Space encoding

One should note that the phase shift becomes time-independent and maximal for a = 1, i.e., at the resonance condition v = vG. The frequency spectrum 4>(a) bears a sine shape with a bandwidth inversely proportional to the number of oscillations of the gradient field (Fig. 4). Such a behaviour was also predicted in Ref. 15. Recording in a systematic way the phase shift as a function of vG without space encoding would be a very fast and efficient method to scan in a whole object the possible frequencies of spin motions. 

Fig. 5. Pulse sequence for MR detection of vibration using a radiofrequency field gradient. A binomial 1331 radiofrequency pulse (pulse length D, interpulse delay r) is applied in-phase with the mechanical wave. Thus the vibration period 7V is equal to 4(D + r). The number of cycles can be increased to ensure a better frequency selectivity. The constant RF field gradient generated by a dedicated RF coil allows space encoding without using conventional static field gradients (from Ref. 16 with permission from Elsevier).

In this pharmacophoric context, rather than comparing molecular structures or substructures to each other, the binding pattern of a ligand to its binding site is characterized by location and tolerance constraints in 3D space encoding for different kinds of interactions. Those include vectors... 

With the help of (3.2.1), it is readily seen that co2q does not depend on the orientation angles a and of the principal axes system. Therefore, the transition corresponds to a narrow resonance which can be favourably exploited for space encoding in imaging. 

Spin-warp imaging denotes the most common form of Fourier imaging with data acquisition in Cartesian k-space coordinates [Edel]. Instead of a variable evolution time t for phase encoding, the gradient amplitude is stepped during t in order to halt phase evolution from spin interactions other than with the applied space-encoding gradient. 

Fig. 6.2.3 [Wehl] Principle of spectroscopic Fourier imaging with slice selection. To separate spatial and spectroscopic responses, the spectroscopic evolution must be constant during the space-encoding period fj. The spectroscopic signal is acquired during the detection time tz in the absence of a gradient.

Fig. 7.1.1 Generation of contrast the initial magnetization is filtered by rf excitation (TX) before space encoding by gradients G. In the absence of gradients the free-induction decay is detected (RX) for the extraction of spectroscopic information.

The second term in the second line of (7.2.8) provides the familiar definition of the k vector for space encoding (cf eqn (2.2.23)), because... 

Fig. 7.2.17 Flow imaging by phase encoding. A bipolar flow-encoding gradient is applied for slice selection to image through-plane flow v (x, y). Both phase and frequency gradients for space encoding are flow compensated.

Fig. 7.2.32 [Dum3] Imaging with homonuclear polarization transfer based on the INEPT sequence. Slice selection and space encoding are incorporated into the filter.

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