GB2101334A - NMR spectroscopy - Google Patents

Abstract

In a method of heteronuclear decoupling in high resolution pulsed NMR spectroscopy, during acquisition of signals emanating from a nuclear species to be observed (e.g. carbon- 13), irradiation of an interfering nuclear species (e.g. protons) is effected by means of a train of composite pulses (R1, R2, R1, R2, etc.) each of which approximately inverts the longitudinal magnetisation thereof. The pulses are of two types (R1, R2, etc. and R1, R2, etc.) differing only by having opposite r.f. phases and the train constitutes a repeated sequence which consists of 2<N> pulses of each type (where N is a positive integer) and which has a form chosen in accordance with specific rules to ensure effective decoupling. A preferred form for the composite pulses consists of three constituent pulses of appropriate durations and with negligible intervals between them, the first and third pulses having the same r.f. phase which differs by 90 DEG from that of the second pulse. <IMAGE>

Description

SPECIFICATION NMR spectroscopy This invention relates to methods of heteronuclear decoupling in high resolution pulsed nuclear magnetic resonance (NMR) spectroscopy.

A NMR spectrum is subject to splitting of the desired nuclear signals into multiplets as a result of coupling between the spins of the nuclear species to be observed and those of other nuclei present in the sample under observation. Such heteronuclear coupling is characteristic of the grouping of nuclei in a molecule and is independent of static external conditions. In particular, coupling is independent of the strength of the static magnetic field used in the NMR technique, and the effect for a specific pair of nuclear species can be represented by a constant J. In simple cases the constant J defines the spacing between any two adjacent lines of the resultant multiplet and is therefore measured in units of frequency.

It is particularly important for a nuclear species of low natural abundance such as 13C to obtain the maximum sensitivity and resolution of each chemically shifted line and clearly the creation of broad multiplets as a result of coupling reduces the line signal and makes the line position uncertain. The prevention or reduction of this interaction is known as decoupling and involves the application, during the acquisition from a sample of signals resulting from resonance of the nuclear species to be observed, of a perturbing field having a frequency in the region of resonance of the interfering nuclei. Commonly these nuclei are protons. In order to cover the range of proton resonance frequencies which are present in any specific chemical system it is usual to apply modulation in some form and a number of schemes have been proposed.The effect of the perturbing field may be regarded as the production of rapid transitions between the spin levels of the proton. The lifetime of each spin state is then short compared with the time 1/J and ideally not net coupling effect is observed. It should be noted that this condition is much more stringent than that required for saturation of the spin system, in which transitions need only be induced at a rate which is fast compared with the inverse of the relaxation times.

In practice no general and valid theory of wideband decoupling has been available and the idealised conditions have been only partially satisfied. For example it is believed that in a pulse modulation scheme designed to cover the target proton frequency range, an implicit dependence on proportionality between the degree of decoupling at a particular frequency and the value of the Fourier component at that frequency cannot be justified. Consequently conventional procedures which result in a considerable degree of decoupling can leave uncompensated residual interactions sufficient to broaden the 13C lines significantly and so reduce resolution and sensitivity.

It is an object of the invention to provide a procedure in which such residual interactions are substantially reduced.

According to the invention there is provided a method of heteronuclear decoupling in high resolution pulsed NMR spectroscopy in which, during the acquisition from a sample of signals resulting from resonance of a nuclear species to be observed, the sample is irradiated with radio frequency energy substantially at the resonant frequency of an interfering nuclear species, the irradiation being in the form of a train of composite pulses each of which is effective to cause at least approximate inversion of the longitudinal magnetisation in respect of the interfering nuclear species, the composite pulses being of two types which differ only by virtue of the r.f. phase for one type being opposite that for the other type and the train being in the form of a repeated sequence which consists of 2N pulses of each type, where N is a positive integer, said sequence being derivable from a basic sequence consisting of two of said composite pulses by a logical expansion process consisting of at least one step of deriving a higher order sequence from a lower order sequence so that said higer order sequence is a cyclic permutation of a composite sequence which consists of M different subsequences, where M is an even number not greater than four, each of said sub-sequences being related to said lower order sequence by a relationship selected from (a) at the cyclic permutation of an even number of pulses, (b) the cyclic permutation of an odd number of pulses, (c) the cyclic permutation of an even number of pulses combined with the interchange of the two types of pulse, and (d) the cyclic permutation of an odd number of pulses combined with the interchange of the two types of pulse, with the selection being subject to the conditions that: (A) if M is four then the four types of relationship (a), (b), (c) and (d) respectively apply to the four sub-sequences constituting said composite sequence, and (B) if M is two then the four types of relationship (a), (b), (c) and (d) respectively apply to the four sub-sequences constituting a notional sequence composed of said composite sequence and a composite sequence of a similar kind which is related to said composite sequence by the cyclic permutation of an even number of pulses.

If desired, the train of composite pulses may also be applied during the period immediately prior to the excitation of resonance of the nuclear species to be observed, in order to establish a wide-band Overhauser enhancement.

