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Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth

100%

Poleszczuk J., Foryś U.

Applicationes Mathematicae

2009

tom 36

nr 3

313-331

We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic cell dynamics, while in the second one we use the Gompertz type of growth. Simulations of solutions show that a vascular dormant state of the tumour can be reached in two different ways. In addition in each case efficiency of treatments is different.

Tumour angiogenesis model with variable vessels' effectiveness

100%

Poleszczuk J., Skrzypczak I.

Applicationes Mathematicae

2011

tom 38

nr 1

33-49

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.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Poleszczuk J.

1 Foryś U.

1 Skrzypczak I.

1 2011

1 2009

Wyniki wyszukiwania

Angiogenesis process with vessel impairment for Gompertzian and logistic type of tumour growth

Tumour angiogenesis model with variable vessels' effectiveness