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.

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 2.14). 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).