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

Abstract

AbstractA model was developed for long term metformin tissue retention based upon temporally inclusive models of serum/plasma concentration ($$ C $$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 $$ C $$C have a peripheral venous first arrival of drug-times parameter, early $$ C $$C peaks and very slow washouts of $$ C $$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 ($$ CL $$CL), and functions of time, f(t), for drug mass remaining (M), apparent volume of distribution ($$V_{d}$$Vd), as well as $$t_{1/2}\ f(t)$$t1/2f(t) for $$ C $$C, $$ M $$M and $$V_{d}$$Vd. The GPC models of $$ C $$C yielded metformin $$ CL $$CL-values that were 84.8% of total renal plasma flow (RPF) as estimated from meta-analysis. The GPC $$ CL $$CL-values were significantly less than the corresponding NC and E2 $$ CL $$CL-values of 104.7% and 123.7% of RPF, respectively. The GPC plasma/serum only model predicted 78.9% drug $$ M $$M average urinary recovery at 72 h; similar to prior human urine drug $$ M $$M collection results. The GPC model $$t_{1/2}$$t1/2 of $$ M $$M, $$ C $$C and $$V_d$$Vd, were asymptotically proportional to elapsed time, with a constant limiting $$t_{1/2}$$t1/2 ratio of M/C averaging 7.0 times, a result in keeping with prior simultaneous $$ C $$C and urine $$ M $$M collection studies and exhibiting a rate of apparent volume growth of $$V_d$$Vd that achieved limiting constant values. A simulated constant average drug mass multidosing protocol exhibited increased $$V_d$$Vd and $$t_{1/2}$$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.