Statistical Modeling of a Pharmacokinetic System

Abstract

The aim of the article is to investigate the drug concentration behavior in a three-compartment open pharmacokinetic model which describes the disposition of an antibiotic drug used in Lyme disease, coumermycin A ₁.

We study a system of random differential equations representing this model. The three rate constants that are used in the system of differential equations are simulated using the trivariate truncated normal probability distribution. The initial values of the rate constants that are used in the simulation are calculated from the pharmacokinetic profile of coumermycin A ₁ determined in four human subjects based on the serum level data obtained from the report of a clinical study. The extensive numerical solutions for the system of random differential equations under different combinations of the covariance structure and the initial conditions are developed.

Numerical comparisons of the deterministic characterizations of the drug concentration as a function of time of the individual compartments to study the effect of various combinations of the covariance structure and the initial conditions on these characterizations are presented. A similar comparison between the deterministic and the stochastic characterizations is also presented.

Keywords:

• Deterministic-Stochastic characterizations
• Drug concentration
• Pharmokinetic models
• Rate constants
• System of random differential equations

Mathematics Subject Classification:

• Primary Pharmokinetic analysis
• Secondary Stochastical modeling