Method and apparatus for post-acquisition correction of NMR spectra

Abstract

An analytical and mathematical method is described for post-acquisition correction of NMR spectra distorted by static and dynamic field inhomogeneities caused by defects in the main superconducting coils and coldhead operation in a typical cryogen-free magnet. For dynamic inhomogeneities, the method and system apply a variant of a general reference deconvolution method complemented by specific mathematical analysis of spectral parameters. For static inhomogeneities, the system and method apply delayed Fourier processing. This system and method contributes to the general field of NMR spectroscopy and enables the more widespread use of cryogen-free magnets in high-resolution NMR spectroscopy. The method and system used are suitable for fast-scan NMR spectroscopy, in which dynamic distortions in spectra caused by rapid frequency sweeps are removed using a single-resonance reference. Based on the independence of dynamic distortions and NMR properties of the material under study, the phase of the complex quadrature free induction decay (FID) signal of a reference single-resonance sample can be used to extract dynamic field distortions from any spectrum obtained with the same dynamic distortion magnet.

Description

[Technical Field]

[0001] The present invention relates to a method and apparatus for post-acquisition correction of NMR spectra distorted by dynamic and static field inhomogeneities in cryogen-free magnets. [Background technology]

[0002] Nuclear magnetic resonance spectroscopy is a spectroscopic technique that observes the spin states of atomic nuclei, providing information about the interaction of local magnetic fields with nearest-neighbor atoms. It typically involves measuring the absorption of electromagnetic radiation in the radio frequency range from less than 4 MHz to 900 MHz or higher. In practice, NMR signals are generated by placing the sample under analysis in a magnetic field and exciting the sample's nuclei with radio waves at the magnetic resonance frequency. The intramolecular magnetic field around atoms within a molecule changes their resonance frequency, from which information about the molecule's electronic structure and its individual functional groups can be extracted. Because the field is unique or highly characteristic of each compound, NMR spectroscopy has become established as a definitive method for identifying single-molecule organic compounds in modern organic chemistry research.

[0003] NMR spectroscopy typically involves three steps. 1) Alignment (polarization) of magnetic nuclear spins in an applied constant magnetic field 2) Perturbation of the alignment of nuclear spins by a weak oscillating magnetic field, usually called a radio frequency (RF) pulse 3) Detection and analysis of electromagnetic waves emitted by the nuclei of the perturbed sample

[0004] NMR spectroscopy is a powerful tool for analyzing chemical structures at the atomic level. Due to its relatively low sensitivity and the requirement for high resolution, NMR requires a strong and uniform magnetic field. The latter is usually generated by a superconducting magnet operating at liquid helium temperatures. The majority of superconducting magnets are so-called liquid magnets, in which the main superconducting coil is immersed in a liquid helium reservoir that allows the coil wire to remain superconducting. As a result of natural evaporation, the liquid helium requires regular replenishment. As helium sources are currently approaching depletion, this traditional technique is becoming increasingly expensive.

[0005] The solution to this problem is the use of so-called dry cryogen-free magnets, in which the main superconducting coils are maintained in a superconducting state by heat exchange with a cold-head cryostat placed in a vacuum and operating with helium gas pumped in a closed-circuit cycle. This modern technology makes it possible to avoid the expense of helium consumption and is already widely used in dual electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) systems.

[0006] Another strong advantage of dry, cryogen-free magnets is that they allow for relatively short field settling times by warming up the magnet quickly to equalize the magnetic fields outside and inside the superconducting windings. This allows for different magnetic fields to be used for short periods of time, so that several magnetic fields can be applied in one day. Cryogen-free magnets are also more compact, allowing probes to be inserted from the top of the magnet rather than the traditional bottom in liquid cryomags, making them more gravitationally stable.

[0007] An inherent feature of cryogen-free magnets is mechanical vibration caused by coldhead operation. The latter can generate dynamic distortions that are manifested in time-periodic perturbations of the main magnetic field. This is particularly evident when the main magnet is not perfectly rigid, but its various parts can move mechanically relative to one another. In this case, the dynamic distortions might be expected to be proportional to the main magnetic field.

[0008] The operating frequency of the coldhead is on the order of 1-2 Hz. The effects of these frequencies are not noticeable in the low-resolution NMR typical of solids and some liquids. In these cases, the broadening caused by coldhead operation is well within the typical width of the NMR spectrum produced by anisotropic NMR interactions and relaxation processes. The latter can be on the order of several kHz or more, unless special high-resolution techniques are applied.

[0009] In contrast, the operating frequency of the coldhead is comparable to the typical width of a high-resolution NMR spectrum, which tends to produce significant distortion broadening, especially in the liquid state, but also in solids under MAS, CP, or spin separation. Strong dynamic field inhomogeneity can be a significant drawback to the use of cryogen-free magnets in high-resolution NMR spectroscopy, where high field uniformity and stability are key requirements.

[0010] In fact, static field inhomogeneities caused by imperfections in the main coil windings as well as in the assembly of the various parts of the magnet together are not fully avoidable even after shimming, a time-consuming and iterative procedure that only removes field inhomogeneities to a certain extent. It is highly desirable to maximally reduce the effects of both dynamic and static field inhomogeneities in experimental high-resolution NMR spectra.

