Purpose

Echo-planar time-resolved imaging (EPTI) is a valuable tool for brain microstructure detection by generating a series of distortion-free diffusion and relaxometry images ^1-6. Recently, subspace reconstructions have been developed as an SNR-efficient approach to reconstruct highly under-sampled EPTI data ^4-8. A critical step in the subspace reconstruction is to generate the subspace bases, which can be estimated by simulating the relaxometry process with varying parameters (T₂, T₂^*, ∆B₀) and then extracting the bases from the simulated signal. However, the human tissue components and microstructures are very complex and may not be fully captured by the numerical simulation. In this study, we will explore a data-driven subspace-based EPTI reconstruction, by estimating bases from acquired calibration data.

Methods

Data acquisition.
Data were acquired on a GE 3.0T Premier MRI scanner, equipped with a 48-channel head coil. Low-resolution fully sampled EPTI scans without (b=0) and with (matched b-values as the to-be-reconstructed high-resolution EPTI scan and applied in x/y/z directions) diffusion encoding were conducted as a calibration scan to estimate the needed subspace bases (Fig.1A), similar to Ref. ⁸. A navigator was acquired at the end of each readout to record the physiological motion-induced phase (P_i) of each shot. The b=0 calibration scan was also used to estimate the coil sensitivity map (S_j) and the B₀ inhomogeneity-induced phases at each TE_k (P_{B0, k}). The high-resolution diffusion-prepared EPTI was highly under-sampled with only 4 shots and denser sampling was deployed around k_y=0 to generate the navigator to facilitate the inter-shot phase correction and subspace reconstruction (Fig.1B). The TE of the spin echo (TE_SE) was set at the 1^st readout (Fig.1B and 1C). Detailed imaging parameters are shown in Table 1.
Experiment 1: A multi-shell acquisition was conducted to test the diffusion-dependent relaxometry estimation and the TE-dependent diffusion estimation.
Experiment 2: To test the universality of the data-driven bases, we reconstructed the high-resolution EPTI data of one subject with the bases estimated from calibration scans of the same and a different subject with matched scan parameters (TEs, TR, N_k, b-value).
Basis estimation.
The basis estimation pipeline is shown in Fig.2A-2C. The low-resolution b=0 and diffusion calibration data were reconstructed with Tikhonov and locally low-rank (LLR) constraints, which is reasonable given the low under-sampling factor or no under-sampling in the calibration scan (R_net=1). The reconstructed b=0 and diffusion calibration images were decomposed by principal component analysis (PCA) to generate the needed magnitude subspace bases (N_m=4 bases were used here).
Subspace reconstruction.
The estimated bases were fed into the subspace reconstruction (Fig.2D-2F):
$$\underset{\mathbf{c}}{\mathrm{min}}\left|\left|\textbf{G}_{\mathit{i}}\textbf{F}\textbf{S}_{\mathit{j}}\textbf{P}_{\mathrm{B_{0}},\mathit{k}}\textbf{P}_{\mathrm{bias}}\textbf{P}_{\mathit{i}}\mathbf{\phi}\mathbf{c}-\textbf{d}_{\mathit{i,j,k}}\right|\right|^{2}+\lambda\left|\left|R\left(\mathbf{c}\right)\right|\right|_{*}$$
where the first term is data consistency and the second term is LLR regularization onc, λ is the regularization parameter, ϕ (N_k×N_m, with N_m≪N_k) is the bases, c (N_m×1) is the coefficients, d_i,j,k is the k-space data at TE_k, P_bias is the phase bias from dynamic B₀ drift and eddy current, P_i is the motion-induced phase, P_B0,k is the B₀ inhomogeneity induced phase at different TE_k, S_j is the sensitivity map, F is Fourier transform, G_i is the under-sampling operator of each shot, i, j, k, and m are the indices for shot, coil, TE, and basis, respectively. The subspace reconstruction was implemented using the alternating direction method of multipliers (ADMM) algorithm ⁹ and P_bias was updated during the iterations.

Results

Fig.3 shows the high-quality reconstruction results of Experiment 1, including (A-C) mean images of b=0, 1, and 2 ms/μm² at the shortest (TE=50 ms) and longest TEs (TE=103 ms), and the T₂^* maps.
Fig.4 displays the directionally-encoded color (DEC) maps and the line representation of the principal and 2^nd fiber orientations estimated from BedpostX¹⁰ in a selected ROI (red box) in 7 different TE groups. Gradual, consistent changes in the 2^nd fiber orientations (red arrowheads) are observed over different TEs, which may be indicative of the presence of microstructural components with different T₂^*.
Fig.5 shows good agreement between the reconstruction with bases estimated from calibration data of the same subject, a different subject, and both subjects. Images reconstructed with the simulated bases show more discrepancy compared to those with bases from acquired data.

Discussion & Conclusion

As a proof-of-concept, we demonstrate the efficacy of a data-driven subspace reconstruction method for distortion-free diffusion-relaxometry EPTI. The data-driven subspace basis estimation does not make strong assumptions about the relaxometry process, which is particularly important for regions with complex components and microstructures and may allow more accurate estimation of microstructural information. This universality test indicates that bases can be estimated from a few pre-calibration scans and do not need to be repeated on each subject, which may further improve the scan efficiency.