Green’s Function Total Field Inversion for Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) is a magnetic resonance imaging technique that quantifies tissue magnetic susceptibility by deconvolving the measured signal phase data. Accurate background field removal is essential for QSM, especially in surface regions of the brain, such as the cerebral cortex, where the background field interference is substantial. Existing methods have errors in estimating background field near the boundary of an organ, such as those of the brain, due to assumptions or loss of low-frequency information. A novel Green's function total field inversion (gTFI) method is proposed here to model the background field using integral equations composed of Green's function and boundary conditions, thereby eliminating the need for traditional filtering, assumption or regularization. The gTFI method simultaneously determines the background field at the boundary and the tissue susceptibility from the measured phase data. Numerical simulations and in vivo experiments demonstrate that the gTFI effectively separates the background field and reconstructs whole-brain QSM images without boundary erosion, offering superior performance over existing methods, particularly in cortical regions.