Especially at high magnetic field strengths, subject motion is becoming a limiting factor for reaching the theoretically possible high resolutions of medical images, particularly in long scans. Several methods were proposed to address this problem.¹ In this work, motion is tracked using NMR field probes, in a setup similar to ². This approach to motion tracking was so far only evaluated by assessing the quality of prospectively corrected images.³ In this study we used field probes to measure the motion of a phantom, and compared the estimated motion parameters against the trajectories obtained with a high accuracy optical tracking camera system.

The NMR field probes use Hexafluorobenzene (C6F6) as an NMR active liquid. The probes are connected to a tuning matching board and are excited by a custom-built transmit/receive-chain based on microelectronic components assembled onto a PCB board.⁴ The signals are demodulated on the PCB board inside the scanner bore and transmitted to and from the board via a shielded Ethernet cable. The demodulated signal is filtered and then digitized at a sampling rate of 500 kS/s using a commercial ADC (NI PCIe-6363, National Instruments, Austin, TX, USA). Due to the external hardware, the setup does not occupy any channels of the MR Scanner as, for example, is the case in ¹. The optical camera system that we used is a commercially available system (KinetiCor Inc, HI, USA) that uses a single Moiré Phase Tracking (MPT) marker for measuring motion .⁵ The measurements were carried out with a 9.4 T human MRI scanner (Siemens Magnetom). The position of each probe was determined via 3 block gradients along each axis (5 mT/m, 0.5 ms). The phase φ of the field probe signal was used to determine the field strength using the following equation $$$\int_0^t B(\vec{r},t)d\tau = \phi(\vec{r},t) + \omega_d$$$. The acquired phases were corrected for their respective B₀ offset.

For the motion measurement, four field probes were attached to a custom-made bite bar (s. Figure 1) together with the MPT marker. The bite bar was then attached to a spherical phantom. Motion was induced manually, using a long non-magnetic rod attached to the phantom. 2640 measurements were taken, using a repetition time (TR) of 50 ms. To measure the stability and accuracy of the position measurement of both systems, an additional measurement was taken without any induced motion.

We used a Newton’s Method regression algorithm to correct the measured field probe positions for errors due to gradient nonlinearities. The previously measured ⁶ spherical harmonics coefficients up to the 4th order were used for finding the actual positions. The translations were calculated from the centroid of the probes’ positions and the x-y-z pose of the MPT marker respectively. Rotations were calculated in respect to the isocenter in both tracking modalities using a modified version of the Kabsch algorithm ⁷.

The accuracy measurements of translations in the absence of induced motion yielded a standard deviation of σ_x,y,z = [6.6 µm, 2.12 µm, 4.7 µm] for the MPT system and σ_x,y,z = [59.9 µm, 63.8 µm, 54.2 µm] for the field probes. The standard deviations for the rotations (in Euler angles) were σ_rx,ry,rz = [0.0062°, 0.0081°, 0.0059°] for the camera and σ_rx,ry,rz = [0.031°, 0.021°, 0.027°] for the field probe measurements.

Figure 2 shows the comparison of the motion trajectories measured with both modalities.

For both tracking modalities the timing of the motion onsets and directions match well. For translational motion, the amplitudes are in close agreement. Small translational displacements in x-direction and small rotations around the z-axis are close to the noise level, but still, motion below 100 µm or smaller than 0.1° is clearly visible. There is a significant discrepancy for translations in x-direction and the rotations around the y-axis which might be due to uncorrected gradient drifts or unintentional field probe motion relative to the phantom due to a not completely rigid attachment.

Our experimental results suggest that field probes estimate the motion parameters with an order of magnitude less accuracy than the optical tracking system. However, they can concurrently provide additional information such as field fluctuations and the k-space trajectory. Also, they do not require a line of sight to a camera and are thus more flexible in positioning.

In our future research we plan to analyze and compare the strong and weak aspects of both motion tracking systems in actual imaging scenarios. We further plan to design and implement a motion generation stage for reproducible motion that can be used to compare both systems against a ground truth.