Synopsis

Keywords: Data Processing, Spectroscopy

J-resolved ¹H-MRSI provides a unique capability to quantify both brain neurotransmitters and metabolites. This paper presents a novel method to effectively remove water and lipid signals from J-resolved ¹H-MRSI data with limited spatial encodings and without lipid suppression. The proposed method has been validated using data from a healthy subject and a brain tumor patient, producing impressive results.

Introduction

Recently, a new J-resolved MRSI technique has been proposed for fast high-resolution mapping of brain metabolites and neurotransmitters using hybrid FID (free induction decay) and SE (spin echo) acquisitions¹. The method achieves high imaging speed by sampling $$$(\boldsymbol{k},t,t_J)$$$-space “sparsely” in acquiring spatial, spectral, and J-evolution information. More specifically, in the accelerated data acquisition scheme, short-TR FID signals were acquired with extended k-space coverage to achieve high spatial resolution while long-TR SE signals (which encode both chemical shift and J-evolution spectral information) were acquired with limited k-space to reduce data acquisition time. One challenging problem with this fast data acquisition scheme is the removal of lipid and water signals from the SE data. Although several data processing methods have been proposed and used for removing water and lipid signals from ¹H-MRSI data^2-7, they are not adequate for solving the nuisance removal problem associated with fast J-resolved MRSI due to the very limited number of spatial encodings acquired without lipid suppression.
In this work, we provided an effective solution to this problem using a physics-based subspace model to incorporate high-resolution FID reference spectroscopic data⁸. The proposed method has been validated using in vivo data acquired from healthy and brain tumor subjects, producing impressive results.

