Real time MR temperature imaging during thermal therapy is beneficial for monitoring and controlling the treatment. Therefore, high spatiotemporal resolution is required for clinical applications. In recent years, several reconstruction methods have been proposed to explore correlations in temporal dimension for a high acceleration factor, such as reconstruction methods based on k-t space (k-t GRAPPA ¹, k-t SPIRiT ²). However, these methods are not easy to achieve real-time temperature monitoring because the information from the future time points is needed to get unbiased temperature estimation.

In this work, we proposed a novel method, temporal weighted sliding window SPIRiT using motion-insensitive golden angle radial sampling to achieve real time temperature imaging.

Theory: In the proposed method, the k-space data from several previous time frames are used to reconstruct the target temperature map by solving the following optimization problem based on SPIRiT ³:$$argmin( d_{c} ) \quad \parallel W_id_r-Dd_c \parallel^{2}_2+\lambda\parallel(G-I)d_{c}\parallel^2_2$$

where $$$d_c$$$ is the reconstructed Cartesian k-space data of all channels at current time frame, $$$d_r$$$ is the acquired radial k-space data, $$$W_i$$$ is the temporal weight of $$$d_r$$$ at the $$$i$$$th iteration, $$$D$$$ represents a gridding matrix for non-Cartesian sampling which also selects the acquired k-space points out of $$$d_c$$$, $$$G$$$ is the SPIRiT interpolation operator, $$$I$$$ is the identity matrix, $$$λ$$$ is the regularization parameter to adjust data consistency and calibration consistency.

A weighted sliding window covering the present k-space data and several k-space data form previous time frames is used to create a k-space with relatively more acquired points for data consistency and calibration process. In this way, there is no need to take extra k-space data for calibration, which are done by the conventional SPIRiT and k-t SPIRiT. And to avoid temperature estimation bias from data of previous time frames, the weight of k-space data from previous time frames is iteratively reduced while repeatedly solving the above optimization problem.

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 experiment was also performed to evaluate the proposed method. A cooling down process was scanned after the agar phantom was heated to about 50℃ at the beginning of the experiment.

All images were obtained on a 3.0T Phillips scanner (Philips, Best, the Netherlands) with a time-interleaved Golden Angle sampling scheme with following parameters: FOV=16cm, matrix size=80×80, 100 projections, 160 readout points, TR/TE=50/10ms. The correction of gradient errors from radial sampling was performed on all data using TrACR ⁴ and fully sampled data were undersampled with a reduction factor of 8×(12 projections) for reconstruction. The proposed method was compared with frame-by-frame SPIRiT ³ and non-weighted temporal SPIRiT.

Fig. 1 shows the estimated temperature maps and temperature errors using the three methods in simulation. Compared with frame-by-frame SPIRiT and non-weighted temporal SPIRiT, the proposed method results in lower temperature errors in heated region and its surrounding area. The temperature evolution curve of the proposed method agrees well with the fully sampled data (Fig. 2). The results of the phantom cooling down experiment are shown in Fig. 3 and Fig. 4. The proposed method provides closest temperature estimation to the fully sampled data with RMSE of about 0.2℃.

Table1 illustrates the RMSEs of ROI (7×7 voxels in heated region) at three different time frames in the simulation and the phantom cooling down experiment. The RMSE of ROI at the 15th time frame using non-weighted temporal SPIRiT in the simulation reached to 5.16℃ because of temporal delay response. In comparison, the proposed method results in lower RMSEs at the three time frames chosen.

Compared with other approaches, the proposed method improves the accuracy of temperautre estimation, not only by utilizing the information from previous time frames, but also by emphasizing the information of the current time frame via decreasing temporal weights of previous time points. The weighted sliding window uses only the previous data rather than the data collected during the whole monitoring process.

This prospective implementation helps the real-time temperature monitoring to be feasible. In-vivo experiments are under way to further test the feasibility of the proposed method on human data in the presence of respiratory motion.