A mathematical model of tumor oxygen and glucose mass transport and metabolism with complex reaction kinetics

Hypoxia imparts radioresistance to tumors, and various approaches have been developed to enhance oxygenation, thereby improving radiosensitivity. This study explores the influence of kinetic and physical factors on substrate metabolism in a tumor model, based on a Krogh cylinder. In tissue, aerobic metabolism is assumed to depend on glucose and oxygen, represented by the product of Michaelis-Menten expressions. For the base case, an inlet pO(2) of 40 mmHg, a hypoxic limit of 5 mmHg, and a tissue/capillary radius ratio of 10 are used. For purely aerobic metabolism, a hypoxic fraction of 0.16 and volume-average pO(2) of 8 mmHg are calculated. Reducing the maximum oxygen rate constant by 9%, decreasing the tissue cylinder radius by 5%, or increasing the capillary radius by 8% abolishes the hypoxic fraction. When a glycolytic term is added, concentration profiles are similar to the base case. Using a distribution of tissue/capillary radius ratios increases the hypoxic fraction and reduces sensitivity to the oxygen consumption rate, compared to the case with a single tissue/capillary radius ratio. This model demonstrates that hypoxia is quite sensitive to metabolic rate and geometric factors. It also predicts quantitatively the effects of inhibited oxygen metabolism and enhanced mass transfer on tumor oxygenation.