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.
The investigations deal with mass transfer in simulated biomedical systems. The modification of classical diffusion chamber, sequential unit (SU) system, imitated different biomedical setups, boundary conditions. The experiments simulated: diffusion chamber (also with two barriers), transport through the membrane to the blood stream, transport from the stent eluting drug simultaneously to the vessel cells and to the blood stream. The concentrations of substances and the relative mass increases/decreases for SU systems indicate that the order of the curves follows the order of mass transfer resistances. The strong dependence of mass transfer rates versus type of diffusing substance was confirmed. The calculated drug fluxes, diffusion coefficients, permeation coefficients are convergent with literature. Permeation coefficients for complex sequential systems can be estimated as parallel connexion of constituent coefficients. Experiments approved functionality of the SU for investigations in a simulated biomedical system. Obtained data were used for numerical verification.