A Mathematical Model for the Effect of Anti-angiogenic Therapy in the Treatment of Cancer Tumou ...
Channel: Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC)
Date: 15/07/2015

- By: Flora Bacelar, Federal University of Bahia, Brazil
- Date: 2015-07-15 14:30:00
- Description: Mathematical models for the growth of treatment of câncer has been of much interest. The tumour angiogenesis is an important process for tumor growth: when it  reaches a certain size,  the cancer cells provides mechanisms that lead to the growth of endothelial cells that cause blood cells to proliferate and bring oxygen and nutrients to tumour.  In order to affect the angiogenic process, an anti-angiogenic agent is introduced in some cases reducing the growth of endothelial cells.  A model consisting of a system of five ordinary differential  equations, to simulate the interactions between normal cells, cancer cells, endothelial cells, chemotherapy agent and anti-angiogenic agent in tumor growth, is developed. The interaction between the normal cells  and the cancer cells is thought of as a competition for bodily nutrients, the chemotherapy acts as a predator on normal and cancer cells, and the anti-angiogenic agent acts as a predator on endothelial cells. It is also tak
en into account that both the vascularization and the anti-angiogenic action may affect the chemotherapy delivery on cancer and normal cells. By a partial analysis of the cancer-free subspace, it is shown how the anti-angiogenic agent may help the chemotherapy agent in controlling the cancer, leading to a cure state for situations where the chemotherapy alone is not able to eliminate the tumour. This is illustrated by numerical examples.