Pulsed gradients

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...

From a more general point of view, components k-, ]=x,y,z of a wave vector k which describes the influence of all gradient pulses may be defined as follows k i) = yCi,U ) dif For the 2D unaging pulse sequence... 

In order to encode displacement as opposed to average position, the gradient is applied in such a maimer as to ensure that ). Generally, this means applying gradient pulses in bipolar pairs or applying uni-... 

We first examine how this works for the case of coherent flow. A typical pulse sequence is shown in figure Bl.14.9. This sequence creates a spin echo using two unipolar gradient pulses on either side of a 180° pulse. The duration of each gradient pulse of strength G, is . The centres of the gradient pulses are separated by A. 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

If temis of higher order than linear in t are neglected, the transverse magnetization evolves in the presence of the first bipolar gradient pulse according to (equation Bl.14.2 and equation B 1.14.61 ... 

The phase of the transverse magnetization is inverted by tire 180° pulse and the magnetization after the second gradient pulse and therefore at the echo centre is ... 

The echo phase does not depend on the initial position of the nuclei, only on their displacement, vA, occurring in the interval between the gradient pulses. Analysis of the phase of the echo yields a measure of flow velocity in a bulk sample. Spatial resolution is easily obtained by the incorporation of additional imaging gradients. 

This is the factor by which the echo magnetization is attenuated as a result of difhision. More elaborate calculations, which account for phase displacements due to difhision occurring during the application of the gradient pulses yield... 

Bryant D J, Payne J A, Firmin D N and Longmore D B 1984 Measurement of flow with NMR imaging using a gradient pulse and phase differenoe teohnique J. Comput. Assist. Tomogr. 8 588-93... 

Figure 7.25 illustrates the power of magnetic field gradient pulses to eliminate unwanted coherences. The double-quantum filtered COSY spec-... 

Figure 7.25 Homoniiclear double-quantum filtered COSY spectrum (400 MHz) of 8-mMangiotensin II in H,0 recorded without phase cycling. Magnetic field gradient pulses have been used to select coherence transfer pathways. (Reprinted from J. Mag. Reson. 87, R. Hurd, 422, copyright (1990), with permission from Academic Press, Inc.)...

Fig. 1.3 Effect of a pulsed magnetic field zero. During the gradient pulse, the field gradient of strength g on the phase of a signal becomes position-dependent and a phase shift contribution originating from spins at position is accumulated that is proportional to t. Prior to the gradient pulse, all spins position t and time t. After the gradient pulse...

However, in order to be able to apply the inverse Fourier transformation, we need to know the dependence of the signal not only for a particular value of k (one gradient pulse), but as a continuous function. In practice, it is the Fast Fourier Transform (FFT) that is performed rather than the full, analytical Fourier Transform, so that the sampling of k-space at discrete, equidistant steps (typically 32, 64, 128) is being performed. 

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. 1.19 Spin-echo based pulse sequence to each gradient pulse, A the separation between encode velocity change. The gradients are each pair of bipolar gradient pulses and tm the stepped pair-wise independently (2D VEXSY) mixing time between the bipolar gradient pairs, or simultaneously (1 D VEXSY). For a VEXSY The opposite polarity of the bipolar gradient experiment, 7q to k4 are usually applied along pair is realized by an inversion 180° pulse, the same spatial direction. 8 is the duration of...

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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