· Understand the basic principles of quantitative susceptibility mapping (QSM)

· Appreciate the technical challenges of QSM

· Become familiar with emerging applications of QSM in the body

Basic Principles of QSM

Magnetic susceptibility is a quantitative property of all materials. The susceptibility of a material is a quantitative measure of its degree of magnetization in response to an applied magnetic field. Materials with larger absolute susceptibility tend to interact with and distort the applied magnetic field more significantly than materials with smaller susceptibility.

Within human tissue, the presence of certain biomaterials (e.g. iron, gadolinium) causes a large change in the magnetic susceptibility of the tissue, in direct proportion to the concentration of that biomaterial. Thus, knowledge of the magnetic susceptibility of a particular tissue, such as iron-overloaded liver, can be used to determine the concentration of the biomaterial within that tissue.

MRI is inherently sensitive to the magnetic susceptibility of tissue. The susceptibility distribution of the tissue being imaged distorts the main magnetic field. The mathematical relationship between the magnetic susceptibility map and the resultant magnetic field distortion is modeled as a convolution with a known unit dipole kernel.

The goal of QSM is to invert this relationship; that is, to estimate the magnetic susceptibility map from the magnetic field distortion. The field distortion manifests as a phase shift, which can be measured using a gradient-echo acquisition. From these acquired data, a series of steps is performed (i.e. QSM) to estimate the susceptibility map.

General Technical Challenges of QSM

In general, there are two main technical challenges of QSM: 1) background field removal, and 2) dipole deconvolution.

Background Field Removal

The background magnetic field arises from susceptibility sources that are either outside the volume of interest (VOI) or MR-invisible (e.g. air). Nevertheless, the effects of these sources must be removed in order to properly estimate the susceptibility distribution in the VOI. Techniques for background field removal have been developed, particularly for QSM in the brain. These techniques include the projection onto dipole fields (PDF) method as well as the sophisticated harmonic artifact reduction on phase data (SHARP) method.

Dipole Deconvolution

Following background field removal, the magnetic field resulting from the susceptibility distribution of the VOI remains. The dipole deconvolution step deconvolves the unit dipole kernel, to recover the susceptibility distribution. The deconvolution is an ill-posed inverse problem since the dipole kernel contains zeros (in the Fourier domain) at the magic angle (54.74°). Regularization techniques for the dipole deconvolution have been proposed, both in the Fourier domain and in the image domain.

Additional Technical Challenges of QSM in the Body

When performing QSM in the body (i.e. outside of the brain), additional technical challenges must be addressed, including: 1) motion during the acquisition, 2) the presence of fat, and 3) large susceptibility shifts.

Motion

Motion (respiratory, cardiac, etc.) during the acquisition introduces artifacts that can propagate to the estimated susceptibility map. The development of motion-insensitive (e.g. breath-held, free-breathing, cardiac-gated) acquisitions is an active area of research that will be of benefit to QSM in the body.

Presence of Fat

Fat is present throughout the body. Fat introduces additional phase shifts into the MRI signal that can be misinterpreted as originating from the main magnetic field. Errors in the estimated magnetic field map will propagate to the estimated susceptibility map. Water-fat imaging techniques have been developed that properly account for the presence of fat, resulting in unbiased estimates of the magnetic field.

Large Susceptibility Shifts

The concentration of certain biomaterials in the body, such as iron, can be significantly greater than in the brain. High concentrations of these biomaterials cause large shifts in the magnetic susceptibility of tissue, which increases R2* relaxation in those tissues. Pulse sequences must be optimized to properly sample the signal in these regions of rapid signal decay. Research is ongoing to develop and optimize sequences for this regime.

Applications of QSM in the Body

QSM in the body is in the relatively early stages of technical development. However, techniques have been developed that demonstrate the feasibility of QSM throughout the body. These include applications for improved detection of calcifications in the breast, quantification of iron concentration in the liver, detection of inflammation and fibrosis in the kidney, assessment of tissue function in the heart, and quantification of iron in whole-body imaging.

Further technical development as well as clinical studies will be necessary to characterize the accuracy, precision, and reproducibility of techniques for QSM of the body, in order to fully elucidate their value.