In this article, a robust methodology for in vivo T 1 mapping is presented. The approach combines a gold standard scanning procedure with a novel fitting procedure. Fitting complex data to a five-parameter model ensures accuracy and precision of the T 1 estimation. A reduced-dimension nonlinear least squares method is proposed. This method turns the complicated multiparameter minimization into a straightforward one-dimensional search. As the range of possible T 1 values is known, a global grid search can be used, ensuring that a global optimal solution is found. When only magnitude data are available, the algorithm is adapted to concurrently restore polarity. The performance of the new algorithm is demonstrated in simulations and phantom experiments. The new algorithm is as accurate and precise as the conventionally used Levenberg-Marquardt algorithm but much faster. This gain in speed makes the use of the fiveparameter model viable. In addition, the new algorithm does not require initialization of the search parameters. Finally, the methodology is applied in vivo to conventional brain imaging and to skin imaging. INTRODUCTIONThe T 1 parameter is an intrinsic MR property of tissue, and mapping T 1 in vivo is useful in several ways. First, knowledge of T 1 helps in optimizing the MR protocol, e.g., by setting the Ernst angle appropriately. In addition, it provides a tool to evaluate contrast uptake, blood perfusion and volume, as well as disease progression during a longitudinal study. Furthermore, it is often desirable to compare T 1 measurements across subjects and across scanners. Although there are many techniques for T 1 mapping (1), there is also a wide range of reported T 1 values in tissue (2), an inconsistency that raises the issue of reproducibility and standardization. The gold standard for T 1 mapping was developed from NMR experiments performed in the late 1940s (3,4). The method is known as inversion recovery T 1 mapping (IR), and it consists of inverting the longitudinal magnetization M z and sampling the MR signal as it recovers with an exponential recovery time T 1 . Different models have been used for T 1 mapping (1). With all models, the fit is traditionally performed using a Levenberg-Marquardt (LM) algorithm (5). Many methods have been proposed to speed up the scanning and fitting procedures, at the expense of accuracy and precision.In this article, we first justify the need for a fourparameter model when accurate T 1 mapping is desired. We show that this model is equivalent in terms of accuracy and precision of the T 1 estimation to a more general five-parameter model. We propose to solve a nonlinear least squares (NLS) problem to fit complex data to the five-parameter model. The problem is reduced to a search over one dimension, which substantially decreases the computational complexity. When only magnitude data are available, the algorithm is adapted to concurrently restore polarity. We perform Monte-Carlo simulations to compare the proposed algorithms to the conventional LM algorithm and...

Purpose The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this paper. Methods We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, Linearization for Off-resonance Estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN. Results We derive the Cramér-Rao bound (CRB), a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T1 and T2 from phase-cycled bSSFP is difficult, since the CRB is high at common SNR. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares. Conclusion Using LORE-GN we can successfully minimize banding artifacts in bSSFP.

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