On the effect of contrast agent internalization in a two compartment diffusion model

Introduction Contrast agents (CA) are commonly used in MRI to generate a detectable contrast between areas of interest and the surrounding tissue. However, the CA may accumulate in a specific area. In this situation it is possible that the exchange of water molecules between the area with CA and the surrounding tissue is not fast enough to preserve the conditions of the fast exchange limit and diffusion can become a limiting factor on the relaxation rate. An example are CAs internalized in cells. This effect has been investigated for T1 relaxation using an exchange model [1]. In this work diffusion between different compartments was not considered explicitly, but modeled implicitly by size dependent residence times of the spins in the according compartment. The effect of diffusion in similar problems has been treated by different authors [2,3,4,5]. The focus of this work is the behavior of the CAs relaxivity if the CA is not homogeneously dispersed but accumulated in small parts of the volume. This is done in terms of a diffusion model.