Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment

U. Ledzewicz, J. Marriott, H. Maurer, H. Schattler
2010 Mathematical Medicine and Biology  
Two mathematical models for tumor anti-angiogenesis, one originally formulated by Hahnfeldt et al. in [16] and a modification of this model by Ergun et al. [12], are considered as optimal control problem with the aim of maximizing the tumor reduction achievable with an a priori given amount of angiogenic inhibitors. For both models optimal controls contain a segment along which the dosage follows a so-called singular control, a time-varying feedback control. In this paper the efficiency of
more » ... efficiency of piecewise constant protocols with a small number of switchings is investigated. Through comparison with the theoretically optimal solutions, it will be shown that these protocols provide generally excellent suboptimal strategies that for many initial conditions come within a fraction of 1% of the theoretically optimal values. When the duration of the dosages are restricted a priori, for example to a daily or semi-daily regimens, still very good approximations of the theoretically optimal solution can be achieved.
doi:10.1093/imammb/dqp012 pmid:20513667 fatcat:rek46vbqgnaj7igkdlorr236ou