Time Scale Calculus: a new approach to multi-dose pharmacokinetic modeling.

Area of Science:

• Pharmacokinetics
• Mathematical Biology
• Dynamical Systems

Background:

• Pharmacokinetic (PK) models describe drug concentration in the body.
• Multi-dose regimens present complex dynamics due to continuous and discrete events.
• Existing methods can be complex for analyzing multi-dose PK scenarios.

Purpose of the Study:

• To apply Time Scale Calculus (TSC) for modeling multi-dose pharmacokinetic dynamics.
• To derive analytical solutions for blood concentration trajectories under various dosing regimens.
• To demonstrate TSC as a simplified framework for PK analysis.

Main Methods:

• Utilizing Time Scale Calculus (TSC), a framework for systems with continuous and discrete dynamics.
• Formulating standard pharmacokinetic models within the TSC framework.
• Deriving analytical expressions for drug concentrations after multiple doses.

Main Results:

• Analytical solutions for blood concentration were obtained for several PK models under multi-dose regimens.
• TSC effectively models the interplay of continuous drug processes and discrete dosing events.
• The framework allows for the analysis of arbitrary dose regimens and long-term behaviors.

Conclusions:

• Time Scale Calculus (TSC) offers a powerful and simplified approach to pharmacokinetic modeling, especially for multi-dose scenarios.
• This method provides accessible analytical solutions, enhancing the understanding of drug disposition.
• TSC facilitates the study of complex dosing strategies and steady-state drug levels.