Direct Magnetic Field Estimation Based on Echo Planar Raw Data

Gradient recalled echo echo planar imaging is widely used in functional magnetic resonance imaging. The fast data acquisition is, however, very sensitive to field inhomogeneities which manifest themselves as artifacts in the images. Typically used correction methods have the common deficit that the data for the correction are acquired only once at the beginning of the experiment, assuming the field inhomogeneity distribution ΔB₀ does not change over the course of the experiment. In this paper, methods to extract the magnetic field distribution from the acquired k-space data or from the reconstructed phase image of a gradient echo planar sequence are compared and extended. A common derivation for the presented approaches provides a solid theoretical basis, enables a fair comparison and demonstrates the equivalence of the k-space and the image phase based approaches. The image phase analysis is extended here to calculate the local gradient in the readout direction and improvements are introduced to the echo shift analysis, referred to here as "k-space filtering analysis." The described methods are compared to experimentally acquired ΔB₀ maps in phantoms and in vivo. The k-space filtering analysis presented in this work demonstrated to be the most sensitive method to detect field inhomogeneities.