Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation
Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, w...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/2158052 |
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| _version_ | 1832562318457700352 |
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| author | Yong Dam Jeong Kwang Su Kim Yunil Roh Sooyoun Choi Shingo Iwami Il Hyo Jung |
| author_facet | Yong Dam Jeong Kwang Su Kim Yunil Roh Sooyoun Choi Shingo Iwami Il Hyo Jung |
| author_sort | Yong Dam Jeong |
| collection | DOAJ |
| description | Cancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor-immune system to design an optimal chemotherapy strategy. For this, we first propose a mathematical model of tumor-immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman (HJB) equation. Here, we use an upwind finite-difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects. |
| format | Article |
| id | doaj-art-4696155be93d4ae0abd1fb33fbaef397 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-4696155be93d4ae0abd1fb33fbaef3972025-02-03T01:22:56ZengWileyComplexity1099-05262022-01-01202210.1155/2022/2158052Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman EquationYong Dam Jeong0Kwang Su Kim1Yunil Roh2Sooyoun Choi3Shingo Iwami4Il Hyo Jung5Department of MathematicsInterdisciplinary Biology Laboratory (iBLab)Department of MathematicsDepartment of MathematicsInterdisciplinary Biology Laboratory (iBLab)Department of MathematicsCancer chemotherapy has been the most common cancer treatment. However, it has side effects that kill both tumor cells and immune cells, which can ravage the patient’s immune system. Chemotherapy should be administered depending on the patient’s immunity as well as the level of cancer cells. Thus, we need to design an efficient treatment protocol. In this work, we study a feedback control problem of tumor-immune system to design an optimal chemotherapy strategy. For this, we first propose a mathematical model of tumor-immune interactions and conduct stability analysis of two equilibria. Next, the feedback control is found by solving the Hamilton–Jacobi–Bellman (HJB) equation. Here, we use an upwind finite-difference method for a numerical approximate solution of the HJB equation. Numerical simulations show that the feedback control can help determine the treatment protocol of chemotherapy for tumor and immune cells depending on the side effects.http://dx.doi.org/10.1155/2022/2158052 |
| spellingShingle | Yong Dam Jeong Kwang Su Kim Yunil Roh Sooyoun Choi Shingo Iwami Il Hyo Jung Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation Complexity |
| title | Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation |
| title_full | Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation |
| title_fullStr | Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation |
| title_full_unstemmed | Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation |
| title_short | Optimal Feedback Control of Cancer Chemotherapy Using Hamilton–Jacobi–Bellman Equation |
| title_sort | optimal feedback control of cancer chemotherapy using hamilton jacobi bellman equation |
| url | http://dx.doi.org/10.1155/2022/2158052 |
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