A novel method for reconstructing MRI temperature maps from undersampled data is presented. The method, model predictive filtering, combines temperature predictions from a preidentified thermal model with undersampled k-space data to create temperature maps in near real time. The model predictive filtering algorithm was implemented in three ways: using retrospectively undersampled k-space data from a fully sampled two-dimensional gradient echo (GRE) sequence (reduction factors R = 2.7 to R = 7.1), using actually undersampled data from a two-dimensional GRE sequence (R = 4.8), and using actually undersampled data from a three-dimensional GRE sequence (R = 12.1). Thirty-nine high-intensity focused ultrasound heating experiments were performed under MRI monitoring to test the model predictive filtering technique against the current gold standard for MR temperature mapping, the proton resonance frequency shift method. For both of the two-dimensional implementations, the average error over the five hottest voxels from the hottest time frame remained between +/-0.8 degrees C and the temperature root mean square error over a 24 x 7 x 3 x 25-voxel region of interest remained below 0.35 degrees C. The largest errors for the three-dimensional implementation were slightly worse: -1.4 degrees C for the mean error of the five hottest voxels and 0.61 degrees C for the temperature root mean square error.
(c) 2010 Wiley-Liss, Inc.