ADVAN-style analytical solutions for common pharmacokinetic models.

Area of Science:

• Pharmacokinetics
• Computational Biology
• Mathematical Modeling

Background:

• Analytical solutions for compartmental pharmacokinetic models are established but lack practical application for complex dosing and covariate changes.
• Existing methods struggle to efficiently handle discrete time events within and between dosing intervals.

Purpose of the Study:

• To derive and present ADVAN-style analytical solutions for 1, 2, and 3 compartment pharmacokinetic models.
• To enable the analysis of complex dosing regimens and covariate/parameter changes at discrete time points.
• To facilitate the development of open-source pharmacokinetic modeling software.

Main Methods:

• Laplace transforms were employed to derive ADVAN-style analytical solutions for linear pharmacokinetic models.
• Solutions were developed for intravenous and first-order absorption drug administration.
• The derived equations were coded in R and validated against NONMEM for accuracy in handling complex scenarios.

Main Results:

• The ADVAN-style analytical solutions produced time-courses identical to NONMEM outputs for all tested models (to at least four significant figures).
• The derived equations successfully handled complex dosage regimens and discrete covariate/parameter value changes.
• Validation confirmed the accuracy and capability of the new analytical solutions.

Conclusions:

• This work presents ADVAN-style equations for common pharmacokinetic models for the first time.
• These equations overcome implementation challenges of classical analytical solutions and offer speed benefits over differential equation solvers.
• The presented equations fill a literature gap and are expected to aid in the development of open-source pharmacokinetic modeling tools.