Mikhail Kozlov^{1,2} and Gregor Schaefers^{1,3}

^{1}MR:comp GmbH, Gelsenkirchen, Germany, ^{2}Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ^{3}MRI-STaR GmbH, Gelsenkirchen, Germany

### Synopsis

At
64 and 127.7 MHz RF-induced heating on or near nine distal radius implant
systems was investigated. The 3-D temperature distribution after 15 minutes
continuous excitation was obtained for a plane wave incident field. For one implant, random trials followed by a gradient-based
investigation revealed three screw configurations that resulted in a high
maximum temperature rise. Due to the smooth outcome of
random trials followed by a gradient analysis, even relatively small simulation
numbers allowed to reveal the configuration with the highest temperature rise for a given incident electrical
field.

### Introduction

Most of commercially
available implants are multi-component devices. With FDA released guidance FDA-2015-D-2104^{1}, reliability
requirements for RF-induced assessment significantly increased compared to
standard ASTM F2182-11a^{2} used widely in the past. Our goals were to analyze 64 and 127.7
MHz RF-induced heating of a distal radius implant system by: 1) simulating relevant configurations of one plate with longest
length and narrow width of distal end to reveal different hotspot locations; 2) simulating other 8 plates with the screw
configurations derived from analysis done for the first plate.### Method

A system
parameter matrix is shown in Fig. 1a. The plate and screws were placed in the
middle of a box with dimensions 600x600x2400 mm^{3}, filled with a
medium with relative electric permittivity of
78 and electrical conductivity of 0.65 S/m,
representing human muscle. The box was excited from one side by a 64 or 127.7
MHz source (Fig.1b). The
screws were simulated as “nails” (Fig 1.c) to reduce computational complexity while
only slightly increasing the temperature results uncertainty (~15%)^{3}.
A 3-D temperature distribution after 15 minutes continuous excitation
with tangential electric field *E*_{tan}(z)=100 V/m (peak-to-peak) was obtained by 3-D EM and thermal co-simulations. The
maximum temperature rise (**Δ***T*_{max})
was calculated as the highest difference of spatial temperature distribution for
cases with and without the implant.
For the first plate (**N76**) random trials followed by a gradient
based investigation included 30 co-simulations at both 64 and 127.7 MHz. The remaining eight plates were
simulated in only five configurations. Three configurations were derived from the
gradient analysis of the first plate. To obtain a base line level estimation
all plates were also simulated in two configurations: all screws with 24 mm length (**AS24**), and all
screws with 10 mm length (**AS10**).### Results and discussion

30 simulations were less than required to cover an entire
parameter matrix using Monte-Carlo analysis with reasonable uncertainty. However
at both 64 and 127.7 MHz,
three screw configurations resulting in high **Δ***T*_{max} (Fig. 2a-c and
Fig. 3a-c) were revealed. The locations of **Δ***T*_{max} were observed
in the medium in close proximity of: screw #1 with -15° angle, screw #12 with 15° angle, and plate
end face, respectively. **Δ***T*_{max}
variation for these cases was less than 12% and was ~75% higher than the minimum
**Δ***T*_{max}
obtained (Fig. 4). Neighboring configurations suggested by gradient analysis,
for example use of screws #10 or #11 instead of screw #12, resulted in a slightly
decreased **Δ***T*_{max}. For**
N76** , configurations
**AS24** and **AS10** resulted in relatively moderate **Δ***T*_{max}. At 64 MHz one
of randomly selected configurations resulted in 20% smaller **Δ***T*_{max} than
for **AS24** and **AS10**. At 127.7 MHz configuration
**AS24** resulted in the smallest **Δ***T*_{max}
(Fig.5).
For all plates and frequencies investigated: a) **AS24** and **AS10** configurations did not result in the
highest **Δ***T*_{max}; b) **Δ***T*_{max} for
**AS24** was not always higher that **Δ***T*_{max} for
**AS10**. Because gradient analysis was done only for **N76**, there is no guaranty that for other plates the highest **Δ***T*_{max} was
calculated. However because a) all plates were electrically short, b) the
longest plate was investigated by gradient analysis, and c) the gradient
analysis showed smooth behavior of **Δ***T*_{max} across
configurations that resulted in highest **Δ***T*_{max}, a scientific
rationale could be that for other plates, the difference between the highest **Δ***T*_{max} and the
smallest **Δ***T*_{max} for **AS24** and **AS10** should be similar
to this difference for **N76**. Thus based on available
results the highest **Δ***T*_{max}
across all plates was estimated as (3.44+1.55)=4.99°C for 64 MHz and
(2.64+1.43)=4.07°C for 127.7 MHz,
which is a bit higher than the corresponding maximum **Δ***T*_{max} obtained across
all simulations.
Cumulative numerical uncertainty for the given numerical
setup was estimated as less than 10%. However single surrounding tissue
approximation and only one orientation of the plate relative to the incident
field propagation were substantial simplifications of different in-vivo
multi-tissue cases. No uncertainties for these simplifications of very
complex real cases, and possible variation of thermal and electrical properties were
estimated in the given study.### Conclusion

Because of the smooth
outcome of random trials followed by a gradient analysis, even relatively small
simulation numbers allowed to reveal the configuration with the highest **Δ***T*_{max} for a
given *E*_{tan}(z). Our case study provided strong evidence that
3T static field strength cannot be considered as a worst-case for RF-induced heating. The specific results of this study, e.g., dependence
of **Δ***T*_{max} on plate dimension and screw
configuration, cannot be simply extrapolated to other implants.
This investigation without additional physical tests in MR environment is not sufficient to claim MR Conditional according to ASTM F2503.### Acknowledgements

No acknowledgement found.### References

1. FDA-2015-D-2104 “Assessment of
Radiofrequency-Induced Heating in the Magnetic Resonance Environment for
Multi-Configuration Passive Medical Devices”, March 2016, www.fda.gov

2. ASTM F2182-11a, Standard Test Method for Measurement of
Radio Frequency Induced Heating On or Near Passive Implants During Magnetic
Resonance Imaging, ASTM International, West Conshohocken, PA, 2011, www.astm.org.

3. Leewood, et. al “Simplified computational models of
medical devices for accurate RF heating simulations with significantly reduced
computational cost”, ISMRM 2015, p. 301.