Teresa Nolte^{1,2}, Mariya Doneva^{3}, Thomas Amthor^{3}, Peter Koken^{3}, Nicolas Gross-Weege^{2}, Tianyu Han^{2}, Hannah Scholten^{2}, and Volkmar Schulz^{2}

In this study, we evaluate the effect of three potentially confounding
factors (B_{1}^{+} inhomogeneity, slice profile, diffusion) on the outcome of 2D Magnetic
Resonance Fingerprinting measurements in the female breast for
six healthy volunteers. Each of these
factors was included into an MRF dictionary and matching results were compared
to a reference dictionary that excluded the correction. For the given MRF
sequence, both B_{1}^{+} inhomogeneity and slice profile correction affected the
quantitative relaxation times in the female breast, whereas
this was not the case for diffusion.

Magnetic resonance fingerprinting (MRF) extracts multiple
quantitative parameters from a time series of undersampled images with varying acquisition
parameters such as flip angles (FA) or repetition times^{1}. Parametric maps
result from matching the temporal signal evolution in each voxel to a
dictionary of modelled signals. Hence, the accuracy of the results depends on the
extent to which the model replicates the physical reality of the MRF sequence. For
gradient spoiled MRF sequences, dictionary calculation involves Extended Phase
Graph simulations^{2}, which take into account radiofrequency (RF)
excitations, relaxations and re-/dephasing of magnetization induced by spoiling
gradients. However, phenomena like in-plane B_{1}^{+} inhomogeneity, the RF slice profile,
i.e., flip angle distribution along the slice direction^{3,4}, and diffusion
caused by unbalanced gradient moments^{5} can induce a bias in the matching
results.

The purpose of this study is to evaluate in detail the
effect of these potentially confounding factors on the outcome of 2D MRF
measurements in the female breast. The measurements, examining quantitative T_{1}
and T_{2} values of fibroglandular (FG) and fatty tissue, were
previously realized in six healthy female volunteers at 1.5 T. In the breast,
especially B_{1}^{+} inhomogeneity is of importance as strong dielectric effects
occur^{6}. Diffusion is expected to affect mostly FG tissue (apparent diffusion
coefficient of (1.95 ± 0.24) · 10^{-3} mm^{2}/s at
1.5T^{7}).

All B_{1}^{+} maps show higher values in the left breast than in
the right breast, reflected by a strong left-right difference in T_{2} and a slight
difference in T_{1} prior to B_{1}^{+} correction (cf. Figure 1(a)–(d)). For all
volunteers, mean fat T_{2} values – expected to be homogeneous over the whole
breast – were plotted against the corresponding mean B_{1}^{+} values in the right
and left breast, cf. Figure 1(e). For matching to the reference dictionary
(orange data points), a strong left- right gradient is visible, which reduces
to 15% of its original slope when including the B_{1}^{+} correction (blue data
points).

Matching including the slice profile resulted in decreased
T_{2} and slightly increased T_{1} values in both FG and fatty tissue (cf. Figure 2).
The changes in T_{2} are strong despite the relatively rectangular slice profile
of the RF excitation pulses and need further verification.

The simulated diffusion results in Figure 4(a)-(b) show for the test tissue that diffusion is expected to have an influence from spoiling strengths of 12·2π upwards. Accordingly, the difference maps in Figure 4(c)-(d) do not show any decrease in the matched relaxation times when including diffusion with 4·2π spoiling.

In conclusion, we showed that an error analysis is important
to obtain accurate MRF measurement results. For the given MRF sequence, both
slice profile as well as B_{1}^{+} inhomogeneity correction affected the quantitative
relaxation times in the female breast anatomy.

^{1}Jiang Y, et al., MR Fingerprinting Using Fast Imaging
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^{2}Scheffler K. A Pictorial Description of Steady-States in
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^{3}Hong T, Han D, Kim M, Kim D. RF slice profile effects in
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^{4}Ma D, Coppo S, Chen Y, et al. Slice Profile and B1
Corrections in 2D Magnetic Resonance Fingerprinting. Magn Res Med 2017;
78:1781–1789.

^{5}Kobayashi Y, Terada Y. Diffusion-weighting Caused by
Spoiler Gradients in the Fast Imaging with Steady-state Precession Sequence May
Lead to Inaccurate T2 Measurements in MR Fingerprinting. Magn Reson Med Sci
2018. doi:10.2463/mrms.tn.2018-0027.

^{6}Winkler SA, Rutt BK. Practical Methods for Improving B1+
Homogeneity in 3 Tesla Breast Imaging. J Magn Reson Imaging. 2015; 41(4):
992–999.

^{7}Partridge S, Murthy RS, Ziadloo A, et al. Diffusion
tensor magnetic resonance imaging of the normal breast. Magnetic Resonance
Imaging 2010; 28:320–328.

^{8}Nolte T, Gross-Weege N, Truhn D, et al. Undersampled
Spiral Magnetic Resonance Fingerprinting with Water and Fat Blurring
Correction. In: Proceedings of the Joint Annual Meeting of ISMRM/ESMRMB, Paris,
France, 2018. (abstract 4215).

^{9}Sommer K, Amthor T, Koken P, Meineke J, Doneva M.
Determination of the Optimum Pattern Length of MRF Sequences. In: Proceedings
of the 25th Annual Meeting of ISMRM, Honolulu, HI, 2017. (abstract 1491).

^{10}Yarnykh, VL. Actual Flip-Angle Imaging in the Pulsed
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^{12}Weigel M, et al. Extended phase graphs with anisotropic
diffusion. Journal of Magnetic Resonance 205: 276–285 (2010).

^{13}Lecture notes https://web.stanford.edu/class/rad229/Notes/B2-ExtendedPhaseGraphs.pdf,
last access on 8th November 2017.

Figure
1: (a) Time envelope of RF pulse shape that has been employed for the MRF sequence
and (b) resulting slice profile, shown for the maximum FA of the MRF sequence (FA=60°).

Figure
2: Effect of B_{1}^{+} correction on matching results, exemplarily shown for
volunteer 5: (a) and (b) are the T_{1} and T_{2} difference maps, obtained by
subtracting the matching results without correction for B_{1}^{+} inhomogeneity from
the reference results. (c) B_{1}^{+} map, as measured with the actual flip angle
technique. (d) Masks for the FG and fatty tissue region. (e) All volunteers: mean
T_{2} values in fatty tissue plotted against the mean B_{1}^{+} values, calculated
separately for the left and the right breast.

Figure
3: (a) and (b): Effect of slice profile correction on the matching results,
exemplarily shown for volunteer 5. T_{1} and T_{2} difference map, calculated by subtracting the matching
result with slice profile correction from the reference matching result. (c)
and (d): Combined effect of slice profile and B_{1}^{+} inhomogeneity correction on
the matching results. T_{1} and T_{2} difference map, calculated by subtracting the
matching result with slice profile and B_{1}^{+} inhomogeneity correction from the
reference matching result.

Figure
4: Diffusion effects on the outcome of MRF matching, exemplarily shown for volunteer 5. (a) and (b) show
simulation results: For an exemplary tissue (T_{1} =1200 ms, T_{2} = 70 ms), the
signal evolution was simulated with spoiling gradients of increasing spoiling
moment. The signal evolutions were then matched to the reference dictionary.
(c) and (d) show difference maps for T_{1} and T_{2} in the fibroglandular tissue: matching results with diffusion were subtracted from reference
matching results. Apart from some occasional noise, the difference maps are zero
throughout the FG tissue.