فهرست مطالب آمنه طالعی

Tumor resistance to chemotherapy and targeted drugs is one of the main factors of treatment failure. Experimental evidence in recent years shows that the progression of cancer cells to drug resistance does not have to happen by chance, but may be caused by the treatment itself. In this regard, understanding the clinical consequences of resistance caused by treatment in the process of chemotherapy helps to develop appropriate solutions. In this paper, to investigate this issue, we first introduce the general mathematical model of drug resistance in the chemotherapy process in the form of a device of nonlinear ordinary differential equations. Then we perform the numerical simulation of the dynamic behavior of the model in three different cases using the least squares support vector machine approach. In this study, the effects of three drugs with different drug resistance induction coefficients are considered. Finally, we will examine the results of these simulations according to the type of drug prescribed in tumor growth control.

Cells in all tissues of the body are constantly growing and dividinginto new cells. Abnormal proliferation of tissues outside the body leads tocancer. In all tissues of the body, a type of cell, called a stem cell, is foundthat has the ability to become specialized cells in the same tissue to be able tocompensate for damage in tissue disorders. In this paper, based on the existingmathematical model, the optimal control model is very effective for inhibitingthis growth in exchange for prescribing a specific drug (doxorubicin) is presented.In order to minimize the number of cancer cells over time, the cancer controlstrategy has been modeled as a problem from the theory of optimal controlduring the effect of a specific drug on non-cancerous stem cells in this model.To solve this problem and prescribe the optimal dose of the drug, first with thehelp of the maximum principle of Pontriagin and then the analytical solution ofthe first-order differential equations, the optimal solution has been determined.In order to provide the optimal dose of the drug to the patient, the proposedsolution is simulated numerically. This numerical implementation shows how byapplying this amount of drug with a specific dose, how the number of cancercells decreases over time, they will be.

With the development of biosensor technology in various sciences, mathematical modeling of biosensors seems to be an important and necessary issue. In this paper, we present the numerical simulation of the mathematical model of amperometric biosensor based on the enzyme. This model is based on reaction-diffusion equations containing a nonlinear term of the Michaelis-Menten enzymatic reaction. The governing equations are discretized with the multi-quadric radial basis functions collocation method in space variable and semi-implicit backward Euler scheme in time. The effect of the reaction- diffusion parameter on other parameters of the mathematical model and biosensor response is investigated. The direct relationship, the current density with the maximal enzymatic rate, and the coefficient of reaction- diffusion are studied. The more stable effect of biosensor behavior with a thicker of enzyme layer than its similar type with a thinner layer has also been shown. In this study, the maximal enzymatic rate and thickness of the enzymatic layer are considered in the range of 10^-9 to 10^-3 and 0.005 to 0.09 , respectively.