Beat Pilot Tone (BPT): Simultaneous MR Imaging and RF Motion Sensing at Arbitrary Frequencies

A volunteer was asked to perform different breathing types: chest breathing, stomach breathing, rapid-shallow breathing, and breathing with simultaneous bulk motion of the chest (Figure 6). The bulk motion consisted of rotation of within +/- 3 degrees about the head-foot axis and translation between -15mm to 5mm in the left-right and anterior-posterior axes (Figure S2). PT and BPT-Tx were transmitted simultaneously at frequencies of $127.8$ MHz and $2.4/2.5276$ GHz, respectively. The scan was acquired with the semi-flexible GEM anterior array. The data was low-pass filtered and converted to percent modulation units (excluding coils with low means, for which the percent modulation is artificially large). The phase was extracted using the method described in the Supporting Information. The low-pass filter cutoff was $2$ Hz for respiratory motion (Figure 6a) and $14$ Hz for bulk motion (Figure 6c) to better visualize sharp movements.

We further investigated separation between motion types by applying Principal Component Analysis (PCA) to PT and BPT-Rx. We compared the time evolution of three PCs of PT and BPT-Rx for a portion of the data with breathing and bulk motion (Figure 6e). Three PCs were chosen for visualization purposes.

We repeated this experiment with the same volunteer at BPT-Tx frequencies $300/427.6$, $800/927.6$, $1200/1327.6$, and $1800/1927.6$ MHz, with simultaneous PT at $127.8$ MHz throughout. BPT-Tx transmit powers ranged from 10 dBm to 20 dBm at the antenna, while PT was fixed at -36 dBm at the antenna in order to result in the same received level (explained in Section 1.6). Results from selected coils are shown in Figure S3.

To evaluate frequency-dependent cardiac sensing with BPT, we acquired a series of breath-held cardiac scans of a volunteer at BPT-Tx frequencies ranging from $400$ MHz to $2.4$ GHz (Figure 7), chosen to be the same as the EM simulation (Figure 4). The scans were acquired on the same GEM anterior array coil used in the respiratory experiment but with 16 additional posterior coils (GE Healthcare; Waukesha, WI). BPT-Tx and PT were transmitted simultaneously, with PT at 127.6 MHz and -38 dBm and BPT-Tx ranging from 10 to 17 dBm. The scans were acquired with RF excitation and gradients off in order to avoid artifacts (see Section 1.11). BPT-Tx was transmitted using a 2.4 GHz printed circuit-board (PCB) dipole antenna placed at the top of the bore, while PT was transmitted with a waveform generator (SDG6022X; Siglent Technologies; OH, USA) and a small broadband loop placed on the chest. We used a wideband amplifier and band-stop filter for the BPT-Tx setup (Section 1.4). BPT-Rx and PT were acquired with simultaneous photoplethysmogram (PPG) on the subject’s finger as a reference for signal timing and shape.

The PT/BPT magnitude signals were low-pass filtered with a cutoff of $25$ Hz, mean-subtracted, and normalized to unit variance (Figure 7a). Signals from four coils with the greatest energy in the cardiac frequency range [0.9, 3] Hz were plotted. We further compared the signal characteristics of BPT-Rx and PT (Figure 7b). PT from an empirically chosen coil element was low-pass filtered with a cutoff of 2 Hz, while BPT-Rx was filtered with a cutoff of 25 Hz for best visualization.

We performed an additional cardiac experiment to assess whether rigid contact with the coil was necessary to sense BPT-Rx signal at 2.4 GHz. We measured breath-held cardiac BPT-Rx data while the GEM coil was not in physical contact with the subject. A 2.4 GHz dipole PCB antenna at the top of the bore transmitted the BPT at 20 dBm and 2.4/2.5278 GHz. The results of this experiment are in Figure S4.

