Another field gradient pulse is now applied in a sense to counteract the NMR precession that occurred during evolution, tte helix of vectors is gradually unwound, bringing spins from all the slices into phase coincidence at a particular instant to form a spin echo (Fig. 6.2). Ms relies on the fact that the accumulated phase (fa) of spins in any given slice is proportional to the evolution time associated with that slice, and hence to the distance along the tube axis (Fig. 6.1). Ms is a most unusual kind of spin echo: a macroscopic field gradient has been used to refocus the effect of a spectroscopic precession, tte fact that all the slices contribute to the intensity of the echo is crucial. No signal strength is lost as a consequence of the slice-selection process, otherwise the sensitivity of the single-scan method would be diluted by a factor N, and this would be unacceptable. If the sensitivity of the single-scan method is limited in practice, this is not through loss of signal but rather through acceptance of additional noise (see later).

So far we have considered the problem as if only a single chemical site were involved. In any practical case there are several different chemical sites and their accumulated phase handicaps are proportional to their respective chemical shifts. Each chemical site has its magnetization vectors wound into a helix of a different pitch. For example if there are three different chemical shifts flg and flc. the corresponding vectors are brought to a focus at three different times (Fig. 6.3). Consequently there is a separate spin echo for every distinguishable chemical site, and they appear at times proportional to their characteristic chemical shifts. We call this sequence of spin echoes an "echo spectrum". Although it resembles the expected NMR spectrum in the Fi frequency dimension, is a very different animal indeed. For one thing, it displays intensity as a function of time not frequency. In complete contrast to the conventional experiment, no Fourier transformation stage is involved.

Once this echo spectrum has been obtained, the field gradient is reversed, bringing the magnetization vectors back again into focus one by one, but in the reverse order, ttis doubling of the evolution period is unavoidable and has some practical repercussions as far as noise is concerned. To improve sensitivity, this second echo spectrum may be recorded and added to the first one after reversing its sense and correcting some trivial phase shifts. However, the main reason for using a bipolar gradient pair is to avoid cumulative effects, because this detection cycle is repeated many times in order to extract the information from the F2 dimension.

Fig. 6.3. If there are three different chemical shifts Q/\, ^b and Qc, the corresponding vectors are dispersed into helices of different pitches. Allowed to precess in the applied magnetic field gradient, these helices unwind to form spin echoes at different times. This creates an "echo spectrum" that has the same general form as the conventional NMR spectrum

Fig. 6.3. If there are three different chemical shifts Q/\, ^b and Qc, the corresponding vectors are dispersed into helices of different pitches. Allowed to precess in the applied magnetic field gradient, these helices unwind to form spin echoes at different times. This creates an "echo spectrum" that has the same general form as the conventional NMR spectrum


Good resolution in the evolution dimension (Fi) of a conventional two-dimensional experiment imposes a minimum acceptable value for the final evolution time (ii)max- If (ii)maxis too short, the observed resonances are broadened or, worse still, are distorted by sinc-function oscillations. Typically (fi)max would be set somewhere in the range 10-100 ms. It is not possible to work with much shorter times. Sometimes the time-domain data are artificially extended by linear prediction, but this becomes unreliable beyond a factor of about 2, or for noisy data.

Resolution in the "echo spectrum" is not governed by the conventional rules of Fourier transformation; as we have seen, no transformation is performed in this dimension. One of the crucial factors that allows the single-scan experiment to be completed so quickly is that the time allowed for evolution in the presence of the field gradient is very short, typically 500 [is, 1 or 2 orders of magnitude shorter than in conventional spectroscopy, ^e spread of precession phases due to chemical shifts is thus quite limited. In principle, the more intense the applied field gradient during detection, the narrower the spin echo, because magnetization vectors from different slices come into phase quickly and then get out of phase equally rapidly, so the echoes should be quite narrow. In practice, there are other factors that limit resolution in the Fi dimension. Only a small number N of pigeon holes are employed to store the various evolution increments, so there is no advantage to be gained by taking more than N samples across the entire echo spectrum. (We shall see later that sensitivity considerations also require N to be small.) Consequently, the Fi dimension is poorly digitized in comparison with the equivalent conventional NMR spectrum, which would typically use between 103 and 104 samples.

ttis lack of resolution would seem to be the inevitable price to be paid for the speed advantage of the single-scan technique. In fact the practical limit on the number of slices N can be lifted by changing the excitation scheme from the sequence of selective radiofrequency pulses (described earlier) to an adiabatic frequency sweep in the presence of the applied field gradient (Pelupessy 2003). In this manner the sampling can be much finer because the excitation is continuous. Although this is a more effective scheme and could improve resolution in the Fi dimension, finer sampling sacrifices sensitivity, as described later.

