Phase-drift correction PRFS thermometry
In the phase-drift correction PRFS thermometry model, the region of interest (ROI) is selected on the actual thermal target, and its size can be changed arbitrarily. Outer and inner ROI regions represent unheated and heated areas, respectively. The phase difference of the outer ROI can be able to fit the phase drifts arising from extraneous sources apart from the variation of temperature in the inner ROI (ΔΦf) by a first-order polynomial, which can be written as
$$\Delta \varPhi_{f} \approx a_{0} + a_{1} x + a_{2} y$$
(3)
When the observational errors are uncorrelated and the weight coefficient matrix, W, is diagonal, the smooth function can be rewritten as Eq. (4).
$$\left( {X^{T} WX} \right)A = X^{T} W\Delta \varPhi_{f}$$
(4)
where X denotes spatial coordinates, A is the polynomial coefficients that is determined via a weighted least squares fitting. According to the phase-drift correction algorithm, conventional PRFS can be noted as:
$$\Delta {\text{T}} = \frac{{\Delta \varPhi - \Delta \varPhi_{f} }}{{\varUpsilon \alpha B_{0} TE}}$$
(5)
Equation (5) indicates that temperature sensitivity (ΔΦ/ΔT) is related to B0 and TE. At an echo time of 30 ms for a 0.35 T MR scanner, the temperature sensitivity is 1.61°/°C, which is almost 4.3 times smaller than that at 1.5 T under the same TE.
Materials and experimental settings
All imaging experiments were performed on a 0.35 T (PICA, Time Medical Systems, Hong Kong, China) open-configuration whole-body MR scanner with head coil. A 2.45 GHz microwave ablation instrument (METI-IVD, Fuzhong Medical, Nanjing, China) was the heating device. For ex vivo porcine liver ablation experiments, a 15 cm long and 2.5 mm in diameter MR-compatible ablation antenna based on a 50-Ω UT-085 semirigid coaxial cable was used. All tissues were kept stationary for two hours before scanning to equalize with the room temperature. The study was approved by the ethics committee of our institution.
Unheated phantom experiments
For all unheated experiments, it was assumed that the temperature of the object did not change in the course of experiments. This assumption was reasonable because the subject was not affected by the external temperature.
A cubic (12 × 12 × 8 cm3) gel phantom which consisted of 2% agar, 4% gelatin, 0.5% NaCl and 0.05% CuSO4 per 1 L pure water was used in this experiment. Images were realized by GRE sequence in the coronal plane with the following scanning parameters: repetition time (TR) = 50 ms, echo time (TE) = 30 ms, flip angle (FA) = 30°, Matrix size = 128 × 128, field of view (FOV) = 220 mm, number of slices = 3, slice thickness (ST) = 8 mm, slice gap (SG) = 0 mm, acquisition time = 6.4 s/slice. Five images were acquired sequentially without heating to verify the feasibility of MRT. The selected inner ROI contains 30 × 30 pixels, approximately 5.2 × 5.2 cm2. As seen in Fig. 1b, the width of outer ROI was 10 pixels (about 1.7 cm) on every side outside the inner ROI.
Unheated ex vivo porcine liver experiments
Unheated experiments were performed on an ex vivo porcine liver at 0.35 T with TR/TE = 50/30 ms, FA = 30°, Matrix size = 160 × 160, FOV = 256 mm, number of slice = 1, ST/SG = 8/0 mm, acquisition time = 8 s/slice. Only one slice of data was scanned five times due to the irregular shape of porcine liver. The selected inner ROI contains 40 × 40 pixels, approximately 6.4 × 6.4 cm2. Magnitude image from ex vivo porcine liver was depicted in Fig. 2a. As seen in Fig. 2b, the width of outer ROI was on every side outside the inner ROI. In this part, three different size of ROIs were set to determine the impact of ROIs selection on temperature errors. The inner and outer ROIs contain 30 and 15 pixels for ROI selection (RS) 1, 40 and 15 pixels for RS 2, and 30 and 10 pixels for RS 3, respectively.
Ex vivo porcine liver ablation experiments
A 2.45 GHz microwave generator was positioned outside the scanner room and the output power was set at 40 W for 330 s. Independent temperature measurements were obtained by fiber optic temperature probe (PalmSense, Photon Control, Inc, Burnaby, B.C., CA). MR-compatible ablation antenna was inserted into the ex vivo porcine liver. The fiber optic temperature probe, surrounded by the catheter, was oriented parallel to the scanning plane. Images were acquired during microwave ablation procedure by GRE sequence in the coronal plane using the following scanning parameters: TR/TE = 50/30 ms, FA = 30°, Matrix size = 128 × 128, FOV = 200 mm, number of slices = 1, ST/SG = 8/0 mm, acquisition time = 6.4 s/slice. The width of the selected inner and outer ROI were 25 (about 3.9 cm) and 10 pixels (about 1.6 cm), respectively. The ex vivo porcine liver was kept stationary to avoid the effects of movement. In this part, relative temperature changes calculated by the phase-drift correction PRFS method were compared to the temperature values measured by fiber optic temperature probe at the same pixels in order to reveal the accuracy of the algorithm of MRT.
In vivo human brain experiments
The feasibility and repeatability of the phase-drift correction PRFS thermometry was assessed by brain temperature experiments of healthy volunteers at room temperature. Three healthy volunteers were involved in this study and informed consent was written before accepting examinations. Images were scanned by GRE sequence in the transverse plane using the following scanning parameters: TR/TE = 50/30 ms, FA = 30°, Matrix size = 128 × 128, FOV = 256 mm, number of slices = 3, ST/SG = 8/0 mm, acquisition time = 6.4 s/slice. In order to compare with the results obtained by Zou et al. at 3.0 T MR scanner [40], the width of the selected inner and outer ROI (see as Fig. 3b) were both 10 pixels (2 cm), which was the same as the above published literature. The measurements were repeated four times to ensure the accuracy and security of the method for clinical interventional therapy. Student’s t test was used in statistical analysis to compare the root mean square error (RMSE) of temperature error between three volunteer studies.
Data analysis
All images were processed and analyzed off-line by MatLab (R2015a, The MathWorks, Inc, Natick, MA, USA) and ran on a computer with 8 GB of RAM and four core CPU operating at 3.3 GHz. Phase difference mappings were calculated by subtracting the reference phase image from the phase images acquired during the heating process. In the unheated experiments, the temperature RMSEs within the inner ROIs, calculated by conventional and first-to sixth-order polynomial fitting, were compared to choose the best order for phase-drift correction PRFS thermometry. The order of the polynomial to obtain the smallest temperature error was chosen as optimal. For microwave ablation experiments, temperature profile calculated by the phase-drift correction PRFS was compared with the temperature values resulted from the averaging over a nine pixels neighborhood surrounding the tip of the fiber optic temperature probe in the target thermal region. In addition, temperature difference values for unheated experiments could be entailed by the phase difference mappings using theoretical PRF thermal coefficient of − 0.01 ppm/°C [32].