Optimal treatment strategy of cancers with intratumor heterogeneity
Intratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic interaction between normal, drug-sensitive and drug-res...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022625?viewType=HTML |
| _version_ | 1798031822583496704 |
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| author | Haifeng Zhang Jinzhi Lei |
| author_facet | Haifeng Zhang Jinzhi Lei |
| author_sort | Haifeng Zhang |
| collection | DOAJ |
| description | Intratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic interaction between normal, drug-sensitive and drug-resistant cells in response to cancer treatment. Based on the proposed model, we first study the analytical conclusions, namely the nonnegativity and boundedness of solutions, and the existence and stability of steady states. Furthermore, to investigate the optimal treatment that minimizes both the cancer cells count and the total dose of drugs, we apply the Pontryagin's maximum(or minimum) principle (PMP) to explore the combination therapy strategy with either quadratic control or linear control functionals. We establish the existence and uniqueness of the quadratic control problem, and apply the forward-backward sweep method (FBSM) to solve the optimal control problems and obtain the optimal therapy scheme. |
| first_indexed | 2024-04-11T20:02:43Z |
| format | Article |
| id | doaj.art-9dbfa6546aff4a40963774a17af2f00b |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-11T20:02:43Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-9dbfa6546aff4a40963774a17af2f00b2022-12-22T04:05:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-09-011912133371337310.3934/mbe.2022625Optimal treatment strategy of cancers with intratumor heterogeneityHaifeng Zhang0Jinzhi Lei11. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China2. School of Mathematical Sciences, Center for Applied Mathematics, Tiangong University, Tianjin 300387, ChinaIntratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic interaction between normal, drug-sensitive and drug-resistant cells in response to cancer treatment. Based on the proposed model, we first study the analytical conclusions, namely the nonnegativity and boundedness of solutions, and the existence and stability of steady states. Furthermore, to investigate the optimal treatment that minimizes both the cancer cells count and the total dose of drugs, we apply the Pontryagin's maximum(or minimum) principle (PMP) to explore the combination therapy strategy with either quadratic control or linear control functionals. We establish the existence and uniqueness of the quadratic control problem, and apply the forward-backward sweep method (FBSM) to solve the optimal control problems and obtain the optimal therapy scheme.https://www.aimspress.com/article/doi/10.3934/mbe.2022625?viewType=HTMLmathematical oncologydrug resistanceheterogeneityoptimal control |
| spellingShingle | Haifeng Zhang Jinzhi Lei Optimal treatment strategy of cancers with intratumor heterogeneity Mathematical Biosciences and Engineering mathematical oncology drug resistance heterogeneity optimal control |
| title | Optimal treatment strategy of cancers with intratumor heterogeneity |
| title_full | Optimal treatment strategy of cancers with intratumor heterogeneity |
| title_fullStr | Optimal treatment strategy of cancers with intratumor heterogeneity |
| title_full_unstemmed | Optimal treatment strategy of cancers with intratumor heterogeneity |
| title_short | Optimal treatment strategy of cancers with intratumor heterogeneity |
| title_sort | optimal treatment strategy of cancers with intratumor heterogeneity |
| topic | mathematical oncology drug resistance heterogeneity optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022625?viewType=HTML |
| work_keys_str_mv | AT haifengzhang optimaltreatmentstrategyofcancerswithintratumorheterogeneity AT jinzhilei optimaltreatmentstrategyofcancerswithintratumorheterogeneity |