Radiologists and scientists working on MR thermometry.

Microwave ablation is a promising technique to treat many diseases, especially bone tumors where an in-depth treatment is needed with a probe. MR temperature imaging using proton resonance frequency (PRF) shift technique ¹ is currently used to monitor temperature change during the treatment, and high temporal resolution is required for clinical applications. However, the acceleration techniques of data acquisition often suffer from difficulty to estimate temperature-induced phase shift accurately with high acceleration factors.

Thus, in this work, we explored the low rank property of k-t space in dynamic MR temperature imaging and proposed a novel fast reconstruction method AscLR with an ascending-threshold low rank constraint in order to accelerate temperature mapping and obtain more accurate temperature estimation.

Theory: In dynamic MR temperature imaging, there is a low rank property in k-t space because there are only slight temperature-induced phase variations across time. This property is used in the proposed method as a constraint to accelerate temperature imaging by estimating temperature from under-sampled k-space. The main steps of the proposed method are shown in Fig. 1.

During iterations, the conventional threshold methods of singular values used for other applications (fMRI ², cardiac imaging ³ or parametric mapping ⁴ ) such as unchanging hard-threshold either failed to eliminate aliasing artifacts due to under-sampling (large threshold), or lost detail information of temperature-induced phase shifts (small threshold). It is hard to find an appropriate threshold for temperature imaging. A simple and effective solution is to start with a small threshold and iteratively ascend it while repeatedly solving the optimization problem. With the initial small threshold, the aliasing artifacts due to under-sampling are easily eliminated and as the singular value threshold goes up, more detail information of the temperature-induced phase shift is preserved. Meanwhile, the acquired data are preserved to confirm data consistency during the process.

Experiments: A phantom simulation was performed to simulate heat-induced phase shifts with maximum temperature change of 30℃ on a 1% agar phantom.

A phantom heating experiment was also performed on a phantom with a heating process induced by an MR-compatible microwave probe (Nanjing ECO Microwave System Co., Ltd, Nanjing, China). The 2D FFE sequence was implemented to acquire data on a 3.0T Phillips scanner (Philips, Best, the Netherlands).

The fully-sampled data were retrospectively under-sampled using pseudorandom variable density pattern in the ky-t domain with sampling rate of 12.4% (Fig. 2a) and 11.6% in phantom simulation and phantom heating experiment respectively. Temperature maps were calculated using PRF ¹ based on a fully-sampled reference. The proposed method was compared to a widely used acceleration method k-t FOCUSS ⁵.

Imaging parameters for the phantom simulation: acquisition matrix size = 128 × 128, FOV = 200 mm × 200 mm, TR = 50ms, TE = 10ms, flip angle = 15°. Imaging parameters for the phantom heating experiment: acquisition matrix size = 88 × 85, FOV = 160 mm × 160 mm, TR = 50ms, TE = 10ms, flip angle = 15°.

The results of the phantom simulation are shown in Fig. 2. Large temperature errors up to 1.5 ℃ can be observed in the temperature error maps of k-t FOCUSS, while the errors of the proposed method are below 1℃. Fig. 3 and Fig. 4 illustrate the results of the phantom heating experiments. As can be seen, the temperature evolution curve of AscLR agrees better with fully-sampled data than k-t FOCUSS in both experiments.

Table 1 lists the temporal root-mean-square errors (RMSEs), RMSEs of Region of Interest (ROI, 9×9 pixels in heated region), errors of the peak point in temperature evolution curve of the proposed method and k-t FOCUSS. The proposed method results in much less RMSEs than k-t FOCUSS in the three comparisons.

The simulation and the phantom heating experiment demonstrate the efficiency of the proposed method for accelerating temperature mapping. Compared with k-t FOCUSS, the proposed method improves the accuracy of temperature measurement even at a reduction factor of 8 by using the low rank property of dynamic temperature imaging and the ascending threshold. In-vivo experiments will be performed to further investigate the ability of the proposed method in presence of motion.We developed a novel reconstruction method AscLR and validated the feasibility of the proposed method for monitoring temperature changes with improved accuracy while largely reducing the acquisition time with a factor of 8. This method can be applied to calculate temperature changes and thermal absorption after treatment in order to evaluate the curative effects of the ablation.