期刊
MATHEMATICAL BIOSCIENCES AND ENGINEERING
卷 8, 期 2, 页码 355-369出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2011.8.355
关键词
Tumor anti-angiogenesis; optimal control; singular arcs; synthesis
资金
- National Science Foundation [DMS 0707404/0707410, DMS 1008209/1008221]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1008221] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1008209] Funding Source: National Science Foundation
We describe optimal protocols for a class of mathematical models for tumor anti-angiogenesis for the problem of minimizing the tumor volume with an a priori given amount of vessel disruptive agents. The family of models is based on a biologically validated model by Hahnfeldt et al. H and includes a modification by Ergun et al. [6], but also provides two new variations that interpolate the dynamics for the vascular support between these existing models. The biological reasoning for the modifications of the models will be presented and we will show that despite quite different modeling assumptions, the qualitative structure of optimal controls is robust. For all the systems in the class of models considered here, an optimal singular arc is the defining element and all the syntheses of optimal controlled trajectories are qualitatively equivalent with quantitative differences easily computed.
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