Quantitative tissue parameter mapping of fundamental MRI parameters, such as T1 and T2, can aid in the detection of diffuse disease, discriminate between true and mimicked pathology, and improve estimates of derived parameters such as cerebral blood flow. However, the need to acquire multiple encoding steps prolongs the scan time, which can limit the use of parameter mapping. Accelerated parameter mapping is possible using a variety of methods, including parallel imaging, compressed sensing, and MR fingerprinting (MRF)¹. MRF builds a unique dictionary between the evolution of signal and parameters of interest using a pseudo random pulse sequence. However, the problem can be simplified when the dimension of the dictionary is relatively low, such as in T2 mapping, where there is only one parameter of interest. It is then possible to build a similar dictionary, but using conventional sequences, which simplifies the problem. In this work, we propose a dictionary that accelerates T2 mapping by representing T2 signal decay using an appropriate model.

In this work, we build a dictionary that simplifies to a lookup table to accelerate T2 mapping. A related idea was proposed to improve robustness of ASL quantification². The key of the proposed method is to build a monotonic dictionary of scalar values, rather than a dictionary of vectors as in conventional MRF. It contains N elements (dn), one for each T2 value of interest, which is similar to the unique representation of MRF. However, this method uses a pulse sequence designed to discriminate between the values of interest, rather than a randomized pulse sequence as in MRF. For T2 mapping, we simply use the summation of density-normalized signals across multiple TEs:

$$d_n=\sum_i exp\left(-\frac{TE_i}{T2}\right)$$

The summary of the algorithm is as follows:

1. Transform the undersampled k-space to aliased T2-weighted images.

2. Normalize the T2-weighted images by a proton density map, which is initialized by the sliding window method at the first iteration and the aliased image with the shortest TE in following iterations.

3. Calculate the remodeled signal using the above equation pixel by pixel and look up corresponding T2 in the dictionary by linear interpolation.

4. Use the resulting T2 map to estimated T2-weighted images at each TE. A sensitivity map is provided as prior knowledge and used to calculate estimated k-space data based on these images.

5. Replace the missing k-space data with the estimated k-space data.

6. Iterate through the above steps until a stopping criteria is met.

This method was verified on a numerical phantom with four T2 ROIs (50, 80, 120, 250ms)³. The T2-weighted images were simulated at 32 TEs with echo spacing 5ms. Complex Gaussian noise was added, corresponding to SNR 50 for the proton density image. The dictionary was built with T2s from 1 to 300 ms.

A spin echo sequence was used for validation scans of an ex-vivo brain to avoid potential confounding effects of a multi-echo sequence, such as RF inhomogeneity and stimulated echoes. The parameters were as follows: matrix size 128 × 128, FOV 180 mm × 180 mm, TR 500 ms and slice thickness 4 mm. 32 TEs were acquired with echo times spaced by 2 ms. Data processing and image reconstruction were performed using MATLAB 2015a.

Fig. 1 shows the dictionary from the model, which is monotonic. Fig. 2 shows the performance of the proposed method on a simulation phantom. With acceleration factors of 4 to 16, the resulting T2 maps had negligible undersampling artifacts (Fig. 2 top), but increased noise and absolute error (Fig. 2 bottom). NRMSE was 0.09, 0.11 and 0.14 respectively. Similar results of the experiments are shown in Fig. 3. For acceleration factors of 4, 8 and 16, NRMSE values were 0.060, 0.064 and 0.099.

By focusing on one parameter, this method simplifies both data acquisition and parameter map calculation relative to MRF. Because this is a look-up table method that uses linear interpolation, the computational complexity is much less than for compressed sensing methods. The current method is based on minimizing the difference between the acquired and estimated sum of signals weighted by T2 decay. This is a different criterion than least squared error, which likely accounts for some of the residual error as measured by NRMSE. Further work is required to determine how the method would need to be adapted for use with faster multi-echo sequences, including methods to account for non-uniform B1.

In conclusion, the proposed method estimates T2 maps accurately, with high acceleration factors and low computational complexity.