Phase twist

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... 

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 ... 

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

Peaks in homonuclear 2D /-resolved spectra have a phase-twisted line shape with equal 2D absorptive and dispersive contributions. If a 45° projection is performed on them, the overlap of positive and negative contributions will mutually cancel and the peaks will disappear. The spectra are therefore presented in the absolute-value mode. 

The first term is the evolution that would have occurred in the absence of the gradient, and the second term is the position-dependent phase twist. Note that the twist is twice as much as that experienced by a SQC in the same gradient. Thus, the coherence order (in this case p = 2) is encoded in the twist, and this gives us a way to select the coherence at any point during the pulse sequence by simply applying a gradient pulse. 

In general, the effect of a gradient pulse on any operator is to multiply it by a phase factor that represents the position-dependent phase twist ... 

These coherences will have a helical phase twist in the NMR sample tube and will add to give a net signal of zero in the probe coil during the FID. 

The pulse sequence is shown in Figure 11.48. The net twist will be zero only for the desired pathway DQC -> ZQC -> lH SQC. Of course, we have created a new problem the minimum t delay is now twice the time required for a gradient and its recovery. This will lead to a very large phase twist in F, so we can either present the data in magnitude mode, where phase is not an issue, or insert the appropriate spin echoes to refocus the chemical-shift evolution that occurs during the gradients. 

Equation 10.9 represents a complicated line shape, which is a mixture of absorptive and dispersive contributions. Figure 10.11 gives an example of such a phase-twisted line shape. The broad base of the line, caused by the dispersive contribution, and the difficulty in correctly phasing such a resonance make it unattractive for practical use. The phase twist problem can be alleviated by displaying only the absolute value mode... 

FIGURE 10.11 Example of a phase-twisted 2D NMR line. Courtesy of Ad Bax (National Institutes of Health). 

In conventional two-dimensional Hartmann-Hahn experiments, only the transfer of a single magnetization component a is used. In order to avoid phase-twisted lineshapes, the orthogonal magnetization components B and y are eliminated with the use of trim pulses or other filters (see Section XII). If two magnetization components can be transferred with identical transfer functions 7) (t) = the sensitivity of multidimen-... 

This simple phase-incrementation idea, not particularly emphasized by the authors at the time, has more recently had a considerable impact on NMR methodology. First, it was made the basis of one of the standard methods for obtaining pure-phase two-dimensional spectra, replacing the undesirable phase-twist line shape with a pure absorption-mode signal. Secondly, it has provided a neat way to generate an extensive array of simultaneous soft radiofrequency pulses covering an... 

---