Region Expansion of Background Field Removal with Local Spherical Harmonics Approximation for Whole-brain Quantitative Susceptibility Mapping

Purpose: Quantitative susceptibility mapping (QSM) is useful for obtaining biological information. To calculate susceptibility distribution, it is necessary to calculate the local field caused by the differences of susceptibility between the tissues. The local field can be obtained by removing a background field from a total field acquired by MR phase image. Conventional approaches based on spherical mean value (SMV) filtering, which are widely used for background field calculations, fail to calculate the background field of the brain surface region corresponding to the radius of the SMV kernel, and consequently cannot calculate the QSM of the brain surface region. Accordingly, a new method calculating the local field by expansively removing the background field is proposed for whole brain QSM.

Methods: The proposed method consists of two steps. First, the background field of the brain surface is calculated from the total field using a locally polynomial approximation of spherical harmonics. Second, the whole brain local field is calculated by SMV filtering with a constraint term of the background field of the brain surface. The parameters of the approximation were optimized to reduce calculation errors through simulations using both a numerical phantom and a measured human brain. Performance of the proposed method with the optimized parameters was quantitatively and visually compared with conventional methods in an experiment of five healthy volunteers.

Results: The proposed method showed the accurate local field over the expanded brain region in the simulation studies. It also showed consistent QSM with conventional methods inside of the brain surface and showed clear vein structures on the brain surface.

Conclusion: The proposed method enables accurate calculation of whole brain QSM without eroding the brain surface region while maintaining same values inside of the brain surface as the conventional methods.