1 Introduction
Metformin is an oral antidiabetic that reduces blood glucose levels. It is the first-line therapy for type 2 diabetes mellitus (T2DM) and the fourth most commonly prescribed outpatient medication in the USA, with almost 80 million prescriptions in 2017 [
1].
Metformin is a BCS Class III drug of high solubility and very low permeability, positively charged at physiological pH and depends on active transport to cross biological membranes. The metformin rate of absorption is slower than its rate of elimination [
2] and the absorption is restricted to the upper intestine [
3], leading to incomplete absorption of metformin, an oral bioavailability of 50–60%, and the excretion of approximately 30% of an oral dose, unabsorbed, with the feces [
2,
4]. Furthermore, the absorption of metformin is saturable, with higher doses showing decreased dose-normalized plasma concentrations and a decreased fraction excreted to urine [
4,
5]. Following its absorption, metformin is not bound to plasma proteins [
2,
4,
6], not metabolized [
2,
6], and not secreted to bile [
2,
4,
7], but excreted unchanged with the urine by passive glomerular filtration and active renal secretion through the sequential action of organic cation transporter 2 (OCT2) and multidrug and toxin extrusion protein 1 (MATE1). Although there are early reports of MATE2-K expression in the human kidney [
8,
9], a recent quantitative study found only negligible amounts of MATE2-K compared to MATE1 [
10]. Renal clearance is approximately 500 mL/min [
11] with a strong correlation between the renal clearances of metformin and creatinine [
4]. Patients with renal impairment show a marked increase in metformin exposure, with three- to ten-fold higher plasma trough concentrations in chronic kidney disease (CKD) stages 3A-5 [
12]. As a consequence, metformin is contraindicated in patients with a glomerular filtration rate (GFR) < 30 mL/min (i.e., CKD stages 4 and 5) [
13,
14], depriving these patients of metformin as a treatment option.
The impact of genetic polymorphisms on the absorption and disposition of metformin (drug–gene interactions or “DGIs”) has been investigated in a multitude of clinical trials, yielding to some extent contradictory results. The transporters of primary interest in these studies were the plasma membrane monoamine transporter (PMAT), OCT1, OCT2, and MATE1, where variations in OCT2 seem to have the largest impact on the plasma concentrations of metformin [
15‐
19]. The most common polymorphism in the gene encoding for OCT2 is the
SLC22A2 808G>T single-nucleotide polymorphism [
20], which results in an amino acid exchange from alanine to serine (A270S) and presumably increased function, leading to decreased exposure with ~ 13–20% decreased maximum concentration (
Cmax) [
17,
18,
21].
A third factor that impacts metformin exposure is drug–drug interactions (DDIs). Metformin displays a list of 333 DDIs, with 13 major and 293 moderate interactions [
22]. Even though some of these occur on the pharmacodynamic level, pharmacokinetic DDIs are clinically relevant and may call for an adjustment of the co-administration regimen. As metformin is exclusively eliminated by glomerular filtration and secretion through the renal organic cation transport system, co-treatment with a potent inhibitor of this transport pathway, such as cimetidine, decreases the renal clearance of metformin and increases metformin exposure (+ 50% area under the curve [AUC]) [
21,
23]. Metformin is recommended by the US Food and Drug Administration as an OCT2/MATE victim drug for clinical DDI studies [
24].
The aim of this study was to build and evaluate a whole-body physiologically based pharmacokinetic (PBPK) model of metformin, applicable (1) to describe the impact of the metformin-
SLC22A2 808G>T DGI on metformin exposure, (2) to dynamically model the cimetidine-metformin DDI, and (3) to analyze the impact of renal impairment on metformin exposure and generate dose recommendations for different stages of CKD. The newly developed and thoroughly evaluated metformin and cimetidine models will be freely available in the Open Systems Pharmacology PBPK model repository (
https://www.open-systems-pharmacology.org), and the Electronic Supplementary Material (ESM) to this article is compiled to serve as a comprehensive and transparent documentation and reference.
2 Methods
2.1 Software
Physiologically based pharmacokinetic models were developed using PK-Sim
® and MoBi
® modeling software (Open Systems Pharmacology Suite 8.0,
https://www.open-systems-pharmacology.org). Published clinical study data were digitized with GetData Graph Digitizer 2.26.0.20 (© S. Fedorov). Model input parameter optimization (Levenberg–Marquardt algorithm, multiple starting values) and sensitivity analysis were performed in PK-Sim
®. All pharmacokinetic parameters and model performance measures derived from simulated and/or observed data were calculated in R 3.6.1 (The R Foundation for Statistical Computing, Vienna, Austria). Plots were generated in R and RStudio 1.1.423 (RStudio, Inc., Boston, MA, USA).
2.2 Physiologically Based Pharmacokinetic Model Building
Physiologically based pharmacokinetic model building was started with an extensive literature search to collect physicochemical parameters, mechanistic information on absorption, distribution, metabolism, and excretion processes, as well as published clinical studies. The general procedure of PBPK model building, including parameter optimization and generation of virtual individuals and virtual populations, is described in the ESM.