The term 'composite pulse' is used herein in the same sense as in the paper by Freeman et al published in J. Magn. Reson., Vol. 38, page 453 (1908), and refers to a pulse sequence (which may include at least one period of free precession between individual pulses) whose constituent pulses are associated in the sense that the state of the relevant nuclear spins is of interest only when the sequence has been completed. It should be noted that the reference to a train of such pulses is not intended to imply that there is necessarily an interval between successive composite pulses; indeed for the purpose of methods according to the invention it will normally be desirable for there to be no significant delay between successive composite pulses of the train.The term 'longitudinal' refers to the direction of the static magnetic field used in the NMR technique, about which the unperturbed spins of the interfering nuclear species precess.

One form of composite pulse suitable for use in a method according to the invention consists of three constituent pulses with negligible intervals between them, the first and third pulses having the same r.f. phase and each being of nominal duration 7r/2yB2, and the second pulse having a r.f. phase which differs by 900 from that of the first and third pulses and having a nominal duration between n/YB2 and 37r/2yB2, where B2 is the magnetic flux density associated with the r.f.

irradiation and y is the gyromagnetic ratio for the interfering nuclear species; in conventional notation this form of composite pulse may be denoted by 90 (X)a(Y)90 (X), where a has a value between 1800 and 2700 and X and Y refer to orthogonal directions perpendicular to the direction of the static magnetic field (in a reference frame rotating about the last-mentioned direction). This form of composite pulse is effective to achieve population inversion of the interfering nuclear spins in a manner which is relatively insensitive to resonance frequency offsets as compared with the use of a simple 1 800 pulse.The length of the second pulse (given by the angle a) may be chosen according to the desired bandwidth of inversion relative to the irradiating field strength, which is conveniently expressed in units of frequency in accordance with the quantity yB|27r. Thus where a has a value of 1 800 the relative effective bandwidth is about 2(yB2/27r), whereas it is only about half of this where a has a value of 2400; over this narrower offset range, however, the inversion is more accurate than in the case where a has the lower value.

An alternative form of composite pulse which may be used consists of two constituent pulses having the same r.f. phase and each of nominal duration 37r/2yB2), separated by an interim period of duration approximately 2/yB2 during which free precession may occur.

As noted above, in methods according to the invention use is made of two types of composite pulse which differ only by virtue of the r.f. phase for one type being opposite that for the other type. Conveniently the two types of composite pulse may be denoted respectively by R and R; for example if R has the form 900(X)a(Y)900(X) then R will have the form 9001-X)a(-Y)900(-X). In order to achieve the desired decoupling effect, the composite pulses are arranged so as to constitute a repeated sequence in which the two types of pulse occur in equal numbers and which has a form chosen in accordance with specific rules.

These rules are discussed more fully below, but it may be noted here that satisfactory decoupling performance would not be obtained with a repeated sequence of the simplest possible forms that can be envisaged incorporating both both types of pulse, denotable by RR and RR. To achieve such a performance the repeated sequence must incorporate at least two pulses of each type, so that the simplest forms of sequence which may be used in a method according to the invention are those denoted BBWB, RRRR, RRRR, and RRRR; these four sequences are equivalent in effect, as will readily be appreciated when it is noted that the four types of train respectively formed by repeating them differ only at the beginning and end of the train.To put the matter in another way, the four sequences are related to each other by the operation of cyclic permutation, which may in the present case be defined as the transfer of at least one pulse from the end to the beginning of a sequence, with the order of the transferred pulses preserved in cases where the transfer involves more than one pulse; it is to be understood that in the most general cyclic permutation includes the case where the number of transferred pulses is equal to the number of pulses in the sequence, in which case the permuted sequence is the same as the unpermuted sequence.It may also be noted that the sequences RRRR and RRRR are related to each other by the operation of interchanging the two types of pulse R and R (which is equivalent to inversion of the r.f. phase for the whole sequence), and likewise for the sequence RRRR and RRRR; it will be evident that two sequences related to each other in this way are equivalent in effect, since the allocation of the symbols R and R between the two types of pulse is arbitrary. As will be explained below, although satisfactory decoupling can be obtained by using one of the four-pulse sequences just mentioned, improved results can be achieved by using instead a more complex sequence which is appropriately related to one of those sequences.

The theoretical basis for the choise of appropriate sequences is highly complex, and will therefore be presented here only in outline. The underlying consideration is that the relevant effects of the sequences of composite pulses can be expressed in terms of average Hamiltonian theory -- see the paper by Haeberlen and Waugh published in Phys. Rev., Vol, 175, page 453 (1 968). As to this it suffices here to note that in considering the interaction between the respective spins of the nuclear species to be observed and the interfering nuclear species, in the presence of a periodic perturbation of the latter spins with a sufficiently rapid repetition rate one can replace the true interaction Hamiltonian by an average Hamiltonian (denoted H); H is composed of an infinite series of terms which progressively decrease in importance if the repetition rate is rapid enough.When the periodic perturbation corresponds to a sequence of composite pulses, it is found that these terms are easily calculated only if it is assumed that the composite pulses achieve exact inversion of the interfering spins. in practice this is not the case, since no composite pulse will operate perfectly over a wide range of resonance frequency offsets.

