Mahesh Bharath Keerthivasan^{1,2}, Blair Winegar^{2}, Unni Udayasankar^{2}, Ali Bilgin^{1,3}, Maria Altbach^{2}, and Manojkumar Saranathan^{2}

T2-weighted imaging of the brain using single shot sequences such as HASTE suffer from reduced spatial resolution, blurring artifacts and decreased conspicuity of small lesions. We present an analytic framework to design the refocusing flip angles for the HASTE sequence tailored for brain imaging. The flip angles are optimized to minimize SAR and blurring, and maximize SNR. The utility of this sequence is demonstrated by incorporating it in a brain tumor protocol and comparing its performance to conventional T2w Turbo Spin Echo in 21 patients.

**Flip Angle Design: **

A
commercial Siemens HASTE sequence was modified to incorporate the refocusing
flip angle modulation scheme proposed by Busse et al^{8}. In this
scheme, the flip angles are parametrized by four control angles $$$\vec{\alpha} = [\alpha_{min},\alpha_{cent},\alpha_{end},\alpha_{max}]$$$. These
control angles were optimized to achieve the following: (1) maximize the PSF
peak and minimize the mean of the outer edge of PSF to improve the spatial
resolution (2) maximize the signal at the central echo to maximize the SNR (3)
minimize the SAR of the sequence to decrease the imaging TR which is usually
SAR limited. In addition, constraints were added to limit the choice of $$$\alpha_{min}$$$ as it has been shown^{9-11}
to be proportional to signal dephasing due to motion. Since the signal
evolution is insensitive to $$$\alpha_{end}$$$, it
was fixed at 45° and based on^{8} $$$\alpha_{max}$$$ was set to 130°.

Representing the problem as a multi-objective optimization:

$$\max_{\alpha_{min},\alpha_{cent}} psf_{max}(\alpha_{min},\alpha_{cent}) \& \min_{\alpha_{min},\alpha_{cent}} psf_{outer}(\alpha_{min},\alpha_{cent}) \& \max_{\alpha_{min},\alpha_{cent}} sig_{cent}(\alpha_{min},\alpha_{cent})\\ \text{s.t. } \text{ sar }(\alpha_{min},\alpha_{cent}) < \eta;\\ \alpha_{min} > \delta$$

The
objective function can be reformulated by the $$$\epsilon$$$-constraint
method^{11}:

$$\max_{\alpha_{min},\alpha_{cent}} psf_{max}(\alpha_{min},\alpha_{cent}) - psf_{outer}(\alpha_{min},\alpha_{cent}) \\ \text{ s.t. } sig_{cent}(\alpha_{min},\alpha_{cent}) < \tau; \\ \text{ sar }(\alpha_{min},\alpha_{cent}) < \eta; \\\alpha_{min} > \delta$$

The optimization problem was solved using a genetic algorithm implemented in MATLAB. A two-dimensional surface plot of the objective function is shown in Figure 1A showing dependence on the individual parameters $$$\alpha_{min}$$$ and $$$\alpha_{cent}$$$. The flip angle evolution corresponding to the optimal solution along with the T2 decay curve is shown in Figure 1B.

**In vivo Imaging:**

The optimized sequence was implemented and tested on a Siemens 3T scanner. The sequence was added to clinical brain tumor protocol at our institution as an addition to the routine T2w TSE sequence. With the approval of the Institutional Review Board and with informed consent, data was acquired from 21 patients. The sequence parameters are shown in Table 1.

The image quality of the HASTE-VFA and the TSE sequences were assessed by two experienced neuro-radiologists in a blinded fashion, with a 2-week interval to avoid recall bias. Images were graded on a scale of 1-5 and scores were assigned based on the criteria listed in Table 2. Non-inferiority analysis between HASTE-VFA and TSE was done using a one-sided Wilcoxon signed rank test with a non-inferiority margin $$$\Delta$$$=0.5, $$$\alpha$$$=0.025 and Gwet’s AC1 metric was computed to measure the inter-observer variability.

Representative axial images of the brain for 3 subjects are shown in Figure 2. Note that HASTE-VFA generates images at comparable contrast and SNR to the TSE. Figure 3 shows images from 2 subjects where the TSE scan exhibited severe motion artifacts. The proposed sequence is more robust because of the single shot acquisition and shorter scan time, whilst maintaining image quality.

The mean scores for the various criteria are shown in Table 2 along with the p-value from the Wilcoxon test. The median difference in scores between the two sequences for was significantly (p-value < 0.025) less than the non-inferiority margin ($$$\Delta$$$=0.5) for all criteria except SNR and GM-WM conspicuity, implying that HASTE-VFA is not inferior to conventional TSE. The inter-observer reliability between the readers indicate a moderate to strong agreement for all criteria. The high positive percent agreement and overall agreement further affirm the diagnostic utility of HASTE-VFA.

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