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Application of queueing theory to pharmacokinetics

P H Brill, R E Moon

Journal of Pharmaceutical Sciences

|May 1, 1980

Summary

This study analyzes plasma drug concentration using deterministic and stochastic methods. The stochastic model guarantees steady-state drug concentration and its mean always exist, offering a more robust analysis.

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Area of Science:

Pharmacokinetics and Pharmacodynamics
Mathematical Modeling
Stochastic Analysis

Background:

Traditional pharmacokinetic models often rely on deterministic approaches.
Understanding steady-state drug concentration is crucial for therapeutic efficacy.
Existing deterministic models may not always guarantee the existence of steady-state solutions.

Purpose of the Study:

To compare deterministic and stochastic methods for analyzing steady-state plasma drug concentration.
To introduce a novel queueing theoretical stochastic approach.
To investigate the existence and properties of steady-state drug concentration distributions.

Main Methods:

Employed a one-compartment, open pharmacokinetic model with multiple doses and first-order kinetics.
Utilized a classical deterministic technique.
Applied a novel queueing theoretical stochastic analysis involving dam theory with compound Poisson input and a general release rule.

Main Results:

The mean of the steady-state concentration distribution from the stochastic model equals the deterministic steady-state average concentration, when it exists.
The stochastic model ensures the steady-state probability distribution of drug concentration and its mean always exist.
Demonstrated the robustness and broader applicability of the stochastic analysis method.

Conclusions:

The stochastic queueing theoretical model provides a more comprehensive framework for pharmacokinetic analysis.
This method guarantees the existence of steady-state drug concentration and its mean, overcoming limitations of deterministic approaches.
The study highlights the significant ramifications of employing stochastic methods in pharmacokinetic modeling.

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