In quantitative magnetic resonance T1 mapping, the Variable Flip Angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution T1 weighted images in a clinically feasible time. Fast, linear methods that estimate T1 maps from these weighted images have been proposed, such as DESPOT1 and iterative reweighted linear least squares (IRWLLS). More accurate, nonlinear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this work, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR T1 mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise T1 map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared to conventional gradient-based NLLS estimators, while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than efficient implementations of the VARPRO method. Furthermore, NOVIFAST is shown to be robust against initialization.

Purpose: Diffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the voxel contains cerebrospinal fluid. In this work, we introduce the “Diffusion Kurtosis Imaging with Free Water Elimination” (DKI-FWE) model that separates the signal contributions of free water and tissue, where the latter is modeled using DKI. Theory and Methods: A theoretical study of the DKI-FWE model, including an optimal experiment design and an evaluation of the relative goodness of fit, is carried out. To stabilize the ill-conditioned estimation process, a Bayesian approach with a shrinkage prior (BSP) is proposed. In subsequent steps, the DKI-FWE model and the BSP estimation approach are evaluated in terms of estimation error, both in simulation and real data experiments. Results: Although it is shown that the DKI-FWE model parameter estimation problem is ill-conditioned, DKI-FWE was found to describe the data significantly better compared to the standard DKI model for a large range of free water fractions. The acquisition protocol was optimized in terms of the maximally attainable precision of the DKI-FWE model parameters. The BSP estimator is shown to provide reliable DKI-FWE model parameter estimates. Conclusion: The combination of the DKI-FWE model with BSP is shown to be a feasible approach to estimate DKI parameters, while simultaneously eliminating free water partial volume effects.

Purpose: Quantitative T₁ mapping is a magnetic resonance imaging technique that estimates the spin-lattice relaxation time of tissues. Even though T₁ mapping has a broad range of potential applications, it is not routinely used in clinical practice as accurate and precise high resolution T₁ mapping requires infeasibly long acquisition times. Method: To improve the trade-off between the acquisition time, signal-to-noise ratio and spatial resolution, we acquire a set of low resolution T₁-weighted images and directly estimate a high resolution T₁ map by means of super-resolution reconstruction. Results: Simulation and in vivo experiments show an increased spatial resolution of the T₁ map, while preserving a high signal-to-noise ratio and short scan time. Moreover, the proposed method outperforms conventional estimation in terms of root-mean-square error. Conclusion: Super resolution T₁ estimation enables resolution enhancement in T₁ mapping with the use of standard (inversion recovery) T₁ acquisition sequences. Magn Reson Med, 2016.