Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis
We describe optimal protocols for a class of mathematical models fortumor anti-angiogenesis for the problem of minimizing the tumorvolume with an a priori given amount of vessel disruptive agents.The family of models is based on a biologically validated model byHahnfeldt et al. [9] and includes a mo...
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| Language: | English |
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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.2011.8.355 |
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| author | Heinz Schättler Urszula Ledzewicz Benjamin Cardwell |
| author_facet | Heinz Schättler Urszula Ledzewicz Benjamin Cardwell |
| author_sort | Heinz Schättler |
| collection | DOAJ |
| description | We describe optimal protocols for a class of mathematical models fortumor anti-angiogenesis for the problem of minimizing the tumorvolume with an a priori given amount of vessel disruptive agents.The family of models is based on a biologically validated model byHahnfeldt et al. [9] and includes a modification byErgun et al. [6], but also provides two new variations thatinterpolate the dynamics for the vascular support between theseexisting models. The biological reasoning for the modifications ofthe models will be presented and we will show that despite quitedifferent modeling assumptions, the qualitative structure of optimalcontrols is robust. For all the systems in the class of modelsconsidered here, an optimal singular arc is the defining element andall the syntheses of optimal controlled trajectories arequalitatively equivalent with quantitative differences easilycomputed. |
| format | Article |
| id | doaj-art-5d1de1a55a094171b403fd656597c5e5 |
| 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-5d1de1a55a094171b403fd656597c5e52025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018235536910.3934/mbe.2011.8.355Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesisHeinz Schättler0Urszula Ledzewicz1Benjamin Cardwell2Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899We describe optimal protocols for a class of mathematical models fortumor anti-angiogenesis for the problem of minimizing the tumorvolume with an a priori given amount of vessel disruptive agents.The family of models is based on a biologically validated model byHahnfeldt et al. [9] and includes a modification byErgun et al. [6], but also provides two new variations thatinterpolate the dynamics for the vascular support between theseexisting models. The biological reasoning for the modifications ofthe models will be presented and we will show that despite quitedifferent modeling assumptions, the qualitative structure of optimalcontrols is robust. For all the systems in the class of modelsconsidered here, an optimal singular arc is the defining element andall the syntheses of optimal controlled trajectories arequalitatively equivalent with quantitative differences easilycomputed.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.355singular arcsoptimal controltumor anti-angiogenesissynthesis. |
| spellingShingle | Heinz Schättler Urszula Ledzewicz Benjamin Cardwell Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis Mathematical Biosciences and Engineering singular arcs optimal control tumor anti-angiogenesis synthesis. |
| title | Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis |
| title_full | Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis |
| title_fullStr | Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis |
| title_full_unstemmed | Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis |
| title_short | Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis |
| title_sort | robustness of optimal controls for a class of mathematical models for tumor anti angiogenesis |
| topic | singular arcs optimal control tumor anti-angiogenesis synthesis. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.355 |
| work_keys_str_mv | AT heinzschattler robustnessofoptimalcontrolsforaclassofmathematicalmodelsfortumorantiangiogenesis AT urszulaledzewicz robustnessofoptimalcontrolsforaclassofmathematicalmodelsfortumorantiangiogenesis AT benjamincardwell robustnessofoptimalcontrolsforaclassofmathematicalmodelsfortumorantiangiogenesis |