Resolving ambiguity in T1 mapping using complex MRI data
Kees M. van Hespen1, Dirk H.J. Poot1,2, Harm A. Nieuwstadt1, and Stefan Klein1

1Departments of Medical Informatics and Radiology, Erasmus MC, Rotterdam, Netherlands, 2Imaging Science and Technology, Delft University of Technology, Delft, Netherlands

### Synopsis

We have recently developed an optimized T1 mapping protocol for carotid atherosclerotic plaque imaging, using a combination of inversion and recovery prepared acquisitions. This protocol requires less images to be taken (and thus shorter acquisition time) for precise T1 estimation than conventional inversion-prepared or saturation-prepared acquisition schemes. However, estimating T1 from magnitude data, acquired with the optimized settings, causes bimodality of T1 estimates, due to the ambiguity in sign of the inversion prepared magnitude images. Simulations and experiments on a hardware phantom and a volunteer show that the ambiguity resolves when we fit a complex-valued model to the complex data.

### Purpose

Rupture of carotid atherosclerotic plaque is a major cause of stroke. Plaque composition, is believed to be an important indicator for rupture risk. For quantitative assessment of plaque composition, T1 and T2 relaxation times can be used1. In general, T1 can be accurately and efficiently quantified by a combined set of inversion and/or saturation prepared fast spin echo (FSE) acquisitions2. Our aim is to apply such a technique for T1 mapping in the carotid artery wall. Conventionally, the T1 is estimated by fitting a signal model to the acquired magnitude images. However, the removal of the sign information by only considering the magnitude data of inversion prepared images, can lead to ambiguous T1 values when the number of images is low (see Figure 1). In this study, we investigate if ambiguity in T1 estimation can be eliminated by fitting complex-valued data.

### Methods

We focus on T1 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, R1 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 ra the unprepared magnitude, and $\phi_a$ the phase of the signal.

For readout, we use a stabilized 3D FSE acquisition3, 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 T1 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 approach4.

In a Monte Carlo simulation, data was generated using the complex signal model and the optimized parameters, for a range of T1 values (100 through 1500ms) occurring in carotid plaque, B=1.9, ra=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 T1 and agarose to reduce T21. 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.

### Results

Figure 2 shows the distribution of estimated T1 for the Monte Carlo experiment (true T1=846ms). A bimodal distribution can be observed for the T1 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 T1=854±47.6ms and 539±32.6ms. Using Model 2 results in a single mode: T1=846.5±47.7ms. For the entire range of T1 (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 T1 is recovered for all simulated T1.

In the hardware phantom experiment, several tubes show a non-uniform, bimodal T1 map (Figure 4a) when Model 1 is used. In the example tube, Figure 4b, two modes can observed: T1=846.6±10.9ms and 541.5±8.7ms. Using Model 2 results in uniform T1 maps in all tubes. The example tube (Figure 4d) shows a single mode: T1=846.1±12.3ms, which corresponds to the T1 found in the Monte Carlo experiment (Figure 2).

The in vivo example (Figure 5) shows that using Model 1 yields estimates T1=510.61±289.41ms in the carotid wall. With Model 2, T1 values of 939.12±206.75ms are found, which are in accordance with those found in previous studies (700-900ms)1.

### Discussion and conclusion

Ambiguity in T1 values estimated from magnitude data acquired with optimized TI/TR settings was resolved by using complex data. This benefit of using complex data for T1 estimation has previously not been explicitly identified5. Our complex model enables us to use the optimized TI/TR settings, which require less scan time than conventional inversion recovery protocols that require more images for robust estimation. Hence, we conclude that T1 mapping with optimized TI/TR settings is more robust when complex data is used for the fitting.

### Acknowledgements

No acknowledgement found.

### References

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 T1 and T2 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 T1 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 T2 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 T1 mapping. Magn Reson Med, 64(4):1057–67, 2010.

### Figures

Figure 1. Ambiguity in fitting the magnitude of the signal (Red), yielding two possible solutions T1=380ms (Blue, correct solution) and T1=221ms (Ochre, incorrect solution)

Figure 2. Probability of finding an estimate T1, using the magnitude (Blue) or complex model (Red), given a true T1=846ms, B=1.9, Signal-to-noise ratio=30 and bin size=11

Figure 3. Estimated T1 in our Monte Carlo experiment for magnitude (A) and complex (B) data. Yielding incorrect solutions as well as correct solutions when magnitude data is used

Figure 4. Hardware phantom T1 mapping using the magnitude (A,B) and complex (C,D) model

Figure 5. T1 mapping of the carotid artery wall using the magnitude (A) and complex (B) model. Yielding an estimated T1=510.61±289.41ms and 939.12±206.75ms, using the magnitude and complex model respectively

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