Abstract:
Cycling sidebands arising from broadband decoupling of I-S heteronuclei are separated from the decoupled I spectra investigated in a 2D pulse sequence wherein I excitation  50  is followed after the interval δ+t 1  with refocusing π pulse  54  operating on the I spins. After I excitation  50,  the J IS  coupling is inverted by π pulse  52  and immediately following the π pulse  54,  decoupling  56  is turned on and maintained while signal acquisition in the interval t 2  is initiated at δ+t 1  after pulse  54.  Double FT yields a 2D spectrum with sidebands completely displaced to diagonal locii, or alternatively the time domain data may be accumulated into respective t 2  locations by effectively summing over t 1  to yield a single dimensional spectrum free of cycling sidebands.

Description:
This application claims the benefits of Prov. 60/250,792 filed Dec. 01, 2000. 
    
    
     FIELD OF THE INVENTION 
     The invention is in the field of magnetic resonance phenomena and particularly relates to reduction of complexity due to artifact in nuclear magnetic measurements. 
     BACKGROUND OF THE INVENTION 
     For all but the simplest of samples, NMR spectroscopy yields spectral distributions of considerable complexity. One aspect of this complexity arises from the interaction of nuclear spins among themselves, e.g., coupling of spins to yield a resultant angular momentum. Spin decoupling is the generic method of reducing this complexity of NMR spectra so that the chemical shift of one nuclear species may be observed without spectral effects due to another nuclear species. 
     A simple example of the decoupling problem and practice is to be found in the heteronuclear molecule. By convention, the (non-zero spin) nuclear constituents I and S are present and it is desired to study the spectral distribution of the I spins without the spectral complications arising from scalar coupling of the S spins to the I spins. Decoupling is achieved if, while observing the I spins, the S spins are repeatedly inverted. Ideally, if this exchange of S spin states is carried out rapidly in comparison with the I-S coupling, the spin-spin coupling will vanish. 
     In modem approaches to decoupling, the S spins are irradiated with modulated rf pulses in accord with any of several recognized techniques. One class of such pulses are realized as composite pulses, i.e. a sequence of phase shifts over appropriate durations to impose a desired corresponding sequence of rotations of the S spins. Adiabatic sweep pulses are another form of obtaining the desired inversion operation for decoupling the (S) spins. For this purpose, the effective field, B eff  is rotated through an angle θ with respect to the x axis over the range π/2≦θ≦−π/2 such that dθ/dt&lt;&lt;γB eff . These pulse decoupling operations are implemented over a separate RF channel, e.g., independent of the observe channel. This pulse decoupling is generically referenced herein as “decoupling radiation” and with careful design the operation may yield effective decoupling over a wide spectral range (broadband decoupling). It is emphasized that the present invention may be practiced with a wide variety of prescriptions for this decoupling radiation and the invention is not to be confused with a particular type of decoupling radiation. Broadband decoupling is generally described by R. Freeman, “Spin Choreography,” chpt. 7, Oxford Univ. Press, Oxford (1997). 
     Inasmuch as these broadband decoupling techniques comprise cyclic modulated sequences of pulses, artifact in the form of cyclic sidebands will appear in the decoupled spectrum (observe channel) of the instrument at the cycling rate and its harmonics. A number of approaches to suppression of these cycling sidebands have been employed in the prior art. The degree of suppression for these sidebands represents a limit to the examination of true, but weak signals. 
     One prior art method of sideband suppression applies adiabatic inversion to the (S) spins during the interval between excitation and refocusing of the I spins, and again after refocusing of the I spins through the acquisition of the I spectra. Sideband suppression is achieved coherently by incrementing the delay between decoupling and acquisition. Representative discussion may be found in the references: Ē. Kup{hacek over (c)}e, J. Magn. Reson. 129, 219 (1997); R. Freeman and Ē. Kup{hacek over (c)}e, NMR Biomed. 10, 372 (1997); Ē. Kup{hacek over (c)}e and R. Freeman, J. Magn. Reson. A 115, 273 (1995). 
