Time dependent dispersion of nanoparticles in blood vessels

The dispersion of intravasculary injected nanoparticles can be efficiently described by introducing an effective diffusion coefficient Deff which quantifies the longitudinal mass transport in blood vessels. Here, the original work of Gill and Sankarasubramanian was modified and extended to include 1) the variati- on over time of Deff; 2) the permeability of the blood vessels and 3) non-Newtonian rheology of blood. A general solution was provided for Deff depending on space (x), time (t), plug radius (xc) and a subset of permeability parameters. It was shown that increasing the vessel plug radius (thus hematocrit) or permeability leads to a reduction in Deff, limiting the transport of nanoparticles across those vessels. It was also shown that the asymptotic time beyond which the solution attains the steady state behaviour is always independent of the plug radius and wall permeability. The analysis presented can more accurately predict the transport of nanoparticles in blood vessels, compared to previously developed models.