- Magnetic susceptibility differences between tissues produce spatial variation in MRI resonance frequency
(and thus phase) that can be utilized in gradient-echo based sequen­ces for creating tissue contrast

- A non-local relationship exists between measured phase variation and underlying susceptibility distribution

- Creating susceptibility maps from phase data is challenging due to the ill-posed nature of the required field-
to-source inversion

- Anisotropic susceptibility can be evaluated by susceptibility tensor imaging which allows assessment of
tissue microstructure and fiber orientation

- QSM and STI provide a novel quantitative contrast of an intrinsic physical tissue quantity

Magnetic susceptibility describes the magnetizability of a material in response to an applied magnetic field and represents an important physical quantity in the field of MRI. Since the earliest days of MRI, quantification of magnetic susceptibility was considered an important goal as it was anticipated that magnetic susceptibility, similar to T1 and T2 relaxation constants, could be useful to characterize diseased tissue. With the recently introduced method of quantitative susceptibility mapping (QSM) and its conceptual extension to susceptibility tensor imaging (STI), non-invasive and spatially resolved assessment of this physical quantity has become possible by solving the ill-posed inverse problem to determine magnetic susceptibility from local magnetic fields.

Gradient-echo (GRE) sequences are particularly suited in this respect, since their associated phase maps or, equivalently frequency maps, are reflecting the sample’s magnetization and thus its magnetic susceptibility. QSM is made possible by, first, estimating the magnetic field distribution from raw MRI phase data of tissue whose contrast is based on off-resonance phase accumulation during TE so that phase in the final image is largely determined by timing of acquisition at the center of k-space, second, eliminating background field contributions that result from susceptibility sources outside of the area of interest (e.g., brain) and, third, solving the inverse problem from field perturbation to magnetic susceptibility by applying deconvolution with a magnetic dipole field kernel. The latter process implicitly assumes that the magnetic field distribution can be considered as the superposition of dipole fields generated by each voxel whereupon each voxel is represented by a particular value of magnetic susceptibility.

All these steps hinted at above need careful consideration when setting up the imaging and reconstruction pipeline. Demarcation of regions with internal magnetic field variations essential for background field removal as well as identification of unreliable phase values are important details that need special consideration. Several methods to overcome the ill-posed nature of the inversion problem have been developed, which rely either on repeated measurements of the object after having been rotated with respect to the magnetic field and combining data or in case of single orientation imaging on the utilization of non-iterative k-space (e.g., simple k-space thresholding) or iterative image-space based regularization methods. With regularization one seeks to incorporate a priori knowledge into the solution process (i.e. knowledge like, e.g., amount or type of noise, smoothness or sparsity of the solution, or restrictions on the values the solution may take on), which also requires choosing one or more regularization parameters. One major demand on any inversion algorithm is its ability to reconstruct subtle tissue susceptibility variations while simultaneously suppressing artifacts, such as streaking and potential blooming, to avoid that such non-local artifacts are mistaken as pathological abnormalities.

In anisotropic materials or specific biological tissue constituents, like lipid bilayers, proteins, muscle fibers or white matter fiber bundles, susceptibility becomes orientation dependent with respect to an external magnetic field and is then described by a symmetric second rank tensor. To determine the six independent tensor elements requires multiple measurements of frequency offsets at different orientations with respect to the field. With a set of data given one can extract the full tensor, an approach that has been exploited in STI to map white matter fiber orientation as well as to explore fibrous and tubular tissues in the body.

Challenges that have to be met concern subject movement and physiological motion that may introduce phase shifts that cannot be explained within the field-to-susceptibility model ultimately leading to inaccurate susceptibility maps and incorporation of orientation dependent microstructural effects into field-to-susceptibility models.

Mapping susceptibility provides a novel, quantitative contrast of an intrinsic physical tissue quantity that reflects the response of tissue to the presence of a static magnetic field. QSM and STI represent important steps towards more specific imaging of tissue properties and a major addition to the imaging armamentarium with important implications for basic science and clinical applications.