Mathematical modeling and optimal control problems in brain tumor targeted drug delivery strategies

摘要: In this paper, we present a mathematical model that describes tumor-normal cells interaction dynamics focusing on role of drugs in treatment brain tumors. The goal is to predict distribution and necessary quantity delivered drug-therapy by using optimal control framework. interactions tumor normal system reactions–diffusion equations involving the drug concentration, tissues. estimates simultaneously blood perfusion rate, reabsorption rate dosage administered, which affect effects chemotherapy. First, develop framework models competition between under chemotherapy constraints. Then, existence, uniqueness regularity solution state are proved as well stability results. Afterwards, problems formulated order minimize delivery cell burden different situations. We show existence solution, derive conditions for optimality. Finally, solve numerically optimization problems, propose investigate an adjoint multiple-relaxation-time lattice Boltzmann method general nonlinear coupled anisotropic convection–diffusion (which includes developed targeted system).