[0011] The effects of dynamic field distortions resulting from the operation of the cold head of a cryogen-free magnet have been analyzed and experimentally measured and are the subject of a prior application. The applicant has previously suggested an active method for suppressing alternating dynamic field distortions at the appropriate frequency and phase based on the application of additional current to the Z0 coil. This procedure is relatively slow and advantageous prior to standard (deuterium or fluorine) field locking, which requires associated NMR signatures. It requires iterative feedback from the signal and an extra acquisition frequency channel. However, instrumental suppression requires extra hardware equipment and can only partially suppress the field distortions. Summary of the Invention

[0012] The present invention aims to provide an improved method and apparatus for post-acquisition correction of NMR spectra distorted by dynamic and static field inhomogeneities in cryogen-free magnets.

[0013] According to one aspect of the present invention, there is provided a method for post-acquisition correction of NMR spectra distorted by static and dynamic field inhomogeneities, comprising removing dynamic field distortions independent of the NMR properties of the sample by applying a common reference deconvolution of the NMR spectrum through delayed Fourier transform processing. Preferably, the dynamic field distortions are removed by a mutational deconvolution method.

[0014] Advantageously, applying delayed Fourier transform processing makes it possible to remove NMR spectral broadening caused by fast decaying FID signal components from the NMR spectrum.

[0015] In a preferred embodiment, the method comprises removing dynamic field inhomogeneities from the NMR spectrum by Fourier transforming only the absolute portion of the FID signal, thereby providing a Lorentzian single peak shape with no or reduced dynamic field distortion.

[0016] Advantageously, the method comprises removing dynamic distortions caused by coldhead operation by reference deconvolution, in which the phases of the complex quadrature FID signals of a reference monoresonant sample are used to extract the dynamic field distortions from spectra obtained with a typical dynamically distorted magnet.

[0017] The method preferably comprises analyzing the dynamic field inhomogeneity by extracting the phase of the FID signal, applying a Larmor frequency shift, and Fourier transforming the integral term of the FID signal.

[0018] Preferably, the method includes the step of removing dynamic field inhomogeneities from the FID contributions produced by the various nuclei.

[0019] The step of removing the dynamic field inhomogeneities from the FID contributions produced by the various nuclei advantageously removes the inhomogeneities from all chemically shifted portions of the spectrum simultaneously.

[0020] The phase term is preferably extracted from either (i) a single-peak reference signal measured with the same distorted magnet, or (ii) a single peak separated from other peaks in the spectrum.

[0021] The method preferably includes applying a reference deconvolution algorithm to remove dynamic inhomogeneities of the magnetic field by the following operations: (1) Selection of a reference complex FID signal from a single-peak sample; (2) decomposition of the reference signal into amplitude and phase parts and extraction therefrom of the phase term containing information of the dynamic field inhomogeneity; and (3) Cleaning the FID signals of other samples

[0022] A step may be provided for narrowing the spectrum by pre-truncating the time domain signal before taking its Fourier spectrum, thereby removing fast decaying components of the FID signal.

[0023] Advantageously, the method includes the step of removing, preferably to zero, any extraneous baseline between peaks in the spectrum.

[0024] In some embodiments, the method comprises replacing the delay spectrum with a Lorentzian shape that narrows the spectrum.

[0025] The substitution step may include: (i) Fitting an initial phase angle and phase-adjusting the initial signal with an adjustment factor. (ii) Select a time and proceed to a delayed pre-cut signal (iii) Calculating the delayed Fourier spectrum (iv) Removing the baseline

[0026] According to another aspect of the present invention, there is provided a system for post-acquisition correction of NMR spectra distorted by static and dynamic magnetic field inhomogeneities, the system comprising a processing unit configured to remove dynamic magnetic field distortions that are independent of the NMR properties of the sample by applying a general reference deconvolution of the NMR spectrum through delayed Fourier processing.

[0027] Preferably, the processing unit is configured to remove dynamic magnetic field distortions by a mutational deconvolution method.

[0028] Advantageously, the processing unit is configured to remove from the NMR spectrum any spectral broadening effects caused by fast decay of the FID signal components by applying delayed Fourier processing.

[0029] In a preferred embodiment, the processing unit is configured to remove dynamic field inhomogeneities from the NMR spectrum by Fourier transforming the absolute part of only the FID signal, thereby providing a Lorentzian single peak shape without or with reduced dynamic field distortion.

[0030] The processing unit may be configured to remove dynamic distortions caused by coldhead operation by reference deconvolution, in which the processing unit uses the phases of the complex quadrature FID signals of a reference singly resonant sample to extract the dynamic field distortions from spectra acquired with the common dynamic distortion magnet.

[0031] The system preferably comprises an analysis unit configured to analyze the dynamic field inhomogeneity by extracting the phase of the FID signal, applying a Larmor frequency shift, and Fourier transforming the integral term of the FID signal.

[0032] The processing unit is advantageously configured to remove dynamic field inhomogeneities from the FID contributions generated by various nuclei. The processing unit may be configured to remove dynamic field inhomogeneities from the FID contributions generated by various nuclei by simultaneously removing inhomogeneities from all chemically shifted portions of the spectrum. The processing unit may be configured to extract phase terms from (i) a single-peak reference signal measured with the same distorted magnet, or (ii) from a single peak separated from other peaks in the spectrum.

[0033] Advantageously, the processing unit is adapted to apply a reference deconvolution algorithm to remove dynamic inhomogeneities of the magnetic field by: (1) Selecting a reference complex FID signal from a single-peak sample (2) Decomposing the reference signal into amplitude and phase parts and extracting therefrom the phase term containing information on the dynamic field inhomogeneity. (3) Cleaning the FID signal of other samples The processing unit may be configured to pre-cut the time domain signal before taking the Fourier spectrum, thereby narrowing the spectrum by removing fast decaying components of the FID signal.

