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Magnetic susceptibility imaging may provide valuable information aboutchemical composition and microstructural organization of tissue. However, itsestimation from the MRI signal phase is particularly difficult as it issensitive to magnetic tissue properties ranging from the molecular tomacroscopic scale. The MRI Larmor frequency shift measured in white matter (WM)tissue depends on the myelinated axons and other magnetizable sources such asiron-filled ferritin. We have previously derived the Larmor frequency shiftarising from a dense media of cylinders with scalar susceptibility andarbitrary orientation dispersion. Here we extend our model to includemicroscopic WM susceptibility anisotropy as well as spherical inclusions withscalar susceptibility to represent subcellular structures, biologically storediron etc. We validate our analytical results with computer simulations andinvestigate the feasibility of estimating susceptibility using simple iterativelinear least squares without regularization or preconditioning. This is done ina digital brain phantom synthesized from diffusion MRI (dMRI) measurements ofan ex vivo mouse brain at ultra-high field.

The Larmor frequency shift of a white matter magnetic microstructure model with multiple sources