A mathematical model-based analysis of the time-kill kinetics of ceftazidime/avibactam against Pseudomonas aeruginosa

Objectives

To characterize quantitatively the effect of avibactam in potentiating ceftazidime against MDR Pseudomonas aeruginosa by developing a mathematical model to describe the bacterial response to constant concentration time-kill information and validating it using both constant and time-varying concentration-effect data from in vitro and in vivo infection systems.

Methods

The time course of the bacterial population dynamics in the presence of static concentrations of ceftazidime and avibactam was modelled using a two-state pharmacokinetic/pharmacodynamic (PK/PD) model, consisting of active and resting states, to account for bactericidal activities, bacteria-mediated ceftazidime degradation and inhibition of degradation by avibactam. Ceftazidime's effect on the bacterial population was described as an enhancement of the death rate of the active population, with the effect of avibactam being to increase ceftazidime potency. Model validation was performed by comparing simulated time courses of bacterial responses with those from in vitro and in vivo experimental exposures of ceftazidime and avibactam that represented those predicted in an average patient dosed with 2 g/0.5 g ceftazidime/avibactam administered every 8 h as 2 h infusions.

Results

The two-state model successfully described the bacterial population dynamics, ceftazidime degradation and its inhibition by avibactam. For external validation, the model correctly predicted the bacterial response of P. aeruginosa isolates evaluated in in vitro hollow-fibre and in vivo neutropenic mouse thigh and lung infection models.

Conclusions

The PK/PD model and modelled strains successfully replicated the spread in activity when compared with a large selection of P. aeruginosa strains reported in the literature.

A model-based analysis of pharmacokinetic-pharmacodynamic (PK/PD) indices of avibactam against Pseudomonas aeruginosa

OBJECTIVE

The aim of the present work was to use a semi-mechanistic pharmacokinetic-pharmacodynamic (PK/PD) model developed from in vitro time-kill measurements with P. aeruginosa to compare different pharmacodynamic indices derived from simulated human avibactam exposures, with respect to their degree of correlation with the modelled bacterial responses.

METHODS

A mathematical model of the effect of ceftazidime-avibactam on the growth dynamics of P. aeruginosa was used to simulate bacterial responses to modelled human exposures from fractionated avibactam dosing regimens with a fixed ceftazidime dosing regimen (2 or 8 g q8h as a 2-h infusion). The relatedness of the 24-h change in bacterial density and avibactam exposure parameters was evaluated to determine exposure parameter that closely correlated with bacterial growth/killing responses.

RESULTS

Frequent dosing was associated with higher efficacy, resulting in a reduction of avibactam daily dose. The best-fit PD index of avibactam determined from the simulation was fT > C_T of 1 mg/L avibactam and q8h was the longest dosing interval able to achieve 2-log kill: 41-87% (3.3 h to 7.0 h out of 8-h interval, respectively). The avibactam exposure magnitude required to achieve a 2-log kill in the simulations was dependent on the susceptibility of the bacterial isolate to ceftazidime.

CONCLUSIONS

Avibactam activity in combination with ceftazidime against multidrug resistant P. aeruginosa correlated with fT > C_T. Setting a threshold avibactam concentration to 1 mg/L, superimposed over a simulated human-like exposure of ceftazidime, achieved at least 2-log kill for the clinical dose of 500 mg q8h avibactam as a 2-h infusion, depending on the minimum inhibitory concentration of ceftazidime alone.

Potentiation of ceftazidime by avibactam against β-lactam-resistant Pseudomonas aeruginosa in an in vitro infection model

Objectives

This study evaluated the in vitro pharmacodynamics of combinations of ceftazidime and the non-β-lactam β-lactamase inhibitor, avibactam, against ceftazidime-, piperacillin/tazobactam- and meropenem-multiresistant Pseudomonas aeruginosa by a quantitative time-kill method.

Methods

MICs of ceftazidime plus 0-16 mg/L avibactam were determined against eight isolates of P. aeruginosa . Single-compartment, 24 h time-kill kinetics were investigated for three isolates at 0-16 mg/L avibactam with ceftazidime at 0.25-4-fold the MIC as measured at the respective avibactam concentration. Ceftazidime and avibactam concentrations were measured by LC-MS/MS during the time-kill kinetic studies to evaluate drug degradation.

