A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy
In this work we study a family of phenomenological super-macroscopic models describing the tumour angiogenesis and antiangiogenesis therapy, introduced by Folkman and coworkers [ P. Hahnfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumour development under angiogenic signaling: A dynamical theory of tumour growth, treatment response, and postvascular dormancy, Cancer Res. 59 ( 1999) 4770-4775], and depending on two positive parameters alpha is an element of [0, 1] and gamma is an element of [0, 5/3]. Here we extend the model by considering not only vessel-disrupting antiangiogenic therapies, but also drugs purely inhibiting the proliferation of endothelial cells, as well as drugs exerting both these actions. By means of cooperativity theory, we show that in order for the family to describe the biological phenomena under study one has to add a further constraint on the two parameters: gamma   alpha. Finally, in the concluding remarks, we stress some limitations of our super-macroscopic approach, and outline some steps of improvement that might lead to more comprehensive detailed multiscale modelling of tumour angiogenesis. (C) 2008 Elsevier Ltd. All rights reserved.
tumour angiogenesis cooperativity stability