Siyuan Dong1, Henk M. De Feyter2, Monique A. Thomas2, Robin A. de Graaf3, and James S. Duncan4
1Department of Electrical Engineering, Yale University, New Haven, CT, United States, 2Department of Radiology and Biomedical Imaging, Yale University, School of Medicine, New Haven, CT, United States, 3Department of Radiology and Biomedical Imaging, Department of Biomedical Engineering, Yale University, School of Medicine, New Haven, CT, United States, 4Department of Radiology & Biomedical Imaging, Department of Electrical Engineering, Department of Statistics & Data Science, Yale University, New Haven, CT, United States
Synopsis
Deuterium Metabolic Imaging (DMI) is a novel
approach providing 3D metabolic data from both animal models and human
subjects. DMI relies on 2H MRSI in
combination with administration of 2H-labeled substrates. Common to
all MRI and MRSI methods, DMI's resolution is ultimately limited by the achievable
SNR. This work proposes a data-driven method using a deep convolutional autoencoder
to improve the SNR and increase the spatial resolution of DMI. The method was
tested with simulated, phantom and in vivo experiments at various SNR levels to
demonstrate its capability and precision for metabolic mapping using noisy DMI
data.
Introduction
The recently proposed DMI is a non-invasive, easy-to-implement and robust metabolic imaging technique 1. However, acquiring high spatial resolution 2H NMR spectra is often limited due to low SNR inherent to the low metabolite concentrations. Several data processing methods have been proposed to deal with this problem for 1H MRSI techniques 2,3,4,5,6,7,8. 2H NMR spectra acquired following administration of [6,6-2H2]-glucose contain only up to 4 non-overlapping peaks. This relative simplicity makes DMI data a good candidate for a machine learning approach. We therefore combine deep learning with 2H MRSI data acquisition to increase the spatial resolution of DMI without compromising spectral quantification.Methods
To increase spatial resolution of DMI we relied on a
data-driven method using a common architecture in deep learning, autoencoder
(AE), and a technique called transfer learning. AE is a type of neural network
for learning efficient encodings of high-dimensional input data in an
unsupervised manner. Specifically, it minimizes the mean-square-error loss
function
$$L=||\mathbf{f}-D(E(\mathbf{f})))||_2$$
by finding the optimal parameterization of the encoder $$$E(\cdot)$$$ and the decoder $$$D(\cdot)$$$.
Fig.1 shows the described architecture: a deep
convolutional AE. The rationale is based on the notion that 1) compressing a noisy free
induction decay (FID) $$$\mathbf{f}$$$ to a low-dimensional
representation $$$E(\mathbf{f})$$$ removes
insignificant features (noise) and that 2) features of the
representation can be pre-determined from synthesized FIDs.
The method consists of two steps: decoder-learning and
representation-learning. In the decoder-learning step, AE is trained on a large
number of synthesized noiseless FIDs (>10k, 80% training and 20% validation)
which are generated through the standard FID specification
$$f(t)=\sum^M_{m=1}A_m exp(2\pi i(f_m+\delta
f)t)exp(i\phi_m)exp(-\frac{t}{T_m})$$
where the chemical shifts $$$f_m$$$ come from prior knowledge, $$$\delta f$$$ models slight frequency shifts and
$$$M$$$ denotes the expected number of distinct
metabolites. Amplitudes $$$A_m$$$,
lineshape parameters $$$T_m$$$,
phases $$$\phi_m$$$ and $$$\delta f$$$
are each randomly generated from a uniform distribution over a reasonable range.
After the training process, the decoder learns how to map from the
low-dimensional representations to the noiseless FIDs. In the representation-learning
step, the encoder is retrained (decoder frozen) on real DMI FIDs to find the
representations that give the best reconstruction in terms of mean-squared-error.
This is motivated by the idea of transfer learning where the model trained in one
domain is used in another. A forward pass through the trained AE plus phase
correction gives the final reconstruction. The decoder-learning step is only
done once before it can be applied to different datasets with similar metabolic
contents to execute the representation-learning step, which takes only ~2min
for a 32x32x32 DMI dataset.
The algorithm's performance is demonstrated on simulated
data, phantom data and in vivo data. The simulated experiment verifies the
method on 2H NMR spectra containing a peak with Lorentzian lineshape.
The phantom was constructed with multiple NMR tubes (Fig.4B) containing
solutions of varying concentrations of 2H-labeled glucose, acetate
and dimethyl sulfoxide (DMSO). The "ground truth" data were acquired
in 1M solutions of the metabolites, and lower SNR DMI datasets were obtained by
dilution. DMI data of brain glucose metabolism were acquired in vivo after
administration of [6,6-2H2]-glucose in a Fischer 344 rat
implanted with an RG2 brain tumor as described previously 1. The in vivo
DMI data were acquired with 1 to 8 averages, to vary SNR levels. Results and Discussion
The performance of the algorithm on simulated data indicates
that the reconstructed data approach the ground truth, and concentration maps
are visually more diagnosable after reconstruction (Fig.2). The method improves
the precision of the concentration measurement by 2 to 3 folds compared to the unprocessed
data as illustrated by the standard deviation (SD) error bars in Fig.3. The SD
of reconstructed data at SNR=2.5
is roughly that of unprocessed data at SNR=6.2. This implies that higher spatial resolution
DMI datasets can be acquired (~1.4x higher in each direction) without a penalty
in precision of the metabolite concentration estimates. Our newly described
method also performed better than standard singular value decomposition (SVD)
methods, a technique used in some aspects of previously described de-noising
algorithms 2,6,7,8 (Fig. 3).
The algorithm also improved the appearance of phantom (Fig.
4) and in vivo DMI data (Fig. 5), showing that at least a 2-fold reduction in
SNR can be tolerated. A slight reduction in performance is anticipated when
using phantom and in vivo DMI data because of magnetic field inhomogeneity and
multi-peak spectra phase correction.
In its current installation the described algorithm relies
only on the known spectral information. The performance of the method is
anticipated to improve further when spatial information is included, quantified
magnetic field inhomogeneity (B0 map) is incorporated, and a more advanced
learning methodology is designed. Conclusion
A novel data-driven method using a deep convolutional
autoencoder and transfer learning was implemented to improve the spatial
resolution of DMI datasets while maintaining precision in determination of 2H-labeled
metabolite concentrations. The algorithm-based reconstruction resulted in a 2-3
folds increase in SNR, which translates to a 40% increase in spatial resolution
for DMI without any modification to hardware or data acquisition needed. The
technique can be extended to other metabolic imaging techniques (1H
MRSI) by synthesizing different training FIDs. Acknowledgements
The research is supported by NIH grant R01EB025840, R01CA206180 and R01NS035193.References
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