     It is known in prior art to suppress decoupling sidebands by decoupling at two different power levels. A high power spin-lock is applied at the beginning of the decoupling sequence. The sidebands are suppressed coherently by increasing the spin-lock time in small increments. See Ē. Kup{hacek over (c)}e, R. Freeman, G. Wider, and K. Wuethrich, J. Magn. Reson. A 122, 81(1996). 
     It is known to apply decoupling radiation during acquisition of the signal asynchronously throughout the acquisition period. Dispersive components are also removed and spectral distortions are minimized. While a very simple approach, sideband suppression is ordinarily no more than a factor of two by this method. A similar prior art method permutes pulses of the composite pulse decoupling. Although a relatively high degree of sideband suppression is obtained, this is a one dimensional technique, limited to composite pulse decoupling, that randomizes the distribution of the sidebands rather than suppressing them coherently. A. J. Shaka, J. Keeler, and R. Freeman, J. Magn. Reson. 53, 313 (1983). Other methods employ a dispersion of sidebands over a restricted spectral region. A suppression factor of 5-10 may be achieved in favorable situations. See Z. Star{hacek over (c)}uk, Jr., K. Bartu{hacek over (s)}ek, and Z. Star{hacek over (c)}uk, J. Magn. Reson. A 107, 24 (1994); T.-L. Hwang, M. Garwood, A. Tannus, and P. C. M. vanZijl, J. Magn./Reson. A 121,221 (1996); R. W. Dykstra, J. Magn. Reson. 82, 347 (1989). 
     SUMMARY OF THE INVENTION 
     In the present invention, cycling sidebands arising from a periodic modulation technique in a decoupling channel of an RF apparatus are displaced from the main spectrum in a two dimensional technique. The suppression technique of the invention allows the magnetization from the cycling sidebands to evolve during the t 1  interval without any concomitant evolution of the magnetization from the parent peaks. This is achieved by a 180° pulse on the I spins that brings all chemical shifts to a focus at the end of the evolution period. Signal acquisition takes place during the interval t 2  under broadband decoupling conditions where both the parent and sideband signals evolve together. The elemental pulse sequence consists of  90φ-Δ-180 x-Δ-acquire in the observe channel with 180x applied to the S spins at Δ/2 and the desired decoupling radiation applied to S spins at the conclusion of the π x  pulse applied to the observed (I) spins and maintained throughout the acquisition interval t 2 . A conventional phase cycle φ=−x, +x, +y, −y performed with opposite receiver accumulation phases set. The quantity Δ=δ+t 1  represents the indirect dimension with the variation of t 1 . After double fourier transformation (t 2 , t 1 →F 2 , F 1 ) the cycling sidebands will be found displaced in the F 1  dimension symmetrically about the parent spectrum at F 1 =0. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is the context for the invention. 
         FIG. 2  shows a basic pulse sequence for practice of the invention. 
         FIG. 3  shows a 2D spectrum of  13 CH 3 I in  13 CH 3 P(O)(OCH 3 ) 2  in accord with the invention. 
         FIG. 4   a  is a spectrum of a sample using the invention. 
         FIG. 4   b  is a spectrum of the same sample as in  FIG. 4   a  using conventional GARP-1 decoupling. 
         FIG. 5   a  is a spectrum of the sample obtained using adiabatic decoupling according to prior art. 
         FIG. 5   b  is the same as  FIG. 5   a  using the present invention. 
         FIG. 5   c  is the spectral data of  FIG. 5   b  on a x100 ordinate scale. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The physical context of the invention is an NMR apparatus. An idealized illustration is shown in  FIG. 1. A  magnet  10  having bore  11  provides a main magnetic field along the axis of the bore. In order to control the magnetic field with precision in time and direction for selected measurements, there are provided magnetic field gradient coils (not shown). These are driven by gradient power supplies  16 ,  18  and  20 , respectively. Additionally, other shimming coils (not shown) and power supplies (not shown) may be required for compensating residual undesired spatial inhomogeneity in the basic magnetic field. An object for analysis (hereafter “sample”) is placed within the magnetic field in bore  11  and the sample is subject to irradiation by RF power, such that the RF magnetic field is aligned in a desired orthogonal relationship with the magnetic field in the interior of bore  11 . This is accomplished through one or more transmitter coil(s)  12  in the interior of bore  11 . Resonant signals are induced in a receiver coil, proximate the sample within bore  11 . The transmitter and receiver coils may be the identical structure, or separate structures. 
