Analysis And Control Of A Class Of Pharmacokinetic Systems

Pharmacokinetic model is the mathematical description of the drugs’movement process in the complex biological systems, thereby predicting the functional relation of the drug concentration in vivo and the time. Admittedly, mathematical descriptions of different methods have their own advantages and shortcomings. Compartment model is the most basic pharmacokinetic models, which is one of the focus issues in pharmacological research, and also has a wide range of applications in the fields such as pharmaceutical research, development and utilization.Analysis and synthesis of the pharmacokinetic systems is an important content in the biological control field, and has become one of the highly debatable issues in the world.In this thesis, modeling, analysis and synthesis problems of the pharmacokinetic systems are investigated.Firstly, the research purpose and the significance of the study of the pharmacokinetic system are introduced, and then we present the basic problem and research status.Secondly, this thesis has systematically analyzed the motion characteristics, controllability, observability and stability of the corresponding pharmacokinetic system, at first several commonly used methods of the mathematical description are given, thereby describing the compartment model with the description of the system’s state-space. After that, we analyze the compartment model, the concentration formulas are given after the multiple dose administration, and then we discuss the situation when advance or delay administration, present an optimal control problem, and the dose titration method can be given through solving the problem, the controllability, observability and the stability theorem can be obtained naturally.Furthermore, we investigate the simulation of the corresponding pharmaco- kinetic system, the simulation system of the compartment model is set up, and analyze the variation of the drug pharmacokinetics in vivo when the physiological system changes with the corresponding simulation system.Finally, we discuss the open-loop pharmacokinetics system and design the corresponding state-feedback controller, the control problem of the open-loop system can be transformed to the design problem of the dosage regimen naturally, thus according to the method proposed, we design5dosage regimen to achieve the destination which can successfully control the concentration of the drug in compartments. Then we investigate a kind of pharmacokinetics system which is so called target-controlled infusion system (TCI), the PID controller design method is proposed, thereby controlling the drug concentration in the compartments.