[0034] In some embodiments, the processing unit may be configured to remove any extraneous baselines between peaks in the spectrum, for example by cutting off and zeroing out such baselines.

[0035] The processing unit may be configured to replace the delay spectrum by a Lorentzian shape that narrows the spectrum.

[0036] Advantageously, the processing unit is configured to replace the delay spectrum by the following operation: (i) fitting an initial phase angle and phase adjusting the initial signal with an adjustment factor; (ii) selecting a time and advancing a delayed precut signal; (iii) calculating the delayed Fourier spectrum; (iv) Removal of the baseline.

[0037] According to another aspect of the present invention, there is provided an NMR system operated by the methods specified herein, including a system as defined herein.

[0038] Post-acquisition correction of NMR spectra is an important part of NMR spectroscopy, allowing to obtain purified NMR spectra that are clean from unwanted outphasing, broadening and noise.

[0039] Below, analytical and mathematical methods are described for post-acquisition correction of NMR spectra distorted by static and dynamic field inhomogeneities caused by defects in the main superconducting coils and coldhead operation, typical of cryogen-free magnets. For dynamic inhomogeneities, the method and system apply a variant of the common reference deconvolution method, complemented by specific mathematical analysis of spectral parameters. For static inhomogeneities, the system and method apply delayed Fourier processing. This approach has been applied to high-field experimental liquid phases of water and ethanol. 1 H NMR spectra and solid state adamantane. 13 This system and method contribute to the general field of NMR spectrum processing, enabling the more widespread use of cryogen-free magnets in high-resolution NMR spectroscopy.

[0040] In addition to the active instrumental methods for suppressing dynamic field distortions described above, a method for correcting acquired experimental NMR spectra for dynamic and static inhomogeneities in the magnetic field typical of cryogen-free magnets is disclosed. It is shown below that dynamic distortions caused by coldhead operation can be removed by a technique that falls within the general approach well known in the broad context of NMR spectroscopy as reference deconvolution. The disclosed method and system are suitable for fast-scan NMR spectroscopy, in which spectral dynamic distortions caused by rapid frequency sweeps are removed using a single-resonance reference. Based on the independence of dynamic distortions and NMR properties of the material under study, the phase of the complex quadrature free induction decay (FID) signal of a reference single-resonance sample can be used to extract dynamic field distortions from any spectrum acquired with the same dynamic distortion magnet.

[0041] The inventors have found that static magnetic field inhomogeneities can be significantly reduced by delayed Fourier processing. This delayed Fourier processing allows the removal of broadening caused by fast-decaying FID signal components from the spectrum. In high-resolution NMR, especially in liquids, such components are not related to the structure of the compound under analysis but originate from the nuclei of the sample container and static magnetic field inhomogeneities, external artifacts. While the window function method of providing acquisition delay has been previously applied in NMR spectroscopy, the present method and system offer new features and advantages over the art. The efficiency of the new method was demonstrated in experimental liquid conditions of water and ethanol using magnets with significant dynamic and static magnetic field inhomogeneities. 1 H NMR spectra and solid state of adamantane in high magnetic fields. 13 This can be verified by the correction of C spectra. The described approach demonstrates its high efficiency and proves an efficient and favorable perspective for using cryogen-free magnets in high-resolution NMR spectroscopy. The mathematical method disclosed herein has broad applicability and can be used in a broader context for post-acquisition correction of NMR spectra. [Brief explanation of the drawings]

[0042] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings in which: [Figure 1] Figure 1 is a series of graphs showing the magnitude of the distorted (solid line) and cleaned (dashed line) Fourier spectra of an example model of Equation (6) for fixed r = 1 s −1 , b = 4 Hz, and various values ​​of v. [Figure 2] Figure 2 is a series of graphs showing the magnitude of the distorted (solid line) and cleaned (dashed line) experimental NMR spectrum of a liquid pure water sample, and on the right, the magnitude of the distorted magnetic field Fourier spectrum extracted by the disclosed technique. [Figure 3] FIG. 3 is a series of graphs showing the magnitude of the distorted (top) and cleaned (bottom) experimental NMR spectra of an ethanol sample. [Figure 4] FIG. 4 is a series of graphs showing the real part of the initially acquired (top) and post-processed (bottom) single-shot phased 1H NMR spectra of liquid ethanol. [Figure 5] FIG. 5 is a series of graphs showing the real part of the originally acquired (top) and post-processed (bottom) phased naturally occurring 13C MAS NMR spectra of adamantane powder. [Figure 6] FIG. 6 is a schematic diagram of the main components of a preferred embodiment of an apparatus according to the present description. DETAILED DESCRIPTION OF THE INVENTION

[0043] The methods and systems described below operate by a modification of the reference deconvolution method to remove dynamic field distortions that are independent of the NMR properties of the sample. This approach is complemented by analytical calculations of spectral parameters. The dynamics of the macroscopic magnetization of a single nuclear species (spin 1 / 2 or quadrupolar in a symmetric environment) is well described by the Bloch equations.

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[0044] In the formula, m=(m x ,m y ,m z ) T is the magnetization 3-vector, and B=(B x , B y , B z ) T is the 3-vector of the magnetic field, γ is the gyromagnetic ratio of the species, and R is the thermal equilibrium state m th is a diagonal matrix characterizing the relaxation to

[0045] In the absence of radiofrequency irradiation, the small transverse contribution of the magnetic field, B x、y is a strong longitudinal component B z tend to be averaged within the rotating frame of the magnet, allowing the magnetic field components to be kept only along the major z-axis.

