Role of Glucose and Oxygen Concentration on Tumor Cell: A Mathematical Model - Mazumdar, Neeta (Communications in Mathematics and Applications, 2023)
The paper aims at determining the combined effect of oxygen level and glucose concentration on the growth of tumor cells. The tumor cells were identified by Otto Warburg as the cells with increased glycolysis and decreased mitochondrial activity and described their metabolism. The known fact is that tumor tissues, which are in the form of solid tumors or as ascites cells, display a high rate of aerobic and anaerobic glycolysis. In this paper, one-dimensional mathematical model analysing the concentration of oxygen and glucose in the tumor is developed. The analyses of the effect of glucose and oxygen on tumor cells is done. The correlation between proliferating and quiescent cell number vis-à-vis primary nutrient concentration is found. The proposed model helps us to evaluate the consumption rate of nutrients in the cell when the concentration of glucose, oxygen, and lactic acid in the external medium is given and the radius of the necrotic core can be determined by using the model.
Keywords: Glycolysis; Michaelis-Menten kinetics; Crank-Nicholson approximation; Diffusivity; Tumor cell; Tridiagonal system; Lactic acid; Metabolism