Optimization of Synergistic Combination Regimens against Carbapenem- and Aminoglycoside-Resistant Clinical Pseudomonas aeruginosa Isolates via Mechanism-Based Pharmacokinetic/Pharmacodynamic Modeling

ABSTRACT

Optimizing antibiotic combinations is promising to combat multidrug-resistant Pseudomonas aeruginosa. This study aimed to systematically evaluate synergistic bacterial killing and prevention of resistance by carbapenem and aminoglycoside combinations and to rationally optimize combination dosage regimens via a mechanism-based mathematical model (MBM). We studied monotherapies and combinations of imipenem with tobramycin or amikacin against three difficult-to-treat double-resistant clinical P. aeruginosa isolates. Viable-count profiles of total and resistant populations were quantified in 48-h static-concentration time-kill studies (inoculum, 10^7.5 CFU/ml). We rationally optimized combination dosage regimens via MBM and Monte Carlo simulations against isolate FADDI-PA088 (MIC of imipenem [MIC_imipenem] of 16 mg/liter and MIC_tobramycin of 32 mg/liter, i.e., both 98th percentiles according to the EUCAST database). Against this isolate, imipenem (1.5× MIC) combined with 1 to 2 mg/liter tobramycin (MIC, 32 mg/liter) or amikacin (MIC, 4 mg/liter) yielded ≥2-log₁₀ more killing than the most active monotherapy at 48 h and prevented resistance. For all three strains, synergistic killing without resistance was achieved by ≥0.88× MIC_imipenem in combination with a median of 0.75× MIC_tobramycin (range, 0.032× to 2.0× MIC_tobramycin) or 0.50× MIC_amikacin (range, 0.25× to 0.50× MIC_amikacin). The MBM indicated that aminoglycosides significantly enhanced the imipenem target site concentration up to 3-fold; achieving 50% of this synergistic effect required aminoglycoside concentrations of 1.34 mg/liter (if the aminoglycoside MIC was 4 mg/liter) and 4.88 mg/liter (for MICs of 8 to 32 mg/liter). An optimized combination regimen (continuous infusion of imipenem at 5 g/day plus a 0.5-h infusion with 7 mg/kg of body weight tobramycin) was predicted to achieve >2.0-log₁₀ killing and prevent regrowth at 48 h in 90.3% of patients (median bacterial killing, >4.0 log₁₀ CFU/ml) against double-resistant isolate FADDI-PA088 and therefore was highly promising.

INTRODUCTION

Antimicrobial resistance in Gram-negative pathogens and the shortage of new antibiotics in the discovery-and-development pipeline are causing a serious global health crisis (1–4). Multidrug-resistant Pseudomonas aeruginosa is an opportunistic nosocomial pathogen and is prevalent in bloodstream, wound, and respiratory tract infections (5, 6). Resistant isolates of P. aeruginosa have been found in hospitals worldwide and are associated with high rates of morbidity and mortality (5, 6). The high rates of resistant P. aeruginosa isolates present a substantial clinical challenge, especially for antibiotic therapies in severe infections (7). Among the β-lactam antibiotics, carbapenems have been considered a monotherapy treatment of choice due to their rapid bacterial killing and good activity against susceptible P. aeruginosa and other Gram-negative bacteria (6, 8, 9). However, in the last 10 to 15 years, carbapenem resistance has become a major challenge, and numbers of infections by resistant isolates have increased worldwide (6, 9, 10). An aminoglycoside (AGS) can cause substantial bacterial killing in monotherapy against P. aeruginosa, but rapid emergence of resistance occurs in vitro and in patients and is associated with treatment failure in 85% of patients (11, 12).

The extensive decline in new approved antibiotics, especially against Gram-negative pathogens, and the rapid emergence of resistance to all existing antibiotics in monotherapies cause significant challenges (1, 3). Synergistic combination therapy using available antibiotics offers an attractive and tangible option to treat infections by multidrug-resistant P. aeruginosa. In the past, in vitro studies of the combination of β-lactams with aminoglycosides have been conducted. However, these studies were limited in that they usually assessed one β-lactam plus one aminoglycoside and in that the studied isolates were susceptible to both antibiotics tested or were intermediate to one and susceptible to the other antibiotic (8, 13–15). Other studies did not evaluate synergy (16).

Our primary objective was to identify the imipenem (IPM) and aminoglycoside concentrations required to achieve substantial bacterial killing and prevent resistance via 48-h static-concentration time-kill (SCTK) experiments with three double-resistant P. aeruginosa isolates. Second, we aimed to characterize the extent and time course of synergistic bacterial killing and prevention of resistance by a new mechanism-based mathematical model (MBM). For our third objective, this MBM enabled us to rationally optimize combination dosage regimens for critically ill patients with bacteremia via novel, MBM-based Monte Carlo simulations that were based on previously reported human population pharmacokinetic (PK) models in critically ill patients.

