Introduction

The goal of this work is to evaluate the reliability of hazard assessments, performed via numerical simulations, for patients carrying orthopaedic metallic implants exposed to MR gradient fields. While heating produced by radiofrequency (RF) has been investigated intensively [1-3], only few studies address heating of implants by switched gradients [4-6]. This work aims to complement simulation results based on [7,8] by experiments designed to maximize absolute accuracy. Clinically relevant MR conditions were chosen for gradient coil (GC), gradient sequence, implant type, and position.

Experimental Methods

Six orthopaedic prostheses (Table 1) were analysed. They were placed at various realistic orientations and positions inside a 3 T scanner (Siemens Verio) and encapsulated in a polystyrene box. The scanner was operated in normal mode and with minimal RF power. The evolution of implant temperature was recorded for various MR sequences (Table 2). Gradient-coil currents were recorded and denoised to be used in simulations. Three NTC thermistors (diameter 0.5 mm, length 3 mm) with twisted leads were used as temperature sensors. An active low pass filter with cut-off frequency at 10 Hz filtered the signal of a Wheatstone-Bridge. At the end of the day, the sensors were calibrated with a calibrated PT100 thermometer. Whenever possible, blind holes were drilled into the implants to optimize sensor contact. Alternatively, an aluminium socket carrying the sensor was glued to the implant.

Numerical Methods

The measured physical dimensions of the prostheses were used to build voxel models at 1 mm resolution. Simulations were performed at implant position $$$z=300 \text{ mm}$$$ and $$$250 \text{ mm}$$$ since the manufacturer supplied gradient-coil-field map shows a B-field maximum at $$$z=300 \text{ mm}$$$. Spatial power density distribution within the implant due to the GC field was computed following the approach described in [7]. The consequent heating was simulated by adopting a finite difference method with a Douglas–Gunn time split implemented to increase the computational efficiency [8]. Simulations allowed to determine the time evolution of temperature increases in the positions where sensors were located in the experiments.

Results and Discussion

Compared to fibre-optical thermometers, NTCs offer huge advantages in terms of precision and speed but are susceptible to electromagnetic fields. Direct eddy-current heating of sensors was determined to be below 2 mK and the noise at MR condition $$$0.5 \text{ mK} / \sqrt{\text{Hz}}$$$ . Implants were repeatedly heated with different MR sequences for 20 s or 32 s followed by cooling periods of 200 s. A linear baseline was subtracted from the experimental data. Uncertainties of the baseline cause negligible errors < 2 mK during heating but lead to diverting temperatures at the end of the cooling period of up to 30 mK and to 12 mK in Fig 1.
The implants used here were selected with a preference for large cross sections to induced eddy currents. A hip implant’s biarticular head was chosen for the first simulation because it promises the smallest uncertainty in eddy current simulation due to its simple geometry and well-known material properties in contrast to fine structured or porous implants.
Fig 1a shows the temperature evolution at 3 sensor positions in implant #1 (Table 1) during a sagittal EPI sequence for 20 s (Table 2). To quantify the deviation between experiment and simulation we use the root mean square of the temperature difference of all 3 sensors at $$$t=20 \text{ s}$$$. In the case of Fig 1 that is 0.021 K (4.6 % of temperature rise). The same metric applied to other 13 experiments with different positions in the GC, sequences, and orientations results in 0.057 K (8 %). Compared to the estimated experimental uncertainty of 15 % the deviation is rather small. Deviations in the cooling period increase with time. We attribute them to an imperfect baseline subtraction and roughly estimated heat loss coefficient of 3.5 W/(m² K) . Since model validation does not depend on data at $$$t>40 \text{ s}$$$ , this is not a problem.
Fig 1b shows the temperature distribution at $$$t=20 \text{ s}$$$ and the asymmetry causing the difference of the sensors on the rim.
Heating data for a femoral knee implant at various z positions are shown in Fig 2a. The implant was placed on the symmetry axis and heated by a trapezoidal z-gradient. The heating rate shows a quadratic dependency around $$$z = 0$$$, reflecting the $$$(z\frac{\text{d}G_z}{\text{d}t})^2$$$ curve. The maxima at $$$z = ±350 \text{ mm}$$$ are in good agreement with manufacturer-provided gradient maps.

Limitations

With a wall thickness of 3.5 mm the chosen hip implant is rather solid, and the model resolution of 1 mm seems sufficient. Most implants have finer structures, however, and the appropriate model resolution needs to be determined separately for every case. The analysis of experimental uncertainties is still incomplete regarding material properties and gradient-field non-linearities.

Conclusion

Numerical results on gradient heating of an orthopedic implant were successfully validated for different implant positions and five MR sequences. Cooling mechanisms were not investigated but are identical to the extensively studied case of RF heating. Fully simulation-based safety assessments are a valid tool, therefore, to estimate the hazard of gradient-aggressive MR sequences to implant carriers.

Acknowledgements

This work has received funding from the EMPIR programme, co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme, under grant number 17IND01 – MIMAS.