Nuno Saraiva Santos^{1,2}, Rui Pedro A G Teixeira^{3}, Joseph V Hajnal^{3}, and Rita G Nunes^{1,2,3}

Interpretation
of T2-weighted images still remains highly reliant on subjective clinical
evaluation. Quantitative mapping using the gold standard approach (single
spin-echo), although appealing, remains unfeasible in clinical practice.
Multi-SE sequences have emerged as viable solutions allowing much shorter scan
times at the expense of signal contamination by indirect echoes. A method
based on the MR Fingerprinting concept has recently been proposed, estimating
T2 and B1+ maps from pre-computed Echo Modulation Curves. This study evaluated
the performance of this method performing Monte Carlo simulations followed by
an *in vivo* acquisition. The method provided accurate T2 maps, despite highly
biased B1+ estimates.

Visual
evaluation of T2-weighted images is typically performed in the clinic. To
reduce subjectivity^{1}, quantitative T2 mapping has been proposed.
The gold standard approach based on single spin-echo (SE) is very time-consuming
and thus unfeasible in practice as long repetition times are required to avoid
T1-weighting contamination^{2}.

A
commonly-accepted alternative for shortening scan times is to use multi-SE
sequences. However, these present significant signal contributions from indirect
echoes due to B1+ inhomogeneities, hindering the accuracy of exponential decay fitting^{3}.

To
account for these contributions, a method inspired in MR Fingerprinting^{4}
has been proposed, matching the measured signal to predicted
echo-modulation curves (EMC) estimating T2 and B1+ maps^{1}.

Our goal was to evaluate the bias and precision of these estimates.

A pattern-matching technique was implemented in Matlab R2013b (Mathworks,
USA) assigning to each signal an element from a dictionary of pre-computed EMC considering all relevant sequence parameters^{1,4}. In multi-SE these are: echo-train length (ETL), inter-echo spacing (dTE), radiofrequency
(RF) waveforms and flip angles (FA).

To model magnetization evolution, the Extended Phase
Graph (EPG)^{5} formalism was used^{6}. Slice profile
effects were considered using the Shinnar-Le Roux algorithm^{7} as
proposed by Buonincontri^{8}.
A Carr-Purcell-Meiboom-Gill selective acquisition protocol was simulated matching
the *in vivo* protocol (ETL=10, dTE=10 ms and FA = [180° 160°… 160°], 4mm slice thickness) for realistic ranges of T2
and B1+ (20-400 ms and 60-140%); T1 was kept fixed to 1000 ms as
suggested by Ben-Eliezer^{1} - Figure 1.

A Monte Carlo (MC) simulation was carried out generating 10,000 instances of noisy signal (with a signal-to-noise ratio of 30) for each possible [T2, B1+] combination (T2/B1+ steps: 5 ms/5%). Both parameters were estimated using template matching and the mean bias relative to the ground truth values and standard deviation were calculated.

An MC simulation was carried out on a numerical brain phantom (T2 ranging
20-300 ms)^{9}. An inhomogeneous B1+ field was considered (range 60 to 120%) and estimates obtained using the same
EMC dictionary.

To evaluate sensitivity to the acquisition protocol, the EMC corresponding to a T2 of 80 ms and B1+ of 80% were simulated for a set of Multi-SE pulse sequences with varying dTE (range 5-15ms, step 1ms) and FA (range 140°-180°, step 5°). The first refocusing pulse of the echo train was kept at 180° to provide a smooth signal transition.

*In vivo*
brain data were acquired on a Philips Achieva 3T scanner, using the imaging protocol
considered in the simulations, with spatial resolution of 1.6×1.6×4.0mm^{3},
field-of-view 250×250mm^{2}, 6
slices and TR of 4s. For comparison, a T2 map was obtained fitting a
mono-exponential model to the even echoes of each EMC^{10}.
Reference B1+ maps were obtained using Actual Flip-angle Imaging (AFI)^{11}: 3.9mm isotropic resolution, field-of-view 250×250×250mm^{3}, 6
slices, TE/TR 0.78/25ms, TR extension 100ms.

From Figure 1, the T2 parameter has a stronger impact on signal amplitude than B1+. This observation is consistent with MC results – Figure 2. The histograms (panels A-B) for estimates obtained from noisy EMC, corresponding to a true T2 of 100 ms and a B1+ of 75% show a much wider B1+ distribution, which also appears bi-modal contrarily to the distribution of T2 estimates.

From Figures 2C-D, the B1+ bias increases as the true value deviates from 100% reaching up to 15%, whereas T2 bias stays within 4% for true T2 below 300ms. The biases depend mostly on B1+, with little dependency on T2. The distribution spreads (Figure 2E-F) follow a similar pattern.

Consistent results were obtained for alternative acquisition protocols (Figure 3). T2 estimates were more accurate, presenting biases lower than 4 % whereas B1+ biases were below 10% only for FA under 160°.

Numerical brain simulations and *in
vivo* results were also consistent as the accuracy of T2 and B1+
estimates decreased sharply when B1+ deviated from 100% (Figures 4 and 5). T2
estimates obtained using the gold standard approach were systematically larger
(5 to 10 ms) (Figure 5A-C), while the B1+ estimates differed from AFI in most
of the brain (Figure 5D-F). Spatial patterns in T2 error maps (Figures 4-5C) resembled the true B1+ maps, which is consistent with higher estimation errors occurring as B1+ deviates from 100% (Figures 2C-D).

1- Ben-Eliezer N, Sodickson DK, Block KT. Rapid and Accurate T2 Mapping from Multi-Spin-Echo Data Using Bloch-Simulation-Based Reconstruction, Magn Reson Med, 2015; 73:809-17.

2- Huang C, Altbach MI, El Fakhri G. Pattern recognition for rapid T2 mapping with stimulated echo compensation, Magn Reson Imaging, 2014; 32:969-74.

3- Petrovic A, Scheurer E, Stollberger R. Closed-Form Solution for T2 Mapping with Nonideal Refocusing of Slice Selective CPMG Sequences, Magn Reson Med, 2015; 73:818-27.

4- Ma D, Gulani V, Seiberlich N, et al. Magnetic Resonance Fingerprinting, Nature, 2013; 495(7440):187-92.

5- Weigel M. Extended phase graphs: dephasing, RF pulses, and echoes - pure and simple, J Magn Reson Imaging. 2015; 41(2):266-95.

6- http://web.stanford.edu/~bah/software/epg/

7- Pauly J, Le Roux P, Nishimura D, et al. Parameter relations for the Shinnar-Le Roux selective excitation pulse design algorithm. IEEE Trans Med Imaging, 1991;10:53–65.

8- Buonincontri G, Sawiak SJ. MR fingerprinting with simultaneous B1 estimation. Magn Reson Med. 2016;76(4):1127-35.

9- Stöcker T, Vahedipour K, Pflugfelder D, et al. High-performance computing MRI simulations. Magn Reson Med. 2010; 64(1):186-93.

10- Kim D, Jensen JH, Wu EX, et al. Breathhold multiecho fast spin-echo pulse sequence for accurate R2 measurement in the heart and liver. Magn Reson Med, 2009; 62(2):300-6.

11- Yarnykh VL. Actual flip-angle imaging in the pulsed steady state: a method for rapid three-dimensional mapping of the transmitted radiofrequency field. Magn Reson Med, 2007; 57(1):192-200.