     As shown in  FIG. 1 , RF power is provided from first transmitter  24   a  through modulator  26   a , and is amplified by an amplifier  31   a  and then directed via transmit/receive (T/R) isolator  27  to the probe  12  that includes a first RF transmitter coil  12  located within the bore  11 . The transmitter  24   a  may be modulated in amplitude or frequency or phase or combinations thereof, either upon generation or by a modulator  26   a . The conceptual grouping of transmitter  24   a , modulator  24   a , amplifier  31   a , T/R isolator  27  and the receiver is conventionally called the “observe channel”. Additional transmitter  24   b /modulator  26   b /amplifier  31   b  components (“decoupler channel”) are often employed to independently manipulate different gyromagnetic resonators coupled to the species under investigation. These independent spin manipulations are conveniently supported by multiple coils or a multi-resonant coil. Transmit and receive functions are not concurrently active in the observe channel. The identical coil  12  within the probe may be employed for both excitation and acquisition if so desired. Thus, the T/R isolator  27  is provided to separate the receiver from the transmitter  24   a . In the case of separate transmitter and receiver coils, element  27  will perform a similar isolation function to control receiver operation. 
     The modulators  26   a, b  (or the equivalent) are responsive to controller  38  including pulse programmer  29  to provide RF pulses of desired frequency, amplitude, duration and phase relative to the RF carrier at pre-selected time intervals. The pulse programmer may have hardware and/or software attributes. The pulse programmer also controls the gradient power supplies  16 ,  18  and  20 , if such gradients are required. These gradient power supplies may impose gradient pulses or maintain selected static gradients in the respective gradient coils if so desired. 
     The transient nuclear resonance waveform is processed by receiver  28  and ordinarily resolved in phase quadrature through phase detector  30 . The phase resolved time domain signals from phase detector  30  are presented to Fourier transformer  32  for transformation to the frequency domain in accordance with specific requirements of the processing. Conversion of the analog resonance signal to digital form is commonly carried out on the phase resolved signals through analog to digital converter (ADC) structures which may be regarded as a component of phase detector  30  for convenience. 
     It is understood that Fourier transformer  32  may, in practice, act upon a stored (in storage unit of processor  34 ) representation of the phase resolved data. This reflects the common practice of averaging a number of time domain phase resolved waveforms to enhance the signal-to-noise ratio. The transformation function is then applied to the resultant averaged waveform. Display device  36  operates on the acquired data to present the distribution for inspection. 
     Controller  38 , most often comprising one or more digital processors, controls and correlates the time critical operations, such as the performance of pulse sequences in the observe channel and the decoupler channel. Controller  38  ordinarily incorporates an independent time base for maintaining synchrony with resonant spin systems. Overall operation of the entire apparatus within processor  34  includes input  37  from operating personnel, non-time critical calculation and output for further processing or display. 
