Tess E Wallace^{1,2}, Onur Afacan^{1,2}, Tobias Kober^{3,4,5}, and Simon K Warfield^{1,2}

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 B_{0}
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.

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 *j*th coil, $$$\rho(x;\tau)$$$ is
the spin density of the object and $$$\Delta B_0(x)$$$
describes
the field at position $$$x$$$. Spatiotemporal B_{0} 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=T_{FID} (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 functions^{8} 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 (T_{FID}=1 ms, TE_{1}/$$$\Delta$$$TE/TR=4.96/1.48/29 ms, $$$\alpha$$$=20°, FOV=256x256x224 mm,
resolution=4 mm^{3}, 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 (T_{FID}=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).

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