QSM Algorithms

How can we map the magnetic susceptibility sources from local field map?

A local field (or tissue field) is the field generated by the magnetic susceptibility sources from the brain tissue. The assumption of the field generated by a magnetic susceptibility point source is a dipole field. We can then try to compute the susceptibility values by deconvolving the local field with a dipole field. However, due to the fact that the dipole field in the k-space (i.e. the dipole kernel) has zero values on the cone surface at 54.7° and values close to this surface will also be close to zeros. As a result, the number of unknown parameters is more than the measurements we have in the data, leading to the problem ill-conditioned and the resulting QSM map has the so-called streaking artefact. To solve the ill-conditioned problem, most of the QSM algorithms try to add a regularisation term in the QMS dipole inversion problem, imposing spatial smoothness in the QSM map and/or the QSM map has similar anatomical features as shown in the magnitude images in order to reduce the streaking artefact in the QSM result.