Nuclear magnetic resonance has been successfully used in field gradient can be described most readily in a k space (1, 6). Here we use the discrete form of the basic equation biomedicine for imaging and in vivo spectroscopy. However, both NMR modes have been severely limited by the availability of excitation selective only for simple shapes, e.g.,
[1] spherical, cylindrical, or cubic volumes (1-5). Here we demonstrate excitation selective for any arbitrary shape. Such excitation can be used for high-resolution NMR specwhere M / is the vector of (complex) transverse magnetizatroscopy and volume-selective imaging of precisely delinetion after N constant intervals Dt of application of smallated organs, tumors, body parts, etc.
flip-angle pulses Éu l É with phases f l [u l Å Éu l Éexp(if l )] and In general, regions are selectively excited by concerted constant gradients G l ; M 0 is the magnitude of equilibrium modulation of the static field gradients and the amplitude of magnetization and g is the nuclear gyromagnetic ratio. The the radiofrequency field (1,(6)(7)(8)(9)(10). The shape of the selected three-dimensional vector of the real space r indicates the region is determined by the number and type of RF fields dependence of transverse magnetization on 3D coordinates. combined with static magnetic field gradients. For example, In full analogy with the continuous representation of the a single selective RF pulse combined with a single static problem (6), Eq. [1] can be written in a more compact form field gradient selects a plane (5); two selective RF pulses and two static field gradients selectively excite a cross sec-