This consideration is particularly significant in cases where the composite pulse R has a nominal form 900(X)1 800(Y)900(X); as indicated above, although the effective bandwidth is large for this type of pulse, inversion is by no means exact over the full range.

It is therefore appropriate to consider the possibility of improving decoupling by using sequences which will compensate for imperfections in the effects of the individual composite pulses. For this purpose it is convenient to assume that the imperfection in the inversion is quantified by a small parameter a and to expand each of the terms in the average Hamiltonian as a power series in 8; there series will also rapidly converge if 8 is small. In this way one can express the average Hamiltonian H as a sort of matrix, as follows:- H=H,(60) +H0(8 1) +H0(82) + +H(80)+H(ar)+H(82X+ +H2(80) +H2(81)+H2(82)+ + + + Under suitable conditions this will converge towards the right and the bottom.In order to improve the decoupling performance the aim is to make as many terms as possible of this matrix disappear.

The use of two-pulse sequences such as RB or RR does not in general result in cancellation of any terms of this matrix, so that satisfactory decoupling performance cannot be achieved by the use of such sequences. The key feature of the theoretical considerations is thus the development of a set of rules which enable one to construct sequences that can be expected to be more effective than such two-pulse sequences in respect of the decoupling performance. In order to present these rules in a general form it is appropriate firstly to set out some definitions. We denote by C any sequence which consists of an even number (2K) of composite pulses, each pulse being either of type R or type R.Then P denotes the set of K sequences which are related to C by the cyclic permutation of an odd number of pulses, and Q denotes the set of K sequences which are related to C by the cyclic permutation of an even number of pulses (including the case where this even number is 2K). P denotes the set of K sequences which are derived from P by the interchange of the two types of pulse, and Q denotes the set of K sequences which are derived from Q in the same way. It will be appreciated that all the members of these four sets are sequences each consisting of 2K composite pulses.As an illustration, ifC is RRRR, then P consists of RRRR and RRRR 0 consists of RRRR and RRRR,P consists of RRRR or RRRR (and hence is identical to P), and Q consists of RRRR and RRRR (and hence is identical to Q).

It can be shown that, for any given form of C, all members of the sets, P,Q,P and Q are of equivalent effect to C when repeated to form trains of pulses. it is, however, possible to combine members of different ones of these sets in such a way as to produce an expanded sequence E which can be used in place of C to improve the decoupling performance. In order to achieve this improvement, it is necessary in the general case to combine (in any order) four sequences~espectively selected from the sets P,Q,P and Q. The resultant composite sequence E can be shown to have the following properties when considered in relation to the matrix expansion of H set out above: (a) Whatever the form of C, E will be such that at least the term H,(60) is zero.

(b) If C is such that in a particular row of the matrix the terms up to the (m)th are all zero, then E will be such that the same is true and at least the (m+ 1 )th term in that row will also be zero.

(c) If C is such that for each column of the matrix up to the (m)th the terms in that column up to the (n)th are all zero, then E will be such that the same is true and at least the (n+ 1 )th term in each of the relevant columns will also be zero.

The general condition indicated above requires that in order to obtain an improvement in performance over that obtainable with a given sequence C the expanded sequence E must consist of a total of 8K composite pulses. In many cases, however, a degree of improvement can be obtained with an expanded sequence E consisting of only 4K composite pulses. This possibility arises because in such cases two parts of the general fourfold expansion are redundant. Two simple cases in which this applies are as follows: (a) If member of 0 are the same as members of Q or P, then an expansion of the form QP or PO is sufficient to achieve one stage of improvement over C.

(b) If members of Q are the same as members of P or P, then an expansion of the form OQ or QQ is sufficient to achieve one stage of improvement over C.

More general conditions for redundancy may be stated as follows:- (1) If there is a representative of either QP or PO which is related to a representative of either QP or PO by the cyclic permutation of an even number of pulses, then an expansion of the form OP and PO is sufficient.

(2) If there is a representative of either OP orPO which is related to a representative of either QP or PO by the cyclic permutation of an even number of pulses, then an expansion of the form QP orPO is sufficient.

(3) If there is a representative of either OO or QQ which is related to a representative of either PP or PP by the cyclic permutation of an even number of pulses, then an expansion of the form QQ or QQ is sufficient.

It will be seen that in all these cases a suitable expanded sequence E will consist of two subsequences respectively selected from two of the four sets P, Q, P and Q, and will be related by the cyclic permutation of an even number of pulses to a sequence of a similar kind for which the two sub-sequences are respectively selected from the other two of the four sets.

