A fast approach for simultaneous measurement of head motion and induced magnetic field changes using FID navigators
Tess E Wallace1,2, Onur Afacan1,2, Tobias Kober3,4,5, and Simon K Warfield1,2

1Computational Radiology Laboratory, Boston Children's Hospital, Boston, MA, United States, 2Harvard Medical School, Boston, MA, United States, 3Advanced Clinical Imaging Technology, Siemens Healthineers, Lausanne, Switzerland, 4Department of Radiology, University Hospital (CHUV), Lausanne, Switzerland, 5LTS5, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland


Incorrect spatial encoding due to subject motion is a dominant source of artifacts in MRI. Even if changes in head pose are measured and corrected, motion-induced perturbations in the local magnetic field are a further source of image degradation, particularly for imaging at longer echo times and higher field strengths. We propose a fast approach for simultaneously measuring head motion and spatiotemporal B0 changes using FID navigators (FIDnavs) and simulation of the acquisition physics. Rigid-body motion and first-order field coefficients estimated from FIDnavs exhibit a high degree of agreement with ground-truth values in both phantom and volunteer experiments.


Image encoding in MRI relies on accurate knowledge of the underlying magnetic field gradients. Subject motion is therefore a major source of artifacts, and a variety of methods have been proposed to compensate for incorrect spatial encoding due to motion, either by retrospectively correcting the imaging data, or prospectively adjusting the acquisition field-of-view.1,2 However, in certain situations, such as susceptibility-weighted imaging at higher field strengths, this is insufficient, due to the complex effects of head motion on the local magnetic field.3 External field probes4 or dual-echo image navigators5,6 may be used to monitor field changes during the scan, but the latter requires sufficient ‘dead-time’ to be present in the imaging sequence. Free induction decay navigators (FIDnavs) can be acquired extremely rapidly and have been shown to encode substantial motion information7,8 as well as local field changes.9 In this work, we present an extended FIDnav-based framework for simultaneously estimating head motion and induced spatiotemporal magnetic field changes using simulation of the acquisition physics.


The FIDnav signal from channel $$$j$$$ at time $$$\tau$$$ may be expressed as: $$y_j(\tau)=\int_v s_j(x)\rho(x;\tau)\exp(i2\pi\gamma\Delta B_0(x)\tau)dx$$ where $$$s_j(x)$$$ is the complex coil sensitivity profile (CSP) of the jth coil, $$$\rho(x;\tau)$$$ is the spin density of the object and $$$\Delta B_0(x)$$$ describes the field at position $$$x$$$. Spatiotemporal B0 variations, that arise due to background field inhomogeneities and the susceptibility distribution of the object, may be represented by a series of low-order basis functions: $$$\Delta B_0 =\beta (x) b(t)$$$. Given a forward model of FIDnav signals and multi-channel FIDnav measurements, the inverse problem may be solved for the underlying rigid-body motion (6 parameters) and field changes (4 first-order field coefficients; Fig.1).

Phantom Validation: A pineapple was scanned at 3T (Siemens Healthcare, Erlangen, Germany) and FIDnavs were measured from a 32-channel coil while first-order shim currents were systematically altered from -4 to 4 $$$\mu$$$T/m (step-size 1 $$$\mu$$$T/m). Two 3D FLASH reference scans with TE=TFID (1 ms) and alternating readout gradients were also acquired using both surface and body coils for estimation of the CSPs and proton distribution. The phase difference between images with opposite readout polarities was calculated to mitigate the effects of gradient delays on the phase of the simulated FIDnavs. Motion of the coils relative to the object was simulated by re-evaluating fitted biharmonic spline functions8 and changes in the field basis functions were applied to compute the model matrix $$$A$$$ (Fig.1). A phase-constrained weighted least-squares fit was used to solve for the real-valued motion and field parameters $$$u$$$.10

In Vivo Validation: FIDnavs were inserted into a multi-echo 3D FLASH sequence after the non-selective excitation pulse. A volunteer was scanned at 3T using a 32-channel coil after obtaining informed consent. Six low-resolution images were acquired (TFID=1 ms, TE1/$$$\Delta$$$TE/TR=4.96/1.48/29 ms, $$$\alpha$$$=20°, FOV=256x256x224 mm, resolution=4 mm3, RBW=1370 Hz/pix) and the subject was instructed to move their head to different poses between each scan. The complex multi-echo images were registered and field maps were calculated in the head frame of reference using the Hermitian inner product method. FIDnav motion and field estimates were computed as described above. A second volunteer was scanned using a 64-channel coil and FIDnavs (TFID=1 ms) were acquired while the subject performed continuous head nodding. Ground-truth motion measurements were recorded using an electromagnetic tracking system (Robin Medical, Baltimore, MD).


Field coefficients and motion parameters were estimated from FIDnavs with very low absolute errors of 0.07 ± 0.04 $$$\mu$$$T/m, 0.06 ± 0.04 mm and 0.06 ± 0.05° for systematic shim current changes in a phantom (Fig.2). In the first volunteer experiment, FIDnav motion estimates achieved mean absolute errors of 0.29 ± 0.17 mm and 0.85 ± 0.65° for maximum changes of 3 mm and 7° (Fig.3). $$$\Delta$$$B0 maps modelled using FIDnav field coefficients were in excellent agreement with the measured field maps (Fig.4). NRMSE between fitted and measured field maps was 4.0%, compared to 4.8% for FIDnav predictions. For head nodding, FIDnavs from the 64-channel coil achieved an accuracy of 0.21 ± 0.16 mm and 0.29 ± 0.21° for motion amplitudes of 1.7 mm and 3.4°.


The proposed approach enables fast, simultaneous estimation of head pose and related spatiotemporal field changes using FIDnavs. There exists a complex relationship between head pose and B0 field inhomogeneity distribution3 and future iterations could investigate higher-order changes and/or iterative estimation of motion and field parameters, which may further improve accuracy. FIDnavs can be inserted into virtually any sequence with minimal time penalty and are a promising method for retrospective correction of motion and $$$\Delta$$$B0 artifacts as well as real-time field-of-view steering and shimming.


This research was supported in part by the following grants: NIH-5R01EB019483, NIH-4R01NS079788 and NIH-R44MH086984.


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Figure 1. Schematic showing extended FIDnav motion and B0 field measurement framework.

Figure 2. Estimated first-order shim and rigid-body motion parameters in a phantom experiment where the X, Y, and Z shim currents were systematically changed from -4 to 4 uT/m. FIDnav-based measurements are in excellent agreement with the applied values.

Figure 3. Comparison of FIDnav translational and rotational motion estimates and ground-truth motion parameters from rigid-body registration.

Figure 4. Comparison of measured B0 difference maps measured within the brain region for four different positions, relative to the reference position; first-order field coefficients fitted to the measured data and FIDnav-based field maps, demonstrating a high level of agreement.

Figure 5. Translational and rotational motion estimates and field coefficients using the proposed FIDnav-based framework for a volunteer performing continuous head nodding motion. Ground-truth motion estimates from an electromagnetic tracking system are also shown (dotted lines). FIDnav estimates are in good agreement, with a tendency for underestimation of larger-amplitude motion.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)