Incorporating white matter microstructure in the estimation of magnetic susceptibility in ex-vivo mouse brain

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) microstructure by using our previously presented model for solid cylinders with arbitrary orientations to describe axons in terms of concentric cylinders. We show how multi-gradient echo (MGE) and diffusion MRI (dMRI) images can be combined to estimate an apparent scalar susceptibility. Experiments in mouse brains acquired at ultrahigh field shows the mesoscopic contribution due to WM microstructure to be substantial, with a magnitude up to 70% of the total frequency shift in highly anisotropic WM. This in turn changed estimated susceptibility values up to 56% 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.Comment: 33 pages, 7 figure

To mask or not to mask? Improving QSM quality by accounting for spatial frequency distributions and susceptibility sources

Estimating magnetic susceptibility using MRI depends on inverting a forward relationship between the susceptibility and measured Larmor frequency. However, an often-overlooked constraint in susceptibility fitting is that the Larmor frequency is only measured inside the sample, and after background field removal, susceptibility sources should only reside inside the same sample. Here we test the impact of accounting for such effects in susceptibility fitting and demonstrate that such effects should not be ignored.Comment: 22 pages, 5 figure

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

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.Comment: 70 pages, 14 figure

Larmor frequency shift from magnetized cylinders with arbitrary orientation distribution

We present a theoretical framework for the NMR and MRI measured Larmor frequency in media with magnetized microstructure using the mesoscopic Lorentz sphere and the principle of coarse graining. We obtain an analytical expression for infinite cylinders with arbitrary orientation dispersion and show how it depends on the fiber orientation distribution, measurable using diffusion MRI. Through simulations, we scrutinize the framework including the effect of the shape and size of the Lorentz cavity and validate our result for cylinders.Comment: 54 pages, 13 figure