  Accurate estimation of microscopic magnetic field variations induced in
biological tissue can be valuable for mapping tissue composition in health and
disease. Here, we present an extension to Quantitative susceptibility mapping
(QSM) to account for local white matter (WM) magnetic microstructure by using
our previously presented model for solid cylinders with arbitrary orientations
to describe axons in terms of concentric cylinders. Through computer
simulations, we find that our model improves susceptibility estimation compared
to QSM, and Susceptibility Tensor Imaging (STI) are substantially biased by the
unaccounted-for structural anisotropy due to the mesoscopic frequency
contribution, indicating the observed STI tensor might not represent
susceptibility anisotropy as expected. Experiments in mouse brains acquired at
ultrahigh field shows the mesoscopic contribution due to WM microstructure to
be substantial. This in turn changed estimated susceptibility values up to 25%
root-mean-squared-difference in WM compared to standard QSM. Our work
underscores how microstructural field effects impact susceptibility estimates,
and should not be neglected when imaging anisotropic tissue such as brain WM.
