Geodesic
Tumour angiogenesis model with variable vessels' effectiveness
Jan Poleszczuk 1   ; Iwona Skrzypczak 2
1 Institute Applied Mathematics and Mechanics Faculty of Mathematics, Informatics and Mechanics University of Warsaw 02-097 Warszawa, Poland
2 College of Inter-faculty Individual Studies in Mathematics and Natural Sciences University of Warsaw 02-089 Warszawa, Poland
Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 33-49 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We propose a model of vascular tumour growth, which generalises the well recognised model formulated by Hahnfeldt et al. in 1999. Our model is based on the same idea that the carrying capacity for any solid tumour depends on its vessel density but it also incorporates vasculature quality which may be lost during angiogenesis as recognised by Jain in 2005. In the model we assume that the loss of vessel quality affects the diffusion coefficient inside the tumour. We analyse basic mathematical properties of the proposed model and present some numerical simulations.
DOI : 10.4064/am38-1-3
Keywords: propose model vascular tumour growth which generalises recognised model formulated hahnfeldt model based idea carrying capacity solid tumour depends its vessel density incorporates vasculature quality which may lost during angiogenesis recognised jain model assume loss vessel quality affects diffusion coefficient inside tumour analyse basic mathematical properties proposed model present numerical simulations

Jan Poleszczuk  1   ; Iwona Skrzypczak  2

1 Institute Applied Mathematics and Mechanics Faculty of Mathematics, Informatics and Mechanics University of Warsaw 02-097 Warszawa, Poland
2 College of Inter-faculty Individual Studies in Mathematics and Natural Sciences University of Warsaw 02-089 Warszawa, Poland 
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Jan Poleszczuk; Iwona Skrzypczak. Tumour angiogenesis model with variable vessels' effectiveness. Applicationes Mathematicae, Tome 38 (2011) no. 1, pp. 33-49. doi: 10.4064/am38-1-3

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