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[0046] Following equation (1), the complex transverse magnetization

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[0047] The phenomenological transverse relaxation rate r ≥ 0 is introduced. For the initial value m (t = 0) = m0, the solution of equation (2) is

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[0048] The main component of the magnetic field gives rise to a time-independent Larmor frequency contribution to which an extra contribution due to dynamic field inhomogeneities should be added.

[0049] B z (t)=B0+δ(t) This gives us equation (3).

[0050]

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[0051] The complex magnetization m(t) gives rise to the quadrature FID signal obtained after a 90° spin flip. Therefore, equations (3) and (4) allow the following important observations to be made about the experimental FID single-peak complex signal of a liquid sample:

[0052] 1. The dynamic inhomogeneity of the magnetic field is totally contained in the phase Φ(t) of the signal. 2. Dynamic field inhomogeneities enter the signal phase in the form of the time integral Δ(t) of the field distortion δ(t). 3. Static field inhomogeneities and relaxation effects are totally contained in the absolute part of the signal with the form of decay amplitude a(t) = |m(t) / m0|. 4. The NMR spectrum of the entire FID signal shifted by the Larmor frequency is the Fourier spectrum of amplitude a(t) and phase term e iΔ(t) is the convolution with the Fourier spectrum of 5. Thus, an effective recipe for cleaning dynamic field inhomogeneities from NMR spectra is the Fourier transform F of the absolute part a(t) of the FID signal only: a (λ). The result is a Lorentzian single-peak shape, completely cleaned from dynamic field distortions.

[0053] To analyze the inhomogeneity of the dynamic field, we extract the phase of the FID signal, shift the Larmor frequency, and calculate the Fourier transform F of the integral term Δ(t). Δ (λ), then the Fourier transform Fδ(λ) of the dynamic inhomogeneity δ(t) is given by

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[0054] As a simple exemplary mathematical model, one can consider the inhomogeneity of the dynamic field imparted by a single sinusoidal mode.

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[0055] It can then be obtained from equation (4).

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[0056] This leads to a Fourier expansion of the phase term.

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[0057] As can be seen from equation (5), a single harmonic of the field distortion generates a full portion of the fundamental frequency ν in the FID signal. This tends to broaden the Fourier spectrum, creating an unwanted set of extra peaks around the Larmor frequency. The intensity of the distorting harmonics in the spectrum is described by a Bessel function of the first kind with magnitude ζ. For positive k, the Bessel function Jk(ζ) decays to zero for both small and large values ​​of ζ. The magnitude ζ decays with increasing distortion frequency ν, so that high-frequency distortion ν≫b=γα has little effect on the signal and also shifts all distortion harmonics far from the spectral linewidth at the dominant Larmor harmonic. The magnitude ζ grows with decreasing ν, so that low-frequency distortion ν≪b has little effect. Distortion due to intermediate frequencies ν~b can significantly affect the signal. It should also be noted that the intensity Jk(ζ) oscillates around zero with varying ζ, introducing additional quantitative complications to the spectrum.

[0058] The Fourier spectrum of the model signal of equation (3) for the described single sinusoidal dynamic field distortion (shifted by the Larmor frequency) is shown in Figure 1,

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[0059] It is a fixed value r=1s -1 1 is a series of graphs showing the magnitude of the distorted (solid line) and cleaned (dashed line) Fourier spectra of an example model of Equation (6) for various values ​​of , b=4 Hz, and ν.

[0060] In Figure 1, the physically reasonable value r=1s -1 , b = γ, α = 4 Hz are fixed, and some exemplary values ​​of ν are chosen. The fixed value of r corresponds to an effective transverse relaxation time of 1 s. The fixed value of b corresponds to a strain amplitude of α = 94 nT (10 ppb of a 94 nT field) and 1 This corresponds to the gyromagnetic ratio of the H species γ=42.58 MHz / T. The dashed line represents the cleaned / undistorted spectrum for comparison.

[0061] The application of the described cleaning algorithm to an experimental NMR spectrum is shown in Figure 2.

[0062] In Figure 2, the left graph shows the magnitude of the distorted (solid line) and cleaned (dashed line) experimental NMR spectra of a liquid pure water sample at 9.4 T, distorted by coldhead operation and an extraneous single-sine-wave modulation. The right graph shows the magnitude of the distorted Fourier spectrum extracted by the algorithm shown. The star indicates the fundamental coldhead frequency, ν = 1.725 Hz. The large peaks correspond to the modulation frequency, ν: a) ν = 10 Hz, (b) ν = 40 Hz, (c) ν = 100 Hz, and (d) ν = 180 Hz. Referring to the right panel, the group of peaks around a frequency of 20 Hz is due to mechanical components induced by the coldhead operation. The peaks around frequencies of 50 Hz and 150 Hz (i.e., multiplications of the mains frequency) are due to effects induced in the receiving coil by the mains power supply.

[0063] In this figure, a room-temperature water FID signal was acquired in a single shot in a magnetic field of 9.4 T distorted by induced oscillations in the coldhead. To demonstrate the power of this method, an additional artificially generated single sinusoidal modulation was applied to the field-sweeping Z coil. The fundamental coldhead frequency ν ch The peak at ν = 1.725 Hz, as well as the artificially generated frequency ν, are clearly visible in the field distortion spectrum. All distortions are cleaned by going to the magnitude of the signal (dashed line) as described herein.

