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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 56521 (02)
- University: Sharif University of Technology
- Department: Mathematical Sciences
- Advisor(s): Fotouhi, Morteza
- Abstract:
- A major medical revolution that is helping us overcome some of the worst diseases, including cancer, is angiogenesis, which is based on the processes our bodies use to develop blood vessels. Most human cancers have acquired six essential capabilities: self-sufficiency in growth signals, insensitivity to growth-inhibitory signals, programmed cell death escape, unlimited replication potential, persistent angiogenesis, and tissue invasion that can induce metastasis. In other words, the defense mechanism that prevents any of these acquired capabilities must be neutralized before the cells become malignant and invasive tumors. In fact, tumors in the non-vascular growth stage can only grow up to half a square millimeter due to the limitation and lack of oxygen. Most of these cancers will never become dangerous and this stage is what Dr. Folkman, one of the pioneers in the field of angiogenesis, calls so-called cancer without disease. In fact, the body's ability to balance angiogenesis, when it works optimally, prevents cancer cells from being fed by blood vessels, and if we prevent angiogenesis forever, tumors can no longer grow. When the process of angiogenesis begins, cancer cells grow and expand rapidly in the presence of blood vessels and oxygen and can eventually metastasize. Until now, various treatments based on chemotherapy and also anti-angiogenic treatments have been used in medical science, and these two types of treatments are completely different from each other. In this thesis, we are going to investigate the mechanism of angiogenesis and the effect of various treatments on it with mathematical modeling. We also compare the combined effect of some anti-angiogenic treatments and observe that with this solution, compared to the case where we use only one treatment, angiogenesis is inhibited faster
- Keywords:
- Angiogenesis ; Partial Differential Equations ; Cancer ; Tumor Growth ; Mathematical Modeling ; Cancer Cells
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