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Design of drug administration methodologies can be considered as Control problem, in which controlled variables could be drug concentrations/amounts in selected tissues/organs, while manipulated variables could be drugs administration rates. This consideration seems to deal successfully with characteristics of individualized therapies. The Model Predictive Control (MPC) methodology was developed for the chemical industry and nowadays is considered as a cutting edge technology and a reference point in the field of Automatic Control. It can be suitably adapted for dealing with optimal drug administration problems, by incorporating pharmacokinetic models to predict systems dynamics. Moreover, constraints can be imposed in order to ensure that the applied administration rate is selected in a predefined range and also that drugs concentrations lie within the so-called therapeutic window defined by bounds of drugs efficiency and patient's safety. According to the above, in current work they ...
Design of drug administration methodologies can be considered as Control problem, in which controlled variables could be drug concentrations/amounts in selected tissues/organs, while manipulated variables could be drugs administration rates. This consideration seems to deal successfully with characteristics of individualized therapies. The Model Predictive Control (MPC) methodology was developed for the chemical industry and nowadays is considered as a cutting edge technology and a reference point in the field of Automatic Control. It can be suitably adapted for dealing with optimal drug administration problems, by incorporating pharmacokinetic models to predict systems dynamics. Moreover, constraints can be imposed in order to ensure that the applied administration rate is selected in a predefined range and also that drugs concentrations lie within the so-called therapeutic window defined by bounds of drugs efficiency and patient's safety. According to the above, in current work they are presented modeling methodologies of processes that take place during the drug administration to human body. The basic methodology, used in the current work, is the classical nowadays and widely used method of Physiologically Based Pharmacokinetic Models (PBPK Models). Modeling goes beyond the classical study of Dynamical Systems through derivatives of integer order in State Space and extends to modeling through Fractional Dynamics, namely dynamical systems where derivatives are not restricted to integers. Fractional Dynamics offers new abilities in modeling, allowing study of complex, non linear processes, where history plays a significant role in the future evolution of such a system. Its main drawback is the fact that computationally is very difficult if not even impossible to calculate a fractional derivative, in a handy way for Control applications. This is due to its nature, where an even increasing number (infinite in practice) of terms are required to describe past states of the system. In terms of Control of drug administration applications, the goal is to achieve and maintain a desired concentration of the drug in one or more organs of the human body, satisfying at the same time the imposed constraints. Such constraints are inherited from the maximum and minimum bounds for the drug concentration, since it should be adequate enough to preserve its healing properties and on the other hand to protect the patient from side effects. So two main variations of Model Predictive Control are presented, Offset Free MPC and Robust MPC. These methodologies are properly implemented for drug administration applications. At first, the Robust MPC methodology is presented over a patients population for the delivery of an anesthetic agent. The presented methodology gives the ability of calculating a Control Law that can be applied over the patients population, achieving the desired response while satisfying the imposed constraints. Next comes the presentation of a useful and computationally feasible approach for applying Offset Free MPC in a pharmacokinetic model of fractional order, that gives a guarantee for asymptotic stability and an approach for the modeling error as well. A study on applying Offset Free MPC is presented, when very complex pharmacokinetic models are available, consist of hundreds of differential equations. The design of the MPC controller is combined with the development of simplified, reduced order models. The proposed methodology is applied in a case study involving the administration of insulin to regulate Mellitus Diabetes of type I. Next, a web application is presented, developed in the context of the current thesis, allowing the user to formulate a compartmental pharmacokinetic model (Physiologically Based Pharmacokinetic Model, PBPK) for a defined drug. The model can be adapted to take into account the physiological characteristics of each patient. Finally the web application can proceed on the study and the evaluation of different dosing regimens, that could be either user-defined or resulting from the adoption of an automated MPC control system. The current dissertation concludes with the presentation of the conclusions and suggestions on further development of the research in the field of Control Theory towards the optimization and the individualization of drug administration.
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