Prospective motion correction for MRI using EEG-equipment

Mads Andersen^{1,2}, Kristoffer H. Madsen^{1}, and Lars G. Hanson^{1,2}

Motion tracking is based on induced signals from gradient switching in an EEG-cap the subject wears during scanning (see figure 1).

From Faraday’s law, the signal from gradient switching on EEG-channel $$$i$$$ is:

$$V_i(t)=w_{ix} \frac{d\tilde{G}_x}{dt}+w_{iy} \frac{d\tilde{G}_y}{dt}+w_{iz} \frac{d\tilde{G}_z}{dt},\quad [1]$$

where $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$ are linear filtered versions of $$$\frac{dG_x}{dt},\frac{dG_y}{dt},\frac{dG_z}{dt}$$$ due to filters of the EEG-system and uncompensated self-term eddy currents. The weights $$$w_{ix},w_{iy},w_{iz}$$$, depend on geometry, position and orientation of the wire loop, and can thus be formulated in terms of parameters describing the position and orientation of the head. For small changes in head position a linear approximation is valid:

$$\Delta\mathbf{w}=\mathbf{A}\Delta\mathbf{r}_h,\quad [2]$$

where $$$\Delta\mathbf{w}$$$ is a 3Nx1 vector with changes in weights from a reference situation (N EEG-channels), $$$\Delta\mathbf{r}_h$$$ is a 6x1 vector with changes in head parameters, and $$$\mathbf{A}$$$ is a 3N×6 matrix with partial derivatives of the weights with respect to head position parameters, evaluated in the reference position. $$$\mathbf{A}$$$ can be estimated from a training scan, where the subject is moving stepwise, an image volume is acquired for each position, and gradient activity is measured simultaneously. The volumes can be aligned to get $$$\Delta\mathbf{r}_h$$$ for every position, and likewise $$$\Delta\mathbf{w}$$$ can be estimated for each position if $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$ are known.

The weights can be computed during scanning from small time segments, and motion parameters of the head estimated from eq. [2]. The FOV of the scanner can be updated e.g. at the slice repetition frequency, by changing the reference frequency of the scanner and rotating the gradient waveforms (2). The same rotation must be applied to $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$; otherwise the weights will change due to scanner updating.

In this work, the waveforms $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$ were estimated from a pre-scan, where a few repetitions of the target sequence were played out with only one gradient active in each run. Simultaneously the EEG-system was recording on all channels. With only one gradient active, eq. [1] predicts that all channels measure the same waveform with different amplitudes. This scan was therefore used for estimating normalized waveforms. The relative amplitudes of $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$ were estimated from an additional, similar pre-scan were the gradient waveforms were rotated.

**Experiments**

On an EEG-cap, 10 electrodes were pairwise interconnected and put on a structured phantom. Signals were acquired using an MR compatible EEG-system (BrainAmpExG, Brainproducts GmbH) synchronized to the clock of the 3T MRI system (Achieva, Philips Healthcare,Best, Netherlands). A FLASH sequence was used for demonstrating the technique.

The phantom was stationary during the pre-scans for measuring $$$\frac{d\tilde{G}_x}{dt},\frac{d\tilde{G}_y}{dt},\frac{d\tilde{G}_z}{dt}$$$. For training, 15 volumes were acquired with the phantom moved in between (1 volume was discarded). Then followed a test session were the phantom was again moved between acquisitions. For each position of the phantom, 3 volumes were acquired:

1) using the FOV settings of the previous position,

2) with updated FOV of the scanner based on the induced gradient signals from 1 (PMC on), and

3) using the FOV settings of the volume that was realigned to (PMC off).

The weights were estimated from time segments of one full volume repetition period in this work.

Figure 2 shows motion parameters from the experiments. The blue curves are almost completely overlaid by the red curves in both training session and test session, demonstrating the validity of the linear assumption. Visible motion is substantially dampened with PMC on (green). There was little translation in x and y directions in both training and test sessions, and errors in these translation parameters are up to 1.8 mm. Figure 3 shows a coronal slice through the phantom with PMC off and on together with difference images to the reference image. With PMC on the visible motion is much reduced, but the difference images reveals that the correction is not perfect, which is also confirmed from the RMS of the difference volumes in the lowest panel.

These initial results show that prospective motion correction can be accomplished using the spatial information from induced gradient signals in interconnected EEG-electrodes. Further optimization of the training and fitting routines are necessary for reducing the errors. Using more positions in the training or ensuring larger motion in all degrees of freedom during training is a first step expected to lower the errors.

(1) Vestergaard M, Schulz J, Turner R, Hanson LG. Motion tracking from gradient induced signals in electrode recordings. Proceedings of the ESMRMB annual meeting and conference 2011.

(2) Maclaren J, Herbst M, Speck O, Zaitsev M. Prospective motion correction in brain imaging: A review. Magn. Reson. Med. 2013;69:621–636.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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