Kirsten Koolstra^{1}, Peter Börnert^{1,2}, Boudewijn Lelieveldt^{3,4}, Andrew Webb^{1}, and Oleh Dzyubachyk^{3}

In Magnetic Resonance Fingerprinting (MRF), the quality of the parameter maps depends on the encoding capability of the variable flip angle train. In this work we show how the dimensionality reduction technique t-Distributed Stochastic Neighbor Embedding (t-SNE) can be used to obtain insight into the encoding capability of different MRF sequences by embedding high-dimensional MRF dictionaries into a lower-dimensional space and visualizing them as colormaps. Experiments on example dictionaries perform comparison between different sequences and assess the effect of B1+ variations on the encoding capability.

*MRF dictionaries:* Three different flip angle sequences
were used to generate four MRF dictionaries. All sequences consist of 1000 flip
angles and have a constant TR of 15 ms. Sequences shown in Figure 1 contain a
constant pattern of 0.1° angles to reduce T_{2} encoding ability (dictionary
*D _{C}*), a smoothly varying
pattern introduced by Jiang et al.

*t-SNE:* Interpreting each dictionary atom as a
high-dimensional vector, the MRF dictionary was embedded into two- or three-dimensional
space using the Barnes-Hut-SNE algorithm^{5}. The maximum number of
iterations was set to a very high value (10^{5}) to guarantee
convergence. Each experiment was repeated several times to eliminate possible
stochastic effects. Consequently, a color was assigned to each point of the
low-dimensional embedding by mapping its coordinates into either a CIE L*a*b*
color space (for the 3D case) or using a suitable 2D colormap^{6}.
Finally, a color-coded dictionary map was created by assigning the calculated
color value to each (T_{1},T_{2}) pair. All the embeddings were
mapped to a common reference frame to ensure consistency of the color mapping.

1. Ma D, Gulani V, Seiberlich N, et al. Magnetic resonance fingerprinting. Nature. 2013;495(7440):187–192.

2. Sommer K, Amthor T, Doneva M, et al. Towards predicting the encoding capability of MR fingerprinting sequences. Magnetic Resonance Imaging. 2017;41:7–14.

3. Van der Maaten L, Hinton G. Visualizing data using t-SNE. Journal of Machine Learning Research. 2008;9:2579–2605.

4. Jiang Y, Ma D, Seiberlich N, et al. MR fingerprinting using fast maging with steady state precession (FISP) with spiral readout. Magnetic Resonance in Medicine. 2015;74(6):1621–1631.

5. Van der Maaten L. Barnes-Hut-SNE. In Proceedings of the International Conference on Learning Representations, 2013.

6. Teuling AJ, Stöcklic R, Seneviratnea SI. Bivariate colour maps for visualizing climate data. International Journal of Climatology. 2011;31:1408–1412.