Fosfomycin as a potential therapy for the treatment of systemic infections: a population pharmacokinetic model to simulate multiple dosing regimens

Abstract Fosfomycin has emerged as a potential therapy for multidrug‐resistant bacterial infections. In most European countries, the oral formulation is only approved as a 3 g single dose for treatment of uncomplicated cystitis. However, for the treatment of complicated systemic infections, this dose regimen is unlikely to reach efficacious serum and tissue concentrations. This study aims to investigate different fosfomycin‐dosing regimens to evaluate its rationale for treatment of systemic infections. Serum concentration‐time profiles of fosfomycin were simulated using a population pharmacokinetic model based on published pharmacokinetic parameter values, their uncertainty, inter‐individual variability and covariates. The model was validated on published data and used to simulate a wide range of dosing regimens for oral and intravenous administration of fosfomycin. Finally, based on the minimum inhibitory concentration for E. coli, surrogate pharmacodynamic indices were calculated for each dosing regimen. This is the first population pharmacokinetic model to describe the oral pharmacokinetics of fosfomycin using data from different literature sources. The model and surrogate pharmacodynamic indices provide quantitative evidence that a dosing regimen of 6–12 g per day divided in 3 doses is required to obtain efficacious exposure and may serve as a first step in the treatment of systemic multi‐drug‐resistant bacterial infections.


| INTRODUCTION
Antibacterial resistance remains one of the major threats to human health, despite its identification as one of the worldwide priority conditions by the WHO over a decade ago. [1][2][3] Particularly alarming is the rise in number and spread of multi-drug resistant (MDR) bacterial strains and a poor pipeline of new Gram-negative antibiotics. [4][5][6][7] To battle MDR bacteria strains, the reassessment and reintroduction of 'old' antibiotics have emerged as alternative solution to circumvent the long and costly process of developing new antibiotics. 8,9 One of such 'old' antibiotics is fosfomycin, developed more than 40 years ago. 10 Fosfomycin is a broad spectrum antibiotic which exerts its bactericidal activity by irreversibly inhibiting the early stages of the bacterial cell wall synthesis. 11 MDR Gram-negative bacteria are responsible for around twothirds of the deaths by MDR-bacterial infections in Europe. 6 Fosfomycin exhibits in vitro and in vivo antibacterial activity against a wide range of both Gram-positive and Gram-negative bacteria, including several MDR-strains. [12][13][14][15][16][17] Even most of the extensively drug-resistant (XDR) Enterobacteriaceae strains still remain susceptible to fosfomycin, including those expressing extended-spectrum beta-lactamases (ESBL) or metallo-b-lactamases (MBL). [14][15][16]18 In addition, fosfomycin has been suggested as add-on therapy for infections caused by MDR-P. aeruginosa, one of the main pathogens associated with nosocomial-acquired infections. 16,17,19 Fosfomycin has been marketed in different formulations including fosfomycin tromethamine for oral administration and fosfomycin disodium for intravenous administration. 20 In most European countries, only the oral formulation is available and approved as a single 3 g dose for the treatment of uncomplicated urinary tract infections (UTIs) in women. This single-dose regimen is not efficacious for the treatment of systemic MDR bacterial infections, making the prospective evaluation of new oral dosing regimens a necessity. A multiple-dose regimen of oral fosfomycin tromethamine has been proposed for the treatment of complicated UTIs, including those due to MDR-bacteria. 21,22 However, more studies are urgently needed to determine the optimal oral dose regimen to achieve efficacious systemic exposure.
Few pharmacokinetic (PK) models for fosfomycin have been described in literature, which were developed on different study designs, limited numbers of subjects and different model structures. 23

