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## Mathematics and Physics of Emerging Biomedical Imaging (1996) Commission on Physical Sciences, Mathematics, and Applications (CPSMA)

### Citation Manager

. "4 MAGNETIC RESONANCE IMAGING." Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: The National Academies Press, 1996.

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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 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, 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-

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 FRONT MATTER (R1-R18) 1 INTRODUCTION AND SUMMARY (1-12) 2 X-RAY PROJECTION IMAGING (13-22) 3 X-RAY COMPUTED TOMOGRAPHY (23-36) 4 MAGNETIC RESONANCE IMAGING (37-88) 5 SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY (89-104) 6 POSITRON EMISSION TOMOGRAPHY (105-120) 7 ULTRASONICS (121-132) 8 ELECTRICAL SOURCE IMAGING (133-142) 9 ELECTRICAL IMPEDANCE TOMOGRAPHY (143-146) 10 MAGNETIC SOURCE IMAGING (147-156) 11 MEDICAL OPTICAL IMAGING (157-166) 12 IMAGE-GUIDED MINIMALLY INVASIVE DIAGNOSTIC AND THERAPEUTIC INTERVENTIONAL.. (167-186) 13 FRONTIERS OF IMAGE PROCESSING FOR MEDICINE (187-198) 14 A CROSS-CUTTING LOOK AT THE MATHEMATICS OF EMERGING BIOMEDICAL IMAGING (199-230) INDEX (231-238) Color Plates (239-242)