Table 2.
Input parameter sensitivity analysis. The Default Values are the values used for the main simulations, whereas the Adjusted Values were set to realistic values that could occur due to either measurement inaccuracy or experimental design choice. The sensitivity factors were calculated as the percentage error in temperature change per percentage error of input parameter. The measurement standard deviation (% of default value) was derived from literature values [41]. *Phantom was thermally stabilised for two days in the MRI scanner room prior to the experiment. Thus, the initial temperature of the phantom and MRI bore are assumed to be the same (Note that the absolute temperature was measured using fibre optic probes with field dependency [22]. This contains some error as the absolute temperature was measured on the patient table outside of the bore where the field strength is not 0 T). **The positioning error of the fibre optic probe was chosen as the half of the PRF image resolution used in the experiment. ***The standard deviation of the alpha coefficient was derived from three literature studies involving 1–2% agar phantoms [[37], [38], [39]].
| Parameter | Default Value | Adjusted Value | Thermal Elevation using Default Value [°C] |
Thermal Elevation using Adjusted Value [°C] |
Sensitivity Factor | Measurement Std. Dev. (% of default value) [41] |
Uncertainty [%] |
|---|---|---|---|---|---|---|---|
| Simulation parameters driven from Phantom Characterisation | |||||||
| Phantom conductivity [S/m] | 0.6227 | 0.6850 | 0.8643 | 0.8805 | 0.19%/% | 6.42% (0.04 S/m) |
1.20% |
| Phantom permittivity | 47.76 | 52.54 | 0.8643 | 0.8662 | 0.02%/% | 5.86% (2.8) |
1.29% |
| Phantom density [kg/m3] | 1022.22 | 1124.40 | 0.8643 | 0.7882 | 0.88%/% | 0.98% (10 kg/m3) |
0.86% |
| Phantom heat capacity [J/kg/°C] | 3776.3 | 4153.9 | 0.8643 | 0.7882 | 0.88%/% | 4.24% (160 J/kg/°C) |
3.73% |
| Phantom thermal conductivity [W/m/°C] | 0.4864 | 0.5350 | 0.8643 | 0.8618 | 0. 03%/% | 4.11% (0.02 W/m/°C) |
0.12% |
| Phantom heat transfer coefficient (W/°C/m2) | 2.5 | 3.0 | 0.8643 | 0.8642 | 0.01%/% | 40.00% (1 W/°C/m2) |
0.58% |
| Total uncertainties in simulation from Phantom characterisation | 7.78% | ||||||
| Simulation parameters driven from Experiment (PRF thermometry and fibre optic probe) | |||||||
| Stabilised temperature of the phantom and background* [°C] | 18.6 | 22 | 0.8643 | 0.8643 | 0.0%/% | 9.30% (1.73 °C) |
0.00% |
| Measured magnitude of Sii [S11 in dB] |
0.4124 [−7.69 dB] |
0.3928 [−8.11 dB] |
0.8643 | 0.8231 | 1.06%/% | 4.75% (0.42 dB) |
5.03% |
| RF exposure time [s] | 1258 | 1263 | 0.8643 | 0.8675 | 0.93%/% | 1.63% (20.5 s) |
1.52% |
| Exp. Error in fibre optic probe X position [mm] | 0 | 2.5 | 0.8643 | 0.9377 | 3.40%/mm | 2.71 mm ** | 9.21% |
| Exp. Error in fibre optic probe Y position [mm] | 0 | 2.5 | 0.8643 | 0.8515 | 0.59%/mm | 2.71 mm ** | 1.61% |
| Exp. Error in fibre optic probe Z position [mm] | 0 | 5 | 0.8643 | 0.8686 | 0.10%/mm | 5.77 mm ** | 0.57% |
| Total uncertainties in simulation from experiment (PRF thermometry and fibre optic probe) | 17.94% | ||||||
| Parameter used for PRF thermometry calculation | |||||||
| PRF alpha coefficient [ppm/°C] |
0.00988 | 0.01000 | 0.9491 | 0.9401 | 0.14%/% | 6.88% (0.00068***) |
0.95% |