Theory of paramagnetic contrast agents in liposome systems

We develop a theoretical description of nuclear spin relaxation mediated by MRI contrast agents and transport processes in liposome systems. Such systems compartmentalize the physical space such that paramagnetic contrast agents, which enhance relaxation, are trapped in some subvolume. Due to diffusive transport across compartmental barriers, i.e., across liposome membranes, nuclear spins in the whole volume exhibit fast relaxation. The description developed is based on the diffusion-Bloch equations for the nuclear magnetization with appropriate boundary and continuity conditions. From this set of equations a new inhomogeneous differential equation for the local relaxation times is derived. For simple geometries of compartmentalized spaces the equation can be solved analytically. A simple formula for average relaxation times in liposome systems is presented. The resulting relaxation times agree well with observations.