Introduction

Brain MRI is susceptible to motion which causes artefacts in reconstructed images¹, especially with prolonged scanning times for high-resolution MRI, particularly relevant at ultra-high field (UHF)². Data-driven motion correction proposed in DISORDER^3,4 leverages an optimised Cartesian sampling to retrospectively correct for rigid body motion during volumetric acquisitions. Whilst able to correct UHF acquisitions⁵, stable motion estimates require multiple readout lines to be assigned to a single motion state, limiting the temporal resolution of estimates. In this work, we extend DISORDER motion estimation by incorporating external motion information coming from injected Pilot Tone (PT) signals⁶ potentially improving the temporal resolution of motion estimates.

Methods

DISORDER motion correction^3,4 divides the k-space acquisition into temporal groups (sweeps) of readouts (one per repetition time TR) that sample uniformly across k-space. Each sweep $$$n$$$ is treated as a different motion state with rigid motion parameters $$$\textbf{z}_n$$$ that can be jointly optimised together with the image $$$\textbf{x}$$$:
$$(\widehat{\textbf{x}},\widehat{\textbf{z}_n})=argmin_{\textbf{x},\textbf{z}_n}\sum_q\Big\| \textbf{A}_q\textbf{FST}(\textbf{z}_q)\textbf{x}-\textbf{y}_q \Big\|_2^2 \quad\quad(1)$$
where $$$q$$$ is the running variable summing over all sweeps with $$$\textbf{T}(\textbf{z}_q)$$$,$$$\textbf{S}$$$,$$$\textbf{F}$$$,$$$\textbf{A}_q$$$ and $$$\textbf{y}_q$$$ respectively representing associated rigid motion, coil sensitivities, Fourier operator, sampling structure, and measured k-space data. PT is a motion-estimation method leveraging signals collected during data acquisition by each receiver channel from an externally generated mono-frequency RF source: PT signals vary slightly with head position and provide updated motion information with every TR^6,7. For brain MRI at 7T, it was shown that a linear model can be used to predict motion parameters ($$$\textbf{z}_{{TR}_t}$$$) from the PT signal ($$$\textbf{p}_{{TR}_t}$$$)⁸:
$$\textbf{z}_{{TR}_t}=\textbf{C}\textbf{p}_{{TR}_t}\quad \quad(2)$$
where $$$\textbf{p}_{{TR}_t}$$$ is a 33-element complex vector containing 32-channel PT signal for the TR at time $$$t$$$ and a 1 to allow for motion offsets. $$$\textbf{C}$$$ is a 6x33 matrix with coefficients for each of the 6 rigid motion parameters in each row. This allows estimating $$$\textbf{C}$$$:
$$(\widehat{\textbf{x}},\widehat{\textbf{C}})=argmin_{\textbf{x},\textbf{C}}\sum_q\Big\|\textbf{A}_q\textbf{FST}(\textbf{C}\textbf{p}_{q})\textbf{x}-\textbf{y}_q \Big\|_2^2 \quad \quad(3)$$
where $$$\textbf{p}_{q}$$$ is the averaged PT signal within the time window $$$w_q$$$ of shot $$$q$$$. Whereas in Equation 1 each motion state is estimated by optimising for an independent quantity, the matrix $$$\textbf{C}$$$ is assumed to be constant for the full acquisition, which can stabilise motion states over time. Implementation details for solving Equation 3 are shown in Figure 2.
The proposed reconstruction was tested in simulations and validated on 4 healthy volunteers (HV) (aged 25-35yrs, Institutional Research Ethics number HR-18/19-8700) with a mix of deliberate motions and lying still, using a volumetric SPGR acquisition on a 7T scanner (MAGNETOM Terra, Siemens Healthcare, Erlangen, Germany). Sequence parameters: $$$0.5^3mm^3$$$ isotropic resolution, DISORDER random checkered sampling with $$$4.1s$$$ per sweep, $$$TR=8.4ms$$$, echo time $$$TE=4.2ms$$$, flip angle $$$FA=7^{\circ}$$$, field of view (FOV)=248x238x176 (IS/AP/RL), readout along IS, scan duration $$$TA=19min49s$$$ with no repeats and no acceleration. The PT was generated with an RF signal generator (APSIN3000, AnaPico, Glattbrugg, Switzerland) and broadcast into the magnet room from a monopole antenna at a drive level of $$$-20dBm$$$ (Figure 1a) and with an offset to set the signal in the oversampled FOV, which was extracted before removing the oversampling (Figure 1b). Images are first reconstructed using motion parameters obtained from solving Equation 1 and $$$\textbf{C}$$$ was then calibrated using Equation 2 to obtain the final reconstructions from the PT consistent motion parameters. Due to computational constraints, full volumetric data was reconstructed at $$$1mm^3$$$ and the motion information (either temporal motion estimates or the calibrated matrix ) was then used to reconstruct single slabs at $$$0.5^3mm^3$$$.

Results

Figure 3a shows the estimated motion parameters with DISORDER compared to PT predicted motion states. These agree well overall, with cleaner estimates using the PT calibration. Zoomed-in traces (Figure 3b) show the higher temporal resolution motion estimates PT provides (per TR). Example reconstructed images in Figure 4 show successful motion correction using DISORDER, but further improvements using the PT predicted motion information. PT reconstructions for all subjects showed either similar or improved image quality compared to DISORDER.

Discussion

We have investigated and integrated PT signals to improve DISORDER motion correction. PT signal calibration can be achieved using the DISORDER motion states and the two then show a strong correlation, but the PT estimates are more stable and have higher temporal resolution. Replacing DISORDER motion estimates with PT either produced similar results or improved motion correction. As shown in Figure 3, PT can provide per TR motion estimates, which look highly coherent. It seems plausible that motion correction at the TR level could yield further improvements but this has hitherto proved computationally infeasible with the current framework.

Conclusion

We have exploited the use of PT at UHF to improve data-driven motion correction. Our method does not interfere with sequence parameters and can be used in almost any sequence. PT predicted motion states can improve image quality and offer new ways to retrospectively detect and correct for motion at a higher temporal resolution, potentially with individual motion states for each k-space line (i.e. at the TR level).