Synopsis

Using external hardware to track patient motion allows for high frequency, accurate prospective motion correction that is robust to changes in coil set-up and subject anatomy. However, this typically comes at the expense of increased hardware complexity, difficulties in marker placement and in some cases cross-calibration. To address some of these challenges, we have developed a small, battery powered marker that uses the three-dimensional gradient spatial encoding, visible through Faraday induction, for vector-based position and orientation estimates. The device enables wireless, calibration-free prospective motion correction that can be used on an ad-hoc basis in an unmodified scanner.

Introduction

Although various devices have proven the efficacy of accurate, high frequency prospective motion correction, including optical cameras¹, NMR field probes², and the Endoscout³ system, they have had limited impact on clinical scanning, possibly due to increased hardware complexity. Here we present a smart, battery-powered marker that can be used in an unmodified scanner by simply placing it in the imaging volume. The device operates without scanner-specific calibration, external digitisation hardware, or physical connections to the scanner.

Method

A Wireless Radio-frequency triggered Acquisition Device⁴ (WRAD) was constructed (Figure 1). The device incorporates a 3-axis Hall effect magnetometer (MV2, Metrolab) and a 3-axis pickup coil. The potential induced in each of the pickup coils is amplified, filtered, digitised and analysed on the device before being transmitted out of the scanner using a 2.4 GHz radio link. The WRAD’s Analog to Digital Converter (ADC) is triggered by RF pulses ensuring sub-microsecond synchronisation to the gradient time frame⁴. The potential induced in the coils is proportional to the rate of change of the gradient magnetic fields $$$\dot{g}_x$$$, $$$\dot{g}_y$$$ and $$$\dot{g}_z$$$ (Faraday induction). By assuming negligible rates of change of curl and divergence and an axially symmetric z gradient coil⁵, the induced voltage vector $$$\vec{v}$$$ can be written as:

$$\vec{v} =-a\mathbf{R}\left( \left[ \begin{matrix}-\frac{\dot{g_z}}{2}& 0&\dot{g_x}\\0&-\frac{\dot{g_z}}{2} &\dot{g_y}\\\dot{g_x}&\dot{g_y}&\dot{g_z}\end{matrix}\right]\vec{p}+B_0\vec{z}\times\vec{\omega}\right) $$

where $$$\mathbf{R}$$$ is a rotation matrix that transforms a vector from the gradient coordinate frame into the WRAD coordinate frame. The vector $$$\vec{p}$$$ is the position of the centre of the pickup coil assembly in the gradient coordinate frame and $$$a = 0.1164$$$ m² is a constant scaling factor related to the cross-sectional area of the pickup coil and amplifier gain. The second term is related to the angular rate of change ($$$\vec{\omega}$$$) of the WRAD in the static magnetic field $$$B_0$$$. The magnetometer observes the sum of magnetic fields within the scanner bore (which are dominated by the static magnetic field). Once normalised, this vector ($$$\vec{m}$$$) represents the gradient z-axis observed in the WRAD coordinate frame:

$$\frac{\vec{m}}{|\vec{m}|}=\mathbf{R}\vec{z}=\begin{pmatrix}r_{13}\\r_{23}\\r_{33}\end{pmatrix}$$

which is the last column of $$$\mathbf{R}$$$. The magnetometer can therefore be combined with the pickup coil vector to solve for $$$\vec{p}$$$ with three unique gradient combinations (like NMR marker-based methods) because:

$$\frac{\vec{m}}{|\vec{m}|}.\vec{v}=-a\begin{pmatrix}\dot{g}_x&\dot{g}_y&\dot{g}_z\end{pmatrix}\begin{pmatrix}p_x\\p_y\\p_z\end{pmatrix}$$

This result is independent of the angular rate term as it lies orthogonal to the static magnetic field. To solve for $$$\mathbf{R}$$$ and the orthogonal spatial encoding, the angular rate term is eliminated by applying a single bin discrete Fourier transform to the voltages induced during sinusoidal gradient activations (Figure 2). In the special case of pure x- or y-gradient excitations, there is a solution to $$$\mathbf{R}$$$ without having to find $$$\vec{p}$$$ first. The three unique gradient excitations result in two measurements of both the x- and y-displacements and three measurements of the z-displacement. This is well suited to Kalman filter (sensor fusion) based methods. Sensor/gradient biases can therefore be modelled and tracked by adapting Equations 1-2. For the imaging experiments, a non-selective 3D spoiled multi-echo gradient echo pulse sequence with 1 mm³ isotropic resolution and two-fold GRAPPA acceleration was used. In total 7 high bandwidth (650 Hz/pixel) bipolar readouts were acquired with a TR of 20 ms. For each image, the Average Edge Strength⁶ (AES) quality metric was computed. The pulse sequence position and orientation were updated for each line of k-space, delayed by one TR to avoid underflow of the gradient waveform buffer.

Experiment 1) To ensure the WRAD does not degrade image quality by injecting variance into the acquisition through the prospective motion correction feedback, the subject was instructed to remain as still as possible during the image acquisition with and without motion correction active.

Experiment 2) The subject was instructed to adjust the position of their shoulders and limbs to simulate discomfort.

Experiment 3) The subject performed strong movements once every 5 seconds. This combined with cushion relaxation resulted in almost continuous motion.

Results

Experiment 1) Fine cortical folding is more clearly delineated on motion corrected scans even when subjects move very little (Figure 3).

Experiment 2) Use of the WRAD resulted in a high-quality image with a small amount of residual ringing, improving the AES by 48.2% (Figure 4).

Experiment 3) For severe motion, prospective motion correction achieved a diagnostic quality image and improved the AES by 51.8% (Figure 5).

Discussion

Conclusion

Acknowledgements

References

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