Radial acquisitions offer several unique advantages for proton resonance frequency (PRF) shift thermometry. Frequently sampling the k-space center provides motion robust images, as well as the ability to correct for respiration induced off resonance¹. It has been shown that arbitrary high spatial and temporal resolution can be achieved in dynamic MRI by acquiring successive radial spokes separated by the golden angle and applying a sliding k-space filter, similar to the k-space weighted image contrast (KWIC) filter², to the reconstruction³. This work investigates a pseudo-golden angle 3D multi-echo stack of stars acquisition to simultaneously measure PRF shift temperature, T2* and ρ (signal magnitude at TE = 0), correct respiration induced off resonance, and provide water/fat separation with high spatial and temporal resolution.

Experiment: A 3D stack of stars spoiled GRE sequence was modified to acquire multiple echo contrasts using a bipolar readout and a pseudo-golden angle increment. The angle used, based on the ratio of two Fibanacci numbers α = (1 – 233/377)*360 ≈ 137.5066, will repeat the k-space trajectory after 377 views. Experiments were performed in an ex vivo pork phantom on a Siemens 3T Trio scanner to assess the effectiveness of this sequence and reconstruction technique (1.3x1.3x3 mm, FOV = 166 mm, Matrix Size = 128x128x8, Flip Angle = 10, TR = 20 ms, 13 Echoes, TE = 2.46/3.69/4.92/6.15/7.38/8.61/8.84/11.07/12.3/ 13.53/14.76/15.99/17.22 ms). An ambu-bag with two 1 liter saline bags, placed above the phantom, was manually inflated periodically to simulate respiration artifacts. The phantom was sonicated with focused ultrasound (FUS) with 125 electric Watts for 30 seconds while imaging. Four sets of data were collected. Two image sets were acquired without manually simulated respiration or FUS. The first set served as a control. The second provided a baseline of the FUS heating without the respiration artifact. The third and fourth image sets repeated sets one and two while manually simulating respiration.

Reconstruction: The center of k-space was corrected with the method described by (4) using the first and second echoes of each view to calculate the pixel shift needed. The slope of the phase at the center of k-space was used for respiration correction¹. Data was then reconstructed using a sliding filter with 13 innermost lines, with each successive ring using the minimum number of lines to meet the Nyquist criteria, using 377 lines in the outermost ring. The sliding window was advanced 13 views between each reconstruction time point providing a temporal resolution of 1.56 seconds. The k-space sampling pattern was repeated after 29 reconstructed time points. PRF temperatures were calculated using both the first time point and the time point with the same k-space sampling pattern as the reference phase. T2*/ρ maps were calculated using linear regression of the log of the magnitude images along the echo dimension. Water and fat images were produced using the three point Dixon method with the second, third and fourth echoes.

Figure 1 shows the water and fat images produced from the sequence. Figure 2 shows the slope of the phase change through the center of k-space induced by simulated respiration. Figure 3 shows the measured PRF temperature change in an example aqueous tissue voxel for the respiration non-heating case. Data is displayed with and without respiration correction and using the 1st image as the reference phase as well as a sampling pattern based phase reference. Figure 4 shows the standard deviation through time images of the PRF temperature measurements for the same cases as Figure 3. Figures 5a, b and c show the PRF temperature, ρ and T2* values vs time of the hottest voxel while heating with FUS. PRF temperature is shown using both the first image as the phase reference and a sampling pattern based phase reference to calculate the temperature difference.All measurements display a structured artifact based on the k-space sampling pattern used for reconstruction. For this reason, a pseudo and not pure golden angle increment was chosen to cause the artifact to repeat and thus be removable in temperature difference measurements. The method shown here provides promising results for this sequence and reconstruction method for use in free breathing interventional treatments. The respiration correction method also corrects for main field drift. The high bandwidth multi-echo readout removes the need for fat saturation as well as provides T2*/ρ measurements, which could be used as another possible measure of temperature change, especially in adipose tissue which does not exhibit a PRF shift with temperature⁵.