Rapid T1 quantification from high resolution 3D data with model-based reconstruction

Purpose: Magnetic resonance imaging protocols for the assessment of quantitative information suffer from long acquisition times since multiple measurements in a parametric dimension are required. To facilitate the clinical applicability, accelerating the acquisition is of high importance. To this end, we propose a model-based optimization framework in conjunction with undersampling 3D radial stack-of-stars data. Theory and Methods: High resolution 3D T1 maps are generated from subsampled data by employing model-based reconstruction combined with a regularization functional, coupling information from the spatial and parametric dimension, to exploit redundancies in the acquired parameter encodings and across parameter maps. To cope with the resulting non-linear, non-differentiable optimization problem, we propose a solution strategy based on the iteratively regularized Gauss-Newton method. The importance of 3D-spectral regularization is demonstrated by a comparison to 2D-spectral regularized results. The algorithm is validated for the variable flip angle (VFA) and inversion recovery Look-Locker (IRLL) method on numerical simulated data, MRI phantoms, and in vivo data. Results: Evaluation of the proposed method using numerical simulations and phantom scans shows excellent quantitative agreement and image quality. T1 maps from accelerated 3D in vivo measurements, e.g. 1.8 s/slice with the VFA method, are in high accordance with fully sampled reference reconstructions. Conclusions: The proposed algorithm is able to recover T1 maps with an isotropic resolution of 1 mm3 from highly undersampled radial data by exploiting structural similarities in the imaging volume and across parameter maps.