Scaling rules for diffusive drug delivery in tumor and normal tissues.

Delivery of blood-borne molecules and nanoparticles from the vasculature to cells in the tissue differs dramatically between tumor and normal tissues due to differences in their vascular architectures. Here we show that two simple measures of vascular geometry--δ(max) and λ--readily obtained from vascular images, capture these differences and link vascular structure to delivery in both tissue types. The longest time needed to bring materials to their destination scales with the square of δ(max), the maximum distance in the tissue from the nearest blood vessel, whereas λ, a measure of the shape of the spaces between vessels, determines the rate of delivery for shorter times. Our results are useful for evaluating how new therapeutic agents that inhibit or stimulate vascular growth alter the functional efficiency of the vasculature and more broadly for analysis of diffusion in irregularly shaped domains.