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

Carl A Wesolowski; Jane Alcorn; Geoffrey T Tucker

doi:10.1007/s10928-021-09779-4

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

J Pharmacokinet Pharmacodyn. 2022 Apr;49(2):191-208. doi: 10.1007/s10928-021-09779-4. Epub 2021 Oct 24.

Authors

Carl A Wesolowski^{1

2}, Jane Alcorn³, Geoffrey T Tucker⁴

Affiliations

¹ College of Pharmacy and Nutrition, University of Saskatchewan, 104 Clinic Place, Saskatoon, SK, S7N 2Z4, Canada. carl.wesolowski@gmail.com.
² Department of Medical Imaging, Royal University Hospital, College of Medicine, University of Saskatchewan, 103 Hospital Drive, Saskatoon, SK, S7N 0W8, Canada. carl.wesolowski@gmail.com.
³ College of Pharmacy and Nutrition, University of Saskatchewan, 104 Clinic Place, Saskatoon, SK, S7N 2Z4, Canada.
⁴ Department of Human Metabolism, Medical and Biological Sciences, University of Sheffield, Sheffield, UK.

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 min per case. The new algorithm is a more practical research tool. Potential pharmacokinetic applications are discussed.

Keywords: Algorithm; Gamma-Pareto convolution; Mathematica; Metformin; Pharmacokinetics; Statistical distributions.

MeSH terms

Acceleration*
Algorithms*
Animals
Dogs
Kinetics