Mathematical modeling of chronical hypoxia in tumors considering potential doubling time and hypoxic cell lifetime.

PURPOSE To model mathematically how potential doubling time and hypoxic cell lifetime affect the extent of chronical hypoxia in tumor tissue segments. Three capillary geometries were modeled under idealized steady state conditions. MATERIALS AND METHODS The capillary geometries are: tissue surrounding an axial capillary, tissue enclosed by a cylindrical capillary network, and tissue enclosed by a spherical capillary network. The tissue segments are modeled as three-compartment systems, where well nourished cells proliferate near the vasculature and, in so doing, displace 'older' cells into a quiescent compartment and, ultimately into a hypoxic region. The extent of the hypoxic zone is the distance traversed by cells during their hypoxic lifetime before becoming necrotic. The steady state situation, where the necrotic cell loss equals the cell gain caused by cell proliferation was investigated. RESULTS The hypoxic fraction, HF, was found to be inversely proportional to the potential doubling time of the tumor segment, T(pot), and proportional to the hypoxic cell lifetime, T(hypox). The extent of the oxygenated zone depends only on the capillary geometry, the capillary radius, the intracapillary oxygen tension, and the tissue respiration rate. The extent of the hypoxic zone in addition depends on T(pot) and T(hypox). CONCLUSIONS Mathematical modeling of idealized steady state conditions shows that the ratio of hypoxic cell lifetime and potential doubling time, T(hypox)/T(pot), determines the hypoxic fraction, HF, in tumor segments. The extents of the oxygenated and the hypoxic zones can be predicted from the models.