Accurate numerical integration of highly stiff pharmacokinetics models using continuous block implicit hybrid one-step collocation methods

Abstract

The differential equations of pharmacokinetic models, obtained from the formulation based on the Fick's perfusion principle and law of conservation of mass action, deals with absorption, distribution, and elimination of drugs by the body systems. In the formulation, the ordinary differential equations obtained may result into highly stiff systems whereby suitable implicit methods have to be employed to solve accurately drug concentration in the body systems, owing to the complex nature of the exact solutions, if they exist. Further, because of the large and increasing interest in the problems of drug kinetics, it is necessary to apply considerably accurate implicit numerical methods in evaluating and in applying them to specific cases. These solutions are to help determine the distribution of drug concentration in different compartments (parts) of the human body network systems as a fundamental step to help in understanding and improving treatments. This is necessary since drug concentration in each compartment is different from one another because of the differences in drug affinity to tissues. From the study, the solution curves obtained show that drug level in the gastrointestinal tract decreases with the passage of time, while drug concentration in the blood increases from zero and reaches its maximum level and then decreases steadily again. We further, compared the model curves with some experimental data plots published in scientific papers. The results obtained from the study can be used extensively for various drug diffusion problems arising in pharmaceutical studies. The presented results widen the applicability of the continuous block implicit hybrid one-step collocation methods to diffusion process which have good number of applications in the drug control, drug dosage and other related problems in pharmaceutical and biomedical industries.