Model-Based Reconstruction for Joint Estimation of $T_{1}$, $R_{2}^{*}$ and $B_{0}$ Field Maps Using Single-Shot Inversion-Recovery Multi-Echo Radial FLASH

Purpose: To develop a model-based nonlinear reconstruction for simultaneous water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or fat fraction (FF) mapping using single-shot inversion-recovery (IR) multi-echo radial FLASH. Methods: The proposed model-based reconstruction jointly estimates water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF maps, as well as a set of coil sensitivities directly from $k$-space obtained with a single-shot IR multi-echo radial FLASH sequence using blip gradients across echoes. Joint sparsity constraints are exploited on multiple quantitative maps to improve precision. Validations are performed on numerical and NIST phantoms and with in vivo studies of the human brain and liver at 3 T. Results: Numerical phantom studies demonstrate the effects of fat signals in $T_{1}$ estimation and confirm good quantitative accuracy of the proposed method for all parameter maps. NIST phantom results confirm good quantitative $T_{1}$ and $R_{2}^{*}$ accuracy in comparison to Cartesian references. Apart from good quantitative accuracy and precision for multiple parameter maps, in vivo studies show improved image details utilizing the proposed joint estimation. The proposed method can achieve simultaneous water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF mapping for brain (0.81 $\times$ 0.81 $\times$ 5 mm$^{3}$) and liver (1.6 $\times$ 1.6 $\times$ 6 mm$^{3}$) imaging within four seconds. Conclusion: The proposed model-based nonlinear reconstruction, in combination with a single-shot IR multi-echo radial FLASH acquisition, enables joint estimation of accurate water-specific $T_{1}$, $R_{2}^{*}$, $B_{0}$ field and/or FF maps within four seconds. The present work is of potential value for specific clinical applications.