PRELUDE & FUGUE - EPI Distortion Correction

Distortion of EPI-based functional images is a particular problem for high field (3T and higher) MR scanners. The inhomogeneities in the magnetic field caused by susceptibility differences at air-tissue interfaces (predominantly air-filled sinuses) result in both signal loss and geometric distortion of images. Such artefacts are particularly noticeable in the inferior temporal and frontal lobes and restrict the use of standard FMRI or diffusion imaging techniques in these areas. In addition, the distortions can also lead to global errors in registration, if not accounted for, causing errors in the spatial localisation of activations (or white matter tracts) from any brain region, including those where there is little or no distortion present.

One approach to solving this problem is to use a measured field-map to ``unwarp'' the distorted images by performing pixel shifts in the phase-encode direction [25] (see fig. 11); although this cannot restore lost signal (intensity), it can correct for local geometric distortion. Such methods require the acquisition of a B0 field map which we obtain from a phase-difference image. This first requires ``phase unwrapping'' to compensate for the fact that MR phase measurements are wrapped within the range 0:2$\pi$. A general N-dimensional phase-unwrapping technique [21] was developed for this task, based on optimising a global cost function that penalises large, spatially-localised phase changes. To improve speed and robustness, an efficient implementation (PRELUDE - Phase Region Expanding Labeller for Unwrapping Discrete Estimates) using region-based labelling and merging techniques was created. This technique has proved to be robust and reliable over a wide range of MR phase images, including high-resolution venogram studies.

Following phase unwrapping, the field map values are used to determine the pixel shift in the phase-encode direction. However, noise or artefacts in the field map are highly problematic for pixel shift methods such as this and in our implementation (FUGUE - FMRIB's Utility for Geometrically Unwarping EPIs) a range of regularisation options are available. Initial tests have showed that simple Gaussian smoothing is usually adequate [20] but this is dependent on the field map sequence and SNR. More recent research at FMRIB has been investigating applications of the field map as a cost function weighting for registration. In addition, alternative approaches, which do not require a field map, are being examined. We have been exploring a physical model-based method that calculates a field map from a structural MR image using a perturbation solution of Maxwell's equations [24]. This approach would allow studies where no field maps are available to benefit from the above distortion correction approaches, whilst still being derived from the individual subject's own anatomy. Such constraints could also be beneficial in other data-driven approaches to distortion correction within time-series, such as [1], and integration of these techniques is being explored.

Figure 11: An example of field-map-based distortion correction for EPI: structural image, field map, original EPI, unwarped EPI