Mathematical modeling of chronical hypoxia in tumors considering potentialdoubling time and hypoxic cell lifetime

Purpose: To model mathematically how potential doubling time and hypoxic ce ll lifetime affect the extent of chronical hypoxia in tumor tissue segments . Three capillary geometries were modeled under idealized steady state cond itions. Materials and methods: The capillary geometries are: tissue surrounding an axial capillary, tissue enclosed by a cylindrical capillary network, and ti ssue enclosed by a spherical capillary network. The tissue segments are mod eled as three-compartment systems, where well nourished cells proliferate n ear the vasculature and, in so doing, displace 'older' cells into a quiesce nt compartment and, ultimately into a hypoxic region. The extent of the hyp oxic zone is the distance traversed by cells during their hypoxic lifetime before becoming necrotic. The steady state situation, where the necrotic ce ll loss equals the cell gain caused by cell proliferation was investigated Results: The hypoxic fraction, HF, was found to be inversely proportional t o 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 d epends only on the capillary geometry, the capillary radius, the intracapil lary oxygen tension, and the tissue respiration rate. The extent of the hyp oxic zone in addition depends on T-pot and T-hypox. Conclusions: Mathematical modeling of idealized steady state conditions sho ws that the ratio of hypoxic cell lifetime and potential doubling time, T-h ypox/T-pot, determines the hypoxic fraction, HF, in tumor segments. The ext ents of the oxygenated and the hypoxic zones can be predicted from the mode ls. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.