Data Fitting

Dictionary-based techniques such as MP2RAGE do not typically use conventional minimization algorithms (e.g. Levenberg-Marquardt) to fit signal equations to observed data. Instead, the MP2RAGE technique uses pre-calculated signal values for a wide range of parameter values (e.g. T₁), and then interpolation is done within this dictionary of values to estimate the T₁ value that matches the observed signal. This approach results in rapid post-processing times because the dictionaries can be simulated/generated prior to scanning and interpolating between these values is much faster than most fitting algorithms. This means that the quantitative image can be produced and displayed directly on the MRI scanner console rather than needing to be fitted offline.

MP2RAGE is an extension of the conventional MPRAGE pulse sequence widely used in clinical studies Haase et al., 1989Mugler & Brookeman, 1990. A simplified version of the MP2RAGE pulse sequence is shown in Figure 2.14. MP2RAGE can be seen as a hybrid between the inversion recovery and VFA pulse sequences: a 180° inversion pulse is used to prepare the magnetization for T₁ sensitivity at the beginning of each TRMP2RAGE, and then two images are acquired at different inversion times using gradient recalled echo (GRE) imaging blocks with low flip angles and short repetition times (TR). During a given GRE imaging block, each excitation pulse is followed by a constant in-plane (“y”) phase encode weighting (varied for each TR_MP2RAGE), but with different 3D (“z”) phase encoding gradients (varied at each TR). The center of k-space for the 3D phase encoding direction is acquired at the TI for each GRE imaging block. The main motivation for developing the MP2RAGE pulse sequence was to provide a metric similar to MPRAGE, but with self-bias correction of the static (B₀) and receive (B₁^-) magnetic fields, and a first order correction of the transmit magnetic field (B₁⁺). However, because two images at different TIs are acquired (unlike MPRAGE, which only acquires data at a single TI), information about the T₁ values can also be inferred, thus making it possible to generate quantitative T₁ maps using this data.

To produce T₁ maps with good accuracy and precision using dictionary-based interpolation methods, it is important that the signal curves are unique for each parameter value. MP2RAGE can produce good T₁ maps by using a dictionary with only dimensions (T₁, S_MP2RAGE), since S_MP2RAGE is unique for each T₁ value for a given protocol Marques et al., 2010. However, as was noted above, S_MP2RAGE is also sensitive to B₁ because of $\theta_{1}$ and $\theta_{2}$ in Equations 2.13, 2.14, 2.15, and 2.16. The B₁-sensitivity can be reduced substantially with careful MP2RAGE protocol optimization Marques et al., 2010, and further improved by including B₁ as one of the dictionary dimensions [T₁, B₁, S_MP2RAGE] (Figure 2.15). This requires an additional acquisition of a B₁ map Marques & Gruetter, 2013, which lengthens the scan time.

The MP2RAGE pulse sequence is increasingly being distributed by MRI vendors, thus typically a data fitting package is also available to reconstruct the T₁ maps online. Alternatively, several open source packages to create T₁ maps from MP2RAGE data are available online Marques, 2017Hollander, 2017, and for new users these are recommended—as opposed to programming one from scratch—as there are many potential pitfalls (e.g. adjusting the equations to handle partial Fourier or parallel imaging acceleration).