Methods

Using the hybrid data acquisition scheme¹, the acquired J-resolved MRSI datasets include FID data, $$$d_{\text{FID}}(\boldsymbol{k},t,t_J),t_J=0$$$, with extended k-space coverage, and dual-echo SE data, $$$d_{\text{SE}}(\boldsymbol{k},t,t_J),t_J\in\{TE_1,TE_2\}$$$, with limited k-space coverage for two TEs (to encode J-evolution information), as illustrated in Fig. 1.
To effectively leverage the high-resolution FID data for water and lipid removal from the SE data, we used a joint representation of the FID and SE MRSI signals with the following union-of-subspaces model⁸:
$$\hspace{27.5em}\rho(\boldsymbol{x},f,J)=\sum_{m=1}^{M}\sum_{\ell=1}^{L_m}{u_{m,\ell}(\boldsymbol{x})v_{m,\ell}(f,J)}, \hspace{27.5em}(1)$$
where $$$v_{m,\ell}(f,J)_{\ell=1}^{L_m}$$$ is a set of pre-determined spectral subspaces for the $$$m^{th}$$$molecule, e.g., water and lipid, and $$$u_{m,\ell}(\boldsymbol{x})_{\ell=1}^{L_m}$$$ a set of spatial coefficients shared by FID and SE data. The FID/SE-shared coefficients and learned spectral subspaces enabled the translation of high-resolution FID reference to SE data, which provided essential spatiospectral information for the reconstruction and removal of water and lipid signals from low-resolution SE data.
Determination of Water and Lipid Subspaces
To capture the inconsistencies between FID and SE data, we estimated FID/SE joint subspaces with physics prior information and training data. First, we used the following spectral model for water and lipid signals⁹:
$$\hspace{24.2em}\rho(t,J)=[c^\text{w}\phi^\text{w}(t,J)e^{-R_{2,\text{w}}^*t}+c^\text{f}\phi^\text{f}(t,J)e^{-R_{2,\text{f}}^*t}]h(t,J),\hspace{24.2em}(2)$$
where $$$c^\text{w}$$$ and $$$c^\text{f}$$$ denote the concentrations for water and lipids; $$$\phi^\text{w}(t,J)$$$ and $$$\phi^\text{f}(t,J)$$$ the resonance structures for water and lipids¹⁰ that capture the physical differences between the FID and SE signals; $$$R^*_{2,\text{w}}$$$ and $$$R^*_{2,\text{f}}$$$ the apparent relaxation constants; $$$h(t,J)$$$ the lineshape function that absorbs experimental variations between FID and SE signals, e.g., field drifts. The resonance structures were determined using quantum mechanical simulation and the Bloch equation, which reduced the learning complexity to determine the joint subspaces. Then the empirical distribution of spectral parameters, i.e., $$$c^\text{w},c^\text{f},R^*_{2,\text{w}},R^*_{2,\text{f}},h(t,J)$$$, were estimated from training data with high spatial resolution. With the estimated spectral parameters, a dictionary of synthetic FID and SE signals was generated using the signal model in Eq. (2), and their joint subspaces were extracted using singular value decomposition.
Estimation of Spatial Coefficients
With the pre-learned joint subspaces, we estimated the corresponding spatial coefficients from FID/SE imaging data by solving the following optimization problem:
$$\hspace{24.2em}\hat{U}=\text{arg}\min_U\left\lVert\begin{bmatrix}d_{\text{FID}}\\d_{\text{SE}_1}\\d_{\text{SE}_2}\end{bmatrix}-\begin{bmatrix}\Omega_{\text{FID}}FV_{\text{FID}}\\\Omega_{\text{SE}_1}FV_{\text{SE}_1}\\\Omega_{\text{SE}_2}FV_{\text{SE}_2} \end{bmatrix}U\right\rVert^2_2+R(U),\hspace{24.2em}(3)$$
where $$$d_{\text{FID}},d_{\text{SE}_1}$$$ and $$$d_{\text{SE}_2}$$$ denote the collected data, $$$U$$$ the high-resolution FID/SE shared spatial coefficients, $$$V_{\text{FID}},V_{\text{SE}_1}$$$ and $$$V_{\text{SE}_2}$$$ the pre-determined subspaces, $$$\Omega_{\text{FID}},\Omega_{\text{SE}_1}$$$ and $$$\Omega_{\text{SE}_2}$$$ the sampling operators, $$$F$$$ the Fourier operator, and $$$R(\cdot)$$$ the regularization functional. This optimization problem was solved using the conjugate gradient method. With the estimated spatial coefficients $$$\hat{U}$$$, the nuisance signals were reconstructed and removed from J-resolved ¹H MRSI data. Finally, the neurotransmitters and metabolites signals were obtained from nuisance-removed hybrid FID/SE data using the union-of-subspaces model^9,12.

Results

To validate the proposed method, J-resolved ¹H-MRSI data were acquired from a healthy volunteer and a brain tumor patient on a 3T scanner (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany) using the hybrid FID/SE acquisition scheme¹.
Figures 2 and 3 compared lipid and water removal results obtained by the proposed method, with FFT, Papoulis-Gerchberg (PG) algorithm (for lipid removal)², HSVD algorithm (for water removal)⁴, and SE-only subspace-based nuisance removal method⁷. The results demonstrated that the proposed method achieved the most effective lipid and water removal among all methods.
Figure 4 shows the metabolite maps and spectra obtained in a test-retest experiment. As can be seen, high-resolution nuisance-free metabolic signals were reconstructed. Besides, the reconstructed maps and spectra were highly reproducible, indicating the good stability of the proposed method.
Figure 5 shows the results obtained from a brain tumor patient. Noticeable reduction in NAA and elevation in lactate were observed in the lesion, without contamination from nuisance signals.

Conclusions

We proposed a novel method to remove nuisance signals from J-resolved ¹H-MRSI data acquired with limited spatial encodings and no lipid suppression. The proposed method was validated using in vivo data, producing highly reproducible nuisance-free metabolite maps. This new method may provide an effective and robust solution to the nuisance removal problem often associated with fast J-resolved ¹H-MRSI of the brain.

Acknowledgements

No acknowledgement found.

References

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