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 ðtÞ 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. Keywords Metformin Á Pharmacokinetics Á Mathematical modelling pdf Á Clearance Á Serum concentration Á Drug mass Á Loading dose regimen Abbreviations AUC Area under the curve C(t) Concentration (model) CDF Cumulative density function CI Confidence interval, default 95% C in ðtÞ Concentration, constant infusion CL Plasma or serum clearance C max Local peak concentration C obs ðtÞ Observed concentrations (vector) C SS Steady-state concentration, terminal C in ðtÞ CV% Coefficient of variation D Dose mass df Degrees of freedom DF(n) Fractional dose multiplier D R An acronym of dosing rate E1 Monoexponential c e Àk t E2 Biexponential ED n Exponential density of n terms E PAH Renal extraction fraction PAH GD Gamma distribution GM Geometric mean GPC Gamma Pareto distribution H-MRT Harmonic mean residence time Electronic supplementary material The online version of this article (

Comment on: “The pharmacokinetics of metformin in patients receiving intermittent haemodialysis” by Sinnappah et al.

“…This uncertainty underlines the need to clarify whether or not metformin undergoes some metabolism and to consider the impact of an ultra-long extensive distribution process on its accumulation and removal. 2,3 The tissue distribution of metformin involves active import by organic cation transporters 4 and is suggested to account for a 21% shortfall in urinary recovery of unchanged drug at 72 h after intravenous dosage. 2,5 Based on the inhibition (IC 50 ) of NADH: ubiquitone oxidoreductase, metformin is estimated to be concentrated 1000-fold in mitochondria relative to extracellular fluid.…”

“…2,3 The tissue distribution of metformin involves active import by organic cation transporters 4 and is suggested to account for a 21% shortfall in urinary recovery of unchanged drug at 72 h after intravenous dosage. 2,5 Based on the inhibition (IC 50 ) of NADH: ubiquitone oxidoreductase, metformin is estimated to be concentrated 1000-fold in mitochondria relative to extracellular fluid. 6 If there is negligible renal and metabolic clearance, no biliary/ intestinal secretion, 5 protracted distribution and haemodialysis over 4-6 h every 44 h removes only 9-35% of a dose, 1 then replacement with a dose of 250-500 mg, even though only half of it may be absorbed, 5 would be predicted to result in excessive accumulation eventually.…”

“…Relatively small increments in trough plasma drug concentration will tend to obscure greater rises in tissue drug concentrations. 2,5 The development of lactic acidosis is likely to be significantly delayed and relatively insensitive to the concentration of drug in plasma. 2,5 Estimates of the dialysis clearance of metformin range from 68 to 230 ml/min 1 Renal clearance in healthy subjects is probably close to renal plasma flow, i.e., 600 ml/min.…”

“…2,5 The development of lactic acidosis is likely to be significantly delayed and relatively insensitive to the concentration of drug in plasma. 2,5 Estimates of the dialysis clearance of metformin range from 68 to 230 ml/min 1 Renal clearance in healthy subjects is probably close to renal plasma flow, i.e., 600 ml/min. 2,4 In this case the fraction of normal dose would be 0.008 to 0.028, suggesting that, ultimately, the maintenance dosage in patients should not exceed about 40 mg/day.…”

“…2,5 Estimates of the dialysis clearance of metformin range from 68 to 230 ml/min 1 Renal clearance in healthy subjects is probably close to renal plasma flow, i.e., 600 ml/min. 2,4 In this case the fraction of normal dose would be 0.008 to 0.028, suggesting that, ultimately, the maintenance dosage in patients should not exceed about 40 mg/day. While metformin is generally a safe drug and we agree that the dosage recommended by Sinnappah et al 1 may be reasonable in the short-to medium-term, in the absence of specific knowledge of the impact of renal impairment on its active absorption and distribution, subsequent tapering of the dose seems prudent to prevent excessive accumulation and delayed toxicity, 2,9 especially if concomitant risk factors develop over time.…”