Development and qualification of a pharmacodynamic model for the pronounced inoculum effect of ceftazidime against Pseudomonas aeruginosa

Abstract

Evidence is mounting in support of the inoculum effect (i.e., slow killing at large initial inocula [CFUo]) for numerous antimicrobials against a variety of pathogens. Our objectives were to (i) determine the impact of the CFUo of Pseudomonas aeruginosa on ceftazidime activity and (ii) to develop and validate a pharmacokinetic/pharmacodynamic (PKPD) mathematical model accommodating a range of CFUo. Time-kill experiments using ceftazidime at seven concentrations up to 128 mg/liter (MIC, 2 mg/liter) were performed in duplicate against P. aeruginosa PAO1 at five CFUo from 10(5) to 10(9) CFU/ml. Samples were collected over 24 h and fit by candidate models in NONMEM VI and S-ADAPT 1.55 (all data were comodeled). External model qualification integrated data from eight previously published studies. Ceftazidime displayed approximately 3 to 4 log(10) CFU/ml net killing at 10(6.2) CFUo and concentrations of 4 mg/liter (or higher), less than 1.6 log(10) CFU/ml killing at 10(7.3) CFUo, and no killing at 10(8.0) CFUo for concentrations up to 128 mg/liter. The proposed mechanism-based model successfully described the inoculum effect and the concentration-independent lag time of killing. The mean generation time was 28.3 min. The effect of an autolysin was assumed to inhibit successful replication. Ceftazidime concentrations of 0.294 mg/liter stimulated the autolysin effect by 50%. The model was predictive in the internal cross-validation and had excellent in silico predictive performance for published studies of P. aeruginosa ATCC 27853 for various CFUo. The proposed PKPD model successfully described and predicted the pronounced inoculum effect of ceftazidime in vitro and integrated data from eight literature studies to support translation from time-kill experiments to in vitro infection models.

FIG. 1.

Model for growth and bacterial killing of one subpopulation (model C). Symbols are defined in Table 1.

FIG. 2.

Mechanism-based model for ceftazidime against P. aeruginosa that describes the phenotypic tolerance at high initial inocula by cell-to-cell communication via signal molecules (model D). Symbols are defined in Table 2.

FIG. 3.

Time-kill data (symbols) and model fitting from NONMEM with model D (lines) for ceftazidime against P. aeruginosa at various initial inocula: 10⁶ (A), 10⁷ (B), and 10⁸ CFU/ml (C) (only the 10⁷ inoculum was studied up to 48 h).

FIG. 4.

Observed versus fitted bacterial counts from NONMEM. (A) Fittings of model C (data from the regrowth of the resistant population were excluded from analysis); (B) fittings of model D (using data at log CFUo of 6, 7, and 8); (C) predictions of model D during the leave-one-inoculum-out procedure (data from a preliminary run at log CFUo of 5 and 9 are included); (D) external predictions of a preliminary run at concentrations of 0 and 128 mg/liter.

FIG. 5.

Observed total and resistant population (triangles indicate a resistant population determined on agar plates containing 8 mg/liter ceftazidime), predicted (using the parameter estimates shown in Table 2), and fitted bacterial counts (lines) of the in vitro PD model study by Henrichfreise et al. (28) for model D.

FIG. 6.

External model qualification of model D (Fig. 2) integrating literature data on P. aeruginosa ATCC 27853 from seven studies. (A) Estimation data set (including data from Barcley et al. [1, 2], Cappelletty et al. [9], McGrath et al. [43], Shalit et al. [55], and Mouton et al. [46]); (B) in silico predictions for time-kill data from Tam et al. (61) at 10⁸ CFUo and in vitro PD model data from Cappelletty et al. (9) for various continuous-infusion (CI) and intermittent-dosage regimens, data from McGrath et al. (43), and data from Mouton et al. (46); (C) observed versus predicted counts and observed versus fitted bacterial counts, with in silico predictions from Mouton et al. (46) shown separately.

FIG. 7.

Probability of successful replication (doubling) as a function of the initial inoculum for a range of constant ceftazidime concentrations (the simulation was based on parameter estimates from NONMEM); a probability of 100% represents perfect growth, 50% represents net stasis due to every second doubling being successful, and 0% represents the fastest possible killing; see Materials and Methods for details.