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Learning-based Separation of Macromolecules and Metabolites in Ultrashort-TE FID MRSI with Auxiliary SE MRSI Data

Yibo Zhao^1,2, Yudu Li^1,3, Wen Jin^1,2, Rong Guo^1,4, Yao Li⁵, Jie Luo⁵, and Zhi-Pei Liang^1,2
¹Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL, United States, ²Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, United States, ³National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, Urbana, IL, United States, ⁴Siemens Medical Solutions USA, Inc., Urbana, IL, United States, ⁵School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China

Synopsis

Keywords: Data Processing, Data Analysis

Motivation: Macromolecules have significant spectral overlap with metabolites, confounding accurate quantification of metabolites in ultrashort-TE MRSI.

Goal(s): To develop a novel method for effective and reliable separation of metabolites and macromolecules from ultrashort-TE FID MRSI data.

Approach: We translated auxiliary macromolecule-free SE metabolite signals to FID signals using a learning-based approach. The translated metabolite reference was incorporated in the spectral model of FID MRSI data through generalized series modelling. Macromolecules signals were modelled with probabilistic subspaces.

Results: The proposed method has been validated using numerical simulation and experimental data from healthy subjects and a tumor patient, producing encouraging results.

Impact: This work provides a novel approach to exploiting the characteristic spectral features in FID and SE MRSI experiments for effective separation of metabolites and macromolecules.

Introduction

Macromolecules (MM) generate broad baseline signals in ultrashort-TE FID MRSI data, overlapping with most metabolites and confounding their biological interpretation¹. Reliable separation of MM and metabolites is thus highly desirable, but has been challenging due to low SNR and severe spectral overlap^2-5. To address this problem, parametric model fitting methods exploiting prior information of metabolites and MM (resonance structure and relaxation properties) have been proposed^6-8, but these methods are usually susceptible to modelling errors and noise perturbations. Deep-learning-based methods have shown promise in separating MM and metabolite signals^9-12, yet may suffer from instabilities, especially when the size of training data is limited^13,14.

Here we propose a novel method to separate metabolites and MM signals in ultrashort-TE FID MRSI data. Auxiliary long-TE SE MRSI data was incorporated to provide MM-free metabolite signals, which was translated from SE to FID data as a reference. The proposed method has been validated in simulation and experimental data, producing encouraging results.

Methods

We used a hybrid FID/SE MRSI acquisition scheme¹⁵: the FID data was acquired in ultrashort TE and high spatial resolution, while the auxiliary SE data was acquired with two TEs. As illustrated in Figure 1, this data acquisition scheme generates three datasets (FID, SE1, SE2) that can effectively differentiate metabolites and MM based on the fast-decay nature of MM. We represented the FID MRSI data $$$\rho(\boldsymbol{x},t)$$$ using the following model:
$$\rho(\boldsymbol{x},t)=\sum_{p=-P}^{P}\alpha_p(\boldsymbol{x})\rho^{(\mathrm{ref})}(\boldsymbol{x},t)e^{-2\pi{\Delta}ft}+\sum_{r=1}^{R}c_r(\boldsymbol{x})\phi_r(t),\\\mathrm{subject~to~}c_{r}\sim\mathrm{Pr}(c_r)$$
where $$$\rho^{(\mathrm{ref})}(\boldsymbol{x},t)$$$ represents the SE-translated reference metabolite signals, $$$\alpha_p(\boldsymbol{x})$$$ the generalized-series (GS) model coefficients, $$$\phi_r(t)$$$ the pre-learned MM basis functions, $$$c_r(\boldsymbol{x})$$$ the corresponding spatial coefficients with probabilistic constraints $$$\mathrm{Pr}(c_r)$$$. The GS model^16,17 enables efficient incorporation of metabolite spectral information encoded in the long-TE SE data, while effectively compensating the difference between FID and SE acquisitions. The probabilistic subspace model^18-23 significantly reduced the degrees-of-freedom of MM signals with pre-learned bases and probabilistic constraints.

We obtained the metabolite reference signal $$$\rho^{(\mathrm{ref})}(\boldsymbol{x},t)$$$ by translating SE data to FID with physics-based and data-driven priors. More specifically, we adopted the following spectral model for the SE signals of the $$$m$$$^th metabolite $$$s_m(t,\mathrm{TE})$$$²¹:
$$s_m(t,\mathrm{TE})=a_m{\cdot}e^{-\mathrm{TE}/T_{2,m}}{\cdot}\psi_m(t,\mathrm{TE}){\cdot}e^{-t/T_{2,m}}{\cdot}h(t),$$
where $$$a_m$$$ denotes the concentration, $$$\psi_m(t,\mathrm{TE})$$$ the resonance structure, $$$T_{2,m}$$$ the transverse relaxation time, and $$$h(t)$$$ the lineshape function. The model parameters $$$\theta=\{a_m,T_{2,m},h(t)\}$$$ were determined from SE data with prior distribution constraints $$$\mathrm{Pr}(\theta)$$$ learned from SE training data. Afterwards, the FID metabolite reference was synthesized as follows:
$$s_{m}^{\mathrm{(FID)}}(t)=a_m{\cdot}w_m{\cdot}\psi_{m}^{\mathrm{(FID)}}(t){\cdot}e^{-t/T_{2,m}}{\cdot}h(t).$$
Here the resonance structure has been replaced to that of FID data, $$$\psi_{m}^{\mathrm{(FID)}}(t)$$$, and a relaxation term obtained by the Bloch-equation-simulated steady-state FID signals, $$$w_m$$$, has been added. This strategy effectively compensated for the physics-induced differences between FID and SE signals. Residual FID/SE discrepancies were further compensated using the GS model.