We compared BPT-Rx from breath-held scans of a volunteer to dBCG acquired with a tri-axial accelerometer placed on the chest as well as to PT, ECG, and PPG [46] (Figure 8). The accelerometer setup (Figure 8b) was the same as in the coil vibration experiment, but with the accelerometer on the subject’s chest. We used a 2D SPGR sequence with RF and gradient excitation turned off, BW=$62.5$ kHz and TR=$8.7$ ms to allow data transfer from the Arduino. As in the cardiac motion experiment, a semi-flexible GEM receiver coil was used, and PPG was measured from the subject’s finger. ECG was also acquired with electrodes on the chest. The accelerometer signals were high-pass filtered with a cutoff of $4$Hz, then integrated twice to obtained displacement.

We performed a least-squares fit to compare dBCG and BPT-Rx quantitatively by regressing the multi-coil BPT-Rx signals to dBCG measured on the left-right axis. Magnitude BPT data were low-pass filtered with a cutoff of $15$Hz, and all signals were de-meaned before the regression. We denote the resulting signal as BPT-dBCG (Figure 8e).

To investigate the effect of coil characteristics on BPT-Rx, we additionally measured cardiac signal from a breath-held volunteer scan using a flexible coil array marketed as the AIR coil (GE Healthcare; Waukesha, WI). BPT-Tx and PT were transmitted simultaneously at frequencies 1.8/1.9298GHz and 129.8MHz, with transmit powers of approximately 10dBm and -44 dBm at the antenna, respectively. 129.8 MHz was chosen because PT modulation is empirically more pronounced than at 127.8MHz yet still in the receiver BW. BPT-Tx was transmitted using the setup described in Figure 3 and a 4G LTE antenna, while PT was transmitted with a waveform generator (SDG6022X; Siglent Technologies; OH, USA) and a small broadband loop, with both BPT and PT transmitters placed on the coil. Data was acquired with RF and gradient excitation turned off. Results from a single coil are shown in Figure S5.

We measured head motion on a volunteer with simultaneous MIMO BPT and PT while acquiring a series of low-resolution 3-dimensional images on a rigid 22-channel head-neck coil (GEM HNU; GE Healthcare; Waukesha, WI) that was not touching the subject. The arrangement of coil elements is shown in Figure S7. The goals of the experiment were two-fold: first, to evaluate the sensitivity and accuracy of BPT-Rx and PT in detecting head motion, and second, to introduce and evaluate MIMO capability for both BPT-Rx and PT.

For the first goal, we explored whether PT and BPT-Rx could capture the lower-dimensionality of nodding and shaking out of the larger space of possible head positions. We performed a calibration scan and an inference scan. In the calibration scan, the subject moved in a raster fashion to sample all translations and rotations within +/- 3mm and +/- 4 degrees (Figure S6a). During the inference scan, the subject shook their head “no” and nodded their head “yes” (Figure S6b). Both scans were acquired using a 3D SPGR sequence (FOV=42 $\times$ 42 $\times$ 27cm, FA=5, BW=250kHz, acceleration=2.5$\times$). The calibration scan was acquired at $\sim 1$ frame per second with 115 frames, and the inference scan at $\sim 0.4$ frames per second with 50 frames.

The transmit setup consisted of two 2.4 GHz dipole PCB transmit antennas placed on the top and side of the head coil with cardboard in between the antenna and the coil to prevent detuning (Figure 9a). The frequencies were 2500/2372.39, 2400/2527.78 for BPT-Tx and 127.58, 127.81 MHz for PT with transmit powers of +15dBm and -42 dBm respectively. Two SDRs and two dual-channel RF transmit devices (SynthHD; Windfreak Technologies, LLC; FL, USA) were used to transmit all tones. The SDRs and one SynthHD produced two sets of BPT-Tx, while the second SynthHD produced the PTs. Each BPT-Tx chain consisted of a power combiner, narrow-band WiFi amplifier, and high-pass filter (Figure 3). An additional combiner (ZFSC-2-372-S+; Minicircuits; NY, USA) was used to combine the two BPT-Tx tones with a PT, yielding three tones on each antenna.

To evaluate the accuracy of BPT-Rx and PT, we obtained ground-truth motion estimates by registering the low-resolution image timeseries. The registration estimates were Savitzky-Golay filtered (window=11 samples, order=4) and compressed to 3 PCs for visualization purposes. The PCs (reg-PCs) explained $99\%$ of the variance of the data. An affine registration, recording translation and rotation, was performed using the SimpleElastix Python package with default settings [47].