It will be appreciated that any particular expanded sequence E derived by means of the foregoing rules can be replaced with equivalent effect by a sequence related to E by cyclic permutation and/or interchange of the two types of composite pulse. It will further be appreciated that any particular expanded sequence E can itself be treated as the starting sequence C for a further step of expansion in accordance with the foregoing rules; in theory, the expansion process can be continued indefinitely, with successive improvements in performance associated with the respective stages of expansion.

The rules discussed above are of a general character, so that in theory one can take as the starting point for such an expansion process any sequence consisting of an even number of composite pulses. In practice, however, it is desirable to use sequences which are as short as possible for a given degree of improvement in decoupling performance. Accordingly it is appropriate to focus further attention solely on cases where the starting point for the expansion process is a basic sequence consisting of only two composite pulses.Suppose one starts with C in the form RR. In this case P and 0 are both RR and P and 0 are both; thus an expansion of the form QQ (i.e. RRRR) is sufficient to ensure that the term H0(# ) will vanish. The sequences RRRR RRRR and RRRR will of course be equally effective, having regard to the consideration relating to cyclic permutation and/or interchange of the two types of pulse.Exactly the same conclusions can be reached about the four useful four-pulse sequences by starting with C in one of the forms RR, RR and RR; in the first of these cases, for example, P and Q are both RR and Q and P are both so that an expansion of the form OP (i.e. RRRR) can be seen to be sufficient, and so on.

To illustrate how the expansion process can be continued, consider the case where C is RRRR. In this case Q=Q, so that an expansion of the form QP is sufficient to achieve a degree of improvement over C in decoupling performance.

The expanded sequence E may then take the form RRRRRRRR; with this form both the term H0(#1) and H1(#0), in addition to the term H0(#0), will be zero. (In setting out the form of the sequence E in the preceding sentence a gap has been left between successive four-pulse sub-sequences; it is emphasised that this convention in the notation is used throughout the description solely for ease of comprehension, and is not intended to imply that in practice there would be any significant intervals between the sub-sequences).For the next step of the expansion process, if one takes C to be of the form RRRRRRRR then neither of the simple redundancy conditions (a) and (b) is satisfied and one must have regard to the more general conditions (1) to (3).

Considering condition (3) in particular, a representative of QQ is RRRR RRRR,%RRRRRR and a representative of PP is RRRR RRRR RRRR RRRR. These two are related by the cyclic permutation of four pulses. so that an expansion of the form QQ is sufficient. Accordingly for the 1 6-pulse sequence RRRR RRRR RRRR RRRR the terms Ho(82), H,(S') and 7-i2(a ) will additionally be zero. The same is of course true of cyclic permutations of this sequence, such as RRRR RRRR RRRR RRRR. It will be noted, however, that the last mentioned sequence cannot be regarded, as can the 1 6-pulse sequence from which it is derived, as simply made up of the four useful fourpulse sequences.The expansion process can of course be carried on from the 1 6-pulse stage, leading for example to 64-pulse sequences such as RRRR RRRR RRRRRRRRRRRRRRRRRRRRR RRRR RRRR RRRR RRRR RRRR BRWBBRRRWBRR RRRR for which H1(8k) will be zero for all values of (j+k) not greater tahn four.

In the illustrative exposition set out in the preceding paragraph, each step in the expansion process leading to the 64-pulse sequence involves a doubling of the length of the relevant sequence, since account is taken in each case of one of the redundancy conditions. It may be noted, however, that one could also regard the 1 6-pulse sequence RRRR RRRR RRRR RRRR as a fourfold expansion (of the form QPQP) of the sequence RRRR, and likewise for the quoted 64pulse in relation to that 1 6-pulse sequence.

Although the expansion process could in theory be extended indefinitely to sequences of even higher orders, other factors (which are not taken into account in the foregoing discussion but are considered further below) are likely to restrict the practical utility of very long sequences, and it is thought that few cases will arise in practice in which it would be advantageous to use sequences of more than 64-pulses.

In the foregoing discussion reference is made to the repetition rate of the periodic perturbation of the interfering spins. In respect of the fourpulse sequences such as RRRR the theory is based on the assumption than 27rJT 1, where T is the total duration of the sequence and J is the spin coupling constant (expressed in frequency units). A similar consideration applies in respect of expanded sequences derived from such a fourpulse sequence with T being the duration of the four-pulse sequence from which the expanded sequence is derived (and not the total duration of the expanded sequence itself).

The invention will be further discussed, and examples of how it may be performed will be described, with refernece to the accompanying drawings, in which: Figure 1 is a diagrammatic representation of a spectrometer which may be used in practising the invention; Figure 2 represents diagrammatically a decoupling and acquisition pulse sequence for the spectrometer of Figure 1; Figure 3 represents diagrammatically the composite structure of the decoupling pulses of Figure 2; Figure 4 indicates the dependence of the effective decoupling field on resonance offset; Figure 5 represents in a rotating frame a longitudinal inversion trajectory produced by a single 1 800 pulse; Figures 6 and 7 represent in a rotating frame the longitudinal inversion trajectories produced by alternative forms of composite pulse;; Figures 8 and 9 are diagrams.illustrating comparisons between results obtained by means of methods according to the invention and known methods of heteronuclear decoupling; Figure 10 is a diagram illustrating results obtained by means of a method according to the invention; and Figure 11 is a diagram illustrating results in a comparable experiment using a known method of heteronuclear decoupling.

