PCA-aided improvements on FID-based motion tracking calibrated on resting-state EPI data without intentional motion
Rüdiger Stirnberg1, Daniel Brenner1, Willem Huijbers1, Tobias Kober2,3,4, and Tony Stöcker1,5

1German Center for Neurodegenerative Diseases (DZNE), Bonn, Germany, 2Advanced Clinical Imaging Technology, Siemens Healthcare, Lausanne, Switzerland, 3Department of Radiology, University Hospital Lausanne (CHUV), Lausanne, Switzerland, 4Department of Electrical Engineering (LTS5), Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 5Department of Physics and Astronomy, University of Bonn, Bonn, Germany


Accurate and precise head motion tracking has been shown to be feasible using multi-channel free-induction-decay (FID) signals, where positional information is supported by the spatial distribution of the receive coils. Until now, this required subject-specific calibration using simultaneously acquired FID signals and reference motion parameters, e.g. from an external device, while the subject performs controlled motion. In this study, we demonstrate successful calibration of FID navigators using motion parameters extracted from a resting-state fMRI scan without intentional motion. Additionally, extension of the calibration by principal component analysis of the FID data is shown to increase motion prediction accuracy and precision.

Target Audience

Neuroscientists and MR physicists interested in MR-based head motion navigation.


To demonstrate successful calibration of free-induction-decay (FID) motion navigators1 using EPI data acquired under realistic conditions (without intentional motion) and to improve on motion prediction by utilizing principal component analysis.


Recently, the accuracy and precision of head motion estimation by means of (spatially not encoded) FID signals acquired with a multi-channel head coil was compared to a motion-tracking camera system2. It was found that the mapping between (rigid-body) motion parameters Y1(t)…Y6(t) and FID signals, X1(t)…XN(t), can be estimated by linear regression on an individual basis (i.e. per subject):

[Eq. 1] Y = XŸ·β + ε
(Y and ε: Nt×6 matrices, X: Nt×N matrix, Nt: No. of time points, N: No. of input signals, ε: residual errors)

The N×6 coefficient matrix β is subsequently multiplied with new FID input signals X’ to predict corresponding motion Y’. Best results are achieved if both real and imaginary parts of the FID signals are considered in X (optionally + const. + lin. term with respect to time, as adopted here).

Experimental data are acquired using the 52 head elements of a 64-channel head coil on a MAGNETOM Prisma 3T system (Siemens Healthcare, Erlangen, Germany), yielding a total of N=52x2+2=106 input signals. To suppress the effect of signals with minor relevance (e.g. high redundancy) or even detrimental impact (e.g. low SNR), we propose to replace X in Eq. 1 by the first Npc<N principal components (truncated PCA) such that XUŸ·SŸ·VT=:TŸ·VT (S: diagonal Npc×Npc singular value matrix). The N×Npc matrix V maps between input signals X and the Nt×Npc principal component matrix T. Compared to Eq. 1, the proposed approach thus relies on calibration and prediction according to

[Eq. 2] Y = TŸ·β + ε = XŸ·VŸ·β + ε.

In essence, instead of the original two-step procedure

1. solve Eq. 1 for β using calibration data X and Y
2. predict motion Y’=X’Ÿ·β

we propose the following three-step procedure:

1. PCA on calibration signals X to obtain V
2. solve Eq. 2 for β
3. predict motion Y’=X’Ÿ·β’, where β’=VŸ·β

EXPERIMENT: A prototype implementation of a segmented 3D-EPI sequence3 capable of high acceleration using CAIPIRINHA4 sampling as described recently5,6, was modified to include one global excitation pulse (FA=5°) and FID readout (2.5ms) once every volume-TR of 500ms (3mm iso, FA=15°). Two scans, each of approximately 4:30min duration, were acquired (550 volumes). During the calibration scan, the subject looked at a fixation cross, while during the validation scan, the subject responded to visual and auditory stimuli by button presses. The subject was instructed to avoid movement. Reference motion parameters were estimated from the EPI data using FSL’s MCFLIRT7 assuming comparable or higher motion sensitivity than discussed by Tisdal et al.8. The raw FID signals were processed as described previously2. FID-based motion prediction was performed once according to Eq. 1 and once according to the new approach (Eq. 2). For the latter, the reduced number of PCs was set to Npc=24.


Fig. 1 shows unintentional head motion parameters as extracted from the calibration and validation EPIs (Y) together with 26 of 204 FID signals (X) as well as the first 6 of 24 PCs (T=XŸ·V). Fig. 2 shows FID-extracted motion parameters according to the original (FID prediction) and novel (PC prediction) approach. For both methods, the mean average error (MAE) and standard deviation of the error (STD) demonstrate relatively high prediction accuracy and precision2 compared to the ground truth validation data. MAE and STD are smaller by a factor of 2-3 when using the PC approach. The scatter plots and the correlation coefficients, r, indicate a similar trend for each degree of motion separately.


Both approaches perform relatively well considering that no intentional motion was performed during calibration. The novel PC approach is more accurate and precise, and – although not shown here – more robust against peak motion parameters (cf. arrows in Fig. 1) as is observed when limiting the calibration phase to the first 60 or 30 seconds. The high number of 52 head array channels used here may, however, be a prerequisite. A thorough group analysis among different degrees of motion is expected to confirm the single-subject findings.


We have shown that replacing raw FID signals by a reduced set of principal components can improve motion prediction based on multi-channel FID signals without requiring dedicated equipment. Furthermore, even unintentional motion was found to be suited for calibration. FID navigators acquired during normal resting state fMRI scans may thus be suitable to train subsequent motion tracking during anatomical scans.


RS wishes to thank Benedikt A. Poser for his help on enabling online 2D-CAIPIRINHA image reconstruction.


1. Kober et al. Magn. Reson. Med. 66, 2011
2. Babayeva et al. IEEE TMI 34, 2015
3. Poser et al. NeuroImage 51, 2010
4. Breuer et al. Magn. Reson. Med. 55, 2006
5. Narsude et al. ISMRM 2013
6. Zahneisen et al. Magn. Reson. Med. 74, 2015
7. Jenkinson et al. NeuroImage 17, 2002
8. Tisdal et al. Magn. Reson. Med. 68, 2012


Fig. 1 Calibration (top) and validation data (bottom) to test motion prediction. Arrows indicate examples of peak motion during calibration. The FID signals are transformed to the principal components (PC) using the matrix B determined from the calibration data. For clarity, only a quarter of the FIDs and PCs are displayed.

Fig. 2 Predicted motion using the original method based on 104+2 FID signals (top) and the novel method based on 24 PCs (bottom). MAE=mean average error, STD=standard deviation of the error. In the scatter plots of predicted vs. validation motion (right), r denotes Pearsons’s correlation coefficients for x/y/z translation and rotation.

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