The calibration BPT-Rx and PT data were first preprocessed by averaging over each frame and filtering using a Savitzky-Golay filter (window=11, order=4) to reduce noise. Each data set had a dimension of $[115\times 22\times 2]$ corresponding to number of frames, coils and tx antennas, respectively. It was then reshaped to $[115\times 44]$ and compressed to 3 PCs (Figure S6c-d). The inference BPT-Rx and PT data were processed in the same way and then projected onto the learned PCs. The resulting signals explained $\sim$95% of the data variance for both BPT and PT. As in Figure 6e, we plotted each time point in the PC-space (Figure 9d).

To evaluate the MIMO setup quantitatively, we regressed the multicoil BPT-Rx and PT signals to each reg-PC using data from both antennas, top alone, and side alone. A single reg-PC was chosen for plotting (Figure S8), while the correlations with all reg-PCs are reported in Table S3 (bolded values indicate the maximum values). Qualitative plots of the time and PC domain plots using data from both antennas, top alone, and side alone are shown in Figure S9.

The respiratory motion experiment suggests that BPT-Rx is sensitive to changes in breathing and bulk motion (Figure 6). Figure 6a displays the two most modulated coils from BPT-Rx and PT, each scaled within their maximum and minimum percent modulation. The numbered coils are physically arranged as in Figure 6b. We compared the range (max - min) of BPT-Rx and PT modulations. BPT-Rx is 6.3$\times$ more modulated than PT in magnitude and 7.3$\times$ in phase during breathing. When overlaid on a patch of the image over time, both BPT-Rx (top) and PT (bottom) breathing signals appear comparable (Figure 6d).

BPT-Rx is also 4.3$\times$ more modulated than the PT in the bulk motion portion of the experiment in magnitude and 3.2$\times$ in phase (Figure 6c). While the BPT-Rx magnitude shows much sharper peaks for bulk motion than breathing, the PT magnitude is smoother, similar to the breathing signal. Thus, Figure 6a and c suggest that BPT-Rx can achieve greater motion sensitivity than PT, and that bulk motion appears noticeably different from respiration.

Figure 6e further demonstrates that breathing is better separated from bulk motion in BPT-Rx PCs (right) compared to PT PCs (left), with the green dashed line indicating a separating plane. Separation in the PC feature space may be a good metric to distinguish between motion types. For instance, after a training period, this information could be used to reject outliers or prospectively acquire data only during respiratory motion.

We found that BPT-Rx signals from some coils over a broad BPT-Tx frequency range have multiple peaks. The simulation (Figure 4) suggested that standing wave patterns with multiple peaks and nulls are created when transmitting into an empty bore. In a setting with a human subject in the bore, the body modulates the standing wave based on its conductive properties, and this standing wave changes with motion; thus, the setting is much more complex. Figure S3a shows manually chosen coil signals from the respiratory experiment with multiple peaks across a broad range of BPT-Tx frequencies (300/427.6, 800/927.6, 1800/1927.6, 2400/2527.6MHz), with corresponding coil positions in S3b. This result further supports the standing wave mechanism.

On the GEM semi-flexible coil array, BPT-Rx at low frequencies appears to reflect blood volume changes, while BPT-Rx at high frequencies appears more sensitive to surface vibrations of the body. Figure 7a shows PT and BPT-Rx magnitudes from the four coils with the greatest energy in the cardiac frequency range. PT cardiac signal appears noisier and contains a single peak for each heartbeat, a signal shape that arises from blood volume changes [35]. However, the BPT-Rx signals at high frequencies (1.8 and 2.4GHz) are cleaner and appear to contain multiple peaks. Figure 7b further shows the differences between PT, BPT-Rx, and PPG acquired simultaneously. At lower frequencies ($<1.2$GHz), BPT-Rx changes smoothly. At higher frequencies ($\geq 1.2$GHz), BPT-Rx contains multiple sharp peaks. It appears that the sensing mechanism is different — as explained in the next section, we hypothesize that BPT-Rx at high frequencies captures dBCG, which measures millimeter-scale vibrations of the body due to the ballistic forces of blood. Given that intermediate frequencies (464 and 864MHz) may contain more than one peak per cycle but have a similar shape to PT, it is possible that the cardiac signal arises both from both blood volume changes and dBCG. The improved quality of the signal at high frequencies suggests that BPT-Rx cardiac signal can be extracted from the raw data with minimal processing, which makes BPT a promising candidate for real-time cardiac gating applications.

