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.

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 r_a 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, 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 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.

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.

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.