Online Shaping of a Drug's Periodic Administration Trajectory for Efficacy Maximization

This paper addresses the problem of shaping nicotine's administration trajectory for maximization of its cardio-accelerating effects. Pharmacologists explain the interaction of this drug with the human body using a two-compartment model. One compartment, in the model, describes the concentration dynamics of nicotine in the plasma, while the other captures buildup of resistance to the drug's effects. Researchers have employed this model and shown that a periodic delivery trajectory results in an average efficacy level superior to the best achievable steady-state performance. The literature has also studied finding the optimal shape of this periodic drug delivery trajectory and offers different solution methods. While the existing methods depend on the exact knowledge of the drug's model, the human body's metabolism varies from one patient to another, affecting the shape of the maximum efficacy trajectory. This creates a need for online solution methods. This paper addresses this issue by developing two online solution algorithms for the problem: 1) a model-reference, gradient-descent-based regulator that considers parameter uncertainty and 2) a model-free extremum seeking control scheme. The latter controller is shown to converge very slowly. Still, it is included in this paper as a completely model-free option and as a benchmark. In contrast, the first controller converges more quickly, and its convergence to the optimal solution is proved using Floquet theory. Finally, this paper demonstrates the performance of the two methods in a simulation study, and also compares them against the deterministic solutions from the literature.