Introduction

Accurate motion sensing is essential to resolve motion at multiple spatial and temporal scales within the human body. Conventional motion sensing requires on-patient hardware or sequence-specific changes (e.g. navigators) and may be inconsistent between subjects. Recently, Pilot Tone (PT) navigators have been proposed as an alternative method^1-4. Requiring no on-patient hardware, PTs are pure tones within the MR bandwidth that are modulated by patient motion and received by the receiver coils. The PT contains respiratory and cardiac information and can be easily separated from the image^1-4. However, the PT frequency is tied to the Larmor frequency and has a wavelength of 1-4.7m (7T-1.5T), which limits its sensitivity to motion within the body (Figure 1a-b).

In this work, we propose a new approach, Beat Pilot Tone (BPT), that overcomes this limitation. The main idea is that even the most linear preamplifiers still exhibit some second order intermodulation. We transmit two high-frequency tones separated by the desired BPT frequency within the bandwidth of the MR receiver (Figure 1c). These signals are picked up by the receiver coils, mixed at the preamplification stage via intermodulation, then digitized by the receiver chain. Since the MR signal is small (< -30dBm)⁵, little transmit power is necessary to induce an intermodulation at a similar amplitude as the MR. For this work, we leverage consumer grade hardware for the 2.4GHz ISM band as a proof of concept. At this frequency, the wavelength is 12.5cm; therefore, BPT obtains greatly improved (20x) sensitivity to motion compared to PT. We demonstrate our method with a respiratory phantom, a volunteer, and an SNR map.

Methods

Mechanism
The PT and BPT signals are sensitive to motion via two mechanisms:

1. Impedance changes - Subject motion changes the impedance of the coil, causing mainly intensity changes.⁶
2. Multi-path length - The transmitted wave experiences changes in path length, reflections, and attenuation from subject motion, resulting in amplitude and phase modulations.

The wavelength for 2.4GHz (12.5cm) is 19 times smaller than the Larmor wavelength at 3T (234.7cm); therefore, following mechanism 2, even a slight path length change due to motion will result in a much greater signal change in BPT than in PT (Figure 1b).
We transmit two signals at two different frequencies $$$f_T$$$ (2.4GHz) and $$$f_T + f_{BPT}$$$, where $$$f_{BPT}$$$ is an offset frequency within the MR bandwidth, for example, $$$f_{BPT} = f_{larmor} + 100kHz$$$. A beat frequency $$$f_{BPT}$$$ is created via mixing in the preamplifier; this signal is the BPT.

Hardware setup
Figure 2a shows the transmission setup. Each transmit frequency was controlled by an Ettus Research B200 software-defined radio (SDR; National Instruments, TX, USA) and synchronized to the system 10MHz clock. The ~10dBm signals were combined, amplified by 17dB, high-pass filtered, and transmitted by a panel antenna placed inside the bore above the subject (Figure 2b). For comparison, a PT close to the Larmor frequency was transmitted using a waveform generator (Siglent SDG6022X, Siglent Technologies, OH, USA). The calculated power output of the BPT was approximately 20dBm at the antenna. The gains of the PT and BPT were adjusted to similar received levels.

Acquired scans
All scans were acquired on a GE 3T MR750W system using a 2D axial balanced SSFP sequence. Phantom scans were acquired on a pneumatic phantom using a 32-channel body coil (TR=3.6ms, FA=35). Two scans were acquired on a volunteer (TR=4.6ms, FA=35): a head scan using a 22-channel head-neck coil and an abdominal scan using a 32-channel body coil. In the first scan, the volunteer moved their head up and down (anterior/posterior). In the second scan, the volunteer breathed normally. To evaluate SNR, a uniform phantom was scanned with BPT, PT, and no PT using a 2D SPGR sequence (TR=34ms, FA=30, resolution=0.9mm). An SNR map was computed using the method developed by Kellman et al⁷.

Reconstruction
The BPT signal forms a line in ky-f space after taking a Fourier transform along the readout direction (Figure 2c). To reconstruct the BPT signal, we demodulate the raw data by the BPT frequency ($$$f_{BPT}$$$) for each TR and each coil. To avoid phase wrapping and inconsistency between the BPT hardware and MR system, we subtract the phase of a reference coil from each of the coil signals.

Results

Figure 3b shows the results of the motion phantom experiment, where the y-axis is the signal amplitude divided by the mean. The BPT shows 20x greater modulation in magnitude and in phase than the PT.

Figure 4 shows the results of the in-vivo experiments. Figure 4b shows the signals from the three most modulated coils for the head motion experiment. The small (~cm) scale motion (black arrows) is evident in the BPT magnitude and phase, but difficult to see in the PT magnitude and phase. Figure 4e shows that both the BPT and PT capture respiratory motion comparably to bellows.

Figure 5 shows the computed SNR maps. The SNR maps (5a) and line profiles (5b) are nearly identical between conditions.

Conclusion

We have proposed BPT, a new, flexible motion sensing method that offers high sensitivity to small-scale motion within the body without on-subject hardware. We demonstrated that BPT outperforms PT in detecting motion while not affecting image SNR.

Acknowledgements

We sincerely thank Alan Dong for suggesting the beat frequency idea, and acknowledge Karthik Gopalan, Jason Stockmann, and Jonathan Polimeni for their code to compute image SNR. We acknowledge support from NIH grants U01 EB025162, R01HL136965, and U01EB029427.