Limitations of the permeability-limited compartment model in estimating vascular permeability and interstitial volume fraction in DCE-MRI.

Dynamic contrast-enhanced magnetic resonance imaging commonly uses compartment models to estimate tissue parameters in general and perfusion parameters in particular. Compartment models assume a homogeneous distribution of the injected tracer throughout the compartment volume. Since tracer distribution within a compartment cannot be assessed, the parameters obtained by means of a compartment model might differ from the actual physical values.

Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation.

A detailed study is presented for a large class of uncoupled continuous-time random walks. The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed.