Artificial intelligence for high-resolution nuclear MRS under inhomogeneous magnetic fields

Qiu Wenqi^{1}, Wei Zhiliang^{1}, Ye Qimiao^{1}, Chen Youhe^{2}, Lin Yulan^{1}, and Chen Zhong^{1}

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 G_{inh-x}, G_{inh-y}, and G_{inh-z} as the
first-order field inhomogeneity along the X, Y and Z axes, we set the encoding
gradients (G_{x}, G_{y}, and G_{z}) according to k=G_{inh-x}/G_{x}=G_{inh-x}/G_{x }=G_{inh-x}/G_{x}, 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(t_{1}, n, t_{a}), perform 3D FT to obtain the frequency-domain
information S(ω_{1}, ω_{2}, ω_{3}) 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(ω_{1}, ω_{2} and ω_{3})
along both ω_{1} and ω_{2} dimensions according to the correction information, the
high-resolution information can be retrieved by projecting S(ω_{1}, ω_{2} and ω_{3}) on
to the ω_{1}ω_{2} plane.

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 t_{1}/2~90^{o}~t_{1}/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 t_{1}/2~90^{o}~t_{1}/2
and t_{1}/2~180^{o}~t_{1}/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.

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

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