A model combining acid-mediated tumour invasion and nutrient dynamics. (English) Zbl 1163.92319

Summary: We illustrate a mathematical model for the evolution of multicellular tumour spheroids in a host tissue, including the effect of the excess H\(^{+}\) ions and nutrient dynamics. Both the avascular and the vascular case are considered. The model is a nontrivial generalization of the simple scheme proposed by K. Smallbone et al. [The role of acidity in solid tumour growth and invasion. J. Theor. Biol. 235, 476–484 (2005)]. Many different situations may occur, depending on the values of the physical parameters involved. Existence of solutions and qualitative properties are investigated.


92C50 Medical applications (general)
35R35 Free boundary problems for PDEs
Full Text: DOI


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