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)…X_N(t), can be estimated by linear regression on an individual basis (i.e. per subject):

[Eq. 1] Y = XŸ·β + ε
(Y and ε: N_t×6 matrices, X: N_t×N matrix, N_t: 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 N_pc<N principal components (truncated PCA) such that X≈UŸ·SŸ·V^T=:TŸ·V^T (S: diagonal N_pc×N_pc singular value matrix). The N×N_pc matrix V maps between input signals X and the N_t×N_pc 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 recently^5,6, 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 N_pc=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.