TheF2 Dimension

Correlation peaks in a COSY spectrum build up gradually, at a rate determined by the inverse of the relevant spin-spin coupling constant, as antiphase components created by the mixing pulse evolve into detectable magnetization. Consequently the first echo spectrum described earlier shows very little effect of the mixing pulse. But when the detection cycle is repeated at increasing delays after the mixing pulse, coherence is gradually transferred between interacting chemical sites, causing frequency jumps within the Fi spectra, and a consequent intensity modulation. Sampling in this time dimension (t2) is more comprehensive; typically 256 repeated gradient pairs would be applied in order to achieve acceptable digital resolution. Fourier transformation of the intensity of each echo peak as a function of generates the COSY spectrum, displaying correlation peaks that serve to map the spin-spin interactions. tte entire sequence can be completed in less than a second, much faster than the comparable COSY experiment performed by conventional methodology.

Signal-to-Noise Ratio

As mentioned earlier, any measurement completed in a short time suffers a degradation in signal-to-noise ratio compared with a conventional experiment where data is accumulated over a much longer period. Ms loss is inevitable and applies to all fast multidimensional measurements. It is tempting to argue that a technique which temporarily stores signals from different evolution increments in N different slices must dilute the signal strength N times, ttis is «of the case, because each echo collects signal intensity from all the spins in the effective sample volume, not merely from a single slice, ttis is a consequence of the unconventional way in which the Fi spectrum is generated - as a string of spin echoes, each one derived from signals from all N slices.

However there are additional sources of noise in the single-scan method that inevitably arise because the acquisition operation is so fast, ttere are two equiva lent ways to explain this loss of sensitivity, tte first attributes the additional noise to the significantly increased receiver bandwidth ("filter bandwidth"). Bandwidth is determined by the inverse of the receiver dwell time, which is short, typically only 2 i^s. Consequently the band-pass filter in the receiver has to accept a very wide range of frequencies, typically 500 kHz. Ms band contains far more noise than a conventional proton NMR spectrum which would span only about 5 kHz. Noise is proportional to the square root of the bandwidth, so this amounts to a tenfold loss in sensitivity.

tte second (equivalent) explanation is based on considerations of receiver duty cycle, the ratio of the times for which the receiver is active and inactive. Suppose there are N data points in each "echo spectrum" in the F\ dimension, with another N points collected when the gradient is reversed (for practical simplicity this "reflected" echo spectrum is sometimes discarded). Each of these 2N points from the Fi dimension must be examined as a function of ti and the result Fourier transformed to give the F2 spectrum. Only one out of a total of 2N evolution samples is used in any given ti trace, so the receiver duty cycle is effectively 1/(2N). tte signal-to-noise ratio is determined by the square root of the duty cycle, so for a typical case where 2N=100, the sensitivity is degraded tenfold, ttese numbers are quoted merely for guidance; the practical parameters in any particular experiment may well be different. For example, if the "reflected" echo spectra are included, the effective receiver duty cycle would be doubled and, as a consequence, some of the lost sensitivity retrieved.

Both analyses predict a roughly tenfold loss in sensitivity. Here lies the irony - dividing the sample into N slices does not reduce the signal strength (as many would have imagined) but it does increase the noise by the smaller factors V(2N) or Vn. ttis is why resolution in the Fi dimension has to be a compromise. It is N that limits the attainable resolution, but if it is too large, the sensitivity suffers.

Any transients induced by the intense field gradient pulses may also contribute noiselike artifacts, although this problem could be mitigated by technological improvements in the equipment used for generating gradients. Although in principle a single-scan measurement benefits from the fact that the initial state has the full equilibrium Boltzmann spin populations without the need to introduce a relaxation delay, this advantage is sacrificed when multiscan averaging is required. Furthermore, some applications in biochemistry require a presaturation period for water suppression, slowing down the process appreciably.

Consequently the lack of sensitivity is probably the limiting factor in the application of the single-scan method to samples where concentration is inherently limited, such as proteins. At the present time, two-dimensional spectra of proteins would probably require unrealistically high concentrations, unless further sensitivity enhancement schemes can be incorporated. Nevertheless, the enormous increase in speed of the single-scan technique naturally suggests some exciting new applications, particularly for time-dependent studies. It has recently been used for monitoring two-dimensional spectra from samples in continuous-flow schemes such as liquid chromatography (Shapira et al. 2004).

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