Nan Wang^{1}, Congyu Liao^{1}, Siddharth Srinivasan^{1}, Xiaozhi Cao^{1}, Justin Haldar^{2}, and Kawin Setsompop^{1}

^{1}Stanford University, Stanford, CA, United States, ^{2}University of Southern California, Los Angeles, CA, United States

EPTI is a highly accelerated time-resolved imaging method for rapid quantitative imaging. To improve the spatiotemporal encoding efficiency of EPTI, we developed a “circular” EPTI sampling trajectory (cEPTI), designed to efficiently traverse a tight circular k-space coverage with full ramp-sampling. A systematic approach was also developed to characterize the noise and effective resolution of the EPTI acquisition and used to guide the optimization of cEPTI’s k-t sampling trajectory. The optimized cEPTI was demonstrated to be capable of producing a 50ms time-resolved series of distortion-free sharp brain images with varying T2* weightings at 1 mm in-plane resolution from a 195ms scan.

$$\widehat{\mathbf{U}}=\arg\min_{\mathbf{U}}\|\mathbf{MFSB}\mathbf{\Phi}\mathbf{U}-\mathbf{d}\|_{2}^{2}+LLR(\mathbf{U}), (1)$$

With acquired k-space data $$$\mathbf{d}$$$, undersampling mask $$$\mathbf{M}$$$, Fourier transform $$$\mathbf{F}$$$, coil sensitivity $$$\mathbf{S}$$$, B

The reconstruction quality is highly dependent on the pre-estimated B

$$g=\frac{1}{\sqrt{R}}\frac{\left(A_{a}^{H}\Psi^{-1}A_{a}\right)^{-1}}{\left(A_{f}^{H}\Psi^{-1}A_{f}\right)^{-1}}, (2)$$

with undersampling factor $$$R$$$, noise covariance $$$\Psi$$$, undersampling imaging model $$$A_{a}=\mathbf{MFSB}\mathbf{\Phi}$$$ and full-sampling imaging model $$$A_f=\mathbf{FSB}\mathbf{\Phi}$$$.

The PSF $$$x_{a}$$$ from a point source input $$$\delta$$$ is characterized as:

$$\widehat{x_{a}}=\underset{x_{a}}{\operatorname{argmin}}\left\|A_{a}\left(x_{a}\right)-A_{a}(\delta)\right\|^{2}, (3)$$

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Figure 1: (A) demonstration of cEPI trajectory. The
maximum frequency encoding is a function of PE step with circular modulation, resulting
in an increasing shortening of echo spacing from center to outer k-space. (B) With shorter k_{x} and full ramp sampling, the readout of cEPI to traverse the entire k-space is 75% of the readout from standard EPTI. (C) The k_{y}-t sampling pattern for standard 5-shot EPTI, 3-shot ACE-EPTI, 3-shot ACE-cEPTI, and cEPTI. (D) demonstration of low-rank subspace recon. In this work, three subspaces were used, resulting in three corresponding coefficient maps.

Figure 2: 1/g-factor for standard EPTI, ACE EPTI, ACE cEPTI and cEPTI at different readout length of 40 ms, 50 ms, and 60 ms. The 1/g-factor for all the sampling schemes increase with the increase of readout length. ACE-EPTI and ACE-cEPTI demonstrated an overall lower 1/g-factor . For 3-shot cEPTI, the 1/g-factor shows similar performance compared to the 5-shot standard EPTI at 40ms readout. The scan time for 5 shot EPTI at 40 ms is 5*(40+15)=275 ms, where the extra 15 ms is for RF pulse and fat-sat pulse. The scan time for 3-shot cEPTI at 50 ms is 3*(50+15)=195, which is 70% of the standard EPTI.

Figure 3: The PSF characterization for standard EPTI, ACE-EPTI, ACE-cEPTI and cEPTI at different readout length of 40 ms, 50 ms, and 60 ms. The point source input was place in the first, second, and third coefficient maps, respectively. For 5-shot standard EPTI, and sharp PSF can be recovered for any coefficient from 40-60 ms. The PSF from ACE-EPTI and ACE-cEPTI cannot be fully recovered, penetrating into other coefficient maps. For cEPTI, with readout length >= 50 ms, a sharp PSF can be recovered without blurring-out or penetration.

Figure 4: Simulation results for 5-shot standard EPTI, ACE-EPTI, ACE-cEPTI and cEPTI at readout length = 50 ms. The representative images at different echo times with various T2*-weighting were displayed for all sampling schemes. The first row displays the full images from cEPTI. Zoomed-in areas are shown for better visualization. The error maps display the normalized error of the combination of all-echo images between a certain undersampling scheme and the ground truth. The simulation results indicate that cEPTI can produce sharp image with small error (RMSE = 3.09%).

Figure 5: In vivo demonstration. The images acquired using 5-shot standard EPTI, ACE-EPTI, ACE-cEPTI and cEPTI were successfully reconstructed. The proton density and T2* maps were evaluated for each case. The ACE-EPTI showed blurry images at later echo time, which is in the agreement with theoretical characterization and simulation. The images and maps produced by 3-shot cEPTI are in similar quality compared to 5-shot standard EPTI. This is a promising initial in vivo demonstration of cEPTI technique.