Generalized Non-Linear SENSE Shimming

Introduction: With the SENSE Shimming (SSH) approach (1) a method was introduced recently that allows for estimating B0 field inhomogeneities based on a reference image and a series of points on a single free induction decay (FID). The temporal evolution of the FID data is explained by field inhomogeneities, starting from the reference image, making use of the encoding properties of the different sensitivities of a coil array. The original approach takes into account the slope of the FID data only at the echo time of the reference image (TE). As a consequence it cannot distinguish between effects caused by relaxation and those caused by inhomogeneities. It can therefore only be used for estimating inhomogeneity variations, relative to a baseline measurement. We here present an extension to the method, which takes into account a larger range of the FID in order to explain not only B0 inhomogeneities but relaxation as well. Since the signal equation is non-linear, the linear fitting of the original approach has to be replaced by a non-linear optimization. Methods: The SSH method as presented in (1) assumes the slope of FID data on a sufficiently small time scale to depend only on the B0 field inhomogeneities; relaxation is assumed to be negligible. The signal of an FID seen by coil n at time t is described by