In the following description it is assumed for the sake of definiteness that the nuclear species to be observed is carbon-13, with protons constituting the interfering nuclear species.

Referring to Figure 1, a sample (not shown) containing these species is placed in a region of substantially uniform magnetic field B0 which is produced between a pair of pole pieces 1 0. A pair of coils 12 arranged on an axis perpendicular to the direction of field B0 receives r.f. pulses from a transmitter 14 to produce the required field B, for excitation of 13C resonance. The transmitter 14 contains gating and delay elements for the control of duration and relative phase of the r.f. pulses.

The coils 12 also serve to pick up the free induction decay signals from the sample, these signals being fed to a receiver 1 6 in which they are coherently detected, the detected signals being sampled to provide data from which the 13C spectrum can be derived by conventional Fourier transformation. A further coil 18, which is shown for convenience as having an axis perpendicular to both B0 and Br, is used to produce a portion decoupling field B2. The coil 18 is energised by a transmitter 2G having similar control facilities to those of the transmitter 14.For a field B0 of about 2.1 tesla the proton decoupling transmitter frequency occupies a band near 90 MHz while the 13C excitation frequency of the transmitter 14 is near 23 MHz, while for a field 8o of about 4.7 tesla the corresponding figures are respectively 200 and 50 MHz. The required decoupling bandwidth depends on the chemical shifts which are present in the sample material and on the strength of field B,, but typically a bandwidth of several kHz will be appropriate when 8o has one of the values quoted above.

The transmitter 20 generates a continuous wave signal whose phase is changed at intervals (between levels of relative phase 0., 900, 1 800 and 2700) in a repetitive pattern such that the output of the transmitter 20 constitutes a train of composite pulses with negligible intervals between them.The composite pulses are of two types R and R, respectively having the nominal forms 900(X)a(Y)900(X) and 900(-X)a(-Y)900(-X) with a equal to either 1800 or 2400, and the repetitive pattern of phase changes is chosen so as to correspond to one of the expanded sequences discussed above, for example the four-pulse sequence RRWR or the 1 6pulse sequence RRRR RRRR RRRR RRRR. It will be appreciated that the actuai duration of each composite pulse (and hence the repetition period for a sequence with a given number of such pulses) will vary inversely in accordance with the value chosen for the strength of the decoupling field B2.For instance, where this value corresponds to about eight kHz when expressed in units of frequency the duration of a composite pulse of the form 900(X)1800(Y)900(X) will be about 0.125 millisecond, so that the repetition period for a 16-pulse sequence will be about two milliseconds. In some cases, however, it may be desired to use low decoupling powers, corresponding say to a value for the field strength as low as one kHz; for this value, the corresponding figures would be about one millisecond for the duration of the composite pulse and 1 6 milliseconds for the repetition period of the 1 6-pulse sequence. In such cases one is particularly likely to wish to use a value of 1 800 rather than 2400 for the angle a, in order to obtain the benefit of the greater effective bandwidth for the decoupling. By way of comparison it may be noted here that, in order to obtain a complete 13C spectrum, it will normally be necessary for the intervals at which the free induction decay signals are sampled to be no greater than about 0.1 millisecond when the field Bo has a value of 4.7 tesla.

The transmitter 20 is of course switched on throughout the period during which data are being acquired from the signals resulting from the 13C resonance excited by a pulse from the transmitter 14. As a further contribution to sensitivity, the transmitter 20 may also be switched on during the period immediately prior to this pulse to provide nuclear Overhauser enhancement.

Figure 2 illustrates the arrangement in a case where the sequence used is RRRR and the transmitter 14 is switched on to apply 900 13C.

acquisition pulse (as indicated on the lower axis 24) at the same time as the transmitter 20 is switched on to initiate the train of composite pulses (as indicated on the upper axis 22). For the purposes of illustration only, the two types of composite pulse R and R are respectively shown above and below the axis 22, with the pulses of each type serially numbered; the initial sequence constituted by the pulses R1, R2, R1 and R2 is of course identical with the sequence constituted by the pulses R3, R4, R3 and R4, and so on. The free induction decay signals are indicated by the oscillatory line following the 900 13C pulse.

The structure and production of the train of composite pulses shown in Figure 2 is illustrated in Figure 3 for the case of a=2400 with reference to the repetitive pattern of phase changes of the continuous wave signal generated by the transmitter 20, the phase angles of 900 and 2400 of course referring to the constituent pulses which make up the composite pulses.

