With numerous MRI applications lasting several minutes, MRI is prone to patient motion. In-plane motion can be corrected in post-processing when motion is tracked. Motion navigators^1-8 use additional gradient waveforms every TR or in separate interleaved TRs whereas marker-based methods, MRI-based⁹ or optical^10-12, use markers placed on the body for motion tracking. Marker-based techniques may suffer from false positives due to difficulties in fixing the marker, while motion navigators may affect the sequence timing due to the additional waveforms/TRs. Arguably the most commonly used technique is the PROPELLER, which acquires data in an overlapping manner and estimates motion from the overlapping data. Nevertheless, the overlapping acquisition increases the scan time by 57%, compared to a non-overlapping approach^13,14. Other techniques keep sequence timing unaltered^15,16 but cannot track rotational motion. Previously, we introduced a motion navigator that uses nonlinear gradient fields to encode translational and rotational motion¹⁷. The technique uses the simultaneous multi-dimensional encoding capabilities of NLGFs to encode motion using a single echo and with a time-penalty of less than one millisecond. In this abstract, we demonstrate the effectiveness of the technique experimentally for both rotational- and translational-motion.

Experiments were performed using a 3T scanner with an 8-channel receiver-array [Siemens Healthcare, Erlangen, Germany; sensitivities characterized as outlined in ¹⁸] and a Z2-harmonic ($$$x^2/2+y^2/2-z^2$$$) gradient insert (Resonance Research Inc, Billerica, MA, USA) controlled using a transmit-array architecture. In the first experiment, translational motion tracking capabilities of the method were tested. A circular cylindrical phantom (Model No: 8624186 K2285, diameter: 12 cm, Siemens Healthcare, Erlangen, Germany) was imaged using a spin-echo sequence and motion encoded at 8 different locations. Spin-echo parameters were; resolution, 128x128; flip-angle, 90-degrees; echo-time, 11ms; repetition-time, 500ms. Motion navigator parameters were NLGF amplitude, 30mT/m²; readout duration, 6.25 ms; readout samples, 256. In the second experiment, a custom-phantom with a rounded rectangular cross-section was imaged at 8 locations and orientations for tracking both rotational and translational motion. By randomly selecting k-space lines and corresponding motion encoding data from these datasets, composite image k-space and motion datasets were generated separately for each experiment. The maximum rotation angle was determined to be 9.8-degrees. Spin-echo images were obtained using a single-channel coil. All images were reconstructed to 256x256 resolution. Navigator images were reconstructed using Kaczmarz with 5 iterations and λ=0.02 to prevent the algorithm from converging to erroneous local minima due to the non-unique nature of the spatial encoding matrix (Figure 1) while motion-compensated images were reconstructed using two iterations and since spatial encoding functions were orthogonal for spin-echo images.

The NLGF and the disturbance in the static magnetic field were determined using a field mapping sequence¹⁷ and a larger phantom (diameter: 20cm). Spatial and temporal polynomial fitting were performed on the disturbance field and the difference between the two measurements to assess the true nature of the applied NLGF (Figure 2).

Finally, simulations demonstrate the applicability of the method in oblique-slices.

For translational motion, the maximum deviation from the actual motion values (determined using images reconstructed from full spin-echo datasets at each location) was less than 0.35mm in the Right-Left direction and 0.11mm in Anterior-Posterior, with the standard deviations being 0.21mm and 0.06mm, respectively (Figure 3).

For rotational motion, the mean and the standard deviation of the estimation error were -0.07-degrees and 0.23-degrees, respectively (Figure4).

With the proposed scheme, the outer-most and inner-most edges of the imaged object are determined via frequency encoding while the other edges are determined using parallel imaging¹⁷. Hence, the method would benefit from a receiver-array with more coils. Nevertheless, phantom locations were selected to be offset in the Posterior direction to test the efficacy of the method when the object is closer to a subset of coils (effective number of coils decreases). Hence, frequency encoding was more effective in the A-P direction, yielding a lower estimation error.

Simulations (Figure5) show that motion tracking can be performed in oblique slices and other field shapes also can be used for 2D navigation using a single-echo as long as the field varies along at least two directions simultaneously.

The maximum field generated inside a (10cm)³ isotropic volume was 0.3mT. By increasing the NLGF-amplitude such that the maximum field generated by the linear gradient fields of the system (40mT/m) is not exceeded inside the same volume, the navigator data can be acquired in less than half a millisecond, reducing the navigator length to less than a millisecond including the rewinder-waveform.

Motion navigation using nonlinear gradient magnetic fields¹⁷ was demonstrated experimentally with sub-pixel and sub-degree accuracy for translational and rotational in-slice rigid motion.