Introduction

The RF transmit in MRI can couple to conductive leads of implanted devices, resulting in RF-induced heating at lead tips^1-4. Detection of the amplification in RF power around lead tips responsible for this heating has been demonstrated with thermo-acoustic ultrasound (TAUS) using the MR scanner's RF body coil and an inexpensive single-element ultrasonic transducer^5,6. The temperature-dependence of the lead tip TAUS signal could also allow for TAUS lead tip temperature monitoring during MRI⁷.

The TAUS pressure signal is formed by thermo-elastic expansion resulting from RF absorption. For TAUS temperature monitoring during MRI to be practical, only a minimal lead tip temperature rise should be required to generate detectable TAUS signals. Here, we characterize the TAUS signal generated as a function of RF power at a lead tip, and we consider the signal that can be generated while constraining lead tip heating.

Theory and Methods

The local specific absorption rate $$$SAR(\vec{r},t)$$$ in MRI can be expressed as a product of the SAR spatial profile $$$G(\vec{r})$$$ and the RF transmit power $$$P(t)$$$. The excited TAUS pressure signal $$$p$$$ is then described using the acoustic wave equation $$\left(\nabla^2-\frac{1}{v_s^2}\frac{\partial^2}{\partial t^2}\right)p\left(\vec{r},t\right)=-\frac{\beta\rho}{C}G(\vec{r})\frac{\partial P(t)}{\partial t},$$ in tissue with speed of sound $$$v_s$$$, thermal expansion coefficient $$$\beta$$$, specific heat $$$C$$$, and density $$$\rho$$$. The frequency content of $$$P$$$, set by the envelope of the RF transmit, determines which acoustic frequencies are excited. For frequency-modulated continuous-wave (FMCW) TAUS acquisition schemes, a chirp signal is used to amplitude-modulate the RF transmit, effectively encoding signal depth with frequency (Figure 1)^6,8,9.

We first consider FMCW TAUS acquisitions for a simple lead tip geometry for which key properties can be defined analytically. For induced rms current $$$I_{rms}$$$ on a thin insulated wire driving a spherical electrode (Figure 2), the current density, time-averaged SAR, and steady-state temperature rise (no perfusion) around the electrode are $$\vec{J}(r)=\frac{I}{4\pi r^2}\hat{r},$$ $$SAR_{avg}(r)=\frac{I_{rms}^2}{16\pi^2r^4\sigma\rho},$$ $$\Delta T(r)=\frac{I_{rms}^2}{16\pi^2\sigma kR_0}\left[\frac{1}{r}-\frac{R_0}{2r^2}\right],$$ where $$$r$$$ is the distance from the center of the electrode of radius $$$R_0$$$, and $$$\sigma$$$ and $$$k$$$ are respectively the electrical and thermal conductivities of the tissue. Assuming acoustic waves are reflected from the electrode surface and neglecting acoustic attenuation, the frequency-domain TAUS pressure $$$\bar{p}$$$ is $$\bar{p}(r,\omega)=\frac{v_s\beta\rho\bar{P}(\omega)}{2Cr}\int dr'r'G(r')\left(e^{-j\frac{\omega}{v_s}\left|r-r'\right|}-\frac{1-j\frac{\omega}{v_s}R_0}{1+j\frac{\omega}{v_s}R_0}e^{-j\frac{\omega}{v_s}\left(\left|r+r'\right|-2R_0\right)}\right),$$ where $$$\bar{P} $$$ is the spectrum of $$$P$$$ for the FMCW RF transmit and $$$G$$$ has the same spatial dependence as $$$SAR_{avg}$$$. This frequency-domain response gives the amplitude of the TAUS signals generated when the RF transmit is amplitude-modulated at different frequencies.

To determine similar relationships for a realistic lead geometry, a model lead tip was characterized in COMSOL Multiphysics (Figure 3). First, the SAR spatial profile was determined with a 64 MHz RF simulation. Heat-transfer simulations (no perfusion), using the SAR spatial profile as a heat source distribution, determined the steady-state maximum temperature rise versus lead tip power absorption. Acoustic simulations determined the frequency-domain TAUS response.

For both a spherical electrode (R₀=1mm) and the model lead tip, we simulated the TAUS signal generated by FMCW acquisitions using a 2.5ms RF transmit of a 100% AM signal. Assuming periodic TAUS acquisitions every 1s, the fractional transmit duty cycle D was 0.25%, and the time-averaged SAR and maximum steady-state temperature rise were reduced by a factor of D for a given induced lead tip power. With these parameters, we calculated the lead tip power corresponding to a maximum steady-state temperature rise of 0.25^oC. To determine the time-domain TAUS signal at a certain position, the frequency-domain response of the TAUS signal at that position ($$$\bar{p}(\vec{r},\omega)/\bar{P}(\omega)$$$) was calculated, and then the inverse FFT of the frequency response was convolved with the baseband content of $$$P$$$ for the desired FMCW excitation. FMCW postprocessing (mixing with time-reversed chirp, windowing, IFFT) recovered SNR and resolution. The recovered signal level was quantified by comparison to the rms value of white Gaussian noise following FMCW postprocessing.

The tissue properties used for calculations and simulations were $$$v_s$$$=1500m/s, $$$\beta$$$=4e-4K^-1, $$$C$$$=4000J/kg/K, $$$\rho$$$=1000kg/m³, $$$\sigma$$$=0.5S/m, $$$k$$$=0.5W/m/K.

Results and Discussion

The excited thermo-acoustic pressure amplitude varies significantly with the transmit modulation frequency for both the spherical electrode and the model lead tip (Figures 2c,d and 3c,d). The frequency response depends on the lead geometry (Figure 2d), and acoustic interference patterns form according to the excited acoustic wavelength (Figure 3c). The pressure level decreases with distance from the lead tip (Figures 2c,3d).

For a spherical electrode with R₀=1mm and D=0.25%, an induced current of 89mA_rms during RF transmit, corresponding to 1.26W at the lead tip (3.15mW time-averaged), results in a worst-case steady-state temperature rise of 0.25^oC and a maximum temperature rise of 63mK per FMCW transmit. Figure 4a shows the FMCW time-domain signals at r=3cm for acquisitions using different chirp bandwidths at this power level.

For the model lead tip with D=0.25%, 1.88W power deposition at the lead tip (4.7mW time-averaged) caused a 0.25^oC maximum steady-state temperature rise and a maximum 50mK rise per FMCW transmit. Figure 5a shows 2.5ms FMCW time-domain signals for this power level.

FMCW postprocessing of the time-domain signals determined the intensity vs distance (Figures 4b,5b).

Conclusion

We characterized the TAUS signals generated from lead tips as a function of RF power deposition and the excited acoustic frequencies for FMCW TAUS acquisitions. Detectable signal levels can be generated without inducing significant temperature increases.

Acknowledgements

This work was supported by the NIH under grants 5R01EB012031, 2R01EB008108, and P01CA159992, and by the William R. Hewlett Stanford Graduate Fellowship.