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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 591-603. doi: 10.3934/mbe.2011.8.591
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New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model

  • 1.
    University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and Mechanics, Banacha 2, 02-097 Warsaw
  • Received: 01 March 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : 34A12, 34C60, 34D05, 34A34, 37N25, 92C50.

  • 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.

    Citation: Jan Poleszczuk, Marek Bodnar, Urszula Foryś. New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 591-603. doi: 10.3934/mbe.2011.8.591

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  • 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.


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    3. U. Ledzewicz, H. Schättler, Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments, 2012, 153, 0022-3239, 195, 10.1007/s10957-011-9954-8
    4. F. A. Rihan, M. Safan, M. A. Abdeen, D. Abdel Rahman, Qualitative and Computational Analysis of a Mathematical Model for Tumor-Immune Interactions, 2012, 2012, 1110-757X, 1, 10.1155/2012/475720
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