Theoretical analysis of the sensitivity of dipolar field signal to local field variations by perturbative expansion of the magnetization

A perturbation method based on the integral form of the Bloch equation is used to calculate the distant dipolar field (DDF) signal formed by the correlation spectroscopy revamped by asymmetric z-gradient echo detection (CRAZED) sequence in the presence of a susceptibility-induced field. The properties of the DDF signal are analyzed through the series expansion of the magnetization, and the first order DDF result is applied to study the use of the DDF effect to probe sub-voxel field distributions. Numerical calculations are carried out with the sub-voxel field distributions modeled by rectangular tubes of uniform frequency shifts (the block model) and cylinders of a finite susceptibility difference (the blood vessel model) using the parameters for brain at 9.4 T. The DDF signal is found to exhibit features arising from the sub-voxel structures.