2.3 Physiologically Based Pharmacokinetic Model Evaluation
Model performance was evaluated with multiple methods. First, predicted population plasma concentration–time profiles were compared with the data observed in the respective clinical studies. As the clinical data from literature is mostly reported as arithmetic means ± standard deviation, population prediction arithmetic means and 68% prediction intervals were plotted, which corresponds to the range of ± 1 standard deviation around the mean, if normal distribution is assumed. In addition, the predicted plasma concentration values of all studies were plotted against their corresponding observed values in goodness-of-fit plots.
Furthermore, model performance was evaluated by comparison of predicted to observed AUC and Cmax values. All AUC values were calculated from the time of drug administration to the time of the last concentration measurement (AUClast).
As quantitative measures of model performance, mean relative deviation (MRD) of all predicted plasma concentrations (Eq.
1) and geometric mean fold error (GMFE) of all predicted AUC
last and
Cmax values (Eq.
2) were calculated. MRD and GMFE values ≤ 2 characterize an adequate model performance.
$${\text{MRD}} = 10^{x} ;\, x = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{k} (\log_{10} c_{{{\text{predicted}},i}} - \log_{10} c_{{{\text{observed}},i}} )^{2} }}{k},}$$
(1)
where
cpredicted,i is the predicted plasma concentration,
cobserved,i is the corresponding observed plasma concentration, and
k is the number of observed values.
$${\text{GMFE}} = {10}^{x} {; }\, x = \frac{{\mathop \sum \nolimits_{i = 1}^{{\text{m}}} { }\left| {{\log}_{{{10}}} { }\left( {\frac{{{\text{predicted PK parameter}}_{i} }}{{{\text{observed PK parameter}}_{i} }}} \right)} \right|{ }}}{m}{,}$$
(2)
where predicted PK parameteri is the predicted AUClast or Cmax value, observed PK parameteri is the corresponding observed AUClast or Cmax value, and m is the number of studies.
Finally, the physiological plausibility of the parameter estimates and the results of sensitivity analyses were assessed. A detailed description of the sensitivity calculation is given in the ESM.
2.4 Modeling the Impact of Polymorphism
The impact of genetic polymorphism on the pharmacokinetics of metformin was implemented by splitting the polymorphic transporter in question into two transporters with half of the initial reference concentration each, corresponding to the two homologous chromosomal alleles in diploid humans. Each “wild-type” allele present in the simulated population (one in heterozygous individuals and two in homozygous individuals) was modeled with the transport rate constant identified during the initial model development. Each “variant” allele was modeled with an adapted transport rate constant that was identified based on clinical studies of metformin in homozygous “variant” individuals.
2.5 Drug–Drug Interaction Modeling
For mechanistic DDI modeling, the type of interaction (competitive inhibition, mechanism-based inhibition, induction) and the interaction parameters were extracted from in-vitro literature. These parameters were incorporated into the perpetrator PBPK model, to dynamically describe the impact of the perpetrator on the victim drug. The mathematical implementation is shown in the ESM.
The DDI modeling performance was assessed by comparison of predicted vs observed victim drug plasma concentration–time profiles when administered alone and during co-administration. In addition, predicted DDI AUC
last ratios (Eq.
3) and DDI
Cmax ratios (Eq.
4) were evaluated.
$${\text{DDI AUC}}_{\text{last}} {\text{ ratio}} = \frac{{{\text{AUC}}_{{{\text{last}}}} {\text{ victim drug during co-administration}}}}{{{\text{AUC}}_{{{\text{last}}}} {\text{ victim drug control}}}}.$$
(3)
$${\text{DDI }}C_{{\max}} {\text{ ratio}} = \frac{{C_{{\max}} {\text{ victim drug during co-administration}}}}{{C_{{\max}} {\text{ victim drug control}}}}.$$
(4)
As a quantitative measure of the prediction accuracy, GMFE values of the predicted DDI AUC
last ratios and DDI
Cmax ratios were calculated according to Eq. (
2).
2.6 Modeling of Renal Impairment
To model the impact of renal impairment on the pharmacokinetics of metformin, a literature search was conducted to identify the pathophysiological changes that occur in conjunction with renal impairment, including their extent at the different stages of CKD. In a next step, these differences in anatomy and physiology were implemented to create renally impaired individuals and to describe the published clinical studies of metformin in patients with CKD.
4 Discussion
A comprehensive whole-body PBPK model of metformin has been thoroughly built and evaluated, integrating the current knowledge on the mechanisms controlling the pharmacokinetics of this widely prescribed drug. The established model has been evaluated for prediction of the effects of the SLC22A2 808G>T polymorphism, the cimetidine-metformin DDI, and the impact of renal impairment, a frequent co-morbidity in patients with T2DM.
Several other PBPK models of metformin have been published previously [
41‐
44], but our newly developed model is the first to integrate PET-measured human in-vivo metformin kidney concentrations, clinical data of microdose studies, and a mechanistic description of the saturable transporter-dependent absorption of metformin. The limitations of the presented model result from our lack of knowledge regarding the metformin pharmacokinetic processes in the liver and the expression levels of the different transporters throughout the body. As shown in Fig.
