Resolving ambiguity in T1 mapping using complex MRI data

Kees M. van Hespen^{1}, Dirk H.J. Poot^{1,2}, Harm A. Nieuwstadt^{1}, and Stefan Klein^{1}

We focus on T_{1} mapping based
on a set of inversion and saturation
prepared acquisitions. The magnitude signal model is as follows:

Model 1: $$S=|A(1-Be^{-TIR_{1}}+(B-1)e^{-R_{1}TR})|$$

where B* *is the inversion
efficiency, TI the inversion time, TR the repetition time, R_{1} the relaxation
rate and A the unprepared magnitude. The complex signal model is given by:

Model 2: $$S=r_{a}e^{i\phi_{a}}(1-Be^{-TIR_{1}}+(B-1)e^{-R_{1}TR})$$

with r_{a} the unprepared
magnitude, and $$$\phi_a$$$_{} the phase of the signal.

For
readout, we use a stabilized 3D FSE acquisition^{3}, which leads to black blood
imaging suitable for carotid wall analysis. The preparation in each acquisition
consists of the saturation by the preceding readout, possibly followed by an
inversion pulse. Parameters TI and TR were optimized numerically, so as to
maximize the time efficiency of the entire protocol, resulting in: TI/TR = {91/973, 429/3725, -/1074, -/907}ms.
From this set of four inversion/saturation prepared images we estimate T_{1} by
either a) fitting Model 1 to the magnitude data, or b) fitting Model 2 to the
complex-valued data. Fitting was done with a maximum likelihood estimation
approach^{4}.

In a Monte Carlo simulation, data
was generated using the complex signal model and the optimized parameters, for
a range of T_{1} values (100 through 1500ms) occurring in carotid plaque, B=1.9,
r_{a}=1000, $$$\phi_{a}$$$=0, and Gaussian noise, $$$\mu$$$=0 and $$$\sigma$$$=33, was added to
the real and imaginary parts for each of 10.000 independent realizations.

In a hardware phantom experiment,
12 tubes were filled with water and different concentrations of gadolinium
trichloride to reduce T_{1} and agarose to reduce T_{2}^{1}. For our imaging protocol
we used an echo-train-length of 18, echo spacing of 6ms and an acquired
voxel-size of 0.625x0.71x2mm$$$^{3}$$$.

In an *in vivo* example, a healthy volunteer is scanned with the
aforementioned protocol and parameters.

Figure 2 shows the distribution
of estimated T_{1} for the Monte Carlo experiment (true T_{1}=846ms).
A bimodal distribution can be
observed for the T_{1} estimates when Model 1 is used. After setting a manual
threshold to sort the estimates to one of the modes, we fit a normal
distribution to each mode with a built-in function of Matlab (normfit). Using
Model 1, the modes are T_{1}=854±47.6ms and 539±32.6ms. Using Model 2 results in a single mode: T_{1}=846.5±47.7ms. For the entire range of T_{1} (See Figure 3a), a bimodal
distribution is observed. Bimodality was assumed if the means of the assumed
modes were more than two $$$\sigma$$$ apart. When Model 2 is used, the ambiguity
issue is resolved (Figure 3b) and the correct T_{1} is recovered for all simulated
T_{1}.

In the hardware phantom
experiment, several tubes show a non-uniform, bimodal T_{1} map (Figure 4a) when
Model 1 is used. In the example tube, Figure 4b, two modes can observed: T_{1}=846.6±10.9ms
and 541.5±8.7ms. Using Model 2 results in uniform T_{1} maps in all tubes. The
example tube (Figure 4d) shows a single mode: T_{1}=846.1±12.3ms, which corresponds to
the T_{1 }found in the Monte Carlo experiment (Figure 2).

The *in vivo *example (Figure 5) shows that using Model 1 yields estimates T_{1}=510.61±289.41ms in the carotid wall. With Model 2, T_{1} values of 939.12±206.75ms are found, which
are in accordance with those found in
previous studies (700-900ms)^{1}.

1. B. F. Coolen, D. H. Poot, M.
I. Liem, L. P. Smits, S. Gao, G. Kotek, S. Klein, and A. J. Nederveen. Three-dimensional quantitative T_{1}
and T_{2} mapping of the carotid artery: Sequence design and in vivo feasibility.
Magn Reson Med, 2015.

2. N. Stikov, M. Boudreau, I. R. Levesque, C. L.
Tardif, J. K. Barral, and G. B. Pike. On the accuracy of T_{1} mapping: searching
for common ground. Magn Reson Med, 73(2):514–22, 2015.

3. R. F.
Busse, H. Hariharan, A. Vu, and J. H. Brittain. Fast spin echo sequences with very
long echo trains: design of variable refocusing flip angle schedules and
generation of clinical T_{2 }contrast. Magn Reson Med, 55(5):1030-7, 2006.

4. D. H. Poot, and S. Klein. Detecting Statistically Significant Differences in Quantitative MRI Experiments, Applied to Diffusion Tensor Imaging. IEEE Transactions on Medical Imaging, 34(5): 1164-1176, 2015.

5. J. K. Barral, E. Gudmundson, N. Stikov, M.
Etezadi-Amoli, P. Stoica, and D. G. Nishimura. A robust methodology for in vivo
T_{1} mapping. Magn Reson Med, 64(4):1057–67, 2010.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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