Rapid, High-resolution and Distortion-free $R_{2}^{*}$ Mapping of Fetal Brain using Multi-echo Radial FLASH and Model-based Reconstruction

Purpose: To develop a rapid, high-resolution and distortion-free technique for simultaneous water-fat separation, $R_{2}^{*}$ and $B_{0}$ mapping of the fetal brain at 3T. Methods: A 2D multi-echo radial FLASH sequence with blip gradients is adapted for data acquisition during maternal free breathing. A calibrationless model-based reconstruction with sparsity constraints is developed to jointly estimate water, fat, $R_{2}^{*}$ and $B_{0}$ field maps directly from k-space. This approach was validated and compared to reference methods using numerical and NIST phantoms and data from nine fetuses between 26 and 36 weeks of gestation age. Results: Both numerical and experimental phantom studies confirm good accuracy and precision. In fetal studies, model-based reconstruction yields quantitative $R_{2}^{*}$ values in close agreement with those from a parallel imaging compressed sensing (PICS) technique using Graph Cut (intra-class correlation coefficient [ICC] = 0.9601), while providing enhanced image detail. Repeated scans confirm good reproducibility (ICC = 0.9213). Compared to multi-echo EPI, the proposed radial technique produces higher-resolution (1.1 $\times$ 1.1 $\times$ 3 mm$^{3}$ vs. 2-3 $\times$ 2-3 $\times$ 3 mm$^{3}$) $R_{2}^{*}$ maps with reduced distortion. Despite of differences in motion, resolution and distortion, $R_{2}^{*}$ values are comparable between the two acquisition strategies (ICC = 0.8049). Additionally, the proposed approach enables synthesis of high-resolution and distortion-free $R_{2}^{*}$-weighted images. Conclusion: This study demonstrates the feasibility of using multi-echo radial FLASH combined with calibrationless model-based reconstruction for motion-robust, distortion-free $R_{2}^{*}$ mapping of the fetal brain at 3T, achieving a nominal resolution of $1.1 \times 1.1 \times 3$ mm$^{3}$ within 2 seconds per slice.