On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach
Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist o...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017014 |
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| _version_ | 1832590041375834112 |
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| author | Urszula Ledzewicz Shuo Wang Heinz Schättler Nicolas André Marie Amélie Heng Eddy Pasquier |
| author_facet | Urszula Ledzewicz Shuo Wang Heinz Schättler Nicolas André Marie Amélie Heng Eddy Pasquier |
| author_sort | Urszula Ledzewicz |
| collection | DOAJ |
| description | Effects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models. |
| format | Article |
| id | doaj-art-4987a5f1239943bcae04b73d84b9296c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4987a5f1239943bcae04b73d84b9296c2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114121723510.3934/mbe.2017014On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approachUrszula Ledzewicz0Shuo Wang1Heinz Schättler2Nicolas André3Marie Amélie Heng4Eddy Pasquier5Institute of Mathematics, Lodz University of Technology, 90-924 Lodz, PolandDept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo, 63130, USADept. of Electrical and Systems Engineering, Washington University, St. Louis, Mo, 63130, USAService d'hématologie et Oncologie Pédiatrique, Centre Hospitalo-Universitaire Timone Enfants, AP-HM, Marseille, UMR S_911 CRO2 Aix Marseille Université, Marseille, FranceService d'hématologie et Oncologie Pédiatrique, Centre Hospitalo-Universitaire Timone Enfants, AP-HM, Marseille, UMR S_911 CRO2 Aix Marseille Université, Marseille, FranceChildrens Cancer Institute Australia, Lowy Cancer Research Centre, University of New South Wales, Randwick, NSW, AustraliaEffects that tumor heterogeneity and drug resistance have on the structure of chemotherapy protocols are discussed from a mathematical modeling and optimal control point of view. In the case when two compartments consisting of sensitive and resistant cells are considered, optimal protocols consist of full dose chemotherapy as long as the relative proportion of sensitive cells is high. When resistant cells become more dominant, optimal controls switch to lower dose regimens defined by so-called singular controls. The role that singular controls play in the structure of optimal therapy protocols for cell populations with a large number of traits is explored in mathematical models.https://www.aimspress.com/article/doi/10.3934/mbe.2017014cancer chemotherapytumor heterogeneitydrug resistanceoptimal controlsingular controlsmetronomic chemotherapy |
| spellingShingle | Urszula Ledzewicz Shuo Wang Heinz Schättler Nicolas André Marie Amélie Heng Eddy Pasquier On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach Mathematical Biosciences and Engineering cancer chemotherapy tumor heterogeneity drug resistance optimal control singular controls metronomic chemotherapy |
| title | On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach |
| title_full | On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach |
| title_fullStr | On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach |
| title_full_unstemmed | On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach |
| title_short | On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach |
| title_sort | on drug resistance and metronomic chemotherapy a mathematical modeling and optimal control approach |
| topic | cancer chemotherapy tumor heterogeneity drug resistance optimal control singular controls metronomic chemotherapy |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017014 |
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