Mo Shahdloo^{1}, Daniel Papp^{2}, Urs Schüffelgen^{1}, Karla L. Miller^{2}, Matthew Rushworth^{1}, and Mark Chiew^{2}

^{1}Wellcome Centre for Integrative Neuroimaging, Department of Experimental Psychology, University of Oxford, Oxford, United Kingdom, ^{2}Wellcome Centre for Integrative Neuroimaging, FMRIB, Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, United Kingdom

Dynamic B0 field inhomogeneities due to vigorous body motion - after mechanical head stabilisation - introduce severe artefacts in accelerated fMRI of awake behaving non-human primates (NHPs) by invalidating the calibration data used for unaliasing reconstruction. Here, we propose a method to estimate dynamic field perturbations via model-based frame-to-frame comparison of EPI reference navigators. These estimates can be used to improve reconstruction quality by matching each data frame to the calibration data, and simultaneously correcting the geometric distortions. The proposed method successfully estimates field perturbations and improves reconstruction quality in accelerated NHP fMRI, without the need for sequence modification or extra acquisitions.

Recently, multi-channel free induction decay navigators (FIDnavs) have been used to successfully estimate low‐spatial‐order dynamic field changes in fMRI

To mitigate these issues, we used reference EPI navigators to estimate dynamic field perturbations, without the need for contrast-matched reference images. These short navigators that sample the central line of k-space three times at each TR are already present in typical EPI sequences for correcting Nyquist ghost artefacts. Here, we used the spatial encoding provided by multi-channel navigators to estimate first order field perturbations in every TR. Field estimation quality is demonstrated in phantom and in vivo experiments, and improved reconstruction performance through significant reduction of residual aliasing is demonstrated using simulations of accelerated fMRI in NHPs.

$$S(k_x+\delta_x,k_y+\delta_y)=G_x^{\delta_x/\Delta_x}G_y^{\delta_y/\Delta_y}S(k_x,k_y)$$

$$s_j^0(t)=\int_x\int_y\rho_j(x,y)e^{-j2\pi[k_x(t)x+k_y(t)y]t}e^{-i\Delta\omega^0t}dxdy$$

where $$$\rho_j$$$ is the coil-sensitivity-encoded object magnetisation, and $$$\Delta\omega$$$ is the off-resonance. Field perturbations in NHP fMRI are mainly caused by motion in body parts that are distant from the imaging volume, and have low spatial frequency

$$\Delta\omega^n=\Delta\omega^0+2\pi[b_xx+b_yy]$$

yielding the navigator signal as:

$$s_j^n(t)=\int_x\int_y\rho_j(x,y)e^{-j2\pi[[k_x(t)+b_x]x+[k_y(t)+b_y]y]t}e^{-i\Delta\omega^0t}dxdy$$

Linear field perturbation is thus manifested as linear shifts in k-space:

$$S_j^n(k_x,k_y)=S_j^0(k_x+b_x,k_y+b_y)$$

where $$$S_j^n$$$ is the k-space data at frame $$$n$$$.

We modelled the shifted k-space data from the multi-channel three-line navigators using GRAPPA operators (illustrated in Fig.1):

$$\begin{bmatrix}S_{j,1}^n\\S_{j,2}^n\\S_{j,3}^n\end{bmatrix}=\begin{bmatrix}G_x^{\alpha}G_y^{\beta}&0&0\\0&G_x^{\alpha}G_y^{\beta}&0\\0&0&G_x^{\alpha}G_y^{\beta}\end{bmatrix}\begin{bmatrix}S_{j,1}^0\\S_{j,2}^0\\S_{j,3}^0\end{bmatrix}$$

and solved for $$$\alpha=b_x/\Delta_x$$$ and $$$\beta=b_y/\Delta_y$$$ using data from $$$N_c$$$ channels. Nelder-Mead simplex gradient-free nonlinear solver was used

To examine the perturbation estimation accuracy, a bottle phantom was scanned on a 3T scanner using a 15-channel NHP receive coil and an EPI sequence with parameters: TE/TR= 30/2000ms,FA=90,FOV=192mm,1.5mm isotropic resolution. To mimic dynamic field perturbations, separate scans were performed where first-order shim terms (X,Y) were manually adjusted up to ±20μT/m in 5μT/m increments across scans.

To test the method in vivo, we acquired 50 frames of brain data from an awake macaque monkey using scan parameters matched to the phantom scan. We estimated field perturbation at each TR and distorted the fully-sampled reference using conjugate-phase reconstruction (CP)

To demonstrate the effect of calibration inconsistency correction on reducing residual ghosting and unaliasing artefacts, data and navigators at the reference frame were distorted via CP, assuming a linear field perturbation (0.00±9.62Hz, mean±std across the FOV). Perturbation was estimated and data were corrected via inverse operators. Inconsistent and corrected frames were retrospectively undersampled at R=2,4 and GRAPPA-reconstructed. Multiband data were simulated with MB=2,R=3 by collapsing the data across slices and reconstructed using split-slice-GRAPPA

Figure 3 shows the estimated distortions in vivo for two representative frames. The method accurately estimates the distortions in vivo.

Figure 4 shows the effect of field perturbation leading to calibration inconsistency, and correcting for it, on the accelerated reconstructions. Considerable ghosting artefacts arise from calibration inconsistency that cannot be corrected in post processing. The proposed method corrects the inconsistency, reduces artefact power, and corrects for geometric distortion in a single step.

M.C. is supported by the Royal Academy of Engineering (RF201617\16\23). The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z).

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