Three-dimensional dynamic contrast-enhanced ultrasound imaging opens the door for the characterisation of vascular networks. This work focusses on a stable finite-element algorithm to retrieve local properties of the vascularity based on the convection-dispersion equation. We show that, even at low spatial and temporal resolution, local convective-dispersion behaviour can be captured. Moreover, we present a probabilistic tractography strategy to visualise convective pathways and provide an in-vivo example.