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.

💡 Research Summary

Purpose
The authors aimed to develop a rapid, high‑resolution, distortion‑free method for simultaneous water‑fat separation, R2* and B0 mapping of the fetal brain at 3 T.

Methods
A 2‑D multi‑echo radial FLASH sequence was designed with inter‑echo blip gradients that rotate the radial spokes in the echo dimension. Thirty‑five echoes were acquired over three TRs, yielding 1,050 spokes and a nominal voxel size of 1.1 × 1.1 × 3 mm³ within approximately 2 s per slice. To reconstruct the undersampled data, a calibration‑less model‑based algorithm was formulated as a nonlinear inverse problem. The signal model incorporates water (W), fat (F) with a six‑peak spectrum (z), off‑resonance (fB0) and transverse relaxation (R2*):

M(TE) = (W + F·z)·exp(i2πfB0·TE)·exp(−R2*·TE).

The forward operator combines this model with coil sensitivities and the sampling mask. The cost function includes a data‑consistency term and regularization: joint ℓ1‑Wavelet sparsity on (W,F,R2*) and Sobolev smoothing on fB0 and coil maps. Optimization was performed with IRGNM‑FISTA on a GPU (RTX A6000), requiring 5–10 min per dataset.

Validation was performed in three stages: (1) numerical phantom with ground‑truth R2* (10–200 s⁻¹), fat fraction (5–95 %), and off‑resonance (±50 Hz); (2) NIST T1 phantom; (3) in‑vivo fetal scans (nine subjects, 26–36 weeks gestation). For comparison, the same radial data were also reconstructed with a parallel imaging/compressed sensing (PICS) pipeline followed by Graph‑Cut water‑fat separation, and a conventional multi‑echo EPI protocol was acquired.

Results
Numerical simulations showed mean absolute errors of –0.03 % (fat fraction), –0.17 s⁻¹ (R2*) and 0.01 Hz (B0) across all parameter ranges, with robustness to increasing noise levels. In the NIST phantom, ROI analysis confirmed negligible bias. In fetal data, the model‑based R2* maps correlated strongly with the PICS‑Graph‑Cut reference (ICC = 0.9601) and demonstrated excellent repeatability (ICC = 0.9213) across repeated scans. Compared with multi‑echo EPI, the radial approach delivered higher spatial resolution (1.1 mm vs. 2–3 mm) and markedly reduced geometric distortion, while R2* values remained comparable (ICC = 0.8049). Visual inspection revealed finer anatomical detail and distortion‑free R2*‑weighted images.

Conclusion
The study demonstrates that a multi‑echo radial FLASH acquisition combined with a calibration‑less, model‑based reconstruction provides motion‑robust, distortion‑free, high‑resolution R2* mapping of the fetal brain at 3 T. The technique achieves 1.1 × 1.1 × 3 mm³ resolution in 2 s per slice, simultaneously yields water‑fat separation and B0 maps, and outperforms conventional multi‑echo EPI in both image quality and quantitative accuracy. This approach holds promise for advanced fetal neuroimaging applications such as developmental assessment, hemorrhage detection, and R2*‑weighted functional MRI. Future work may extend the method to 3‑D volumes, incorporate automated motion correction, and evaluate clinical impact in larger cohorts.