Fit fluctuating blood drug concentration: a beginner's first note

Area of Science:

• Pharmacokinetics
• Mathematical Biology
• Computational Science

Background:

• Linear pharmacokinetics models typically use sums of exponential functions.
• These models struggle to accurately represent fluctuating (oscillating) blood drug concentrations observed clinically.
• Existing hypotheses for fluctuating drug levels lack comprehensive mathematical exploration.

Purpose of the Study:

• To introduce and evaluate mathematical equations from other fields for modeling oscillating drug concentrations in pharmacokinetics.
• To demonstrate that analytical solutions for compartmental pharmacokinetic models can incorporate sinusoidal functions.

Main Methods:

• Proposed and adapted equations featuring decaying exponential sinusoidal functions for pharmacokinetic modeling.
• Generated fluctuating curves using these proposed equations.
• Analyzed the differential equation system for compartmental models to identify analytical solutions.

Main Results:

• The proposed decaying exponential sinusoidal functions theoretically fit fluctuating pharmacokinetic curves.
• Generated curves using these equations demonstrated their potential suitability for clinical pharmacokinetic data.
• Proven that analytical solutions for compartmental models inherently include decaying exponential and sinusoidal functions.

Conclusions:

• The precise analytical solution for compartmental pharmacokinetic models involves a sum of decaying exponential and sinusoidal functions.
• Previous models using only sums of exponential functions represent only an approximation.
• This research offers a more accurate mathematical framework for understanding oscillating drug concentrations.