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Figure 4.1. Resolution, expressed as the reciprocal of imaging voxel volume,

achieved in MR brain images by means of a volume head coil in scan times

of less than 20 minutes and SNR sufficient to delineate anatomic structures.

#### 4.1 Principles of Magnetic Resonance Imaging

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 ^{23}Na or ^{ 31}P). 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, *M*0 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-