A k-space-based method to measure and correct for temporal B0 field variations in MR temperature imaging

Abstract

Purpose: Present a method to use change in phase in repeated Cartesian k-space measurements to monitor the change in magnetic field for dynamic MR temperature imaging.

Methods: The method is applied to focused ultrasound heating experiments in a gelatin phantom and an ex vivo salt pork sample, without and with simulated respiratory motion.

Results: In each experiment, phase variations due to B₀ field drift and respiration were readily apparent in the measured phase difference. With correction, the SD of the temperature over time was reduced from 0.18°C to 0.14°C (no breathing) and from 0.81°C to 0.22°C (with breathing) for the gelatin phantom, and from 0.68°C to 0.13°C (no breathing) and from 1.06°C to 0.17°C (with breathing) for the pork sample. The accuracy in nonheated regions, assessed as the RMS error deviation from 0°C, improved from 1.70°C to 1.11°C (no breathing) and from 4.73°C to 1.47°C (with breathing) for the gelatin phantom, and from 5.95°C to 0.88°C (no breathing) and from 13.40°C to 1.73°C (with breathing) for the pork sample. The correction did not affect the temperature measurement accuracy in the heated regions.

Conclusion: This work demonstrates that phase changes resulting from variations in B₀ due to drift and respiration, commonly seen in MR thermometry applications, can be measured directly from 3D Cartesian acquisition methods. The correction of temporal field variations using the presented technique improved temperature accuracy, reduced variability in nonheated regions, and did not reduce accuracy in heated regions.

Keywords: MRI field drift monitoring; PRF temperature phase correction; respiration monitoring.

FIGURE 1

Segmented EPI sequence and definition of $t_n$, $t_m$, and $t_l$

FIGURE 2

Standard deviation in phase versus 1/SNR. The deviation from linear and saturation occurs at about an $\text{SNR}=5$ and below

FIGURE 3

Coronal ${\text{T}}_1$-weighted views of the gelatin phantom (A) ex vivo salt pork sample (B) in the breast-specific MR-guided focused system. The position of the focused ultrasound transducer is shown with white, dashed lines indicating the acoustic beam path. The volunteer is positioned on top of the system (ie, out of the plane)

FIGURE 4

Data from the edge and central planes of k-space from a 10-slice 3D segmented EPI phantom study. A, k-Space magnitude scaled to show signal at edges. B, k-Space phase. C, Phase of complex phase difference between current time frame and time average of 20 time frames in the dynamic sequence

FIGURE 5

The phase of the complex phase difference k-space after averaging over the readout samples and over all coils as described in Equations (21) and (23). Each $k_y/k_z$ rectangle shows the phase evolution over the time of a complete image volume. This image volume is replicated over time. (Note: A column of zeros is inserted between every block of $k_z$ measurements to assist in visualization.) A,B, The gelatin phantom. C,D, The ex vivo salt pork sample. B,D, A breathing volunteer lying above the phantom. The volunteer is outside of the image FOV but contributes a respiratory phase

FIGURE 6

The phase measurements due to field drift and respiration sorted in time order from the four experiments. In each rectangle, the measurements vertically are from the echo train, showing the phase evolution during the 7 $k_y$ encodings of each echo train in these studies, and the measurements horizontally are the 22 sets of echo trains. For these images, phase evolution with $k_z$ is not shown

FIGURE 7

Change in ${\mathbf{\text{B}}}_{\mathbf{0}}$ (in Tesla) as a function of time for the four experiments. A,B, The gelatin phantom heating study. C,D, The heating of the ex vivo salt pork sample. A,C, With no breathing human. B,D, A breathing human above the phantom/sample. Measurements are shown for the central $k_z$ plane

FIGURE 8

The SD and RMS error (RMSE; in °C) over time for each image voxel for the four experiments. A,B, The gelatin phantom heating study. C,D, The heating of the ex vivo salt pork sample. A,C, No breathing human. B,D, A breathing human above the phantom. In each row, the first and second image are the SD of the uncorrected and corrected temperature images, respectively, and the third and fourth images are the RMSE of the temperature images without and with correction. The yellow rectangle in the first image shows the region of interest used for obtaining the average and SD of the SD and RMSE measurements

FIGURE 9

Bar chart of average SD and RMSE in time of the temperature measurements without and with corrections shown in Figure 8 for the four experiments. The measurements are averaged over the regions indicated in Figure 8. The SD of the measurements over the rectangle are plotted as the error bars

FIGURE 10

Temperature measurements versus time for the four experiments. A–D, top row: The temperature at the hottest point (solid lines) and a background point (dashed lines), with and without correction for the four experiments. E–H, bottom row: The average temperature in a 3×3 region of interest (ROI) around the hottest and background points