Magnetic susceptibility

Materials have a property called magnetic susceptibility () that reflects their ability to become magnetized in response to an external magnetic field Schenck, 1996. The change in magnetic field Bz (the subscript “z” is shown to make it explicit that we are referring to the component parallel to the B₀ field) is proportional to the magnetic susceptibility value, the magnetic field strength, and can be affected by the geometry and location of the tissues. It can be modeled as a convolution of the difference in magnetic susceptibility with the component parallel to the magnetic field induced by a unit magnetic dipole ($d=\frac{\left( 3\text{cos}^{2}\left( \theta \right)-1 \right)}{4\pi\left| \textbf{r} \right|^{3}}$) in spherical coordinates where $\textbf{r}$ is the position vector and is the angle with B₀ Rochefort et al., 2008.

The dipole kernel (d) is illustrated in Figure 5.2 along with the dipole kernel (D) in the k-space domain often used in QSM.

When a subject is introduced in the scanner, it interacts with the B₀ field and distorts it. Therefore, a perfectly homogeneous field in an empty bore will usually have an inhomogeneous B₀ field once a patient is introduced. This is the reason why active shimming is required when a patient is introduced in the scanner. Although these inhomogeneities happen everywhere in the body, stronger field variations occur at the boundaries of strong susceptibility differences such as air (slightly paramagnetic: $+\chi$) and water/tissue (diamagnetic: $-\chi$).

The following figure shows different susceptibility distributions in ppm for a homogeneous cylinder within a larger homogeneous cylinder placed in a homogeneous background (top) and a brain (bottom). The corresponding B₀ field maps are simulated at 7 T and shown in Figure 5.3. In the brain, the B₀ field inhomogeneities are dominated by air-tissue boundaries. On the right-hand panel, the slow varying spatial variations (also called background field) were removed to show the local field variations.