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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.

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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Numerical parameter sensitivity.
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fig5: Numerical parameter sensitivity.

Mentions: In order to find the parameter factors that exert a strong impact on model outcome, we use the numerical parameter sensitivity analysis. For the sensitivity analysis, one parameter value in the model is increased and decreased by 20 percent and the other parameter values are fixed. After 5 days, we plot tumor sizes depending on the model parameters. In Figure 5, the solid red line and blue line represent change rates of tumor cell numbers when a special parameter value was decreased 20 percent and when parameter value was increased 20 percent, respectively. From this we can check that during 5 days, tumor size is highly sensitive to parameters a (tumor growth), d (strength of immune system), and α1 (rate of IL-2 and DC induced CD8+T cell activation) in order of list.


Optimal treatment strategy for a tumor model under immune suppression.

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

Numerical parameter sensitivity.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4129922&req=5

fig5: Numerical parameter sensitivity.
Mentions: In order to find the parameter factors that exert a strong impact on model outcome, we use the numerical parameter sensitivity analysis. For the sensitivity analysis, one parameter value in the model is increased and decreased by 20 percent and the other parameter values are fixed. After 5 days, we plot tumor sizes depending on the model parameters. In Figure 5, the solid red line and blue line represent change rates of tumor cell numbers when a special parameter value was decreased 20 percent and when parameter value was increased 20 percent, respectively. From this we can check that during 5 days, tumor size is highly sensitive to parameters a (tumor growth), d (strength of immune system), and α1 (rate of IL-2 and DC induced CD8+T cell activation) in order of list.

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.

Show MeSH
Related in: MedlinePlus