Analysis of oxygen transport to tumor tissue by microvascular networks.

We present theoretical simulations of oxygen delivery to tumor tissues by networks of microvessels, based on in vivo observations of vascular geometry and blood flow in the tumor microcirculation. The aim of these studies is to investigate the impact of vascular geometry on the occurrence of tissue hypoxia. The observations were made in the tissue (thickness 200 microns) contained between two glass plates in a dorsal skin flap preparation in the rat. Mammary adenocarcinomas (R3230 AC) were introduced and allowed to grow, and networks of microvessels in the tumors were mapped, providing data on length, geometric orientation, diameter and blood velocity in each segment. Based on these data, simulations were made of a 1 mm x 1 mm region containing five unbranched vascular segments and a 0.25 mm x 0.35 mm region containing 22 segments. Generally, vessels were assumed to lie in the plane midway between the glass plates, at 100 microns depth. Flow rates in the vessels were based on measured velocities and diameters. The assumed rate of oxygen consumption in the tissue was varied over a range of values. Using a Green's function method, partial pressure of oxygen (PO2) was computed at each point in the tissue region. As oxygen consumption is increased, tissue PO2 falls, with hypoxia first appearing at points relatively distant from the nearest blood vessel. The width of the well-oxygenated region is comparable to that predicted by simpler analyses. Cumulative frequency distributions of tissue PO2 were compared with predictions of a Krogh-type model with the same vascular densities, and it was found that the latter approach, which assumes a uniform spacing of vessels, may underestimate the extent of the hypoxic tissue. Our estimates of the maximum consumption rate that can be sustained without tissue hypoxia were substantially lower than those obtained from the Krogh-type model. We conclude that the heterogeneous structure of tumor microcirculation can have a substantial effect on the occurrence of hypoxic micro-regions.