Introduction

In MRI, motion sensing plays a crucial part in obtaining clean images that are robust to physiological motion. Conventional motion sensing requires sequence dependent solutions (e.g., navigators) or sensors on the subject (e.g., bellows). The Pilot Tone (PT) navigator has been established as a promising alternative^1-4. PTs are pure tones within the MR bandwidth that are modulated by patient motion and received by the receiver coils. However, the PT must be placed outside the imaging band, which requires knowledge of the MR bandwidth and center frequency. For that reason, PT is not always feasible or convenient. In this work, we overcome this limitation by spreading the energy of the PT over a larger bandwidth. Our proposed method, the Spread Spectrum Modulated Pilot Tone (SSMPT), adds a small amount of noise to the entire imaging band which can then be estimated and removed from the image while remaining robust to changes in MR parameters.

Methods

Motivation
This methodology is motivated by the Direct Sequence Spread Spectrum (DSSS) where a pure tone is spread over many frequencies by multiplying the tone with a pseudo-random sequence (PRS) of +1 and -1. The PRS is chosen because its autocorrelation looks like a scaled discrete-time delta function, which is useful for demodulation, and because the spectrum of the PRS is evenly spread out over a large bandwidth. This yields a noise-like artifact rather than a zipper artifact that appears in PT (Figure 1). A spread spectrum allows the SSMPT to remain robust to MR parameters such as bandwidth and center frequency.

Model
A PRS $$$R[n]$$$ of length $$$M$$$ is transmitted repeatedly during the acquisition. Each received k-space readout can be written as $$y[n] = k[n] + AR_N[n-d]$$where $$$y[n]$$$ is the received readout, $$$k[n]$$$ is the unmodulated k-space line of length $$$N$$$, $$$A$$$ is the amplitude of the motion signal that we wish to recover, and $$$R_N[n-d]$$$ is the true PRS shifted by $$$d$$$ samples and truncated to be of length $$$N << M$$$. $$$k[n]$$$ and $$$d$$$ are unknown. We recover the desired quantity $$$A$$$ by cross-correlating each received line $$$y[n]$$$ with the PRS and taking the maximum value,$$ A \approx \max_n \frac{1}{N} R[n] \star y[n] $$ where $$$\star$$$ denotes cross-correlation. Because the sequence $$$R[n]$$$ is a PRS, and thus has desirable autocorrelation properties, we assume that $$$ R[n] \star R[n -d ] \approx M\delta[n - d]$$$ and $$$R[n] \star k[n] \approx 0$$$. However, in practice, the variation in $$$k[n]$$$ is large at the center of k-space, which violates this assumption. In order to combat this, we remove the peak by interpolating the problematic motion estimate points with a degree 10 polynomial. Finally, the motion estimate is lowpass filtered and is used to subtract the SSMPT noise to obtain a clean, corrected image. Figure 2 describes this pipeline in detail.

Simulation
The SSMPT technique was verified in simulation using a 2-D Cartesian k-space acquisition. For each k-space line, the SSM-PT was added with a random phase to emulate the scanner environment. To simulate respiratory motion, the SSMPT was amplitude modulated with a frequency of 0.3Hz. Figures 3b) and 3e) show that a weaker SSMPT causes a very large error in the motion estimate at the center of k-space, and that a stronger SSMPT gives a better motion estimate. Figures 3c) and 3f) show that the SSMPT removal process performs well but yields small streak-like artifacts due to discrepancies between the motion estimate and the true motion.

Results

Acquisition
To test the SSMPT technique in-vivo, images were acquired on a GE 3T MR750W system with a healthy volunteer. A software-defined radio (USRP-B200, National Instruments, TX, USA) was used to transmit the SSMPT. A single-slice, free-breathing abdominal SSFP scan (FA=35, TR=4.4ms, resolution=1.9mm) was acquired using SSMPT, conventional PT, and the bellows for respiratory sensing. The antenna was placed on top of the 32-channel combined anterior and posterior coil array.

Motion Estimation
The SSMPT is compared against the standard PT. Both are transmitted at the same transmit power. Images were reconstructed using a sum of squares on all but 4 coils due to noise. From Figures 4b) and 4e), we see that the SSMPT is comparable to the PT in measuring respiratory signals. After removing the SSMPT from the image, Figure 4f) shows that just a small amount of the noise persists.

In Figure 5, we derive motion estimates from the SSMPT under different transmit strengths. All the motion estimates perform well in comparison to the bellows signal. Figures 5d) and f) show the images after noise removal. Under a lower transmit gain, the recovered image quality is improved.

Conclusion

SSMPT spreads a pure tone over the entire imaging band. This allows SSMPT to remain more robust to changes in MR sequence parameters. The SSMPT noise artifact can be estimated and removed, preserving image quality. Simulated and in-vivo results suggest that SSMPT is comparable to the standard PT and Bellows for motion estimation while being more flexible for practical use.

Acknowledgements

We thank Alan Dong for his insights and useful discussions on Spread Spectrum Modulation.