A series acceleration algorithm for the gamma-Pareto (type I) convolution and related functions of interest for pharmacokinetics

TL;DR

This paper introduces a fast, practical algorithm for computing the gamma-Pareto type I convolution distribution, improving efficiency and precision in pharmacokinetic modeling of drugs like metformin in dogs.

Contribution

The paper presents a novel series acceleration algorithm with separate routines for short and long times, significantly reducing computation time and enhancing accuracy.

Findings

Algorithm completes in about 3 minutes per case.

Improves precision at long times in pharmacokinetic calculations.

Facilitates practical application in pharmacokinetic research.

Abstract

The gamma-Pareto type I convolution (GPC type I) distribution, which has a power function tail, was recently shown to describe the disposition kinetics of metformin in dogs precisely and better than sums of exponentials. However, this had very long run times and lost precision for its functional values at long times following intravenous injection. An accelerated algorithm and its computer code is now presented comprising two separate routines for short and long times and which, when applied to the dog data, completes in approximately 3 minutes per case. The new algorithm is a more practical research tool. Potential pharmacokinetic applications are discussed.