Before presenting results which have been obtained with the arrangement just discussed, it is appropriate to consider in more detail the constitution of the composite pulses in relation to the requirement for inversion of the proton magnetisation axis, particularly having regard to the inherent defects of using a nominally 1 800 pulse in any practical system. Exact inversion by means of a single 1 800 pulse becomes impossible for a proton at a particular site when the decoupling frequency is significantly offset from resonance.Such resonance offset, which is a most important problem in decoupling, is equivalent to introducing an additional component of field along the Z axis (i.e. parallel to field B,). The relevant effective field then becomes appreciably stronger than B2 and is directed at an angle to the transverse (XY) plane.

The effect of resonance offset is indicated in Figure 4 which shows the XZ plane of a three axis reference frame, considered to be rotating about the Z axis in synchronism with the frequency of the decoupling transmitter. The B2 field vector is represented along the X axis and the extent of resonance offset is represented by a component of field AB in the +Z direction. The effective field Beff, equal to (AB2+B22) 1/2, is tilted by the angle O with respect to the X axis, where 0=tan B/B2).

Clearly a similar tilt would be observed with respect to the Y axis of the phase of field B2 were shifted through 900. The consequence is that during a B2 pulse the proton magnetisation vector rotates about the axis of B eff instead of about the axis X (or Y). Referring now to Figure 5, field Beff is represented as inclined on an axis 28 at the angle o to the X axis. It is apparent that a path 30 representing the trajectory of a vector rotated about axis 28 by a single 1 800(X) pulse (which in the absence of defects would produce perfect inversion) will deviate progressively further from an initially followed line of longitude and from the --Z pole.

The possibility of inversion error correction by means of a composite pulse of the form 90 (X)cz(Y)90 (X) can be visualised with reference to Figure 6 in which a path 32 corresponds to the first part of path 30, reproduced from Figure 5. If a 900(X) pulse is applied by calculation from B2, the rotation of the vector in the field Beff must be greater than 900, since rotation varied inversely with the field value.

Path 32 may therefore be expected to terminate at a point below the XY plane. However, because rotation occurs about the tilted Beff axis 28 the distance over the upper hemisphere is increased and path 32 is consequently found to terminate at a point 34 which is close to the XY plane. For purpose of illustration, point 34 is shown as being slightiy above the XY plane. It is apparent that a further point 36 can be identified, symmetrically disposed with point 34 about the Y axis, from which a second 900(X) pulse identical to the first pulse will continue to rotate the vector about axis 28 to the --Z pole. A further pulse is now required to produce a transition between points 34, 36 by rotation of the vector with respect to the Y axis.

Such a pulse must therefore be phase-shifted by 90O relative to the two 900 pulses. In the presence of offset, rotation in fact occurs about a tilted axis 38 in the ZY plane. If axis 38 intercepts the notional sphericai surface of the system at a point 40 and if the offset is considered to be small, then for unit radius the distances from the Y axis to the points 34, 36 and 40 are all equal to 0. For a substantially planar element of the spherical surface the angle subtended at point 40 by points 34, 36 is thus 900. As a first estimate therefore a pulse of 2700(Y) is required to produce the desired transition from point 34 to point 36, as indicated by an arc 42.

The estimate is oversimplified partiy because, for practical values of resonance offset, a planar geometrical representation is no longer adequate and partly because of the increase in the true angle of rotation over the nominal rotation value of the pulse, under the influence of the enhanced field B eff Computer simulation has been used to make a more refined estimate and indicates that a pulse of nominal angle 2400(Y) is preferable. As indicated above, the use of this angle gives rise to good inversion over a reasonable range of values of resonance offset, but for the reason already mentioned it may be preferred in some cases to make the nominal angle of the central constituent pulse of the composite pulse as small as 1800(Y).

The initial and final constituent pulses of the composite pulse have been considered only to be of similar nominal angle 900(X) and in general it will be convenient to maintain symmetry. It is evident, however, that small variations from 900(X) could be accommodated by a variation in the rotation angle of the central pulse and it is probable that markedly asymmetric sequences can be found which will be satisfactory.

The condition required for the operation of the invention is therefore only that the elements of the composite pulse have the combined result that inversion is sufficiently complete for effective decoupling.

It has also been found that an alternative form of composite pulse is effective in which two symmetrical pulses are separated by a period of free precession. The trajectory is indicated in Figure 7. Starting as before from the +Z pole a 2700(X) pulse produces a rotation indicated by a path 48, initially following path 30 (Figure 5) and continuing round the rear surface of the lower hemisphere. Path 48 terminates at a point 50 near to the XY plane and is displaced by 6 from the -Y axis. A second rotation in a corresponding trajectory 52 which is required to terminate close to the -Z pole must start from the region of a point 54, which is located symmetrically with point 50 about the -Y axis.It is not generally appreciated that following a 2700(X) pulse in the presence of an inclined field B a self-corrective precession of the magnetisation will occur from the displaced position 50 towards the -Y axis. A time delay between the pulses can therefore be determined which allows precession to continue until the transition is completed from point 50 to point 54. It can be shown that the delay must be set equal to 2/yB2 to allow precession through an angle of approximately 26 radians, where 6 has the value shown in Figure 4.Provided that 6 is not too large the 26 relationship remains true whatever the valye of the offset AB. This alternative composite pulse is more sensitive than the three-pulse composite to the correct setting of the pulse parameters but has the advantage that r.f. phase shifting of the B2 pulse by 900 is not required so that the spectrometer need not have this facility; a 1800 phase modulation facility is, however, still needed, since the alternative form of composite pulse would of course be used in sequences of the kind referred to in the description of the spectrometer illustrated in Figure 1.Although showing an improvement over conventional noise decoupling, the use of the relevant sequences with the alternative form of composite pulse provides less effective decoupling than is the case when the composite pulse has the form 900(X)a(Y)900(X); in the following description, therefore, attention will be confined to the latter case.

