ROLE OF TUMOR VASCULAR ARCHITECTURE IN NUTRIENT AND DRUG-DELIVERY - AN INVASION PERCOLATION-BASED NETWORK MODEL

Delivery of diffusible nutrients and drugs in tissues is limited in pa rt by the distance over which substances must diffuse between the vasc ular space and the surrounding tissues and by upstream losses prior to local delivery by the blood. By examining the fractal behavior of two -dimensional vascular networks in the murine dorsal skinfold chamber p reparation, we have identified distinct architectural features of norm al and tumor vascular networks that lead to fundamentally different tr ansport behavior. Normal capillaries which are relatively straight and regularly spaced are well modeled by the widely used Krogh cylinder m odel. In contrast, the fractal dimensions of tumor vascular networks s uggest that the tortuous vessels and wide range of avascular spaces fo und in tumors are better represented by invasion percolation, a well-k nown statistical growth process governed by local substrate properties . Based on these observations, we have constructed a percolation-based model of tumor vascular growth that enables us to predict the effects of network architecture on transport. We find that the number of avas cular spaces in tumors scales with the size of the spaces so that ther e will exist a few large avascular spaces and many smaller avascular s paces between vessels. We also End that the tortuosity of the vessels, as reflected by the elevated minimum path dimension, produces regions of locally flow-limited transport and reduces flow through the tumor as a whole. Our model helps to explain the long-standing paradox that tumor vasculature has a higher geometrical resistance than normal vasc ulature despite increases in vessel diameter. A comparison to oxygenat ion measurements in normal and tumor tissues shows that our model pred icts the architectural obstacles to transport in tumors more accuratel y than the Krogh cylinder model. Our results suggest that clinical int erventions that yield more regular vascular geometry may be useful as a supplement to those that improve arterial availability or decrease r ates of consumption by the tissue. (C) 1996 Academic Press, Inc.