Fetal brain imaging is moving from anatomy to connectivity research, requiring advanced neuroimaging modalities such as functional and diffusion MRI. These generally rely on echo planar imaging (EPI), which is highly sensitive to distortion due to static magnetic field (B0) inhomogeneity. Correction of geometric distortion in the fetus can be performed using a B0 field map¹. Distortion corrected EPI can then be used for motion corrected 3D slice-to-volume reconstruction (SVR) [e.g. ^2,3,4]. However, the acquisition of the B0 field map itself is vulnerable to motion artefacts. In this work we propose an alternative solution to address this problem by including a distortion-correction step in SVR for fetal EPI data.

The fetal head is composed of tissues of very similar magnetic susceptibility. However, significant sources of field variation may exist in reasonably close proximity to the fetal head (e.g. as a result of gas bubbles in maternal gut). Thus although the B0 field is frequently non-uniform, its variation, $$$\Delta B$$$, is generally smooth in the fetal brain region and since there are only weak internal sources (such as from fetal blood), $$$\Delta B$$$ approximately obeys the Laplacian equation⁵ $$$\nabla^2 (\Delta B) = 0$$$. The EPI slices are acquired as regular stacks in scanner coordinate $$$y$$$, but are distorted due to $$$\Delta B$$$. As the fetus moves, the fetal head volume, $$$V(x)$$$, undergoes a rigid motion, $$$M_t$$$, in time $$$t$$$, such that anatomical location $$$x$$$ in the fetal head is related to scanner coordinate $$$y$$$ by $$$y= M_t x$$$. Due to the B0 field variation $$$\Delta B$$$, the fetal head will not appear in the acquired image in location $$$y$$$, but will be shifted by a spatially varying distance $$$d(y)=(\gamma \cdot \Delta B(y)/bw)\cdot \Delta y$$$, where $$$\gamma$$$ is gyromagnetic ratio, $$$bw$$$ is the bandwidth per pixel and $$$\Delta y$$$ is the pixel width in the direction of the shift. This shift always occurs in the phase-encoding (PE) direction, which can be expressed as a unit vector $$$\mathbf{p}$$$. The acquired, distorted, EPI data $$$S_t$$$ can thus be related to the moving model of the fetal head by: $$S_t(y_{it}+d(y_{it}) \cdot \mathbf{p}) = V(M_t^{-1}y_{it})$$ where $$$y_{it}$$$ is the grid of the acquired slice $$$S_t$$$. If the EPI dataset contains two orthogonal sets of stacks with orthogonal PE directions, the distortion $$$d$$$ can be found by estimating volume $$$V$$$ from the first set of stacks and then registering the EPI stacks of the second set to the simulated stacks $$$V(M_t^{-1}y_{it})$$$ using non-rigid registration⁶ with a Laplacian constraint. The sets of stacks can then be switched so that the distortion field can be estimated from both sets jointly. The distortion estimation is interleaved with motion estimation, which is performed by registration of distortion corrected EPI slices to a brain volume $$$V$$$, constructed from all corrected EPI stacks. The proposed SVR method with distortion correction was tested on three spin-echo diffusion datasets of fetal head with diffusion gradients set to zero (dMRI b=0smm^-2, TE 121ms, TR 8500ms, FoV 290x290x128mm³, voxel size 2.3x2.3x3.5mm³, slice overlap 1.75mm), each consisting of four transverse and four coronal stacks with orthogonal PE directions. We compared the reconstructed EPI volumes to motion-corrected ssFSE volumes³ (which are not affected by distortions) using local normalised cross correlation (LNCC).

SVR of the EPI data without distortion correction resulted in a mean LNCC of 0.69. The proposed method increased this to 0.78, while correction using an acquired field map resulted gave 0.76. Examples of reconstructed volumes are presented in Fig. 1.In this abstract we presented a slice-to-volume reconstruction method for EPI which includes distortion correction in the form of non-rigid registration with a Laplacian constraint, which was motivated by the expected properties of the local B0 field. We showed that the proposed method can perform better than field map correction and therefore registration-based distortion correction is a viable alternative to the acquisition of a B0 field map.