[0064] This technique works well for a single nuclide that does not interact with other nuclei in the sample. In general, to apply it to more complex spectra, one can analyze the FID signal from a nuclear spin species I that undergoes scalar spin-spin interactions with m other nuclear species I(k), k = 1, m. This situation is typical for solution NMR, which is characterized by nuclear J-coupling due to intramolecular chemical bonds. In this case, spin interactions within the same nuclide and the non-time-dependent part of interactions between different species are removed from the NMR spectrum.

[0065] The effective spin Hamiltonian is (in frequency units)

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[0066] In the formula, I z , I z (k) is the z-component of the associated angular momentum operator, Ω and γ are the Larmor frequency and gyromagnetic ratio of the nucleus under consideration, respectively, δ(t) is the time-dependent perturbation of the main magnetic field, and J k is the strength of the J coupling.

[0067] According to the Hamiltonian in equation (7), the complex transverse magnetization m of nuclide I that contributes to the FID signal is I (t) can be calculated as follows:

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[0068] From equation (8) and equation (4), the same phase term e, which includes the dynamic field inhomogeneity, iΦ(t) appears as a common factor in all FID contributions produced by the various nuclei. Therefore, it can be simultaneously removed from all chemically shifted parts of the spectrum. The phase term can be extracted from another single-peak reference signal measured with the same distorted magnet, or from a single peak well separated from the other peaks in the spectrum. Equation (8) also shows that dynamical inhomogeneities cannot be removed or extracted directly from the multiplet, since information about J-couplings is lost along with the field distortion.

[0069] From the above analysis, it follows that the following reference deconvolution algorithm is reasonable for cleaning dynamic inhomogeneities of the magnetic field:

[0070] (1) From a single peak sample to a reference complex FID signal m ref (t) selecting (2) decomposing the reference signal into amplitude and phase components;

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[0071] The result will be a Lorentzian multi-peak NMR spectrum cleaned from dynamic field inhomogeneities. As a control, the signal from a single-peak water sample or a single peak well separated from other peaks in a more typical NMR spectrum can be used.

[0072] To illustrate the method, an experimental NMR spectrum of a liquid ethanol sample, acquired in a single shot in a 9.4 T magnetic field distorted by coldhead operation, was processed. The results of the simulation are shown in Figure 3. In this simulation, a single peak of a well-chemically resolved OH group was selected as the basis for the described deconvolution algorithm.

[0073] Referring to Figure 3, this graph shows the magnitude of the distorted (top) and cleaned (bottom) experimental NMR spectra of an ethanol sample in a 9.4 T magnetic field distorted by coldhead operation. The three main chemical shift peaks corresponding to OH (left), CH (middle), and CH (right) groups are plotted separately to show details of splitting due to J-coupling and dynamic ELD distortion. The well-resolved single OH peak (left) was used as a reference for the deconvolution algorithm.

[0074] Narrowing static broadening by pre-cutting the FID signal

[0075] The disclosed technique is based on pre-truncating the time domain signal before taking its Fourier spectrum in order to narrow the spectrum by removing fast decaying components of the FID signal that broaden the spectrum.

[0076] First, consider the FID signal.

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[0077] This is due to the frequency ω k is formed from n harmonics with m different rates r j The time-dependent complex amplitude a characterizing poly-exponential decays with ≥ 0 k (t) with a decay rate r j The existence of is a result of static inhomogeneities in the magnetic field as well as spin-spin relaxation processes. The technique makes use of the assumption that the macroscopic magnetization is aligned along the static field before the 90° spin-flip pulse. At t=0, after the 90° pulse, the transversely inverted signals are phase-aligned, so that all complex amplitudes a kj can be considered to have the same phase φ.

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[0078] The Fourier transform F(λ) of the signal s(t) compensated for the initial phase φ is calculated as follows:

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[0079] As can be seen from equation (11), the real part of the Fourier spectrum is:

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[0080] By choosing a certain delay time τ, the initial part of the signal is set to zero, which leads to a pre-cut signal.

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[0081] The latter corresponds to multiplication by a stepped window function that is zero for t∈[0,τ) and equal to 1 for t≧τ. The Fourier transform Fτ(λ) of the precut signal s′τ compensated for the initial phase φ is calculated as follows:

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[0082] The real part is as follows:

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[0083] Comparing equation (14) with equation (12), the amplitude |a kj | is the extra coefficient e -rjτ β kj (λ) is obtained. j The larger the delay τ, the smaller the associated amplitude in the delayed spectrum. As a result, the spectral peaks become narrower. Thus, by going from the initial signal in equation (10) to the delayed signal in equation (13), a large rate r j The time delay τ should be chosen to be long enough to eliminate unwanted broadening, but not too long to maintain a reasonably large signal-to-noise ratio. kj Due to the presence of (λ), the delay spectrum is no longer Lorentzian and there is an extra baseline between the peaks, b τ(λ) is generated.

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[0084] This extra baseline is undesirable, does not contain useful spectral information, and should be removed from the spectrum. There are several ways to do this, two of which are described below as examples.

[0085] The first method is to simply clip the baseline to zero. According to equations (14) and (15), if the delay time τ is long enough, the contributions of fast decay rates tend to be removed from the spectrum, leaving the contributions of the slowest rates,

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[0086] According to equation (17), the spectral peak λ = ω k Baseline b at τ (λ) is much smaller than the peak intensity.

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[0087] Therefore, baseline decoupling simply narrows the spectrum and preserves all relevant spectral information, both qualitative and quantitative.

