MRI - 3 - Body cross-section Frequency Encode Gradient...

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Body cross-section Frequency Encode Gradient (FEG) \ Net frequency at gradient location - .--- al 3 u .- - n 5 Composite frequency Receiver coil $. Digitization I v Fourier Transform Position (position decoder) FIGURE 15-9. The frequency encode gradient (FEG) is applied in an orthogonal direc- tion to the SSG, and confers a spatially dependent variation in the precessional fre- quencies of the protons. Acting only on those spins from the slice encode excitation, the composite signal is acquired, digitized, demodulated (Larmor frequency removed), and Fourier transformed into frequency and amplitude information. A one-dimensional array represents a projection of the slice of tissue (amplitude and position) at a specific angle. (Demodulation into net frequencies occurs after detection by the receiver coil; this is shown in the figure for clarity only.) Demodulated MR Signal Corresponding Fourier Transformation 2 cycleslcm Amplitude: 0.75 180" phase shift 3 cycleslcm Amplitude: 0.5 pig1 Composite a J , waveform --__ I +t L 0 05 1(1 15 -5 4-3-2-1 0 12 3 45 Distance (cm) Frequency (cycleslcm) or position
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Phase gradient amplitude discretely applied 256 times Resulting phase shift after gradient removed FIGURE 15-11. The phase encode gradient (PEG) produces a spatially dependent variation in angular frequency of the excited spins for a brief duration, and generates a spatially depen- dent variation in phase when the spins return to the Larmor frequency. Incremental changes in the PEG strength for each TR interval spatially encodes the phase variations: protons at the null of the PEG do not experience any phase change, while protons in the periphery experience a large phase change dependent on the distance from the null. The incremental variation of the PEG strength can be thought of as providing specific "views" of the three-dimensional volume because the SSG and FEG remain fixed throughout the acquisition. SEG -q,-npdd% Localize (z) Localize (y) FEG p Localize (x) Echo Generate echo DAQ RUUYIWUU Acquire data - TE - HGWE 15-12. A typical spin-echo pulse sequence diagram indicates the timing of the 556, PEG, and FEG during the repetition time (TR) interval, synchronized with th@ RF pulses and the data acquisition (DAQ) when the echo appears. Each TR Inter- val is repeated with a different PEG strength (th~s appears as multiple lines in the illustration, but only one PEG strength is applied as indicated by the bold line in this example).
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I Phase encode gradient I I Frequency encode gradient I I MR signal I Frequency Domain k-space Spatial Domain image space FIGURE 15-15. MR data are acquired into the spatial frequency domain k-space matrix, the repos- itory of spatial frequency signals. Each row in k-space represents spatially dependent frequency vari- ations under a fixed FEG strength, and each column represents spatially dependent phase shift vari- ations under an incrementally varied PEG strength. Data are placed in the k-space matrix in a row determined by the PEG strength for each TR interval. The grayscale image is constructed from the
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MRI - 3 - Body cross-section Frequency Encode Gradient...

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