Influence of diffusion on transverse relaxation rates and phases of an ensemble of magnetic spheres.

In quantitative susceptibility mapping, the tissue susceptibility is determined from the magnitude and phase of the gradient echo signal, which is influenced by the interplay of complex susceptibility and diffusion effect. Herein, we analytically analyze the influence of diffusion on magnitude and phase images generated by randomly arranged magnetic spheres as a model of intracerebral iron depositions. We demonstrate that both gradient and spin echo relaxation rate constants have a strong and nonlinear dependence on diffusion strength and give empirical formulas for magnitude and phase. This may be used in the future to improve QSM processing methods. In addition, we show that, in theory, combined acquisitions of gradient and spin echo can be used to determine the dimension of the magnetic spheres and the diffusion strength.