     Turning now to  FIG. 2 , the pulse sequence of the invention is shown. Following the excitation pulse  50  on I-spins, evolution of the hetero-nuclear spin-spin coupling (J IS ) is refocused by the first π-pulse  52  on S-spins. At the point where the J IS  coupling is fully refocused a π-pulse  54  on I-spins is applied. Note that this pulse does not affect evolution of the J IS  coupling. The purpose of this pulse is simply to refocus the I-spin chemical shift evolution. Just after the π-pulse on I-spins, hetero-nuclear S-spin decoupling  56  is switched on. During the following t 1  period the J IS  coupling evolves in the presence of the decoupling field. The interval Δ=δ+t 1  is equal on either side of the 180° I pulse  54  with the constraint that the fixed delay δ is equal or greater than the width of the (preferably composite) 180° S pulse  52 . That is, the frequency-modulated components of magnetization (the cycling sidebands) evolve and accumulate phase shifts that eventually determine the initial phases of the signals detected during the acquisition period. In complete contrast, the magnetization from the parent signals is refocused by the 180° pulse and starts the acquisition interval with zero phase shift, just as in a conventional pulse-acquire experiment. Consequently, in the resulting two-dimensional spectrum, the cycling sideband frequencies appear in the F1 dimension while the parent peaks are all confined to the trace at F 1 =0. This essentially means that only evolution of decoupling sidebands is observed during the t 1  period. Once the chemical shift refocusing is accomplished the I-spin spectrum is acquired. Parent signals and decoupling sidebands both have evolved during t 2  with the consequence that the sidebands are dispersed along diagonals that pass through the corresponding chemical shift frequencies on the trace F1=0. Since the time-domain signals evolving during t 1  have no imaginary parts, the spectrum is symmetrical about the line F1=0, with the sidebands falling along two symmetrically related diagonals, reminiscent of those observed in “reflected” two-dimensional J spectra, as discussed for example in NMR Biomed. 10, 372 (1997) or J. Magn. Reson. A 115, 273 (1995). The inventive experiment is known by the acronym, as DESIRE—decoupling sideband-resolved spectroscopy. 
     The technique was tested using a partially decomposed mixture of  13 CH 3 J (δ H =1.95 ppm,  1 J CH =151 Hz),  13 CH 3 P(O)(OCH 3 ) 2  (δ H =3.5 and 1.25 ppm,  1 J CH  =129 Hz), which contained a fair number of impurities. The 2D spectrum of this mixture recorded using the pulse sequence of  FIG. 2  is shown in FIG.  3 . This data was obtained at 500 MHz, in this case using the well known GARP-1 decoupling of  13 C. The decoupled proton spectrum appears at F1=0 and the responses at 1.25 and 1.95 ppm are coupled to  13 C. The indirect dimension (t1) was realized in 128 increments, each of which was phase cycled over 4 scans. The inversion pulse applied to S was a composite pulse comprising 90° (x) 180° (y) 90° (x). The strongest sidebands, appearing on F1 at +/−210 Hz from the main  13 CHJ peak were phased by adjusting the value of the delay δ to 2.5 ms. The distribution along the top of the 2D spectrum is from the initial increment and shows the spectral complexity where sidebands are not suppressed. 
     The trace along the zero frequency in F1 represents a sideband free spectrum of the main resonances referred to as the main spectrum below. The peaks that appear at non-zero frequencies in F1 represent the decoupling sidebands. Their frequency in F1 corresponds to their relative distance from the parent peak in F2. Hence the decoupling sidebands show diagonal patterns that cross over at the position of the main peak. The cross peaks allow identification of any residual or partially suppressed sideband peaks that may appear in the main spectrum. 
     In  FIG. 4  the main spectrum (b) from a DESIRE experiment of 128 transients (using conventional synchronous GARP-1 decoupling) is compared with a conventional synchronous GARP-1 decoupled spectrum ( FIG. 4   a ). A dramatic reduction of sideband intensity has been achieved. Both spectra have been truncated at 2.5% of the most intense MeJ peak. 
     The degree of sideband suppression in the DESIRE experiment largely depends on a) the number of increments in t 1 , b) the length of the decoupling sequence, c) length of individual (composite) inversion pulse in the decoupling sequence and d) overall stability of the system (hardware). In order to minimize relaxation losses, the delays Δ and t 1  need be as short as possible. A high degree of sideband suppression can be achieved if the t 1  is set to an integer multiple of the duration of decoupling sequence, including the phase cycle or supercycle. The optimum number of increments (n i ) is determined as:
 
 n   i =2 kmN,   (1)
 
where m is a positive integer, usually m=1, k is the number of phase cycling steps in the decoupling sequence, and N is a positive integer, a power of two, that corresponds to the highest order harmonic that needs to be eliminated. The time increment in F1 is calculated as T d /(2N), where T d  is the length of a single (composite) inversion pulse in the decoupling sequence. It is known that sub-harmonic sidebands can only be eliminated if k is an even number. Hence the decoupling sequences employing some of the iterative phase cycling schemes where k is an odd integer may require doubling the number of increments (m=2) to achieve a complete elimination of sub-harmonic sidebands.
