Introduction

Sensors consisting of orthogonally arranged gradient pickup-coils fixed to the subjects head have proven useful for motion tracking when combined with interleaved gradients or tones.^1,2 Pilot studies have shown that tracking is possible during simultaneous EEG-fMRI using only EEG-equipment sensitive to field changes.^3-8 With a modified EEG setup including carbon wire loops, and after a short calibration scan, motion tracking is achieved using native gradients of a high-resolution T1w 3D-GRE sequence, requiring only a short calibration scan and mounting of the cap. The method is validated with retrospective correction for three healthy subjects, with direct comparison to interleaved 3D navigators (NAVs)⁹.

Methods

Gradient switching induces voltages in the wire loops and it follows from Faraday's law that the recorded time signal of channel $$$i$$$ can be described as: $$\mathit{v}_i(t)=\mathit{w}_{ix}\frac{\partial\tilde{\mathit{g}}_x(t)}{\partial t}+\mathit{w}_{iy}\frac{\partial\tilde{\mathit{g}}_y(t)}{\partial t}+\mathit{w}_{iz}\frac{\partial \tilde{\mathit{g}}_z(t)}{\partial t}+\mathit{\eta}_i(t)$$
with $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)=\left[\frac{\partial \tilde{\mathit{g}}_x(t)}{\partial t},\frac{\partial\tilde{\mathit{g}}_y(t)}{\partial t},\frac{\partial \tilde{\mathit{g}}_z(t)}{\partial t}\right]$$$ representing filtered time derivatives of gradient activity, and $$$\pmb{\mathit{w}}_i=\left[\mathit{w}_{ix},\mathit{w}_{iy},\mathit{w}_{iz}\right]$$$ being weights that depend on wire loop geometry, position, and orientation. $$$\mathit{\eta }_i(t)$$$ is measurement noise. $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)$$$ is recorded for any sequence, for each of the gradients $$$\mathit{g}_x(t)$$$, $$$\mathit{g}_y(t)$$$, and $$$\mathit{g}_z(t)$$$, in a static phantom pre-scan (Figure 1) where RF and the remaining gradient systems are deactivated, and is determined as the primary component from singular value decomposition (SVD) across wire loop channels $$$i=[1,2,\ldots ,I]$$$. $$$\pmb{\mathit{w}}_i$$$ is determined for a new signal snippet using a general linear model expressed by $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)$$$. Additional nuisance regressors are appended to $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)$$$ to model $$$\mathit{\eta }_i(t)$$$. These are determined in the pre-scan by sampling RF contributions without gradients (Figure 1,RF), and by modelling eddy currents and cross talk by including non-primary components from the aforementioned SVD. Additionally, mechanical vibrations are modelled with a low-frequency harmonic expansion [120-400Hz] fitted to periods free of gradient ramping (Figure 2), and are subtracted.

The relation between weights $$$\pmb{\mathit{w}}$$$ ($$$3I$$$ vector) and subject pose $$$\pmb{\mathit{r}}$$$ (position and orientation, six degrees-of-freedom), is determined in a short subject-specific calibration scan with instructed free head movement during a dynamic series of rapid 3D-EPI. Small changes in subject pose from a reference position corresponds to small changes in $$$\pmb{\mathit{w}}$$$ in the linear approximation:
$$\Delta\pmb{\mathit{w}}=\pmb{\mathit{A}}\Delta\pmb{\mathit{r}}$$
where $$$\Delta\pmb{\mathit{w}}=\left[\Delta\pmb{\mathit{w}}_{1},\Delta\pmb{\mathit{w}}_{2},\ldots ,\Delta\pmb{\mathit{w}}_{I}\right]$$$, and $$$\Delta\pmb{\mathit{r}}=\left[\Delta x,\Delta y,\Delta z,\Delta \theta ,\Delta \phi,\Delta \psi \right]$$$. The elements of $$$\pmb{\mathit{A}}$$$ ($$$3I\times 6$$$ matrix) are found by jointly solving the linear approximation for a number ($$$\geq 6$$$) of calibration positions by least squares estimation, using motion parameters from rigid alignment of the 3D-EPI volumes (SPM12 volume realignment, UCL, UK).

The developed method was evaluated in-vivo using three healthy volunteers. An 80s calibration scan, and four structural T1w 3D-GRE images (all with NAVs), were acquired for each subject (3T Achieva MRI, Philips Healthcare, Best, Netherlands). Subjects were instructed to remain stationary during 2 structural scans, and to perform various amounts of voluntary motion for 2 scans. The structural scans were retrospectively corrected using the RetroMoCoBox¹⁰ with pose estimates from either rigid alignment (SPM12) of NAVs⁹ (recorded every 1561ms interleaved^11,12 with acquiring slices of k-space), or from carbon wire loop (CWL) recordings. Loop recordings during interleaved navigators were excluded from pose estimation for fair comparison between the two methods. The sequence used during calibration was identical to the interleaved NAVs with sequence parameters TE/TR: 5.8/14ms, duration per dynamic: 472ms, tip angle: 2°, voxel size: 7.1×8.2×7.2mm, matrix: 36×31×32. Sequence parameters for the T1w 3D-GRE images were TE/TR: 3.5/6.5ms, tip angle: 14°, voxel size: 1×1×1mm, matrix: 240×240×240, outer/inner phase-encoding order: center-out/linear.

CWL voltages were sampled with a high bandwidth EEG sampling system (80kHz sampling, HP/LP-cutoffs: 100Hz/16kHz, NeurOne Tesla, Bittium Biosignals Ltd, Kuopio, Finland), and an EEG-cap (Easycap, Germany) with 9 channels interconnected to the reference electrode with resistive carbon wire forming inductive loops evaluated for safety. CWL motion estimation was based on signals from two consecutive dynamics with 50% overlap yielding 1561ms tracking frequency.
Average Edge Strength (AES) was calculated before and after retrospective correction using the AES toolbox¹³, averaging over sagittal, coronal, and axial orientation. Before calculation, reference, corrupted, and corrected images were transformed to a common reference frame using sinc interpolation.

Results

Figure 3 and 4 show retrospectively corrected volumes with instructed-, and uninstructed movement respectively. Table 1 shows AES for each structural scan, before and after retrospective correction. The average improvement to AES in volumes with instructed movement was 12/13% for CWL and NAVs, respectively, and -0.39/1.8% in volumes where the subject was instructed to lay still. The average mean absolute difference (MAD) for all structural scans between CWL pose estimates and NAVs estimates were [0.13,0.33,0.12]mm and [0.28,0.15,0.22]deg, revealing close similarity between the two.

Discussion & Conclusion

While comparable in terms of improvements to image sharpness (visually and calculated AES), CWLs can offer decreased tracking noise, especially in anterior/posterior direction, where NAVs are most sensitive to field fluctuations. Neither method introduced noise in motion-free scans. No line-of-sight or sequence modification was needed for CWL. The method is suited for prospective updating, which requires scanner interfacing and updating of three columns of $$$\dot{\tilde{\pmb{\mathit{G}}}}(t)$$$ whenever the field-of-view is updated⁵. Residual artifacts from local Nyquist violations in k-space may improve with prospective updating, and reacquisition. CWLs for EEG artifact rejection have recently become commercially available, and may be suited for the method.

Acknowledgements

Malte Laustsen is supported by the Sino-Danish Center for Education and Research.