A robust optimal control framework for controlling aberrant RTK signaling pathways in esophageal cancer

This study presents a new framework for obtaining personalized optimal treatment strategies targeting aberrant signaling pathways in esophageal cancer, such as the epidermal growth factor (EGF) and vascular endothelial growth factor (VEGF) signaling pathways. A new pharmacokinetic model is developed taking into account specific heterogeneities of these signaling mechanisms. The optimal therapies are designed to be obtained using a three step process. First, a finite-dimensional constrained optimization problem is solved to obtain the parameters of the pharmacokinetic model, using discrete patient data measurements. Next, a sensitivity analysis is carried out to determine which of the parameters are sensitive to the evolution of the variants of EGF receptors and VEGF receptors. Finally, a second optimal control problem is solved based on the sensitivity analysis results, using a modified pharmacokinetic model that incorporates two representative drugs Trastuzumab and Bevacizumab, targeting EGF and VEGF, respectively. Numerical results with the combination of the two drugs demonstrate the efficiency of the proposed framework.