Comparison of the gamma-Pareto convolution with conventional methods of characterising metformin pharmacokinetics in dogs

Abstract

A model was developed for long term metformin tissue retention based upon temporally inclusive models of serum/plasma concentration (C) having power function tails called the gamma-Pareto type I convolution (GPC) model and was contrasted with biexponential (E2) and noncompartmental (NC) metformin models. GPC models of C have a peripheral venous first arrival of drug-times parameter, early C peaks and very slow washouts of C. The GPC, E2 and NC models were applied to a total of 148 serum samples drawn from 20 min to 72 h following bolus intravenous metformin in seven healthy mongrel dogs. The GPC model was used to calculate area under the curve (AUC), clearance (CL), and functions of time, f(t), for drug mass remaining (M), apparent volume of distribution (Vd), as well as t1/2f(t) for C, M and Vd. The GPC models of C yielded metformin CL-values that were 84.8% of total renal plasma flow (RPF) as estimated from meta-analysis. The GPC CL-values were significantly less than the corresponding NC and E2 CL-values of 104.7% and 123.7% of RPF, respectively. The GPC plasma/serum only model predicted 78.9% drug M average urinary recovery at 72 h; similar to prior human urine drug M collection results. The GPC model t1 / 2 of M, C and Vd, were asymptotically proportional to elapsed time, with a constant limiting t1 / 2 ratio of M/C averaging 7.0 times, a result in keeping with prior simultaneous C and urine M collection studies and exhibiting a rate of apparent volume growth of Vd that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased Vd and t1 / 2 with elapsing time, effects that have been observed experimentally during same-dose multidosing. The GPC heavy-tailed models explained multiple documented phenomena that were unexplained with lighter-tailed models.