Zepeng Wang^{1,2} and Fan Lam^{1,2,3}

^{1}Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, IL, United States, ^{2}Beckman Institute for Advanced Science and Technology, Urbana, IL, United States, ^{3}Cancer Center at Illinois, University of Illinois at Urbana-Champaign, Urbana, IL, United States

Diffusion-weighted MRSI (DW-MRSI) is a unique quantitative
molecular imaging modality that can potentially provide exclusive cell-type and
compartment-specific microstructural information in vivo. However, DW-MRSI studies have been largely limited to single voxels or very low
resolutions in basic science and clinical applications due to several fundamental technical challenges. Here, we further enhanced the performance and
robustness of the recently proposed subspace imaging method by synergizing improved acquisition and data processing
strategies. Higher b-value DE and 3D metabolite mean diffusivity mapping more
immune to physiological motions at a 6.9x6.9x8 mm^{3} nominal resolution
were achieved in less than 20-mins.

We introduced flow-compensated DE gradients

Reconstruction from data acquired at higher b-values is more challenging due to the reduced SNR. Straightforward application of spatial constrained and/or low-rank constrained reconstruction can fail to recover the multi-b-value spatiospectral function faithfully. We propose here to use learned subspaces

With the multi-dimensional spatial-temporal-diffusion reconstruction, metabolite diffusion coefficients can be estimated using concentrations quantified from individual DEs. However, this leads to an increased number of unknown parameters, which does not fully take advantage of the data dependencies (across DEs) and fitting of higher-b-value data is less reliable due to lower SNR. Inspired by the approach in [18], we proposed a spectral fitting strategy using metabolite-specific multi-b-value subspace models. Specifically, we model the reconstruction as:

$$ \hat{\rho}(\mathbf{r},t,\mathbf{b})=\sum_{l_{NAA}=1}^{L_{NAA}}c_{l_{NAA}}(\mathbf{r})v_{l_{NAA}}(t,\mathbf{b})+\sum_{l_{Cr}=1}^{l_{Cr}}c_{l_{Cr}}(\mathbf{r})v_{l_{Cr}}(t,\mathbf{b})+\sum_{l_{{Cho}}=1}^{L_{{Cho}}}c_{l_{Cho}}(\mathbf{r})v_{l_{Cho}}(t,\mathbf{b})+\sum_{l_{{other}}=1}^{L_{{other }}}c_{l_{other}}(\mathbf{r}) v_{l_{other}}(t,\mathbf{b}),(1) $$

where $$$t$$$ and $$$\mathbf{b}$$$ denote the chemical shift and DE dimensions. The metabolite-specific multi-b-value basis $$$\{v_{l_{x}}(t,\textbf{b})\}$$$ with model orders $$$l_x$$$ are learned subspaces incorporating lineshape adaptation to $$$\hat{\rho}\left(\mathbf{r},t,\mathbf{b}\right)$$$ (details omitted). The separated metabolite components were then subject to a multi-b-value joint parametric fitting to determine the metabolite ADCs, i.e.,

$$S_{m}(t,\mathbf{b})=e^{i \varphi_{\mathrm{b}}} e^{-t^{2}/g} e^{-\mathbf{b}\times ADC_{m}}c_{m} \phi_{m}(t)e^{\left(i2\pi\delta f_{m}t-t/T_{2}^{*}m\right)},(2)$$

where $$$S_{m}(t,\mathbf{b})$$$denotes the multi-b-value FIDs, $$$\phi_{m}(t), ADC_{m}, c_{m}, T_{2}^{*}m, $$$ and $$$\delta f_{m}$$$denote basis, ADC, concentrations, relaxation parameters and frequency shift for that specific metabolite. $$$g$$$ is a global Gaussian lineshape parameter and $$$\varphi_{\mathrm{b}}$$$ captures b-value dependent phases. Note that different diffusion models can also be used depending on acquisitions and specific applications.

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Figure1: Improved data acquisition with better data quality. (a) Flow-compensated (FC) DW gradient pairs were integrated into a double spin-echo DW-MRSI sequence. (b) Comparison of water images and spectra generated by DW-MRSI sequence using previously shown bipolar gradients^{13} (row 1) and FC gradients (row 2). Reduced ghosting artifacts (indicated by red and green arrows) and better water lineshapes can be observed, indicating better data quality.

Fig.2 Strategy for learning multi-b-value signal subspace. Metabolite resonance structures (by simulations) and parameters (with physiologically meaningful distributions) are input to the parametric model to generate a large amount of b-value-dependent training data (**S**, 2nd column). Then the multi-b-value subspace can be extracted and adapted to in vivo data accounting for experimental variations (3rd column). The noise-level residuals for the projection evaluations shown on the most right column support the fidelity of the subspace representation.

Figure3: High-resolution 3D in vivo mean diffusivity
(MD) maps of NAA, Cr, and Cho estimated from volunteer 1. T1 weighted images from
several slices across the overall image volume are shown on the top. MD maps fitted using the proposed processing strategy (row 1) and method in [13] (row 2) are compared
here. Clear improvement of MD estimates can be seen using the proposed reconstruction
strategy. Apparent white matter and gray matter contrast can also be visualized in the proposed MD maps (row 1), which indicates the better performance of our strategy.

Figure4: Representative spatially resolved high
quality spectra from volunteer 1 with a 3 b-value ([0,1500,3000] s/mm^{2})
acquisition. Voxel locations are labeled with different markers in the T1
weighted image on the left, with blue voxel (row 1) from gray matter rich region
and red voxel (row 2) from white matter rich region. The multi-b-value spectra
from different DE directions are shown in different columns.

Figure5: Results from a single DE direction, 5
b-value ([0, 800, 1600, 3200, 4000] s/mm^{2}) acquisition.
(a) T1-weighted image (row 1) along with ADC maps of NAA, Cr, and Cho from representative
slices of the imaging volume. (b) spatially resolved spectra from different
locations (marked with different symbols in T1w image) showing the capability of the proposed
method in producing high-quality data at higher b-values with lower SNRs.

DOI: https://doi.org/10.58530/2022/3524