Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy
We consider the problem of minimizing the tumor volume with a priorigiven amounts of anti-angiogenic and cytotoxic agents. For oneunderlying mathematical model, optimal and suboptimal solutions aregiven for four versions of this problem: the case when onlyanti-angiogenic agents are administered, com...
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| Format: | Article |
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AIMS Press
2011-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.307 |
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| author | Urszula Ledzewicz Helmut Maurer Heinz Schättler |
| author_facet | Urszula Ledzewicz Helmut Maurer Heinz Schättler |
| author_sort | Urszula Ledzewicz |
| collection | DOAJ |
| description | We consider the problem of minimizing the tumor volume with a priorigiven amounts of anti-angiogenic and cytotoxic agents. For oneunderlying mathematical model, optimal and suboptimal solutions aregiven for four versions of this problem: the case when onlyanti-angiogenic agents are administered, combination treatment witha cytotoxic agent, and when a standard linear pharmacokineticequation for the anti-angiogenic agent is added to each of thesemodels. It is shown that the solutions to the more complex modelsnaturally build upon the simplified versions. This gives credence toa modeling approach that starts with the analysis of simplifiedmodels and then adds increasingly more complex and medicallyrelevant features. Furthermore, for each of the problem formulationsconsidered here, there exist excellent simple piecewise constantcontrols with a small number of switchings that virtually replicatethe optimal values for the objective. |
| format | Article |
| id | doaj-art-7309ee021e49466a90b7efe6c10d7207 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7309ee021e49466a90b7efe6c10d72072025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018230732310.3934/mbe.2011.8.307Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapyUrszula Ledzewicz0Helmut Maurer1Heinz Schättler2Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653We consider the problem of minimizing the tumor volume with a priorigiven amounts of anti-angiogenic and cytotoxic agents. For oneunderlying mathematical model, optimal and suboptimal solutions aregiven for four versions of this problem: the case when onlyanti-angiogenic agents are administered, combination treatment witha cytotoxic agent, and when a standard linear pharmacokineticequation for the anti-angiogenic agent is added to each of thesemodels. It is shown that the solutions to the more complex modelsnaturally build upon the simplified versions. This gives credence toa modeling approach that starts with the analysis of simplifiedmodels and then adds increasingly more complex and medicallyrelevant features. Furthermore, for each of the problem formulationsconsidered here, there exist excellent simple piecewise constantcontrols with a small number of switchings that virtually replicatethe optimal values for the objective.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.307combination therapytumor anti-angiogenesisoptimal and suboptimal controls. |
| spellingShingle | Urszula Ledzewicz Helmut Maurer Heinz Schättler Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy Mathematical Biosciences and Engineering combination therapy tumor anti-angiogenesis optimal and suboptimal controls. |
| title | Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy |
| title_full | Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy |
| title_fullStr | Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy |
| title_full_unstemmed | Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy |
| title_short | Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy |
| title_sort | optimal and suboptimal protocols for a mathematical model for tumor anti angiogenesis in combination with chemotherapy |
| topic | combination therapy tumor anti-angiogenesis optimal and suboptimal controls. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.307 |
| work_keys_str_mv | AT urszulaledzewicz optimalandsuboptimalprotocolsforamathematicalmodelfortumorantiangiogenesisincombinationwithchemotherapy AT helmutmaurer optimalandsuboptimalprotocolsforamathematicalmodelfortumorantiangiogenesisincombinationwithchemotherapy AT heinzschattler optimalandsuboptimalprotocolsforamathematicalmodelfortumorantiangiogenesisincombinationwithchemotherapy |