(Part of this work was presented as a poster presentation at ASM Microbe, 16 to 20 June 2016, Boston, MA [74].)

RESULTS

All three studied clinical isolates were carbapenem resistant (Table 1). Isolate FADDI-PA088 was tobramycin resistant (MIC, 32 mg/liter) and amikacin susceptible (MIC, 4 mg/liter), whereas isolate FADDI-PA001 was tobramycin susceptible, with an MIC of 4 mg/liter (i.e., the highest MIC deemed susceptible by European Committee on Antimicrobial Susceptibility Testing [EUCAST] breakpoints), and amikacin resistant (MIC, 32 mg/liter). Isolate FADDI-PA022 was resistant to both tobramycin and amikacin. The log₁₀ mutation frequencies on 3× MIC agar plates (Table 1) indicated the presence of an aminoglycoside-resistant population for FADDI-PA088 and an imipenem-resistant population for FADDI-PA001 before the initiation of antibiotic therapy.

TABLE 1.

MICs and log₁₀ mutation frequencies in cation-adjusted Mueller-Hinton II broth^a

Strain	MIC (mg/liter)			Log10 mutation frequency at 3× MIC
	Imipenem	Tobramycin	Amikacin	Imipenem	Tobramycin	Amikacin
FADDI-PA088	16	32	4	<−7.6	−5.5	−5.4
FADDI-PA001	32	4	32	−4.75	<−7.8	<−7.8
FADDI-PA022	16	8	>32	<−7.3	<−7.3	NS

^aNS, not studied.

Extensive and synergistic killing of isolate FADDI-PA088 was observed with imipenem-plus-aminoglycoside combinations. In monotherapy, the highest clinically achievable concentrations of imipenem, tobramycin, and amikacin yielded at least 3.0-log₁₀ killing by 6 h, which was, however, followed by regrowth. Excitingly, as little as 1 mg/liter tobramycin (i.e., 1/32 of the MIC) achieved synergy with imipenem at 24 mg/liter and prevented regrowth over 48 h (Table 2 and see Fig. 2A1). Amikacin at 1.0 mg/liter demonstrated synergy in combination with 24 mg/liter imipenem and prevented regrowth over 48 h (Table 2 and see Fig. 2A2).

TABLE 2.

IPM concentrations required in combination with tobramycin or amikacin to achieve synergistic bacterial killing and prevention of regrowth of three P. aeruginosa isolates^b

^aTobramycin monotherapy yielded considerable killing. Thus, this combination was not synergistic.

^bIPM and AGS concentrations are shown as fold MICs. Cells shaded in green represent ≥2-log₁₀ more killing than the most active monotherapy (i.e., meeting the empirical definition of synergy), and cells shaded in blue represent 1.0- to 2.0-log₁₀ more killing than the most active monotherapy.

FIG 2.

Observed (markers) and individual fitted (lines) viable counts for imipenem combined with an aminoglycoside (tobramycin or amikacin) against three P. aeruginosa isolates. Observed viable counts below the limit of detection (i.e., below 1.0 log₁₀ CFU/ml) were plotted as zero.

Against FADDI-PA001, imipenem at 36 mg/liter and tobramycin at 32 mg/liter achieved 2-log₁₀ killing by 6 h in monotherapy, followed by extensive regrowth. No killing was observed with amikacin monotherapy. Imipenem at 14 mg/liter plus tobramycin at 32 mg/liter, imipenem at 24 mg/liter plus tobramycin at 16 to 32 mg/liter, and imipenem at 36 mg/liter plus tobramycin at 4 to 16 mg/liter yielded synergy (i.e., ≥2-log₁₀ more killing than the most active monotherapy) over 24 to 48 h (Table 2 and see Fig. 2B1). Imipenem at 36 mg/liter was required to achieve synergy at 24 h with 16 to 64 mg/liter amikacin. Imipenem at 36 mg/liter combined with 64 mg/liter amikacin prevented regrowth over 48 h (Table 2 and see Fig. 2B2).

In SCTK experiments with FADDI-PA022, 24 mg/liter imipenem and 32 mg/liter tobramycin were the most active monotherapies, with 3.2-log₁₀ and 2.3-log₁₀ killing at 6 h. However, initial killing was followed by extensive regrowth at 48 h. Imipenem at 8 mg/liter plus tobramycin at 32 mg/liter and imipenem at 24 mg/liter plus 16 to 32 mg/liter tobramycin yielded at least 5-log₁₀ killing and prevented regrowth over 48 h (Table 2 and see Fig. 2C).