3d, the liver concentration–time profile following the intravenous
11C-metformin microdose is not adequately described. The uptake of metformin into the liver is modeled via OCT1, but, in accordance with the literature, no process for metformin metabolism or secretion to bile has been implemented. An unspecific hepatic metabolic clearance was tested, but did not improve the model (causing underestimation of the plasma concentrations in studies with therapeutic doses), supporting the idea that metformin is not metabolized. The plasma concentrations following the oral
11C-metformin microdose, and consequently also the measured tissue concentrations, are underpredicted for the 2 h of the oral PET study (see the ESM). However, the administered microdoses (1.445 µg intravenously and 0.856 µg orally) were more than 300,000 and 500,000 times below the lowest therapeutic dose of 500 mg. Given that the metformin pharmacokinetics are completely governed by saturable transport processes and that the plasma, whole blood, kidney, and muscle concentrations following the intravenous microdose are well described, this underprediction might be caused by a missing process for metformin absorption.
The effect of the
SLC22A2 808G>T polymorphism is difficult to assess from the literature. In-vitro studies report a decreased metformin transport rate [
29], equal activity [
20], as well as increased transport velocity [
17] for the variant OCT2 protein. In-vivo, two studies report decreased clearance by renal secretion in Korean and Chinese 808TT individuals [
21,
29], whereof the Chinese study nevertheless shows a non-significantly lower metformin plasma
Cmax for the 808TT group. However, two different studies report increased clearance by renal secretion in American and European individuals [
17,
18], with corresponding decreases in metformin exposure in association with the minor allele. Given that OCT2 and MATE1 are working sequentially to transport metformin through the kidney, it is difficult to distinguish their impacts on renal secretion. Therefore, statements regarding the effect of polymorphisms or co-medications on OCT2 function should not be based on plasma concentrations or renal secretion alone, without concomitant assessment of MATE1 genotype/activity or kidney concentrations. This also holds true for the DDGI results by Wang et al. [
21] (Fig.
5f), where the observed lack of cimetidine-metformin DDI in
SLC22A2 808TT individuals is difficult to explain, because (1) this DDI is mainly caused by inhibition of MATE1, (2) the MATE1 genotypes were not analyzed in this study, and (3) so far there are no in-vitro results available on the impact of cimetidine on MATE1 variants. Another explanation for the weak effect of cimetidine in the
SLC22A2 808TT group might be reduced transport of cimetidine by this OCT2 variant into the kidney and therefore less inhibition of MATE1, as previously proposed [
30].
To model the renal impairment, renal secretion was decreased in proportion to the impaired GFR, based on the “intact nephron hypothesis”, which postulates that structurally damaged nephrons stop contributing to both passive renal filtration and active secretion, and that the remaining intact nephrons continue to function in glomerulo-tubular balance with appropriate adaptation to the patient’s needs [
35]. This hypothesis has been successfully applied in previous PBPK analyses of renal impairment [
36,
42,
45,
46]. The inhibition of liver drug uptake by uremic toxins in renal impairment has been postulated by Zhao et al. [
38], based on the fact that the clearance of many nonrenally eliminated drugs is decreased in CKD, and based on their PBPK analysis of repaglinide in CKD4.
We used an empirical approach to model the inhibition of liver and muscle uptake as a function of the degree of renal impairment. The inhibition of the basolateral intestinal permeability/transport in CKD is purely hypothetical, but was essential to describe the shape and elimination phase of the clinically observed data. The induction of OCT2 and MATE1 was demonstrated in hyperuricemic rats [
40]. To confirm and refine these hypotheses, in-vitro studies of OCT1 and PMAT inhibition by uremic solutes are needed, to identify the toxins involved and to assess their inhibitory potential; the expression and role of transporters at the basolateral membrane of the intestinal mucosa has to be investigated; and the clinical relevance of OCT2 and MATE1 induction by uric acid in humans needs to be established.
Future applications include the modeling of further DGIs and DDIs, and ultimately, the individualized dose recommendation for real patients with multiple polymorphisms, co-medications, and co-morbidities. Although the effects of some of these interactions do not reach statistical significance in the blood, their impact on kidney or liver concentrations might well be substantial and of therapeutic relevance. The model application with the most immediate medical benefit is the generation of dose recommendations for renally impaired patients with T2DM. Chronic kidney disease is a frequent co-morbidity, but physicians are reluctant to prescribe metformin to patients with reduced renal function because of the contraindication given in most guidelines and fear of lactic acidosis caused by metformin accumulation [
47]. These contraindications are based solely on the estimated GFR of the patient, even though for patients with stable renal disease, a dose adjustment based on renal function, with monitoring of the metformin plasma concentrations, would be perfectly feasible. A reduced dose of 500 mg metformin daily was reported to be safe for creatinine clearances as low as 20 mL/min [
48] and in a group of CKD4 patients [
12], which is in line with the presented model-based recommendation of 200 mg three times daily for CKD4 patients with T2DM.