Phase 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. 

For phase encoding the phase twist is most connnonly varied by incrementing in a series of subsequent transients as tiiis results in a constant transverse relaxation attenuation of the signal at the measurement position. The signal intensity as a fiinction of G is... 

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 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 ... 

The recipe for the first building block of NMR imaging, the phase encoding, thus goes like this apply a phase gradient of effective area k acquire the signal S(k) repeat for a number of different equidistant values of k perform the inverse... 

Fig. 1.4 Phase encoding scheme in three ween the rf pulses and before the acquisition of dimensions. Three pulsed gradients in ortho- the echo signal. In practice, the gradients are gonal directions are applied and are varied often applied simultaneously. The indices 1, 2 independently of each other (symbolized by the and 3 represent orthogonal directions with no diagonal line). The actual timing of the gradi- priority being given to a particular choice of ents is arbitrary provided they are placed bet- combinations.

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. 1.11 Typical basic three-dimensional negative intensity directly before the actual imaging sequence with slice selection, frequen- read gradient. The shape of the 180° rf pulse cy encoding and phase encoding in three ortho- is drawn schematically to indicate that a soft gonal directions. The compensating lobe for pulse is used, the read gradient is drawn as a rectangle with...

Just as we obtain the spin density distribution q(i), and hence the projection of the investigated object, in phase encoded imaging, we can reconstruct P(R, A) by... 

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.

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