Mathematical modelling of the Warburg effect in tumour cords.
The model proposed here links together two approaches to describe tumours: a continuous medium to describe the movement and the mechanical properties of the tissue, and a population dynamics approach to represent internal genetic inhomogeneity and instability of the tumour. In this way one can build models which cover several stages of tumour progression. In this paper we focus on describing transition from aerobic to purely glycolytic metabolism (the Warburg effect) in tumour cords. From the mathematical point of view this model leads to a free boundary problem where domains in contact are characterized by different sets of equations. Accurate stitching of the solution was possible with a modified ghost fluid method. Growth and death of the cells and uptake of the nutrients are related through ATP production and energy costs of the cellular processes. In the framework of the bi-population model this allowed to keep the number of model parameters relatively small.
Astanin
Sergey
S
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. astanin@calvino.polito.it
Preziosi
Luigi
L
D002452:Cell Count; D045744:Cell Line, Tumor; D002470:Cell Survival; D003198:Computer Simulation; D018450:Disease Progression; D006019:Glycolysis; D006801:Humans; D008954:Models, Biological; D009369:Neoplasms / Q000378:metabolism* / Q000473:pathology*