Imipenem combinations suppressing resistance.

Emergence of resistance was defined as viable counts of resistant bacteria higher than those of the growth control (see Fig. 3, broken black horizontal line). All monotherapies (except imipenem monotherapies for FADDI-PA088) demonstrated, in part extensive, resistance emergence quantified on antibiotic-containing agar plates (3× MIC) for all three isolates (see Fig. 3; see also Fig. S2 in the supplemental material). The emergence of resistance was very extensive for aminoglycoside monotherapies, primarily for higher aminoglycoside concentrations in broth (tested range, 0.5 to 64 mg/liter).

FIG 3.

Resistant subpopulations of imipenem and aminoglycosides (tobramycin and amikacin) on 3× MIC agar plates at 48 h for treatment and control arms. All monotherapies resulted in the amplification of resistant subpopulations that grew on 3× MIC drug plates. The highest achievable clinically relevant concentrations of imipenem combined with tobramycin or amikacin suppressed the amplification of resistance over 48 h.

Clinically relevant concentrations for the combination of imipenem with tobramycin or amikacin suppressed resistance over 48 h against FADDI-PA088 and FADDI-PA022. For isolate FADDI-PA088, despite the presence of a preexisting aminoglycoside-resistant subpopulation (2.1 to 2.3 log₁₀ CFU/ml at 0 h), 14 mg/liter imipenem plus ≥16 mg/liter tobramycin or ≥4 mg/liter amikacin and 24 mg/liter imipenem plus 1 to 16 mg/liter tobramycin or amikacin suppressed resistance to both imipenem and aminoglycosides (see Fig. 3A). Against isolate FADDI-PA022, imipenem at 8 mg/liter plus 32 mg/liter tobramycin and imipenem at 24 mg/liter in combination with 16 and 32 mg/liter tobramycin displayed suppression of resistance to both imipenem and aminoglycosides (see Fig. 3C). Isolate FADDI-PA001 harbored a preexisting imipenem-resistant subpopulation (3.1 log₁₀ CFU/ml at 0 h); imipenem at 24 mg/liter plus 32 mg/liter tobramycin and imipenem at 36 mg/liter in combination with 16 mg/liter tobramycin (or 64 mg/liter amikacin) suppressed resistance to both imipenem and the aminoglycosides over 48 h (see Fig. 3B).

Mechanism-based modeling.

Our MBM contained three preexisting bacterial populations with different susceptibilities to imipenem and the aminoglycosides (Fig. 1). This MBM simultaneously described the effects of imipenem plus tobramycin and of imipenem plus amikacin and yielded unbiased and precise curve fits for all monotherapies and combinations (Fig. 2; see also Fig. S1 in the supplemental material). The coefficient of correlation for the observed versus individual fitted log₁₀ viable counts was ≥0.976 against all three isolates.

FIG 1.

The IPM^S/AGS^S population is susceptible to both imipenem and the aminoglycoside, the IPM^R/AGS^I population is imipenem resistant and has intermediate susceptibility to the aminoglycoside, and the IPM^I/AGS^R population is aminoglycoside resistant and has intermediate susceptibility to imipenem. The maximum killing rate constants (K_max) and the antibiotic concentrations causing 50% of K_max (KC₅₀) are explained in Table 3. The effect of aminoglycosides on the outer membrane (i.e., the aminoglycoside enhancing the target site penetration of imipenem) was applied to all three strains. The outer membrane effect terms I_max,OM and IC_50,OM are explained in Table 3. A life cycle growth model (61, 64) was utilized for each of the three populations to describe bacterial growth and replication.

Mechanistic synergy due to the aminoglycoside enhancing the target site concentration of imipenem (i.e., the effect of the aminoglycoside on the outer membrane) occurred for all three populations of FADDI-PA088. Synergy was present for two of the three bacterial populations (SS, i.e., IPM^S/AGS^S, and IR, i.e., IPM^I/AGS^R) for FADDI-PA001 and FADDI-PA022 (Fig. 1). The inclusion of mechanistic synergy for the RI (i.e., IPM^R/AGS^I) population did not improve the model performance for these two isolates. Mechanistic synergy was expressed as a decrease in the KC_50,IPM (the imipenem concentration causing 50% of K_max) of the respective bacterial populations with increasing aminoglycoside concentrations (see Fig. 4). A decrease in the KC_50,IPM in the MBM is equivalent to an increase of the imipenem target site concentration.

