Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity
We consider cancer chemotherapy as an optimal control problem with the aim to minimize a combination of the tumor volume and side effects over an a priori specified therapy horizon when the tumor consists of a heterogeneous agglomeration of many subpopulations. The mathematical model, which accounts...
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AIMS Press
2016-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016040 |
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| author | Shuo Wang Heinz Schättler |
| author_facet | Shuo Wang Heinz Schättler |
| author_sort | Shuo Wang |
| collection | DOAJ |
| description | We consider cancer chemotherapy as an optimal control problem with the aim to minimize a combination of the tumor volume and side effects over an a priori specified therapy horizon when the tumor consists of a heterogeneous agglomeration of many subpopulations. The mathematical model, which accounts for different growth and apoptosis rates in the presence of cell densities, is a finite-dimensional approximation of a model originally formulated by Lorz et al. [18,19] and Greene et al. [10,11] with a continuum of possible traits. In spite of an arbitrarily high dimension, for this problem singular controls (which correspond to time-varying administration schedules at less than maximum doses) can be computed explicitly in feedback form. Interestingly, these controls have the property to keep the entire tumor population constant. Numerical computations and simulations that explore the optimality of bang-bang and singular controls are given. These point to the optimality of protocols that combine a full dose therapy segment with a period of lower dose drug administration. |
| format | Article |
| id | doaj-art-ea832f66f2f24d28baf3deda9c70a154 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-ea832f66f2f24d28baf3deda9c70a1542025-01-24T02:37:49ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-07-011361223124010.3934/mbe.2016040Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneityShuo Wang0Heinz Schättler1Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo, 63130Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo 63130We consider cancer chemotherapy as an optimal control problem with the aim to minimize a combination of the tumor volume and side effects over an a priori specified therapy horizon when the tumor consists of a heterogeneous agglomeration of many subpopulations. The mathematical model, which accounts for different growth and apoptosis rates in the presence of cell densities, is a finite-dimensional approximation of a model originally formulated by Lorz et al. [18,19] and Greene et al. [10,11] with a continuum of possible traits. In spite of an arbitrarily high dimension, for this problem singular controls (which correspond to time-varying administration schedules at less than maximum doses) can be computed explicitly in feedback form. Interestingly, these controls have the property to keep the entire tumor population constant. Numerical computations and simulations that explore the optimality of bang-bang and singular controls are given. These point to the optimality of protocols that combine a full dose therapy segment with a period of lower dose drug administration.https://www.aimspress.com/article/doi/10.3934/mbe.2016040bang-bang controlscancer chemotherapysingular controls.tumor heterogeneityoptimal control |
| spellingShingle | Shuo Wang Heinz Schättler Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity Mathematical Biosciences and Engineering bang-bang controls cancer chemotherapy singular controls. tumor heterogeneity optimal control |
| title | Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| title_full | Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| title_fullStr | Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| title_full_unstemmed | Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| title_short | Optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| title_sort | optimal control of a mathematical model for cancer chemotherapy under tumor heterogeneity |
| topic | bang-bang controls cancer chemotherapy singular controls. tumor heterogeneity optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016040 |
| work_keys_str_mv | AT shuowang optimalcontrolofamathematicalmodelforcancerchemotherapyundertumorheterogeneity AT heinzschattler optimalcontrolofamathematicalmodelforcancerchemotherapyundertumorheterogeneity |