A mathematical study of the interaction between oxygen and lactate in an <i>in vivo</i> and <i>in vitro</i> tumor

Micro-environmental acidity is a common feature of the tumor. One of the causes behind tumor acidity is lactate production by hypoxic cells of the tumor. Hypoxia is a direct result of the establishment of oxygen gradients. It is commonly observed in the tumor in an in vitro experimental setup and also in vivo situation. Here, we propose a mathematical model to analyze the production of lactate by hypoxic cells, and it is used as an alternative fuel by normoxic cells in tumor tissue in vitro and in vivo conditions. Also, we study the effects of unequal oxygen concentrations at the tumor boundaries on lactate status in the tumor. The effects of necrotic core on lactate accumulation is examined. The results are in good agreement with experimental data and are in align with the theoretical findings of previous studies. The analytical results show that lactate levels are elevated in an in vivo tumor compared to that in an in vitro tumor. Also, during the onset of necrotic core formation, the effects of necrotic core on lactate levels are noticed. Knowledge of the lactate status in a patient’s tumor may be helpful in choosing the appropriate and effective medicines for cancer treatment.