The Optimal Individual Dosing Regimen Design

Traditional individual dosing method includes six parts: determining the initial dosing regimen, collecting blood, measuring plasma concentration, establishing pharmacokinetic model, estimating parameters and determining the final dosing regimen. Among them, establishing pharmacokinetic model and determining the final dosing regimen are main issues this paper studied. This studies should be based on Pharmacokinetic model establishment, now most literatures use differential equation to build pharmacokinetic model, has not highlighted the impulsive effect of dosing, cannot describe the whole dosing process accurately; the metabolic process of drugs in vivo is in line with homogeneous Markov processes, seldom literature uses Markov chain to describe pharmacokinetic process, so this paper is to boldly attempt to build pharmacokinetic mode by Markov chain and impulsive dosing style, at the same time, build impulsive differential equation dosing model, statistical data according to plasma concentrations, determining pharmacokinetic model which has the minimum error through residual analysis method. In dosing regimens design, currently, most dosing regimen determined finally just ensures the reasonableness of dosing, making the plasma concentration within therapeutic window, this paper is to employ optimization theory, considering the accumulation extent of toxin in vivo, to determine the optimal dosing regimen, which get a good efficacy and the least side effect. Aiming at these problems, main works of this paper as follows:1. Establish impulsive differential Equation pharmacokinetic model. Firstly, build periodic impulsive differential Equation pharmacokinetic model; then, give the expression of dose in each period; finally, the plasma concentration measured patient data is used for statistical analysis, employ the residual method to estimate parameters.2. Establish Markov chain pharmacokinetic model. Firstly, describe intravenous injection n-compartment model with Markov chain, present transition probability matrix and fundamental matrix; secondly, establish periodic Markov chain Pharmacokinetics model with Markov chain and pulse together, give the expression of dose in each period; thirdly, according to the patient’s plasma concentration data, use nonlinear regression to estimate model parameters; finally, use natures of absorbed Markov chain and Markov chain with input to compute operating time of drugs and dose in steady time.3. The optimal individual regimen design. Firstly, use integration of dose in vivo within a course of curing to represent accumulation extent of drug in the body, and give expression of accumulation extent under each model; secondly, give the maximum value of dose in vivo under each model; then, in each model, use optimization theory to determine the optimal dosing regimen that makes the amount of the drug within therapeutic window, has the least accumulation extent of toxin; finally, determine the best dosing regimen for a patient by comparing the fitting degrees for actual data of the two pharmacokinetic model built in this paper, and summarize the design process for the optimal individual dosing regimen.