Abdominal quantitative susceptibility mapping (QSM), especially in small animals, is challenging because of respiratory motion and blood flow that, in addition to noise, deteriorate the quality of the input data. Efficient artefact suppression in QSM reconstruction is crucial in these conditions. Single-step QSM algorithms combine background field removal and magnetic field-to-susceptibility inverse problem regularization in a single optimization equation. Here, we propose a single-step QSM algorithm that uses spherical mean value kernels of different radii for background field removal and structure prior (consistency with magnitude image) with L1 norm for regularization. The optimization problem is solved using the split-Bregman method on the graphic processor unit. The method was compared with previously reported singlestep methods: a method using discrete Laplacian instead of spherical mean value kernels, a method using total variational penalty instead of structure prior, and a method using L2 norm for structure prior. With the proposed method relative to the previous ones, a numerical susceptibility phantom was reconstructed more precisely. In living mice, susceptibility maps with more homogeneous liver, higher contrast between liver and blood vessels, and well-preserved structural details were obtained. In patients, susceptibility maps with more homogeneous subcutaneous fat and higher contrast between subcutaneous fat and liver were obtained. These results show the potential of the proposed single-step method for abdominal QSM in small animals and humans.
Generalized spherical mean value operators on Euclidean space
