How far away from anisotropic microstructure do you need to be for QSM to be faithful?

Motivation: White matter (WM) microstructure can affect estimation of WM susceptibility with QSM. However, as QSM fits all voxels at once, it is less understood how it affects estimation of surrounding tissue. Goal(s): Our goal is to demonstrate the effect of a cylindrical microstructure on surrounding tissue in a digital phantom. Approach: We synthesize a digital phantom with parallel rods surrounded by a rim with random dots. We estimate susceptibility with (QSM+) and without (QSM) account of microstructure. Results: QSM is biased inside the rim, and this error spreads to the surrounding tissue characterized by a power law. QSM+ improved susceptibility fitting. Impact: It may be important to account for microstructure in WM even though one may only be interested in analyzing surrounding tissue like gray matter. Failing to do so could lead to misinterpretation of tissue magnetic susceptibility.