  Magnetic susceptibility imaging may provide valuable information about
chemical composition and microstructural organization of tissue. However, its
estimation from the MRI signal phase is particularly difficult as it is
sensitive to magnetic tissue properties ranging from the molecular to
macroscopic scale. The MRI Larmor frequency shift measured in white matter (WM)
tissue depends on the myelinated axons and other magnetizable sources such as
iron-filled ferritin. We have previously derived the Larmor frequency shift
arising from a dense media of cylinders with scalar susceptibility and
arbitrary orientation dispersion. Here we extend our model to include
microscopic WM susceptibility anisotropy as well as spherical inclusions with
scalar susceptibility to represent subcellular structures, biologically stored
iron etc. We validate our analytical results with computer simulations and
investigate the feasibility of estimating susceptibility using simple iterative
linear least squares without regularization or preconditioning. This is done in
a digital brain phantom synthesized from diffusion MRI (dMRI) measurements of
an ex vivo mouse brain at ultra-high field.
