Analysis of control for a free boundary problem of steady plaques in the artery

摘要

In the earlier paper of Friedman et al. a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells is considered and they satisfy a coupled system of PDEs with a free boundary. The paper adds some control function to that model, allowing the controlled growth of LDL, HDL and plaque. Next, the new dual dynamic programming approach for free boundary problem is developed to formulate sufficient optimality conditions for the optimal steering of drugs. Finally an approximate optimality and numerical calculations are presented.