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

Bianchini, Lorenzo; Fasano, Antonio

Nonlinear Anal., Real World Appl. 10, No. 4, 1955-1975 (2009).

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.

MSC:

92C50	Medical applications (general)
35R35	Free boundary problems for PDEs

Keywords:

mathematical models of cancer

References:

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