Comparative tests have been made between decoupling using a method according to the invention and conventional noise decoupling of two kHz bandwidth (the best choise of the available bandwidths for the instrument concerned) in determining the sensitivity to resonance offset of the 13C spectrum of methyl iodide. Spectra are shown in Figure 8 for an experiment in which the frequency of the B2 signal is displaced in successive steps of 0.5 kHz through a range of eight kHz. The on-resonance condition is at approximately five kHz.The set of curves 54 is obtained by noise decoupling and the set 56 by means of a method as described above with reference to Figures 1 to 3 (i.e. using the sequence RRRR with the angle a equal to 2400), with the field B0 having a value of 2.1 tesla and the strength of the decoupling field B2 corresponding to 6.3 kHz. Normalised peak heights have been calculated which confirm the visuai impression of curves 54, 56 that, while the peaks are similar at five hKz, the peaks of curves 54 fall away quite sharply above and below five kHz but the peaks of curves 56 are displayed at substantially uniform sensitivity over a much wider band.

A further comparative demonstration of the sensitivity obtained is shown in the spectra of ethyl benzene in Figure 9. Spectrum 58, obtained with conventional noise decoupling, shows considerable narrowing of the broad line groupings which would appear in the presence of coupling. Spectrum 60 shows the same groups decoupled by means of a method similar to that used to obtain the set of curves 56 in Figure 8. In this case, however, the strength of the decoupling field B2 corresponded to 3.1 kHz. An improvement in resolution is apparent, but is not readily quantified on the scale of the drawing. An approximate doubling in sensitivity is, however, very clearly indicated by the vertical scales in arbitrary units, with some variation in the improvement dependent on the line group structure.

Figure 10 illustrates results which have been obtained using the arrangement described with reference to Figure 1, the sample material being dimethyl carbonate with the field B0 having a value of 4.7 tesla, the strength of the decoupling field B2 corresponding to 8.3 kHz, the angle a for the composite pulses being 2400, and the pulse sequence having the form RRRR RRRR RRRR RBRB. Figure 11 illustrates results obtained using a similar arrangement, but replacing the decoupling method of the present invention by a known method employing square-wave phase modulation, as disclosed in the paper by Grutzner and Santini published in J. Magn, Reson., Vol. 19, page 173 (1975).In both cases the observed carbon-1 3 signals are plotted as a function of proton resonance offset, the spectral width displayed being 40 Hz. It will be seen that the broad band decoupling performance is much superior in the case of Figure 10, for which the peak heights remain within five percent of that observed for coherent on-resonance decoupling over a range of more than + five kHz.

It is appropriate finally to consider certain factors which may have a bearing on the choice for particular cases of the length of the sequence (in terms of the number of composite pulses in the sequence). Where it is possible to use a relatively high decoupling power, it will normally be possible to obtain the required effective bandwidth for decoupling when using composite pulses with a equal to 2400, and this value will then normally be preferred to 1 800 since it gives more perfect inversion for each composite pulse over the relevant frequency range. In such cases, although the use of the 1 6-pulse sequence offers a considerable improvement in performance over the use of a four-pulse sequence, the theoretical improvement that could be achieved by going to even longer sequences is much less significant.

The main sphere of application of such very long sequences is thus more likely to arise in cases where one wishes to use composite pulses with a equal to 1 800, particularly with a view to obtaining an appropriate effective bandwidth while using a low decoupling power.

The theoretical advantages of using very long sequences must, however, be balanced against certain practical considerations, which are likely to be particularly cogent where a low decoupling power is used. The theoretical treatment of the effect of the relevant sequences of composite pulses shows that at the end of a sequence the state of the interfering nuclear spins is as if the coupling between them and the nuclear spins to be observed were much reduced, and the greater the length of the sequence the closer this reduced interaction approaches zero. In practice, however, it is desirable that decoupling should be as good as possible within the duration of the sequence.

One reason for this is the requirement noted above for sampling the free induction decay signals at a rate which is appreciably greater than the sequence repetition rate even when using the shorter sequences and relatively high decoupling powers. This necessitates the acquisition of data at instants within, and not merely at the end of, each sequence, which results in the generation of artefacts in the spectrum; the intensity of these will be weak if the decoupling is good throughout.

