New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model
In the paper we propose a new methodology in modeling of antiangiogenic treatment on the basis of well recognized model formulated by Hahnfeldt et al. in 1999. On the basis of the Hahnfeldt et al. model, with the usage of the optimal control theory, some protocols of antiangiogenic treatment were p...
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| Format: | Article |
| 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.2011.8.591 |
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| author | Jan Poleszczuk Marek Bodnar Urszula Foryś |
| author_facet | Jan Poleszczuk Marek Bodnar Urszula Foryś |
| author_sort | Jan Poleszczuk |
| collection | DOAJ |
| description | In the paper we propose a new methodology in modeling of antiangiogenic treatment on the basis of well recognized model formulated by Hahnfeldt et al. in 1999. On the basis of the Hahnfeldt et al. model, with the usage of the optimal control theory, some protocols of antiangiogenic treatment were proposed. However, in our opinion the formulation of that model is valid only for the antivascular treatment, that is treatment that is focused on destroying endothelial cells. Therefore, we propose a modification of the original model which is valid in the case of the antiangiogenic treatment, that is treatment which is focused on blocking angiogenic signaling. We analyze basic mathematical properties of the proposed model and present some numerical simulations. |
| format | Article |
| id | doaj-art-540a3f80f4ad41d5a513902ee6302283 |
| 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-540a3f80f4ad41d5a513902ee63022832025-01-24T02:01:39ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-03-018259160310.3934/mbe.2011.8.591New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. modelJan Poleszczuk0Marek Bodnar1Urszula Foryś2University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawUniversity of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawUniversity of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 WarsawIn the paper we propose a new methodology in modeling of antiangiogenic treatment on the basis of well recognized model formulated by Hahnfeldt et al. in 1999. On the basis of the Hahnfeldt et al. model, with the usage of the optimal control theory, some protocols of antiangiogenic treatment were proposed. However, in our opinion the formulation of that model is valid only for the antivascular treatment, that is treatment that is focused on destroying endothelial cells. Therefore, we propose a modification of the original model which is valid in the case of the antiangiogenic treatment, that is treatment which is focused on blocking angiogenic signaling. We analyze basic mathematical properties of the proposed model and present some numerical simulations.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.591angiogenesistumorantiangiogenic treatmentordinary differential equations. |
| spellingShingle | Jan Poleszczuk Marek Bodnar Urszula Foryś New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model Mathematical Biosciences and Engineering angiogenesis tumor antiangiogenic treatment ordinary differential equations. |
| title | New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model |
| title_full | New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model |
| title_fullStr | New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model |
| title_full_unstemmed | New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model |
| title_short | New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model |
| title_sort | new approach to modeling of antiangiogenic treatment on the basis of hahnfeldt et al model |
| topic | angiogenesis tumor antiangiogenic treatment ordinary differential equations. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.591 |
| work_keys_str_mv | AT janpoleszczuk newapproachtomodelingofantiangiogenictreatmentonthebasisofhahnfeldtetalmodel AT marekbodnar newapproachtomodelingofantiangiogenictreatmentonthebasisofhahnfeldtetalmodel AT urszulaforys newapproachtomodelingofantiangiogenictreatmentonthebasisofhahnfeldtetalmodel |