Study On Nonlinear PK/PD Model And Discussion Of Parameter Estimation Method

Pharmacokinetic is a science to deal with the dynamic process of drug in the bodyusing mathematical analysis method, has important theoretical value and is an importantpart of "math pharmacy". It’s development is a great of practical value on the objectiveevaluation of existing drugs, design of new drugs, improvement of drug dosage,providing efficient, low toxic side effects of drugs, especially for guiding the clinicalrational medication, delivery cycle and design of the optimal dosage regimen throughthe study of pharmacokinetics characteristics.Modeling the relationship between the drug concentration and drug response is apowerful and important tool in drug development. Traditionally,ODEs(ordinarydifferential equation)is a widely used method for modeling pharmacokinetic-pharmacodynamic(PK/PD) data, but it cannot statistically describe the system andmeasurement errors. And researchers discover that the relationship of plasmaconcentration and response is not instant in the research of PK/PD, hysteresis betweenthe changes in drug effect and plasma concentration occur. Thus, in this paper, weconstruct a nonlinear model based on SDE with effect compartment to characteristic therelationship of plasma concentration and response after single intravenous dose insulin.Furthermore, this paper proposes a Density-based Monte Carlo filter to estimatethe unobservable variable in the stochastic differential equations involved in PK/PDmodeling. And then the Density-based Monte Carlo filter is compared with ExtendedKalman Filter in estimation effect of unobservable variable through simulationexperiments. And Results show that our proposed method that is Density-based MonteCarlo filter, is significantly better than Extended Kalman Filter (EKF).Moreover, we also construct a robust estimation to estimate the unknownparameters with respect to mean absolute error. And we improve the traditional geneticalgorithm to speed up the convergence with joining weight. At last, Monte Carlosimulations are performed to generate2000data sets. It is found that the proposedmethod is more accurate than the semi-parametric approach.