Artificial intelligence for high-resolution nuclear MRS under inhomogeneous magnetic fields
Qiu Wenqi1, Wei Zhiliang1, Ye Qimiao1, Chen Youhe2, Lin Yulan1, and Chen Zhong1

1Department of Electronic Engineering, Xiamen University, Xiamen, China, People's Republic of, 2Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen, China, People's Republic of


High-resolution multi-dimensional nuclear magnetic resonance (NMR) spectroscopy serves as an irreplaceable and versatile tool in various chemical investigations. In this study, a method based on the concept of partial homogeneity is developed to offer two-dimensional (2D) high-resolution NMR spectra under inhomogeneous fields. Oscillating gradients are exerted to encode the high-resolution information, and a field-inhomogeneity correction algorithm based on pattern recognition is designed to recover high-resolution spectra. The proposed method improves performances of 2D NMR spectroscopy under inhomogeneous fields without increasing the experimental duration or significant loss in sensitivity, and thus may open important perspectives for studies of inhomogeneous chemical systems.


Multi-dimensional (mD) nuclear magnetic resonance (NMR) spectroscopy is considered to be a versatile and powerful method for characterizing the structures and dynamics of molecules[1-3]. However, in some occasions, sufficiently homogeneous magnetic fields are simply unavailable even with advanced shimming techniques. Under this circumstance, adjacent peaks in most kinds of mD NMR spectra take the risk of overlap, thus deteriorating spectral readability and losing information. Recently, the partial homogeneity assisted inhomogeneity correction spectroscopy (PHASICS) has been presented to produce 1D spectra with enhanced resolutions under inhomogeneous magnetic fields [4]. In this study, the PHASICS is equipped with different mixing periods to offer different types of 2D NMR information in unison with a designed 2D field-inhomogeneity correction algorithm to yield high-resolution 2D NMR spectra.


The proposed pulse sequence is shown in Fig. 1. Replacing the step-wise phase encodings in the reported PHASICS [4] with synchronous encoding (denoted as SE-PHASICS), which contains three orthogonal gradients, shortens the acquisition time. Defining Ginh-x, Ginh-y, and Ginh-z as the first-order field inhomogeneity along the X, Y and Z axes, we set the encoding gradients (Gx, Gy, and Gz) according to k=Ginh-x/Gx=Ginh-x/Gx =Ginh-x/Gx, where k is defined as the synchronous coefficient by virtue of a pre-acquired field map. In this way, position-independent high-resolution information can be recorded, and the high-resolution spectrum can be obtained with the aid of a 2D inhomogeneity correction algorithm based on pattern recognition. If the inhomogeneity is mainly along one dimension, SE-PHASICS sequence can be simplified by retaining only single-axial gradient along the same orientation where field inhomogeneity distributes. In this case, high-order terms of inhomogeneous field can be conquered.

The encoded high-resolution information can be recovered by virtue of pattern recognition. As presented in Figure 2, the 2D inhomogeneity correction algorithm is implemented as follows: (1) reconstruct the 3D data D(t1, n, ta), perform 3D FT to obtain the frequency-domain information S(ω1, ω2, ω3) and break it into a series of 2D data; (2) binarize the 2D spectra, apply dilation operator, and then extract the contours of peaks to yield central coordinates of different peaks; (3) compare central coordinates to provide correction information; (4) shifting S(ω1, ω2 and ω3) along both ω1 and ω2 dimensions according to the correction information, the high-resolution information can be retrieved by projecting S(ω1, ω2 and ω3) on to the ω1ω2 plane.

Results and Discussion

A mixture solution comprising of ethyl 3-bromopropionate and 2-butanone in identical volume is used to demonstrate the flexibility and usability of Z-PHASICS. The shimming coils of X1, Y1 and Z1 were detuned to introduce a 3D inhomogeneous field. This inhomogeneity is sufficiently large that diagonal peaks are broadened to overlap each other and cross peaks appear with broad line width in the conventional COSY (Fig. 3c). According to the acquired field map, the magnetic field inhomogeneity was 0.034, 0.038 and 0.097 G/cm along the X, Y and Z axes, respectively. The module of t1/2~90o~t1/2 was used to form the SE-PHASICS-COSY. With the SE-PHASICS, high-resolution information can be restored. Then, the 2D inhomogeneity correction algorithm unravel the high-resolution information. The projection spectra convey high-resolution 2D SECSY, and the COSY spectrum can be recovered from spin echo correlated spectrum via a simple and direct mathematical conversion [5]. The performance of SE-PHASICS suffers from certain deterioration when high-order inhomogeneity terms occur, but is satisfactory when high-order terms are insignificant.

A 200 mM quinine in DMSO-d6 is used to investigate the performance of Z-PHASICS in analyzing more complicated chemical systems. The shimming coils from Z1 to Z7 are detuned simultaneously. Modules of t1/2~90o~t1/2 and t1/2~180o~t1/2 are integrated with Z-PHASICS to construct Z-PHASICS-SECSY and Z-PHASICS-J spectra. Fig. 4b exhibits correlation information clearly and Fig. 4c presents delicate scalar-coupling splitting pattern, providing useful information of chemical systems even under severe inhomogeneity (Fig. 4d).

With the enhanced signal-to-noise ratio and resolution performances under inhomogeneous magnetic fields, the PHASICS based high-resolution 2D spectroscopy constitutes an alternative for conventional techniques. The proposed methods may open important perspectives for studies of inhomogeneous chemical systems.


This work was partially supported by the National Natural Science Foundation of China under Grants 11375147 and 11204256.


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Figure 1. Schematic diagram of 2D spectroscopy developed based on SE-PHASICS

Figure 2. Pilot process of the 2D field-inhomogeneity correction algorithm. Z-PHASICS-COSY spectra of ethyl 3-bromopropionate is used.

Figure 3. Spectra of conventional COSY (a) and SE-PHASICS-COSY (b) and pilot process of inhomogeneity correction (c, d and e). The orginal SE-PHASICS data (c) are corrected to be (d). (e) is recovered high-resolution spin echo correlated spectrum; (b) COSY converted from (e).

Figure 4. (a) Molecular structure and standerd 1D spectrum of quinine, (b and c) are Z-PHASICS-J and Z-PHASICS-SECSY spectra recorded under an inhomogeneous field introduced by detuning shimming coils from Z1 to Z7.; (d) is the convensional single-pluse measurement under the same inhomogeneous field.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)