Magnetic susceptibility anisotropy: Cylindrical symmetry from macroscopically ordered anisotropic molecules and accuracy of MRI measurements using few orientations

White matter is an essential component of the central nervous system and is of major concern in neurodegenerative diseases such as multiple sclerosis (MS). Recent MRI studies have explored the unique anisotropic magnetic properties of white matter using susceptibility tensor imaging. However, these measurements are inhibited in practice by the large number of different head orientations needed to accurately reconstruct the susceptibility tensor. Adding reasonable constraints reduces the number of model parameters and can help condition the tensor reconstruction from a small number of orientations. The macroscopic magnetic susceptibility is decomposed as a sum of molecular magnetic polarizabilities, demonstrating that macroscopic order in molecular arrangement is essential to the existence of and symmetry in susceptibility anisotropy and cylindrical symmetry is a natural outcome of an ordered molecular arrangement. Noise propagation in the susceptibility tensor reconstruction is analyzed through its condition number, showing that the tensor reconstruction is highly susceptible to the distribution of acquired subject orientations and to the tensor symmetry properties, with a substantial over- or under-estimation of susceptibility anisotropy in fiber directions not favorably oriented with respect to the acquired orientations. It was found that a careful acquisition of three non-coplanar orientations and the use of cylindrical symmetry guided by diffusion tensor imaging allowed reasonable estimation of magnetic susceptibility anisotropy in certain major white matter tracts in the human brain.