| Contents |
| In mathematical models for homogeneous tumor populations of chemotherapeutically sensitive cells, optimal controls are bang-bang reaffirming the medical paradigm of maximum tolerated doses (MTD). However, as more aspects of the tumor microenvironment are taken into account---such as tumor heterogeneity, the tumor vasculature or tumor-immune system interactions--- alternatives to this paradigm become a viable option. There is mounting medical evidence that "more is not necessarily better", but that a so-called biologically optimal dose (BOD) should be sought. This, for example, might be realized by specific time-varying, reduced dose rate regimes known under the name of metronomic dosing. It has been shown that chemotherapy administered in such a manner, although having obvious lower cytotoxic effects, exhibits antiangiogenic and immune-stimulatory effects and contributes to resensitizations. In this talk, we shall address modeling aspects of this problem using an optimal control approach. Interestingly, protocols that provide an alternative to MTD strategies appeared as optimal solutions in the analysis of various models for tumor growth in connection with antiangiogenic treatments and tumor immune system interactions as well as in models for heterogeneous tumor populations. We shall discuss a model that encompasses all these features and provides a framework for the analysis of metronomic chemotherapy. |
|