Results

Avibactam alone displayed no antimicrobial activity. MICs of ceftazidime decreased by 8-16-fold in the presence of avibactam at 4 mg/L. The changes in log 10 cfu/mL at both the 10 h and 24 h timepoints (versus 0 h) revealed bacterial killing at ≥1-fold MIC. Significantly higher concentrations of ceftazidime alone, as compared with those of ceftazidime in combination, were required to produce any given kill. Without avibactam, ceftazidime degradation was significant (defined as degradation t 1/2  <   24 h), with as little as 19%   ±   18% of the original concentration remaining at 8 h for the most resistant strain. In combination with avibactam, ceftazidime degradation at ≥ 1-fold MIC was negligible.

Conclusion

The addition of avibactam protected ceftazidime from degradation in a dose-dependent manner and restored its cidal and static activity at concentrations in combination well below the MIC of ceftazidime alone.

Prediction of in vivo and in vitro infection model results using a semimechanistic model of avibactam and aztreonam combination against multidrug resistant organisms

The combination of aztreonam‐avibactam is active against multidrug‐resistant Enterobacteriaceae that express metallo‐β‐lactamases. A complex synergistic interaction exists between aztreonam and avibactam bactericidal activities that have not been quantitatively explored. A two‐state semimechanistic pharmacokinetic/pharmacodynamic (PK/PD) logistic growth model was developed to account for antimicrobial activities in the combination of bacteria‐mediated degradation of aztreonam and the inhibition of aztreonam degradation by avibactam. The model predicted that changing regimens of 2 g aztreonam plus 0.375 and 0.6 g avibactam as a 1‐hour infusion were qualitatively similar to that observed from in vivo murine thigh infection and hollow‐fiber infection models previously reported in the literature with 24‐hour log kill ≥1. The current approach to characterize the effect of avibactam in enhancing aztreonam activity from time‐kill study was accomplished by shifting the half‐maximal effective concentration (EC₅₀) of aztreonam in increasing avibactam concentration using a nonlinear equation as a function of avibactam concentration, providing a framework for translational predictions.

Pharmacodynamics of Ceftazidime and Avibactam in Neutropenic Mice with Thigh or Lung Infection

Avibactam is a new non-β-lactam β-lactamase inhibitor that shows promising restoration of ceftazidime activity against microorganisms producing Ambler class A extended-spectrum β-lactamases (ESBLs) and carbapenemases such as KPCs, class C β-lactamases (AmpC), and some class D enzymes. To determine optimal dosing combinations of ceftazidime-avibactam for treating infections with ceftazidime-resistant Pseudomonas aeruginosa, pharmacodynamic responses were explored in murine neutropenic thigh and lung infection models. Exposure-response relationships for ceftazidime monotherapy were determined first. Subsequently, the efficacy of adding avibactam every 2 h (q2h) or q8h to a fixed q2h dose of ceftazidime was determined in lung infection for two strains. Dosing avibactam q2h was significantly more efficacious, reducing the avibactam daily dose for static effect by factors of 2.7 and 10.1, whereas the mean percentage of the dosing interval that free drug concentrations remain above the threshold concentration of 1 mg/liter (%fT>C(T) 1 mg/liter) yielding bacteriostasis was similar for both regimens, with mean values of 21.6 (q2h) and 18.5 (q8h). Dose fractionation studies of avibactam in both the thigh and lung models indicated that the effect of avibactam correlated well with %fT>C(T) 1 mg/liter. This parameter of avibactam was further explored for four P. aeruginosa strains in the lung model and six in the thigh model. Parameter estimates of %fT>C(T) 1 mg/liter for avibactam ranged from 0 to 21.4% in the lung model and from 14.1 to 62.5% in the thigh model to achieve stasis. In conclusion, addition of avibactam enhanced the effect of ceftazidime, which was more pronounced at frequent dosing and well related with %fT>C(T) 1 mg/liter. The thigh model appeared more stringent, with higher values, ranging up to 62.5% fT>C(T) 1 mg/liter, required for a static effect.