Document Details
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Document Type |
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Thesis |
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Document Title |
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MATHEMATICAL ANALYSIS OF SOME MODELS ON CANCER TREATMENT التحليل الرياضي لبعض نماذج علاج السرطان |
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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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Despite advances in traditional cancer treatments such as surgery, radiation therapy and chemotherapy, these therapies are considered low efficacy and high toxicity for patients. Thus, new therapeutic strategies are urgently needed. Fortunately, the advances in genetic engineering paved the way for a new therapy for cancer, which is called virotherapy. This treatment uses genetically engineered viruses to selectively infect, replicate in, and destroy cancer cells without damaging normal cells. Furthermore, current researches and clinical trials have indicated that these viruses can be delivered as a single agent or in combination with other therapies.
In this thesis, we construct and analyze six mathematical models in the form of ordinary differential equations (ODE) and partial differential equations (PDE) in order to examine the dynamics of virotherapy (alone and combined with other treatments) and understand the interaction between tumor cells and oncolytic viruses. The thesis seeks to gain insight on which key factors lead to treatment success, describe how the immune system influences the outcome of virotherapy treatment, and determine the efficacy of oncolytic viruses combined with radiation therapy in tumor eradication.
First, we present an ODE model (model 1) that includes, in the dynamics of virotherapy, the interaction between uninfected tumor cells and immune response. The model is analyzed qualitatively producing five equilibrium points. One of these equilibriums demonstrates the effect observed in virotherapy, where the immune system demolishes infected cells as well as viruses. Moreover, the existence and local stability of the equilibrium points are established under certain criteria. Furthermore, numerical simulations are performed to display the agreement with the analytical results. Also, parameter analysis is carried out to illustrate which parameters in the model affect the outcome of virotherapy. Then model 1 is extended to include the spatial evolution of cells. Therefore, in model 2, we develop a system of PDE which describes the spatiotemporal dynamics of cancer cells under virotherapy treatment and immune response. We carry numerical simulations of the system and analyze the important biological parameters with a continuous delivery of the virus. The numerical results suggest that high viral infection plays an important role in improving the treatment outcomes. Moreover, strong immune response can improve the result of virotherapy along with high immune killing rate of cancer cells.
In models 3 and 4 we propose systems of ODE embodying the dynamics of aggressive tumor growth under radiovirotherapy treatment. Here, we divied the treatment period into two phases, consequently, we present two mathematical models. First, we formulate the virotherapy model as a Phase I of the treatment. Then, we extend the model to include radiotherapy in combination with virotherapy as a Phase II of the treatment. A comprehensive qualitative analysis are conducted of both models. Furthermore, numerical experiments are performed to support the analytical results. Also, parameter analysis is carried out to investigate the effect of parameters on the outcome of the treatment. Analytical results reveal that radiovirotherapy is more effective and a good alternative to virotherapy which is capable of complete eradication of tumors. Finally, we develop models 3 and 4 by considering the spatial variation of cancer cells. Thus, we propose two models (models 5 and 6) in the form of PDEs to investigate the spatiotemporal dynamics of tumor cells under radiovirotherapy treatment. We first present model 5 for virotherapy and solve it numerically for different values of the parameters with a continuous delivery of the virus. We then extend the virotherapy model to include the effect of radiotherapy in combination with virotherapy (model 6). Numerical investigations are carried out for three modes of the radiation delivery: constant, decaying, and periodic delivery. The numerical results show that the radiovirotherapy leads to a complete tumor eradication provided that the delivery of radiation is constant or periodic. Moreover, we show that there is optimal timing for radiation administration, as well as, an optimal dose that improves the results of treatment. |
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Supervisor |
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Dr. Salma Al-Tuwairqi |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1440 AH
2019 AD |
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Co-Supervisor |
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Dr. Eman Simbawa |
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Added Date |
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Monday, May 20, 2019 |
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Researchers
| نجوى عطيوي الجهني | Al-Johani, Najwa Otaywi | Researcher | Master | |
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