Retrospective estimation of the susceptibility driven field map for distortion correction in echo planar imaging

Echo planar imaging (EPI) sequence used for acquiring functional MRI (fMRI) time series data provides the advantage of high temporal resolution, but also is highly sensitive to the magnetic field inhomogeneity resulting in geometric distortions. A static field-inhomogeneity map measured before or after the fMRI scan to correct for such distortions does not account for magnetic field changes due to the head motion during the time series acquisition. In practice, the field map dynamically changes with head motion during the scan and leads to variations in the geometric distortion. We model in this work the field inhomogeneity with the object and the scanner dependent terms. The object-specific term varies with the object's magnetic susceptibility and orientation, i.e., head position with respect to B0. Thus, the simple transformation of the acquired field may not yield an accurate field map. We assume that the scanner-specific field remains unchanged and independent of the head motion. Our approach in this study is to retrospectively estimate the object's magnetic susceptibility (chi) map from an observed high-resolution static field map using an estimator derived from a probability density function of non-uniform noise. This approach is capable of finding the susceptibility map regardless of the wrapping effect. A dynamic field map at each head position can be estimated by applying a rigid body transformation to the estimated chi-map and the 3-D susceptibility voxel convolution (SVC) which is a physics-based discrete convolution model for computing chi-induced field inhomogeneity.