A further reason is that a number of irreversible processes can interfere with the compensation effected by the sequence, examples being spin relaxation and molecular diffusion; the main relaxation process involved will probably be proton transverse relaxation, which in typical samples has a time constant in the range of about 0.1-1 second. Such irreversible processes have the effect of increasing the width of the decoupled spectral line at the expense of its height.

Both the consideration relating to sampling and that relating to irreversible processes become more significant the greater is the actual duration of the sequence, which of course means that for a given number of pulses in the sequence they become more serious the lower is the decoupling power. Moreover, the second consideration becomes particularly significant for sequences consisting of more than 1 6 composite pulses.

This arises because, in following the rules for constructing the expanded sequences, while one can construct a 16-pulse sequence entirely from four-pulse sub-sequences which in themselves have good decoupling performance, the same is not true for 32-pulse or higher order sequences.

Taking these factors into account, one can conclude that in general the use of an appropriate 16-pulse sequence should always give better results than are obtainable when using four-pulse or eight-pulse sequences, but that the use of longer sequences may not in all cases result in improvement in the overall performance.

This may be illustrated by reference to experimental observations carried out on one particular sample using composite pulses with a equal to 1 800. With a strength of the decoupling field B2 corresponding to eight kHz, it was found that a dramatic improvement in decoupling performance was obtained by using a 16-pulse sequence in place of a four-pulse sequence, and that the use of sequences consisting of 32, 64, 128 and 256 pulses offered further small improvements. At a field strength corresponding to 1.5 kHz, however, the 64-pulse sequence was wound to give a performance marginally better than that obtained with 16-pulse or 256-pulse sequences, while at a field strength corresponding to one kHz, however, the best overall decoupling performance was achieved when using a 16pulse sequence.

Claims (9)

Claims

1. A method of heteronuclear decoupling in high resolution pulsed NMR spectroscopy in which, during the acquisition from a sample of signals resulting from resonance of a nuclear species to be observed, the sample is irradiated with radio frequency energy substantially at the resonant frequency of an interfering nuclear species, the irradiation being in the form of a train of composite pulses each of which is effective to cause at least approximate inversion of the longitudinal magnetisation in respect of the interfering nuclear species, the composite pulses being of two types which differ only by virtue of the r.f. phase for one type being opposite that for the other type and the train being in the form of a repeated sequence which consists of 2N pulses of each type, where N is a positive integer, said sequence being derivable from a basic sequence consisting of two of said composite pulses by a logical expansion process consisting of at least one step of deriving a higher order sequence from a lower order sequence so that said higher order sequence is a cyclic permutation of a composite sequence which consists of M different subsequences, where M is an even number not greater than four, each of said sub-sequences being related to said lower order sequence by a relationship selected from (a) the cyclic permutation of an even number of pulses, (b) the cyclic permutation of an odd number of pulses, (c) the cyclic permutation of an even number of pulses combined with the interchange of the two types of pulse, and (d) the cyclic permutation of an odd number of pulses combined with the interchange of the two types of pulse, with the selection being subject to the conditions that: (A) if M is four then the four types of relationship (a), (b), (c) and (d) respectively apply to the four sub-sequences constituting said composite sequence, and (B) if M is two then the four types of relationship (a), (b), (c) and (d) respectively apply to the four sub-sequences constituting a notional sequence composed of said composite sequence and a composite sequence of a similar kind which is related to said composite sequence by the cyclic permutation of an even number of pulses.

2. A method according to Claim 1, in which said expansion process consists of not more than five steps for each of which M is two, whereby N is equal to the number of said steps.

3. A method according to Claim 2, in which N is one.

4. A method according to Claim 2, in which N is three.

5. A method according to Claim 4, in which said repeated sequence is constituted by four different successive sub-sequences each consisting of two pulses of each type and involving less than three changes of type between successive pulses.

6. A method according to any one of the preceding claims, in which each of said composite pulses consists of three constituent pulses with negligible intervals between them, the first and third constituent pulses having the same r.f.

phase and each being of nominal duration 7r/2yB2, and the second constituent pulse having a r.f.

phase which differs by 900 from that of the first and third constituent pulses and having a nominal duration between 7t/yB2 and 3/2yB2 where B2 is the magnetic flux density associated with the r.f.

irradiation and y is the gyromagnetic ratio for said interfering nuclear species.

7. A method according to Claim 6, in which the nominal duration of said second constituent pulse is 4or/3yB2.

8. A method according to any one of Claims 1 to 5, in which each of said composite pulses consists of two constituent pulses having the same r.f. phase and each of nominal duration 37r/2yB2, said constituent pulses being separated by an interim period of duration approximately 2/yB2, where B2 is the magnetic flux density associated with the r.f. irradiation and y is the gyromagnetic ratio for said interfering nuclear species.

9. A method of heteronuclear decoupling in high resolution pulsed NMR spectroscopy, substantially as hereinbefore described with reference to Figure 1 of the accompanying drawings.