Optimal and suboptimal protocols for a mathematical model for tumor anti-angiogenesis in combination with chemotherapy - Urszula Ledzewicz; Helmut Maurer; Heinz Schättler (Mathematical Biosciences and Engineering)
We consider the problem of minimizing the tumor volume with a priorigiven amounts of anti-angiogenic and cytotoxic agents. For oneunderlying mathematical model, optimal and suboptimal solutions aregiven for four versions of this problem: the case when onlyanti-angiogenic agents are administered, combination treatment witha cytotoxic agent, and when a standard linear pharmacokineticequation for the anti-angiogenic agent is added to each of thesemodels. It is shown that the solutions to the more complex modelsnaturally build upon the simplified versions. This gives credence toa modeling approach that starts with the analysis of simplifiedmodels and then adds increasingly more complex and medicallyrelevant features. Furthermore, for each of the problem formulationsconsidered here, there exist excellent simple piecewise constantcontrols with a small number of switchings that virtually replicatethe optimal values for the objective.