[0088] Another method is to replace the delay spectrum by a Lorentzian shape, which also narrows the spectrum while still preserving all the qualitative and quantitative spectral information. As mentioned above, if the delay time τ is long enough, only the contribution of the slowest rate r remains in the spectrum. According to equation (14), a good approximation can be obtained by

[0089]

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[0090] In the formula, β k (λ) is given by equation (16), and α k is some amplitude. From this, it is possible to find the best fit of the delay spectrum in (14) to the shape in (18) and use this fit to remove the baseline in (15) and obtain a Lorentzian approximation.

[0091]

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[0092] frequency ω k can be taken directly from the delay spectrum in equation (14) as the position of the associated peak. The remaining fitting parameters are the slowest rate r and amplitude α k The latter can also be taken from the delay spectrum in the first fitting approximation. k For a known value of , the standard least-squares fitting algorithm finds α k , which helps to effectively adjust the fitting parameters. It is also contemplated that certain modifications of linear prediction, harmonic inversion and filter diagonalization methods can be applied.

[0093] For an experimental FID signal and associated NMR spectrum, the narrowing algorithm includes (or consists of) the following successive steps: (1) Fit the initial phase φ and the initial signal s(t) with the coefficient e -iφ adjusting the amount by (2) Select a time delay τ and calculate the delayed precut signal s' by equation (13). T Process proceeding to t (3) calculating the delayed Fourier spectrum Fτ(λ); (4) Removing the baseline and simply truncating it or fitting the delay spectrum to the form of equation (18) and then proceeding to a Lorentzian form via equation (19).

[0094] As an example of the application of the described algorithm, the same ethanol sample as in Figure 3 was used, with the dynamic field distortions cleaned accordingly and the spectrum delayed by τ = 100 ms. The results for two different magnetic fields are plotted in Figure 4. Compared to the magnitude of the spectrum delayed by 20 ms shown at the bottom of Figure 3, it can be seen that the extra Fourier acquisition delay allows us to obtain a very narrow, well-phased spectrum while preserving all relevant information on the spectrum and a good signal-to-noise ratio.

[0095] Referring to Figure 4, the graphs show the real parts of the initially acquired (top) and post-processed (bottom) single-shot phased H NMR spectra of liquid ethanol at (a) 1.175 T and (b) 9.4 T. The well-resolved single-peak OH chemical group (left) was used as the deconvolution reference, and a 100 ms Fourier time delay was applied, followed by Lorentzian correction of the baseline. In panel (b) of Figure 4, the three chemical groups (respectively, from left to right) OH, CH, and CH are plotted separately to show details of the splitting due to coldhead distortion and J-coupling.

[0096] Solid-state validation demonstrated that the described method yields proton-decoupled natural abundance α-amyloids of adamantane powder. 13The proposed algorithm was applied to a C MAS NMR spectrum, one of the results of which is plotted in Figure 5. To better demonstrate the efficiency of the proposed algorithm, the coldhead distortion amplitude was increased by a factor of four by applying an AC current to the Z0 coil at the coldhead frequency. The numerical results confirm the good efficiency of the proposed method, even in solid-state high-resolution NMR.

[0097] Referring to Figure 5, these graphs show the initially acquired (top) and post-processed (bottom) phase-adjusted natural abundance spectra of adamantane powder at a dynamic strain field of 9.4 T and a rotor speed of 7.5 kHz. 13 The real part of the C MAS NMR spectrum is shown. A well-resolved single peak of the CH2 chemical group (left) was used as the deconvolution reference, and a 50 ms Fourier time delay was applied. A Lorentzian correction of the baseline was performed. The two chemical groups CH2 (left) and CH2 (right) are plotted separately to show details of the coldhead distortion.

[0098] It should be understood that the above-described experiments were carried out using a prototype superconducting magnet, in which imperfect assembly of its mechanically distinct parts resulted in significant dynamic field inhomogeneities induced by the operation of the coldhead. This magnet, which would normally be considered unsuitable, was tuned to be a good tool for experimental estimation, suppression, and post-acquisition processing of distorted NMR spectra. Even with this imperfect magnet, the techniques disclosed above demonstrated high efficiency.

[0099] conclusion A numerical mathematical method for post-acquisition correction of NMR spectra distorted by both dynamic and static magnetic field inhomogeneities, typical of cryogen-free magnets, is described. It demonstrates the high efficiency and good applicability of the approach for experimental NMR spectra. Together with active methods to suppress dynamic field distortions, the disclosed post-acquisition correction will further aid in the more widespread use of cryogen-free magnets in high-resolution NMR spectroscopy. The presented results are practically universal and can be used in a wide range of NMR spectrum correction procedures.

[0100] Those skilled in the art will appreciate that the methods disclosed herein may in fact be used in a processing system that automatically corrects NMR spectra distorted by the dynamic and static field inhomogeneities of a cryogen-free magnet. A cryogen-free NMR system including such a processing system is also provided.

[0101] 6, which shows a schematic representation of an embodiment of the apparatus showing the major components of the processing system. Those skilled in the art will appreciate that many elements of the apparatus shown may be implemented as hardware or algorithms.

[0102] The processing system comprises an input 210 for receiving an NMR spectrum and a processor unit 200 configured to correct the acquired NMR spectrum and output an improved NMR spectrum at 232, cleaning it from undesired outphasing, broadening, and noise. The system provides post-acquisition correction of NMR spectra distorted by static and dynamic field inhomogeneities caused by defects in the main superconducting coils and coldhead operation, which are typical in cryogen-free magnets. The processing unit 200 comprises modules for performing the steps of this technique, including a module 214 configured to apply a variant of a common reference deconvolution method, complemented by a module 216 configured to perform a specific mathematical analysis of the spectral parameters. In the case of static inhomogeneities, the system is configured to apply delayed Fourier processing.

