Optimal treatment strategy for a tumor model under immune suppression. Kim KS, Cho G, Jung IH - Comput Math Methods Med (2014) Bottom Line: We propose a mathematical model describing tumor-immune interactions under immune suppression.To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions.Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. View Article: PubMed Central - PubMed Affiliation: Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea. ABSTRACTWe propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer. Show MeSH MajorImmunotherapy/methods*Neoplasms/immunology*/therapy*MinorAnimalsCD4-Positive T-Lymphocytes/cytologyCD8-Positive T-Lymphocytes/cytologyComputer SimulationDendritic Cells/immunologyHumansModels, ImmunologicalModels, Theoretical Related in: MedlinePlus © Copyright Policy Related In: Results  -  Collection License getmorefigures.php?uid=PMC4129922&req=5 .flowplayer { width: px; height: px; } fig4: Optimal controls when initial value of tumor cells is 108, (a) A = 1, B = 1, C = 1, (b) A = 1, B = 1000, C = 10, and (c) A = 1, B = 10, C = 1000. Mentions: For the case of exception immunosuppressive effects, we assume that initial values of regulatory T cell, IL-10, and TGF-β and values of parameters α3, γ2, p1, p2, p3, and p4 are all zeroes. We simulate the optimal controlled model in different scenarios. Firstly, we divide into two cases of the initial value of tumor cells, 107 in Figure 3 and 108 in Figure 4. Secondly, Figures 3 and 4 divided into two cases: the model with or without immunosuppressive effects. The optimality system is solved by using the Runge-kutta fourth-order scheme. The optimal strategy is obtained by solving the state system, the adjoint system, and the transversality conditions. We use Forward-Backward method [18–21] to solve the optimal system.

Optimal treatment strategy for a tumor model under immune suppression.

Kim KS, Cho G, Jung IH - Comput Math Methods Med (2014)

Related In: Results  -  Collection

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fig4: Optimal controls when initial value of tumor cells is 108, (a) A = 1, B = 1, C = 1, (b) A = 1, B = 1000, C = 10, and (c) A = 1, B = 10, C = 1000.
Mentions: For the case of exception immunosuppressive effects, we assume that initial values of regulatory T cell, IL-10, and TGF-β and values of parameters α3, γ2, p1, p2, p3, and p4 are all zeroes. We simulate the optimal controlled model in different scenarios. Firstly, we divide into two cases of the initial value of tumor cells, 107 in Figure 3 and 108 in Figure 4. Secondly, Figures 3 and 4 divided into two cases: the model with or without immunosuppressive effects. The optimality system is solved by using the Runge-kutta fourth-order scheme. The optimal strategy is obtained by solving the state system, the adjoint system, and the transversality conditions. We use Forward-Backward method [18–21] to solve the optimal system.

Bottom Line: We propose a mathematical model describing tumor-immune interactions under immune suppression.To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions.Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, Pusan National University, Busan 609-735, Republic of Korea.

ABSTRACT
We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer.

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Related in: MedlinePlus