The MM signals are represented using a probabilistic subspace model. The spectral basis functions and coefficient distributions were pre-learned from inversion-recovery MM training data, and adapted to the imaging data, as described in the previous work²³.

Finally, we reconstructed metabolite and MM signals by estimating the GS coefficients for metabolites and the spatial coefficients for MM:
$$\{\hat{\boldsymbol{\alpha}},\hat{\boldsymbol{\mathrm{C}}}\}=\arg\min_{\{\boldsymbol{\alpha},\boldsymbol{\mathrm{C}}\}}\frac{1}{2}\left\|\boldsymbol{\mathrm{\rho}}-\begin{bmatrix}\boldsymbol{\mathrm{G}}&\boldsymbol{\mathrm{\Phi}}\end{bmatrix}\begin{bmatrix}\boldsymbol{\mathrm{\alpha}}\\\boldsymbol{\mathrm{C}}\end{bmatrix}\right\|_2^2+ \lambda\left\|\boldsymbol{\mathrm{W}}\boldsymbol{\mathrm{C}}\right\|_2^2-\sigma_{\mathrm{noise}}^{2}\log \mathrm{Pr}(\boldsymbol{\mathrm{C}}),$$
where $$$\boldsymbol{\mathrm{\rho}}$$$, $$$\boldsymbol{\mathrm{G}}$$$, $$$\boldsymbol{\mathrm{\Phi}}$$$, $$$\boldsymbol{\alpha}$$$, and $$$\boldsymbol{\mathrm{C}}$$$ represent the matrix forms of FID MRSI data, GS encoding, MM spectral basis, GS coefficients and MM spatial coefficients, respectively. Edge-preserving spatial regularization²⁴ $$$\lambda\left\|\boldsymbol{\mathrm{W}}\boldsymbol{\mathrm{C}}\right\|_2^2$$$ and probabilistic regularization $$$\sigma_{\mathrm{noise}}^{2}\log \mathrm{Pr}(\boldsymbol{\mathrm{C}})$$$ were imposed on the MM spatial coefficients.

Results

Figures 2 and 3 show the Monte Carlo simulation results. Figure 2 compares the uncertainties in metabolite and MM using the conventional nonlinear fitting algorithm⁷ and the proposed method. The proposed method led to negligible bias and noticeable reduction in uncertainties compared to nonlinear fitting method. The tumor MRSI simulation results in Figure 3 further confirmed the reduction in bias and variations provided by the proposed method.

Experimental data were acquired from 3T scanners (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany) at three different sites to evaluate the proposed method. Figure 4 shows the MM reproducibility of the proposed method in 21 healthy subjects. The MM maps obtained from the first and the second experiments match each other well, and Bland-Altman analysis in 42 small subcortical and white matter regions did not reveal significant bias (P>0.05). Figure 5 shows metabolite and MM results obtained from a glioblastoma patient. Noticeably elevated Cho, Gln and Lac were found in the enhancing tumor region, and reduction in most metabolites was found in the edema, with minimal contamination from MM signals.

Conclusion

This work proposes a novel method to separate metabolites and MM in ultrashort-TE FID MRSI with auxiliary SE MRSI data. This method was validated using experimental data acquired from healthy volunteers and a tumor patient, producing encouraging results.

Acknowledgements

This work is supported in part by NIH: P41EB022544 and R01EB033582.

References

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Figures

Figure 1 | Schematic overview of the proposed method. (A) The acquisition of ultrashort-TE FID MRSI data and auxiliary SE MRSI to provide better separation of metabolite and MM signals. (B) Integration of GS model to incorporate the translated metabolite reference and probabilistic subspace model to represent MM to enable reliable and accurate separation.

Figure 2 | Monte Carlo simulation to compare the uncertainties in spectral estimation. Median spectra and shadowed area corresponding to 25%, 50% and 75% percentiles in the simulation are shown. The nonlinear fitting method led to overestimation of MM and large uncertainties, especially for Lac signals and MM signals around 0.9 ppm. The proposed method significantly reduced both bias and estimation uncertainties.

Figure 3 | Monte Carlo simulation using a synthetic tumor MRSI data. (A) Ground truth, nonlinear fitting, FID subspace processing (without auxiliary SE data), and the proposed method results in one realization of Monte Carlo simulation, including Cho, NAA, Lac, and MM_0.94 maps. (B) Bias maps (normalized by the ground truth concentrations) calculated in the Monte Carlo simulation. (C) Coefficient of variation maps calculated in the Monte Carlo simulation. Note that the proposed method produced the smallest bias and coefficients of variations.

Figure 4 | Healthy subject reproducibility study results. (A) T1-weighted (T1w) anatomical images, region of interests (ROIs) and MM_0.94 maps obtained from two subjects in test-retest experiments. (B) Bland-Altman analysis in the 42 ROIs shown above, using healthy subject data acquired from three different sites. The obtained MM_0.94 maps were stable, and no significant bias was found between test and retest experiments.

Figure 5 | Glioblastoma patient results. (A) T1-weighted, contrast-enhanced T1-weighted, T2-weight FLAIR anatomical images, as well as metabolite and MM maps. (B) Localized spectra in normal region, enhancing tumor region and edema regions, before and after removing MM signals. The altered metabolic profile in enhancing tumor and edema (reduced NAA, Cr and mI, increased Cho and Lac) could be better visualized in the MM-removed spectra.

Proc. Intl. Soc. Mag. Reson. Med. 32 (2024)

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DOI: https://doi.org/10.58530/2024/2984