Purpose

Previously, we developed a Wireless Radio frequency triggered Acquisition Device (WRAD1) - an intelligent wireless ‘marker’ capable of self-synchronizing to the gradient time frame with sub-microsecond precision (Figure 1). The WRAD measures the magnetic spatial encoding of the gradient coils, through induction, during a series of sinusoidal blips lasting 880 μs (3D pickup coil, Figure 1). This simplifies cross-calibration and miniaturization so that the additional hardware required for digitizing and processing the signals can be embedded within the ‘marker’ itself. By doing so, the scanner is in its original state when the device is removed. The device can therefore be thought of as “plug and play”, and used only when it is needed. Although the hardware requirements for sampling of the gradient fields through induction are simplified, the interpretation of these measurements is more challenging because they produce a 3-dimensional vector field. To alleviate this problem the WRAD incorporates additional sensors that over constrain the solution. In this work2 we demonstrate how this over-constrained data can be fused to accurately track and correct subject motion, as well as imperfections in the WRAD and gradient coils whilst controlling the output variance of motion parameters.

Methods

The filter we propose relies heavily on a precise estimate of the direction of the static magnetic field (Lb), obtained from a 3-axis magnetometer mounted on the WRAD (Magnetometer, Figures 1-2). We use this estimate to rotate the voltage vectors (3D pickup coils, Figure 2) from the WRAD frame (L) into an intermediate reference frame (M’) that has its z-axis aligned with the static magnetic field. This transform is more intuitively written in unit-quaternion form3:, where
The z-component of the gradient field contributes to the NMR spatial encoding. It is therefore possible to treat the z-component of each voltage in the same way as a frequency shift of an NMR field probe. The direction of the xy-component of the voltage vectors in the intermediate frame are used to encode the remaining degree of freedom in rotation of the WRAD with the filter state n (Figure 2): .
The amplitude of the xy-component of the vector encodes position in a different spatial dimension to its respective z-component (NMR) encoding. For example, the x-gradient coil encodes the z-displacement in the x-direction of the gradient frame (G). The vector field (f) produced by the changing gradients (s) encode the position (p) as follows: where
The bias state vector c (Figure 2) models mechanical misalignments of the x and y gradient coils with respect to the z-gradient coil in the z-direction and the z-gradient coil with respect to the x-gradient coil in the x-direction and y-gradient coil in the y-direction.
We account for a small bias in the magnetometer that could project into the results by introducing a state vector m (Figure 2) that represents a small rotation about the MRI scanner’s x and y axes.
The states m, n, p and c are then tracked using a modular Kalman filter. Here we assume the system is stationary, and therefore treat the other states as constant when updating each vector.
Experiments: 1) A synthetic rotation of the magnetometer with respect to the 3D pickup coil was introduced 5 seconds into a scan to test the estimation of the bias rotation state m.
2) Prospective motion correction of involuntary motion using encoding from only the X and Z gradient coils (sinusoidal navigator; duration of 600 μs per update; 120 T/m/s peak slew rate).
3) Prospective motion correction of deliberate motion using data from all 3 gradient coils (sinusoidal navigator; duration of 880 μs per update; 120 T/m/s peak slew rate).

Results

1) The filter effectively tracks biases caused by magnetometer misalignment (m Enabled, Figure 3).
2) A noticeable improvement in image quality is achieved, particularly in the frontal regions of the brain, even when the subject moved very little during the acquisition (Figure 4).
3) Prospective motion correction dramatically improves image quality for the case of deliberate motion even in the case of strong frequent motion (Figure 5).

Discussion

The proposed method requires a once-off calibration of a global scaling parameter (Volts/mm). This can be considered a device specific calibration. We therefore expect that the same WRAD could be used on multiple scanners without additional setup.

Conclusion

The WRAD provides a simple and effective way of enabling prospective motion correction on an MRI scanner without hardware modifications, calibrations or mounting considerations – such as line of sight. Pulse sequence modifications are, however, still necessary in the current implementation.

Acknowledgements

This work was supported in part by the National Institutes of Health under grants R01HD085813, R01HD093578, R21AG046657, R01HD071664 and R21MH096559, the Bertarelli Foundation, the NRF/DST through the South African Research Chairs Initiative and the University of Cape Town through the RCIPS Explorer fund EX15-009.