However, Figure S4 suggests that rigid contact with the subject may be required to obtain these BPT-Rx results at high frequencies. When the coil is elevated above the subject (Figure S4b), the sharp peaks do not appear as visible (Figure S4d). There is still some cardiac modulation, but it appears weaker. We hypothesize the reasons for this in Section 1.9.4.

Cardiac signals acquired by BPT-Rx at 2.4/2.5278GHz highly correlate with dBCG [49, 50, 46] (Figure 8). This suggests not only that BPT-Rx at microwave transmit frequencies is sensitive to very small vibrations but also that BPT-Rx could offer information about the cardiac cycle that is complementary to MR imaging. dBCG can be measured in many ways, including fiber-optic sensors [51], pneumatic sensors [49], cameras [52], doppler radar [53], or accelerometers [52].

Figure 8c demonstrates the timing of the raw BPT-Rx signal from the coil in Figure 8d relative to low-pass filtered PT (cutoff = 3 Hz), dBCG, PPG, and ECG signals. The timing and peaks of the BPT-Rx signal qualitatively match dBCG. Quantitatively, the regressed BPT-dBCG has a strong correlation of 0.81 with dBCG (Figure 8e) [46]. We hypothesize that BPT senses mechanical vibrations; therefore, BPT-dBCG may be enhanced due to the stiffness of the receiver array and contact with the subject.

One caveat, however, is that dBCG may not be visible with BPT-Rx on all coils. The AIR coil experimental results are shown in Figure S5. The top subplot shows percent modulation of BPT-Rx and PT relative to the mean. While BPT-Rx is approximately twice as modulated as PT, the modulation is still within +/- 1%, which is much smaller than the level of modulation in dBCG ($\approx 30\%$ [46]). Moreover, the signal shape and timing appear very similar between PT and BPT-Rx. We hypothesize that BPT-dBCG is visible in the experiments with the GEM coil because of its mechanical stiffness, which amplifies vibrations of the body when touching it. In contrast, the AIR coil is flexible and may dampen these vibrations. Figure S4 further supports this hypothesis - when the GEM coil is not in physical contact with the subject and thus not vibrating, BCG does not appear visible.

The cardiac results suggest that BPT may be influenced by blood volume changes as well as surface vibrations of the body and the coil. The relative contribution of each of these mechanisms appears to depend on the stiffness of coil, the level of contact with the subject, and the transmit frequencies.

Figure 9c shows the three PCs for the registration parameters (reg-PCs), BPT-PCs, and PT-PCs over time, while Figure 9d shows the same data in the PC space from two viewing angles. The smoothness of the BPT-PC curve in Figure 9c suggests that the BPT-PCs may be less noisy than PT. In 9d, the BPT-PCs overall look very similar to the reg-PCs. Both BPT-PCs and reg-PCs show a crossing behavior that corresponds to the position of the head between nodding and shaking. Moreover, both show smooth trajectories for nodding and shaking. However, the PT-PCs are noisier, with less clear structures to distinguish nodding from shaking.

Quantitatively, MIMO appears to have benefits for BPT-Rx and PT: the regressed BPT-Rx and PT (Figure S8, Table S3) computed with data from both antennas have greater correlation with the reg-PCs than regressed BPT-Rx/PT using data from a single antenna. Regressed BPT-Rx (Figure S8b) has consistently higher correlation than PT (Figure S8a) over all reg-PCs (Table S3). Figure S9 shows the time and PC-domain plots for the top and side antenna data alone, showing qualitative differences between the two datasets. These results suggest that MIMO-BPT has the potential for accurate quantitative rigid motion correction.