A method for calculating quantitative three-dimensional susceptibility maps from field measurements acquired using gradient echo imaging at high field is presented. This method is based on division of the three-dimensional Fourier transforms of high-pass-filtered field maps by a simple function that is the Fourier transform of the convolution kernel linking field and susceptibility, and uses k-space masking to avoid noise enhancement in regions where this function is small. Simulations were used to show that the method can be applied to data acquired from objects that are oriented at one angle or multiple angles with respect to the applied field and that the use of multiple orientations improves the quality of the calculated susceptibility maps. As part of this work, we developed an improved approach for high-pass filtering of field maps, based on using an arrangement of dipoles to model the fields generated by external structures. This approach was tested on simulated field maps from the substantia nigra and red nuclei. Susceptibility mapping was successfully applied to experimental measurements on a structured phantom and then used to make measurements of the susceptibility of the red nuclei and substantia nigra in healthy subjects at 3 and 7 T.
(c) 2010 Wiley-Liss, Inc.