Pharmacokinetics from a dynamical systems point of view

Area of Science:

• Pharmacology
• Systems Biology
• Mathematical Modeling

Background:

• Drug action is influenced by multiple variables, often leading to complex behavior.
• Pharmacokinetic processes, involving drug transport in tissues and organs, can be modeled using dynamical systems theory.
• The arrangement of tissues and organs in the body (parallel, series, feedback loops) influences drug transport dynamics.

Purpose of the Study:

• To present pharmacokinetics from a dynamical systems perspective.
• To characterize drug transport as a stochastic process using density functions.
• To elucidate the relationship between transit time and residence time distributions in the body.

Main Methods:

• Modeling drug transport as a stochastic process using density functions of transit times and blood flows.
• Analyzing the body as a positive feedback system with pulmonary and systemic circulations as transfer functions.
• Utilizing Laplace domain analysis to describe the relationship between transit and residence time distributions.

Main Results:

• Pharmacokinetic behavior is predictable, often dominated by a zero-dimensional point attractor.
• Single-pass drug transport is a stochastic process influenced by transit time distributions, cardiac output, and extraction ratio.
• The closed-loop total body transport function is stochastic, characterized by residence time distributions due to feedback mechanisms.

Conclusions:

• The dynamical systems approach logically derives key pharmacokinetic parameters such as cardiac output, clearance, and volume of distribution.
• This framework provides a comprehensive understanding of drug movement and behavior within the body.
• The approach was successfully illustrated using caffeine pharmacokinetics.