[0103] Although the disclosure herein is directed to cryogen-free NMR systems, it should be understood that it may be applied to any NMR system.

[0104] The apparatus and processing unit comprises: 1) a cryogen-free superconducting magnet 202 (or an alternative suitable magnet) with a warm bore or a cryostat-isolated variable temperature insert (VTI) bore that supports the magnetic field for the NMR experiment; 2) an NMR probe 204 with a suitable (warm or VTI) magnet bore and chemistry suitable for high-quality NMR signal measurement; 3) an NMR spectrometer 206 including a radio frequency source, transmitter and receiver coils and amplifiers, with software to acquire and pre-process the appropriate NMR signal; and 4) a post-acquisition processing unit 210, which may be a hardware desktop computer with a processor and operating system that supports high-level programming languages ​​(e.g., Matlab, Python, etc.) and associated graphical interfaces, allowing software and programming code to be written and executed to perform post-acquisition processing according to the methods described herein.

[0105] 6, the processing unit 210 may include a general reference deconvolution stage 214 configured to remove dynamic field distortions that are independent of the NMR properties of the sample, and to this end configured to apply general reference deconvolution of the NMR spectrum through delayed Fourier processing. Stage 214 may be a mutational deconvolution stage configured to remove dynamic field distortions by a mutational deconvolution method.

[0106] Preferably, a spectral broadening effect removal stage 216 is provided that is configured to remove spectral broadening effects from the NMR spectrum caused by fast decay of the FID signal components by applying delayed Fourier processing.

[0107] This embodiment also provides a dynamic field inhomogeneity removal stage 218 that removes dynamic field inhomogeneities from the NMR spectrum by Fourier transforming only the absolute portion of the FID signal, thereby providing a Lorentzian single peak shape with no or reduced dynamic field distortion.

[0108] The dynamic distortion removal stage 222 is configured to remove the dynamic distortion caused by the coldhead operation by reference deconvolution, in which the processing unit uses the phase of the complex quadrature FID signal of the reference singly resonant sample 220 to extract the dynamic field distortion from the spectrum obtained with a common dynamically distorted magnet.

[0109] The analysis unit 224 is configured to analyze the dynamic field inhomogeneity by extracting the phase of the FID signal, applying a Larmor frequency shift, and Fourier transforming the integral term of the FID signal.

[0110] Dynamic field inhomogeneities are preferably removed from the FID contributions produced by the various nuclei. Stage 218 may be configured to remove dynamic field inhomogeneities from the FID contributions produced by the various nuclei by simultaneously removing inhomogeneities from all chemically shifted portions of the spectrum. The processing unit preferably comprises a phase term extraction stage 226 configured to extract phase terms from (i) a single-peak reference signal measured with the same distorted magnet, or (ii) from a single peak separated from other peaks in the spectrum.

[0111] Advantageously, the processing unit is configured to apply a reference deconvolution algorithm to remove dynamic inhomogeneities of the magnetic field by the following steps: (1) selecting a reference complex FID signal from a single-peak sample; (2) Decomposing the reference signal into amplitude and phase parts and extracting the phase term from them, which contains information about the inhomogeneity of the dynamic field; (3) Cleaning the FID signals of other samples. The processing unit may be configured to pre-cut the time domain signal before taking its Fourier spectrum, thereby narrowing the spectrum by removing fast decaying components of the FID signal.

[0112] In some embodiments, the processing unit comprises a baseline extraction stage 228 configured to remove excess baselines between peaks in the spectrum, for example by truncating such baselines to zero, and may also include a delayed spectrum replacement stage 230 configured to replace the delayed spectrum by a Lorentzian shape that narrows the spectrum.

[0113] Advantageously, stage 230 is configured to replace the delay spectrum by the following steps: (i) fitting an initial phase angle and phase adjusting the initial signal with an adjustment factor; (ii) Selecting a time and proceeding with a delayed pre-cut signal; (iii) calculating the delayed Fourier spectrum; (iv) Removal of the baseline.

[0114] Those skilled in the art will readily understand how to operate this device from the teachings herein.

[0115] The disclosures in UK Patent Application No. GB2302818.6, from which this application claims priority, and in the abstract accompanying this application, are incorporated herein by reference.

Claims

1. A method for post-acquisition correction of NMR spectra distorted by static and dynamic magnetic field inhomogeneities, comprising removing dynamic magnetic field distortions independent of the NMR properties of the sample by applying a common reference deconvolution of the NMR spectrum through delayed Fourier transform processing.

2. The method of claim 1 , wherein the dynamic magnetic field distortion is removed by a mutational deconvolution method.

3. 3. The method according to claim 1, wherein the step of applying a delayed Fourier transform process makes it possible to remove NMR spectral broadening caused by fast-decaying FID signal components from the NMR spectrum.

4. 4. A method according to any one of claims 1 to 3, comprising the step of removing dynamic field inhomogeneities from the NMR spectrum by Fourier transforming only the absolute portion of the FID signal, thereby providing a single Lorentzian peak shape without or with reduced dynamic field distortion.

5. 5. A method according to any one of claims 1 to 4, comprising the step of removing dynamic distortions caused by operation of the coldhead by reference deconvolution, in which the phases of the complex quadrature FID signals of a reference singly resonant sample are used to extract the dynamic field distortions from spectra obtained with a common dynamically distorted magnet.

