Frequency-encoding

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

Once a slice has been selected and excited, it is necessary to encode the ensuing NMR signal with the coordinates of nuclei within the slice. For each coordinate (x andy) this is achieved by one of two very closely related means, frequency encoding or phase encoding [1]. In this section we consider the fonner and in the next, the latter. In tlie section after that we show how the two are combined in the most coimnon imaging experiment. 

Figure 3 describes for nine magnetization vectors the effect of the appHcation of a phase-encoding gradient, G, and a frequency-encoding gradient, G. ... 

A problematic artifact associated with MRI arises when the imaged subject moves duriag acquisition of the / -space data. Such motion may result ia a discontiauity ia the frequency-encoded or phase-encoding direction data of / -space. When Fourier transformed, such a discontiauity causes a blurred band across the image corresponding to the object that moved. Such an artifact ia an image is referred to as a motion artifact. 

In this section, we will describe three building blocks of NMR imaging phase encoding, frequency encoding and slice selection. All three are related to the signal by the fourth equation ... 

One way out of this dilemma is the so-called frequency encoding technique. It is often referred to as an approach that is very different from phase encoding, but... 

Fig. 1.9 Schematic plot of a basic three-dimensional imaging pulse sequence with frequency encoding along one axis (read), and phase encoding along the two remaining orthogonal directions. The choice of directions is arbitrary, as is the position of the phase gradients within the sequence.

Fig. 1.21 Echo Planar Imaging (EPI) pulse sequence. Gradient-echo based multiple echoes are used for fast single-shot 2D imaging. Slice selection along Gs and frequency encoding along C, are utilized. Phase encoding is realized using short blipped gradient pulses along Gp.

Another issue of concern is the amplitude of magnetic field gradients required for solids imaging. For spectra up to a few kHz wide, standard frequency encoding schemes can be used to obtain reasonable spatial resolution. This will not work for broader lines, but it is well known that phase encoding is much more tolerant to line broadening and can be used for spectral widths in excess of 100 kHz with no major loss in spatial resolution. 

P. E. Rapp, Frequency encoded biochemical regulation is more accurate than amplitude dependent control, J. Theor. Biol, 90, 531-544 (1981). 

A. Goldbeter, G. Dupont, and M. Berridge, Minimal model for signal induced Ca + oscillations and for their frequency encoding through protein phosphorylation, Proc. Natl. Acad. Sci. USA, 87, 1461-1465 (1990). 

Theoretical models shed light on additional aspects of pulsatile cAMP signaling in Dictyostelium. First, like Ca + spikes, cAMP pulses are frequency encoded. Only pulses delivered at 5-min intervals are capable of accelerating slime mold development after starvation. Simulations indicate that frequency encoding is based on reversible receptor desensitization [76]. The kinetics of receptor resensitization dictates the interval between successive pulses required for a maximum relay response [78]. Second, cAMP oscillations in... 

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