A fast approach for simultaneous measurement ofhead 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, Department of Radiology, Boston ChildrensHospital, Boston, MA, United States, 2Harvard Medical School, Boston, MA, UnitedStates, 3Advanced Clinical Imaging Technology, Siemens Healthcare AG, Lausanne,

Switzerland, 4Department of Radiology, Lausanne University Hospital and University ofLausanne, Lausanne, Switzerland, 5LTS5, Ecole Polytechnique Federale de Lausanne,

Lausanne, Switzerland

Contact: tess.wallace@childrens.harvard.edu

Synopsis Incorrect spatial encoding due to subject motion is a dominantsource of artifacts in MRI. Even if changes in head pose are measured andcorrected, motion-induced perturbations in the local magnetic field are afurther source of image degradation, particularly at longer echo times andhigher field strengths. In this work, we propose a fast approach for simulta-neously measuring head motion and spatiotemporal B0 changes using FIDnavigators (FIDnavs) and simulation of the acquisition physics. Rigid-bodymotion and first-order field coefficients estimated from FIDnavs exhibit ahigh degree of agreement with ground-truth values in both phantom andvolunteer experiments.

1 Purpose

Image encoding in MRI relies on accurate knowledge of the underlying magneticfield gradients. Subject motion is therefore a major source of artifacts, and a widevariety of methods have been proposed to compensate for incorrect spatial encodingdue to motion, either by retrospectively correcting the imaging data, or prospec-tively adjusting the acquisition field-of-view [1, 2]. However, in certain situations,such as susceptibility-weighted imaging at higher magnetic field strengths, this isinsufficient, due to the complex effects of head motion on the local magnetic field[3]. External field probes [4] or dual-echo image navigators [5, 6] may be used tomonitor 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 mo-tion information [7, 8] as well as local field changes [9]. In this work, we presentan extended FIDnav-based framework for simultaneously estimating head motionand induced spatiotemporal variations in the magnetic field by simulating the un-derlying acquisition physics.

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

2 Methods

The FIDnav signal yj(τ) from channel j at time τ may be expressed as:

yj(τ) =

∫v

sj(x) · ρ(x, τ) · exp(i2π∆B0(x)τ)dx (1)

where sj(x) is the complex coil sensitivity profile (CSP) of the jth coil, ρ(x, τ)is the spin density of the object and ∆B0(x) describes the field at position x.Spatiotemporal B0 variations, that arise due to background field inhomogeneitiesand the susceptibility distribution of the object, may be represented by a series ofspherical harmonic basis functions:

∆B0(x, t) = β(x)b(t) (2)

Given a forward model of FIDnav signal changes and multi-channel FIDnavmeasurements, the inverse problem may be solved for the underlying rigid-bodymotion (6 parameters) and field changes (4 first-order field coefficients; Fig. 1).

2.1 Phantom Validation

A pineapple was scanned at 3T (Siemens Healthcare, Erlangen, Germany) andFIDnavs were measured from a 32-channel coil while first-order shim currents weresystematically altered from -4 to 4µT/m in units of 1µT/m. Two 3D FLASH ref-erence scans with TE = TFID (1 ms) and alternating readout gradients were alsoacquired using both surface and body coils for estimation of the CSPs and protondistribution. The phase difference between images with opposite readout polari-ties was calculated to mitigate the effects of gradient delays on the phase of thesimulated FIDnavs. Motion of the coils relative to the object was simulated by

re-evaluating fitted biharmonic spline functions and changes in the field basis func-tions were applied to compute the model matrix A. A phase-constrained weightedleast-squares fit was used to solve for the real-valued motion and field parametersu [10].

Fig. 2. Estimated first-order shim and rigid-body motion parameters in a phantom ex-periment where the X, Y , and Z shim currents were systematically changed from -4 to4µT/m. FIDnav-based measurements are in excellent agreement with the applied values.

2.2 In Vivo Validation

FIDnavs were inserted into a multi-echo 3D FLASH sequence after the non-selectiveexcitation pulse. A volunteer was scanned at 3T using a 32-channel coil afterobtaining informed consent. Six low-resolution images were acquired (TFID =1ms, TE1/∆TE = 4.96/1.48 ms, TR = 29 ms, α= 20◦, FOV = 256 mm, resolution = 4mm3, rBW = 1370 Hz/pix) and the subject was instructed to move their head todifferent poses between each scan. Reconstructed images were registered and field

maps were computed in the head frame of reference via the Hermitian inner prod-uct between the first and second echoes. A second volunteer was scanned using a64-channel head coil and an FID-navigated 3D FLASH sequence (TFID = 1 ms) wasacquired while the subject performed continuous head nodding. Ground-truth mo-tion measurements were recorded using an electromagnetic tracking system (RobinMedical, Baltimore, MD).

3 Results

Field coefficients and motion parameters were estimated from FIDnavs with verylow absolute errors of 0.07± 0.04µT/m, 0.06± 0.04 mm and 0.06± 0.05◦ for sys-tematic shim current changes in a phantom (Fig. 2). In the first volunteer experi-ment, FIDnav motion estimates achieved mean absolute errors of 0.29± 0.17 mmand 0.85± 0.65◦ for maximum changes of 3 mm and 7◦ (Fig. 3). ∆B0 maps mod-elled using FIDnav field coefficients were in excellent agreement with the measuredfield 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 the64-channel coil achieved an accuracy of 0.21± 0.16 mm and 0.29± 0.21◦ for motionamplitudes of 1.7 mm and 3.4◦ (Fig. 5).

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

4 Discussion

The proposed approach enables fast, simultaneous estimation of head pose andrelated spatiotemporal B0 field changes using FIDnavs. There exists a complexrelationship between head pose and B0 field inhomogeneity distribution [3] andfuture iterations could investigate higher-order changes and/or iterative estimation

Fig. 4. Comparison of measured ∆B0 field maps within the brain region, first-order fieldcoefficients fitted to the measured data and FIDnav-based field maps for four differentpositions, relative to the reference position, demonstrating a high level of agreement.

of motion and field parameters, which may further improve accuracy. FIDnavscan be inserted into virtually any sequence with minimal time penalty and are apromising method for retrospective correction of motion and artifacts as well asreal-time field-of-view steering and shimming.

5 Acknowledgements

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

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