Phase-encoding methods

The phase-encoding methods are considered to be the most robust and quantitative but, as demonstrated below, TOF and rapid image acquisition can be particularly useful in specific applications. 

If the magnetic field gradient is applied for a short time period (i.e., a pulse ), as opposed to continuously during which time data are acquired, instead of imposing a time-independent modified resonance frequency on a nucleus as determined by its spatial position, the nuclear spin is given a phase offset (say fi) after application of the pulse characteristic of its spatial position when the pulse was applied. In the rotating frame of the spin system, this phase offset, (j)i is equal to yg i, where 5 is the duration of the applied gradient, Zi the position of the spin. 

When pulsed magnetic field gradients are applied to study diffusive processes, the MR technique is often referred to as pulsed field gradient or pulsed gradient spin echo (PGSE) MR. Application of PGSE MR techniques to quantify molecular diffusion was pioneered by Stejskal and Tanner 17,18), and the techniques typically probe molecular displacements of 10 -10 m over time scales of the order 10 M s. 

Transport measurements performed using pulsed magnetic field gradients are most clearly understood in the context of a more mathematical framework. It follows from Eq. (2) that the phase shift (i.e., the instantaneous phase offset in resonance frequency) (f) t) acquired (in the rotating frame) following application of 

We also know that the change of position with time of a spin or its associated magnetic moment can be written as 

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The short signal lifetimes of these nuclei (bulk T2 around a hundred ps and T) around a few ms) [14] require the use of pure phase encode methods. The low concentration of these nuclei coupled with the low absolute sensitivity requires a measurement technique that is rapid enough to permit numerous signal averages. 

The fact that multiple quantum coherences can only be measured indirectly by their influence on the amplitude and phase of a subsequently acquired single quantum signal makes this technique a phase-encoding method. The necessity to acquire the spatial information in time-consuming extra dimensions is a penalty in all phase-encoding techniques. However, in the case of double quantum imaging of quadrupolar nuclei like, e.g., H, the wideline information of the single quantum spectrum can be utilized for contrast, because the quadrupolar interaction usually dominates all other spectral features and is a sensitive probe for molecular dynamics and orientations [80-83]. 

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