the interaction of water or other nuclei with macromolecules in tissues. T 1 and T 2 contribute independently to the contrast between different tissues.
There is, in general, no closed-form solution to equation 4.1 (although section 14.1.6 introduces two approximate solutions). Ignoring the relax-