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Document Type |
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Thesis |
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Document Title |
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MATHEMATICAL MODELING OF BRAIN TUMORS (GLIOMA) النمذجة الرياضية لأورام المخ (جلايوما) |
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Subject |
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Faculty of Science |
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Document Language |
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Arabic |
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Abstract |
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Glioma is an invasive brain tumor associated with low survival rates and limited life expectancy. The complexity of glioma includes not only the heterogeneous cell population of the tumor and its location in the brain, but also its interaction with glial cells, neurons, immune system and responses to different kinds of treatments. Mathematical modeling of the impact of these factors on glioma growth can improve treatment strategies to maximize the chance of a cure.
In this thesis, we present four mathematical models using ordinary differential equations aiming to simplify the glioma interaction with the microenvironment and responses to chemotherapy. This thesis investigates whether or not glial cells and the immune system has the ability to eliminate glioma completely. Moreover, it studies the effect of the chemotherapeutic agent on the glioma growth.
The first model describes the competition between glioma and glial cells. Local and global stability conditions are obtained, that is, we found the conditions for the glial cells or the glioma to win the competition. Numerical results showed that untreated glioma invades the brain and destroys the glial cells.
Then the first model is modified to propose the dependence of neurons on glial cells and the attack of chemotherapy on all the cells. The second model shows that the death of glial cells causes the death of neurons, whereas, the growth of glial cells does not contribute to a change in the neural population. Furthermore, the infusion rate of chemotherapeutic agent plays a major role in the local asymptotic stability of all equilibrium points of the model. Moreover, several numerical simulations were conducted to support our theoretical findings. The numerical experiments vary according to the values of the infusion rate.
The third model describes the interaction among glioma cells, microglia and cytotoxic T lymphocytes (CTLs). The existence and the stability conditions of the equilibrium points are analyzed. Numerical results showed that neither microglia nor CTLs have the ability to eradicate the tumor. Because of this, we extended the model by including the chemotherapeutic agent (fourth model). The model has six equilibrium points and one of these points represents a cure state. Through local stability we found a range of values for the infusion rate that guarantee the elimination of glioma, as well as, preventing the glioma from reoccurring. |
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Supervisor |
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Dr. Sarah Al-Sheikh |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1441 AH
2020 AD |
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Co-Supervisor |
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Dr. Hala Ashi |
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Added Date |
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Tuesday, July 7, 2020 |
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Researchers
| دعاء موسى الأحمدي | Alahmadi, Dua Mousa | Researcher | Master | |
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