| PK model
The structural model for intravenous administration was based on a previously reported two-compartment population PK model of fosfomycin, developed on 12 patients scheduled for abscess drainage. 25 The model was parameterized in terms of elimination rate constant (k e ), volumes of distribution for the central (Vc) and peripheral compartments (Vp) and intercompartmental clearance (Q). The rate and duration of infusion were parameterized by Q inf and t inf , respectively.
To include oral administration of fosfomycin tromethamine, the model was extended with a gastrointestinal-(GI) and a transit component (TRANS), based on a PK model published by Segre et al., that was developed after oral and intravenous administration in 5 healthy volunteers. 24 This model was parameterized in terms of rate constants k ij , representing the different rates of drug transfer from the i th compartment to the j th compartment, including a k 10 , representing the first order loss of dose, hence correcting for oral bioavailability.
Additionally, a transfer constant representing biliary clearance of the drug (k b ) was included in the oral PK model. As literature is inconclusive on reabsorption of fosfomycin, 24,29,30 models with and without enterohepatic recirculation were compared to published data in order to evaluate its descriptive impact on the simulations. The PK model structures used for the simulations of different multiple-dose regimens after intravenous and oral administration of fosfomycin are presented in Figure 1.
The two compartment PK model structure used for the simulations of fosfomycin multiple-dose regimens (black), together with the excluded enterohepatic recirculation (gray). CL, clearance; CMT, compartment with associated number; k10, the first-order loss prior to reaching CMT 2; k12, k23, k56, k61, rate constants between compartments; kb, biliary elimination; GI; gastrointestinal; Q, intercompartmental clearance; Q inf infusion rate constant; t inf , infusion time; TRANS, transit; Vc, central volume of distribution; Vp, peripheral volume of distribution Individual PK parameters were simulated according to Equation 1.
where h i is the PK parameter for the i th individual, h TV the typical population PK parameter, and g i the interindividual variability (IIV) for the i th individual.Here, IIV was reported to be log-normally distributed for CL, Vc, and Vp, 25 and incorporated as such in the model; g is assumed to be normally distributed around 0 with its reported variance x 2 .
where subscript LN refers to the log domain, and N refers to the normal domain. Subsequently, h TV was calculated according to Equation 4.

| Covariates
A mean-centered linear relationship between creatinine clearance (CL CR ) and clearance (CL) was reported, 25 and incorporated as such in the simulated clearance for the i th individual (CL i , Equation 5).
where CL TV is the literature derived mean population parameter with its uncertainty (Equation 4), CL CR,i is the creatinine clearance and g i the IIV for the i th individual. The CL CR,i and normalization factor (103) were obtained from Sauermann et al. 32

| Model validation
The validation of the PK models was performed by simulating previ-    3.2 | Simulation of different multiple-dose regimens and calculation of PK/PD Indices Different multiple-dose regimens after oral administration of fosfomycin were simulated using the validated PK model. Figure 4 shows the medians of the predicted PK profiles of 1000 subjects (qd), two times daily (bid) and three times daily (tid). The predicted medians of these different dose regimens as presented in Figure 5 show that the medians of all first doses reached serum concentrations above the MIC. For both dose groups, concentrations only maintain above the MIC for the entire duration of the day following tid dosing. As shown in Table 3

| DISCUSSION
This is the first population PK model to describe the oral pharmacokinetics of fosfomycin, using data from different literature sources.
The study provides quantitative evidence that an oral dosing regimen of 6-12 g per day divided in 3 doses is required to obtain   41 In this regard, further studies are urgently needed to establish the PK-PD relationships of fosfomycin. Microbiological susceptibility information could also be included in Monte Carlo simulations in order to define oral dosing regimens based on potential PK/ PD targets with high probability of microbiological cure. This has been recently reported following intravenous infusion of fosfomycin in the treatment of Klebsiella pneumoniae, 42 and Pseudomonas aeruginosa. 43 Literature review on fosfomycin PK and simulations clearly indicate the need for further clinical research to characterize the PK and PD properties of fosfomycin tromethamine. Previous studies reported potential decreased absorption at higher doses 24,44 and fosfomycin recirculation. 24 In the model building, these concepts were considered but did not improve the descriptive properties of the model with regards to the available data. Also, when administering doses that are higher than the current recommended dose in the clinic, this may result in nonlinear PK. 24,44 Hence, in the design of a future clinical trial, dose regimens as well as sampling times should be chosen to optimally address these potential PK characteristics.
Characterization of these processes is the key to the design of optimal multiple-dose strategies, as saturable absorption or elimination can limit the use of higher doses and recirculation can lead to clinically relevant accumulation.
Simulations and PD indices show that a total daily oral dose of at least 6-12 g of fosfomycin tromethamine are required to achieve a therapeutic concentration to treat systemic infections, based on the epidemiological cut-off value for E. coli. In light of the reported simulations, the population PK model can be used to optimize a new clinical trial to assess the PK, safety, and tolerability of fosfomycin tromethamine in multiple-dose regimens.