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 (V_{d}), as well as t_{1/2} f(t) for C , M and V_{d}. 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 t_{1/2} of M , C and V_d, were asymptotically proportional to elapsed time, with a constant limiting t_{1/2} 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 V_d that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased V_d and t_{1/2} 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.