2696

Temperature rise modelling framework for multiple electrode configurations on parallel transmit systems.

Jagjit S Sidhu¹, Ken Sakaie¹, Pallab K Bhattacharyya¹, and Mark Lowe¹
¹Cleveland Clinic, Cleveland, OH, United States

Synopsis

Keywords: Safety, Safety

Implanted electrodes can induce unsafe heating during MRI. Developing safe MRI protocols can be a burdensome process, involving intensive simulations that are hard to tailor to individual patients. To increase the feasibility of safe imaging of patients with implanted electrodes, we extend previous work, that nulled induced currents when the number of transmitters exceeded the number of electrodes, to account for the case when these are equal or the number of electrodes exceeds the number of transmitters. In such cases, complete nulling (no measured temperature rise) is impossible in all electrodes unless an acceptable induced temperature rise is allowed.

Introduction

Patients with implanted electrodes are typically denied the potential benefit of HF (>3T) or UHF MRI (>7T) due to safety concerns ¹. Higher field strengths provide increased signal-to-noise ratio (SNR) ², which allows for smaller structures to be more clearly visualized. To increase the feasibility of safe imaging of patients with implanted electrodes, Eryaman et al. ³ and Sadeghi-Tarakameh et al. ⁴ demonstrated a method to identify a safe operating point—an implant-friendly (IF) mode ^5,6. The results of ^3,4 were extended to the case of bilateral electrodes ⁷. Here, we extend the formalism presented by Sadeghi-Tarakameh et al. ⁷ to an arbitrary number of electrodes and validate the formalism with a phantom experiment.

Theory

The case of two electrodes and two transmitters is important because bilateral electrodes are common for treating movement disorders ⁸, and two transmitters are common among standard body transmit coils.
$$ A_1 I_{1,1} + A_2 I_{1,2} = J_1 $$
$$ \qquad \qquad \quad \qquad \qquad \quad \qquad \qquad \qquad A_1 I_{2,1} + A_2 I_{2,2} = J_2
\qquad \qquad \qquad \qquad \qquad \qquad \quad \qquad (1) $$
$$$ A_i $$$ is the complex amplitude in transmitter . $$$ I_{j,i} $$$ is the current induced in electrode $$$ j $$$ when transmitter $$$ i $$$ is switched on and includes contributions from the transmitter and the other electrode. $$$ J_j $$$ is the net current induced in electrode $$$ j $$$.
Various studies report a linear relationship between the specific absorption rate (SAR) and measured temperature rise ^9-12. SAR depends on the dissipated power, which in turn depends quadratically ³ on the induced current in each electrode:
$$ \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \Delta T_j \propto | I_j | ^2 \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad (2) $$
$$$ \Delta T_j $$$ is the temperature rise in electrode j. $$$ | I_j | $$$ denotes the magnitude of the induced current in electrode j. Writing the weights and induced currents as $$$ A_1 = \alpha_1 e^{i \phi_1} $$$, $$$ A_2 = \alpha_2 e^{i \phi_2} $$$, $$$ I_{j,1} = \beta_1 e^{i \theta_1} $$$ and $$$ I_{j,2} = \beta_2 e^{i \theta_2} $$$ we find
$$ \qquad \qquad \qquad \quad \quad \qquad \qquad \qquad \qquad \Delta T_j = C + D cos \Psi
\qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad (3) $$
where $$$ C = (\alpha_1 \beta_1)^2 + (\alpha_2 \beta_2)^2 $$$, $$$ D = 2 \alpha_1 \beta_1 \alpha_2 \beta_2 $$$, $$$ \Psi = \theta_1 - \theta_2 + \phi_{rel} $$$ and $$$ \phi_{rel} = \phi_1 - \phi_2 $$$ is the relative phase between the two transmitters. Equation (3) generalizes to any number of transmitters and electrodes.

Methods

Imaging was performed on a Siemens 3T Prisma system equipped with two independent ¹³ and fully integrated whole-body transmit channels (Siemens Healthineers, Erlangen, Germany) with a standard 20-channel head-neck receive-only array. A high SAR T2-TSE sequence with B1+ rms value of 2.1μT and Time-averaged RF power of approximately 20W was acquired to induce heating (axial, 240 mm x 240 mm FOV, 256 x 256 matrix, 32 slices, 4 mm thick, TE/TR=71/6470 msec, 212 Hz/Pixel bandwidth).
To simulate bilaterally implanted electrodes, two 0.8-mm diameter insulated copper wires with exposed tips were secured to the bottom of a cuboid shaped container of approximately 50 cm x 30 cm x 20 cm filled with gel prepared by following ASTM F2182-11a standard ¹⁴. Wire lengths of 85 cm were chosen to maximize heating ¹⁵. Wires were chosen instead of electrodes to exaggerate heating, providing a worst-case scenario ¹⁶. Temperature changes were measured using fluoroptic temperature sensor (model m3300, Luxtron (Lumasense Technologies), Santa Clara, CA, USA) by securely tying probes to the exposed wire tips.
The amplitude of transmitter one was fixed at 0.8 and that of transmitter 2 at 0.4. The phase of transmitter 1 was fixed at 0. The phase of transmitter 2 was varied from 0 to 360⁰ in increments of 30⁰. Matlab ¹⁷ was used to perform a fit of the maximum temperature rise as a function of phase for each wire to equation 2.

Results and Discussion

In Figure 1, we show the temperature as a function of time across the full duration of the TSE. A negligible temperature rise was measured in one wire but unacceptable temperature rise ($$$ > 2°$$$) ¹⁸ was observed in the other. This demonstrates that a safe operating point for one electrode is not necessarily safe for multiple electrodes.
Figure 2 shows the maximum temperature as a function of relative phase. The maximum temperature in each electrode follows the cosine relation predicted by equation (3). A minimum temperature rise can be achieved by appropriate manipulation of the relative phase (arrow, figure 2).

Conclusion

We have generalized the formalism of Eryaman et al. ^3,4,7 to include any number of transmitters and implanted electrodes and tested the formalism on a clinically relevant configuration of two transmitters and two electrodes. As the formalism is analytic, it may provide helpful constraints for finding safe operating points in general, allowing patients to benefit from the higher signal-to-noise ratio at higher field strengths.

Acknowledgements

We acknowledge support from the Imaging Institute of the Cleveland Clinic and from Siemens Healthineers.

References

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Figures

Heating over time in two electrodes differs dramatically. The amplitude of transmitter 1 was set to 0.4, that of transmitter 2 was set to 0.8 and the relative phase was set to 0. One electrode experienced a large temperature rise of over 3°C (solid line) while the other experienced negligible heating (dashed line).

Maximum temperature rise as a function of phase for configuration 3. The dotted and dashed lines indicate fit to the temperature rise with equation 3 for each electrode. The solid (dashed) arrow shows the overall minimum (maximum) temperature rise. A temperature rise ≤2°C is considered safe ¹¹.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

2696

DOI: https://doi.org/10.58530/2023/2696