6. A method according to any preceding claim, comprising the step of analysing the dynamic field inhomogeneity by extracting the phase of the FID signal, applying a Larmor frequency shift and Fourier transforming the integral term of the FID signal.

7. A method according to any one of claims 1 to 6, comprising the step of removing dynamic field inhomogeneities from the FID contributions produced by the various nuclei.

8. 8. The method of claim 7, wherein the step of removing dynamic field inhomogeneities from the FID contributions produced by various nuclei simultaneously removes inhomogeneities from all chemically shifted portions of the spectrum.

9. 9. The method of claim 7 or 8, wherein the phase term is extracted from (i) a single-peak reference signal measured with the same distorted magnet, or (ii) a single peak separated from other peaks in the spectrum.

10. (1) Selecting a reference complex FID signal from a single-peak sample; (2) decomposing the reference signal into amplitude and phase parts and extracting therefrom the phase term containing information on the inhomogeneity of the dynamic field; and (3) Cleaning the FID signals of other samples 10. A method according to any one of claims 1 to 9, comprising applying a reference deconvolution algorithm to remove dynamic inhomogeneities of the magnetic field by:

11. A method according to any preceding claim, comprising the step of pre-truncating the time domain signal before taking its Fourier spectrum, thereby narrowing the spectrum by removing fast decaying components of the FID signal.

12. A method according to any preceding claim, comprising the step of removing extraneous baselines between peaks in the spectrum.

13. 13. The method of claim 12, further comprising the step of truncating such baseline to zero.

14. 14. A method according to claim 12 or 13, comprising replacing the retardation spectrum by a Lorentzian shape which narrows the spectrum.

15. The substitution step (i) fitting an initial phase angle and phase adjusting the initial signal with an adjustment factor; (ii) Selecting a time and proceeding with a delayed pre-cut signal; (iii) calculating the delayed Fourier spectrum; and (iv) Removing the baseline 15. The method of claim 14, comprising:

16. A system for post-acquisition correction of NMR spectra distorted by static and dynamic magnetic field inhomogeneities, comprising a processing unit configured to remove dynamic magnetic field distortions that are independent of the NMR properties of the sample by applying a common reference deconvolution of the NMR spectrum through delayed Fourier processing.

17. 17. The system of claim 16, wherein the processing unit is configured to remove dynamic magnetic field distortions by a mutational deconvolution method.

18. 18. The system of claim 16 or 17, wherein the processing unit is configured to remove spectral broadening effects caused by fast-decaying FID signal components from the NMR spectrum by applying delayed Fourier processing.

19. 19. The system of any of claims 16 to 18, wherein the processing unit is configured to remove dynamic field inhomogeneities from the NMR spectrum by Fourier transforming the absolute part of only the FID signal, thereby providing a Lorentzian single peak shape without or with reduced dynamic field distortion.

20. 20. The system of any one of claims 16 to 19, wherein the processing unit is configured to remove dynamic distortions caused by coldhead operation by reference deconvolution, the processing unit using the phases of the complex quadrature FID signals of a reference singly resonant sample to extract the dynamic field distortions from spectra acquired with a common dynamic distortion magnet.

21. 20. The system according to any one of claims 16 to 19, comprising an analysis unit configured to analyze the dynamic field inhomogeneity by extracting the phase of the FID signal, applying a Larmor frequency shift and Fourier transforming the integral term of the FID signal.

22. The system according to any of claims 16 to 19, wherein the processing unit is configured to remove dynamic field inhomogeneities from FID contributions generated by different nuclei.

23. 23. The system of claim 22, wherein the processing unit is configured to remove dynamic field inhomogeneities from FID contributions generated by different nuclei by simultaneously removing inhomogeneities from all chemically shifted portions of the spectrum.

24. 24. The system of claim 22 or 23, wherein the processing unit is configured to extract the phase term from (i) a single-peak reference signal measured with the same distorted magnet, or (ii) a single peak separated from other peaks in the spectrum.

25. The processing unit (1) Selecting a reference complex FID signal from a single-peak sample (2) Decomposing the reference signal into amplitude and phase parts and extracting therefrom the phase term containing information of the dynamic field inhomogeneity; and (3) Cleaning the FID signals of other samples A system according to any one of claims 16 to 24, configured to apply a reference deconvolution algorithm to remove dynamic inhomogeneities of the magnetic field by:

26. 26. The system of any of claims 16 to 25, wherein the processing unit is configured to pre-truncate the time domain signal before taking the Fourier spectrum, thereby narrowing the spectrum by removing fast decaying components of the FID signal.

27. The system of any of claims 16 to 19, wherein the processing unit is configured to remove any extraneous baselines between peaks in the spectrum.

28. 28. The system of claim 27, wherein the processing unit is configured to truncate the baseline to zero.

29. 29. The system of claim 27 or 28, wherein the processing unit is configured to replace the delay spectrum by a spectrally narrowing Lorentzian shape.

30. The processing unit (i) fitting an initial phase angle and phase adjusting the initial signal with an adjustment factor; (ii) selecting a time and advancing a delayed pre-cut signal; (iii) calculating the delayed Fourier spectrum; (iv) Removing the baseline 30. The system of claim 29, configured to replace the delay spectrum by:

31. NMR system operated by the method of any of claims 1 to 15 and / or comprising the system of any of claims 16 to 30.

32. 32. The NMR system of claim 31, wherein the system is a cryogen-free NMR system.

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