Velocity encoding

Fig. 1.16 Typical motion-compensated, velocity encoding imaging sequence. The basic scheme from Figure 1.11 is amended by additional compensating gradient pulses for the read, phase and slice directions. The velocity encoding pair of gradient pulses of duration 8 and separation A is drawn on a separate line in reality, it is applied along any of the three...

Fig. 2.8.1 Rf and gradient pulse sequence used encoding is along the x axis. By changing the to encode for velocity in a two-dimensional direction of the velocity encoding gradient image in the (x, y) plane normal to the slice pulse pair of duration 6 other directions for direction z. In the example shown the velocity velocity components can be measured.

Fig. 3.3.9 Velocity encoded imaging (upper) and radial velocity distribution (lower) for a flow of water at 2.93 mm3 s- through the fixed bed reactor, taken in the same slice as for Figure 3.3.8. (a) Spherical glass beads of 2 mm in diameter and (b) cylindrical pellets with average equivalent diameter of 2.2 mm.

The molecular translations are spatially resolved by combining the velocity encoding sequence with the conventional spatial imaging encodings. In this velocity imaging", the phase shift of the spins reflects the information about their displacement as well as the spatial position. In this work, a flow-compensation [25] is implemented in the velocity imaging pulse sequence to eliminate the actifacts due to fluid flow. 

Fig. 4.2.5 Unaliased (A) and aliased (B) velocity images for a 0.6% aqueous carboxy-methylcellulose solution obtained by MRI. The vertical axes represent the data obtained in the velocity encoded direction and the horizontal axis represents data obtained in the spatially encoded direction. Aliasing is achieved by setting the velocity encode gradients so large that the maximum phase evolution of a given fluid element for a pulsed gradient step exceeds Ji or 2jt...

Velocity-encoding 2D NMR imaging methods characterize general patterns of spatial velocity distributions and directly visualize different characteristics of flow behavior depending on the properties of the materials and operating param-... 

An example of a velocity-encoding method is the bipolar-gradient method.35 Here, two identical pulses are applied during the dephasing and rephasing periods of a spin-echo sequence. Since the two pulses are in opposite polarity with respect to the time domain, the phase shift (p(t) in Eq. (28) is dominated by the velocity term, i.e. the first-order term of t in the expansion. 

Figure 10 shows the incorporation of the velocity-encoding field gradient pulses in a stimulated-echo imaging pulse sequence which was used in this work. A remarkable advantage of using the stimulated echo is that the relaxation... 

In order to obtain spatial resolution of the molecular translations within each voxel, it is necessary to combine the velocity-encoding gradient sequence shown in Section 3.1.1 with a standard imaging sequence such as frequency or phase encoding. The displacement distribution function, P A (R), must now be generalized to a spatial-displacement joint density function Aso that it describes the total number of spins located at r with displacement R during time A 28... 

In our work, the velocity distribution method is used, where the velocity distribution function PA (v, r) is estimated from the velocity imaging, and the average velocity at a voxel located at r, r, is calculated. Consider the one-component ("-direction) velocity imaging in two-dimensional (z- and A-direction) space illustrated in Fig. 11. In this case, the velocity encoding is parallel to the frequency encoding. The signal intensity from the stimulated echo S(kz, kx, q) is converted to the velocity distribution function PA (fi z, x) by combining Eq. (34) and Eq. (36) ... 

In order to expand the velocity-encoding pulse sequence to two-component velocity measurement in a two-dimensional domain, we can superimpose another series of velocity-encoding gradients on the x-axis in Fig. 11, where phase-encoding is applied for spatial resolution. For steady-state flowing conditions, however, it may be faster and more convenient to use two different pulse sequences independently. After the data for the z-component velocity field... 

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