BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

 BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 56, Issue 4, December 2008

Electronics
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pp 367 - 378

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Direct and indirect control of cancer populations

A. SWIERNIAK
This paper presents a brief survey of our research in which we have used control theoretic methods in modelling and control of cancer populations. We focus our attention on two classes of problems: optimization of anticancer chemotherapy taking into account both phase specificity and drug resistance, and modelling, and optimization of antiangiogenic therapy. In the case of chemotherapy the control action is directly aimed against the cancer cells while in the case of antiangiogenic therapy it is directed against normal cells building blood vessels and only indirectly it controls cancer growth. We discuss models (both finite and infinite dimensional) which are used to find conditions for tumour eradication and to optimize chemotherapy protocols treating cell cycle as an object of control. In the case of antiangiogenic therapy we follow the line of reasoning presented by Hahnfeldt et al. who proposed to use classical models of self-limiting tumour growth with variable carrying capacity defined by the dynamics of the vascular network induced by the tumour in the process of angiogenesis. In this case antiangiogenic protocols are understood as control strategies and their optimization leads to new recommendations for anticancer therapy.
  
Key words: 

biomedical models, optimal control, nonlinear control systems, anticancer therapy.

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Copyright ® Bulletin of the Polish Academy of Sciences: Technical Sciences

December 2008