Imaging modalities exploit tracer-dilution methods to measure bulk haemodynamic parameters such as blood flow and volume at the level of the microcirculation. Here, we ask the question of whether the kinetics of a tracer can reveal morphological information about the vessels through which the tracers flow. The goal is to relate the acquired time-intensity characteristic to details of the vascular structure that lies below the imaging resolution. Two fractal vascular models are developed that represent organized 'kidney-like' and disorganized 'tumour-like' structures. The models are generated using simple rules of branching and fractal geometry in two dimensions. Blood flow and tracer kinetics are simulated using fundamental laws of haemodynamics. The flow conditions are matched in the two models. The fractal box dimensions of the kidney (D(B) = 1.67 +/- 0.01) and the tumour (D(B) = 1.80 +/- 0.01) vasculatures fall in the range given in the literature (D(B) = 1.61 +/- 0.06 and D(B) = 1.84 +/- 0.04, respectively). The tracer kinetic curves of the kidney and the tumour vasculatures have the same initial slope and final asymptote, corresponding to the same flow rate and vascular volume, but have different forms. The difference in the two curves is related to the distribution function of transit times of the vascular models, and is a consequence of the randomness introduced in vessel diameter and length. In principle, the form of the tracer kinetic curve from a contrast imaging study may offer information relating not only to vascular volume and flow rate, but also to the organization of a microvascular network.