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

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.

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.

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.

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.