Magnetic Phase encoding

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

Figure Bl.14.7. Chemical shift imaging sequence [23], Bothx- andj -dimensions are phase encoded. Since line-broadening due to acquiring the echo in the presence of a magnetic field gradient is avoided, chemical shift infonnation is retained in tire echo.

The displacement of a spin can be encoded in a manner very similar to that used for the phase encoding of spatial infonnation [28, 29 and 30]. Consider a spin j with position /-(t) moving in a magnetic field gradient G. The accumulated phase, cpj, of the spin at time t is given by... 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

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. G. Webb 2004, (Optimizing the point spread function in phase-encoded magnetic resonance microscopy), Concept Magn. Reson. 22A, 25-36. 

Pure Phase Encode Magnetic Resonance Imaging of Concrete Building Materials 285 3.4... 

SPRITE is termed a pure phase encode technique because spatial encoding occurs through the application of variable amplitude magnetic field gradients (which yield spatially varying frequencies) applied for fixed periods of time. Variable frequency with a fixed evolution or encoding time yields a variable signal phase. 

Fig. 3.4.1 Schematic description of the three-dimensional SPI technique. Gz, Cx and Gy are the phase encode magnetic field gradients and are amplitude cycled to locate each /(-space point. A single data point is acquired at a fixed encoding time tp after the rf excitation pulse from the free induction decay (FID). TR is the time between excitation (rf) pulses. Notice that the phase encode magnetic field gradients are turned on for the duration of the /(-space point acquisition.

Fig. 3.4.4 Schematic description of the one-dimensional double half k (DHK) SPRITE technique. The phase encode magnetic field gradient, Gz, ramped through half of /(-space beginning at the center and a single data point is acquired at a fixed time (tp) after the rf excitation pulse. The second half of /(-space is acquired after a 5T time delay. The time between rf pulses is TR.

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. 

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