 
     Cycling sidebands that are closer to the parent line are more difficult to eliminate and require longer to evolution times. The inner sidebands are typically caused by a poor inversion profile of the basic 180° pulse in the given decoupling sequence, or because of inaccurate calibration of the radio frequency field. Adiabatic pulses have the advantage of being less sensitive to radio frequency calibration errors. It is essential that the effective bandwidth of the 180°(S) pulse be at least as wide as those in the following decoupling sequence. Alternatively, the same pulses that are used for the S-spin decoupling can also be employed for refocusing J IS , as described earlier: see J. Magn. Reson. 129, 219 (1997). This has the advantage of reducing some of the sidebands at the initial stage. 
     In addition to more conservative use of decoupling power, adiabatic decoupling has the advantage of producing cycling sidebands fewer than those of conventional decoupling schemes, giving a simpler DESIRE spectrum. The degree of sideband suppression achievable with adiabatic decoupling is shown in  FIGS. 5   a-c . A relatively long (T d =2 ms) WURST-40 waveform covering a 20-kHz bandwidth and phase cycled according to the MLEV-4 scheme was employed to produce an extensive pattern of sidebands. This made genuine peaks in the spectrum from minor components essentially impossible to recognize (see  FIG. 5   a ). Sidebands up to the fourth harmonic, N=4 were suppressed. A considerable improvement of sideband suppression was obtained by applying a sine-squared window function in the t 1  dimension. This required doubling the number of increments to n, =64 (m=2). In order to minimize the sub-harmonic sidebands, a 1-ms constant adiabaticity WURST-40 pulse was employed as the 180° pulse. A sideband-free spectrum obtained from the two-dimensional data set is shown in  FIG. 5   b . The vertical scale has been increased by a factor of 100. Only a few residual responses from the sidebands can be identified, the strongest of which is the eighth-order sideband marked by an asterisk (*). Its intensity is only 2.4×10 −5  of the main (CH 3 I) peak, demonstrating a remarkable suppression factor of 1000. 
     From the example 2D spectrum of  FIG. 3 , it is apparent that a simple addition of frequency domain spectra for each symmetrical F1 value of t 1  will cancel various sidebands, while differential information carried by the F1 dimension is available until such spectral addition is carried out. In a more elegant manner, the 2D DESIRE experiment can easily be reduced in an operational sense to a one dimensional decoupled spectrum by simply accumulating corresponding time domain data of the 2D experiment in respective memory locations. This is equivalent to carrying out a summation over t 1  for the t 2  distribution, e.g., Σ t1 {f(t 2 )}. Only one fourier transform is thus required at the conclusion of the 2D experiment. This would also simplify the task of sideband suppression in more complex multidimensional experiments. One application of DESIRE involves dilute species, requiring extensive time-averaging, so there need be no increase in total spectrometer time. 
     To conclude, the inventive technique allows an extremely high degree of sideband suppression in decoupling experiments and provides the means to identify any incompletely suppressed sidebands in the final spectrum. The new method should be useful for detection of minor components in spectra of high dynamic range. Apart from slight loss due to spin-spin relaxation during the short interval 2Δ, the sensitivity should be comparable with that of conventional one-dimensional spectroscopy, and in any case, for decoupled spectra, it is the residual cycling sidebands (rather than noise) that often limit the effective sensitivity. 
     Although this invention has been described with reference to particular embodiments and examples, other modifications and variations will occur to those skilled in the art in view of the above teachings. It should be understood that, within the scope of the appended claims, this invention may be practiced otherwise than as specifically described.