FIG 4.

The outer membrane effect of the aminoglycosides (i.e., the aminoglycoside enhancing the target site penetration of imipenem) resulted in a decrease in the imipenem concentration required for half-maximal bacterial killing of two or three bacterial populations (KC_50,IPM). Results are shown for three P. aeruginosa isolates. The decrease in the KC_50,IPM was dependent on the aminoglycoside (tobramycin or amikacin) concentration. Parameters are explained in Table 3.

Mechanistic synergy was most pronounced for isolate FADDI-PA088: the imipenem concentration required to provide half-maximal killing for all three populations was decreased by 2.4- to 2.9-fold in the presence of 32 mg/liter tobramycin and 32 mg/liter amikacin compared to the situation without an aminoglycoside being present (see Fig. 4A). There was a lesser decrease in the KC_50,IPM noted for FADDI-PA001 (see Fig. 4B). For isolate FADDI-PA022, the imipenem concentration yielding half-maximal killing of the aminoglycoside-resistant population (KC_50,IR,IPM) decreased 1.7-fold in the presence of 32 mg/liter of tobramycin compared to no tobramycin (see Fig. 4C). This decrease in the KC_50,IPM in the presence of an aminoglycoside contributed to the killing of the bacterial populations by imipenem. For all three isolates, we estimated the aminoglycoside concentration required for half-maximal permeabilization of the outer membrane (IC_50,OM,AGS), i.e., the concentration required for 50% mechanistic synergy (Table 3 and see Fig. 4). Similarly, the aminoglycoside concentration required for 80% mechanistic synergy is also illustrated in Fig. 4.

TABLE 3.

Population mean parameter estimates for the imipenem-plus-aminoglycoside (tobramycin or amikacin) combination models against three P. aeruginosa isolates

Parameter	Abbreviation	Population mean value (SE [%]) for strain, treatment
		FADDI-PA088, IPM + AGS	FADDI-PA001, IPM + AGS	FADDI-PA022, IPM + TOB
Log10 CFU, initial inoculum	LogCFU0	7.54 (3.8)a	7.92 (1.2)a	6.99 (1.3)
		7.46 (1.8)b	7.78 (1.0)b
Log10 CFU, maximum population size	CFUmax	9.56 (1.8)	9.23 (0.7)	9.54 (2.9)
Replication rate constant (h−1)	k21	50 (fixed)	50 (fixed)	50 (fixed)
Mean generation time (min)
Population 1 (CFUSS)	k12S−1	26.9 (6.2)	45.3 (10.9)	63.8 (10.8)
Population 2 (CFURI)	k12I−1	873 (8.5)	481 (15.2)	565 (19.9)
Population 3 (CFUIR)	k12R−1	26.9 (6.2)	45.3 (10.9)	63.8 (10.8)
Log10 mutation frequencies
IPM	LogMUT,IPM	−4.73 (5.8)	−4.99 (4.0)	−3.90 (9.4)
AGS	LogMUT,AGS	−7.00 (5.9)a	−7.33 (4.2)a	−7.55 (4.0)
		−6.68 (3.4)b	−6.66 (4.0)b
Killing by IPM
Maximum killing rate constant (h−1)	Kmax,IPM	3.34 (5.5)	3.21 (18.5)	2.23 (10)
Imipenem concn causing 50% Kmax,IPM (mg/liter)
Population 1 (CFUSS)	KC50,SS,IPM	0.992 (33)	33.2 (11.1)	15.2 (25.7)
Population 2 (CFURI)	KC50,RI,IPM	264 (9.7)	118 (17.8)	67.3 (24.2)
Population 3 (CFUIR)	KC50,IR,IPM	23.5 (11)	61.8 (9.0)	52.7 (33.8)
Killing by AGS
Maximum killing rate constants (h−1)
Population 1	Kmax,SS,AGS	11.8 (7.9)	2.84 (15.8)	2.93 (11.8%)
Population 2	Kmax,RI,AGS	3.28 (26.3)	3.14 (15.9)	2.80 (21.2%)
Population 3	Kmax,IR,AGS	11.8 (7.9)	2.84 (15.8)	2.93 (11.8%)
AGS concn causing 50% Kmax,AGS (mg/liter)
Population 1	KC50,SS,AGS	18.6 (39.6)a	16.6 (17)a	54.9 (8.1)a
		4.88 (25.3)b	153 (12.7)b
Population 2	KC50,RI,AGS	849 (5.7)a	228 (16.7)a	568 (10.9)a
		280 (15.7)b	738 (8.3)b
Population 3	KC50,IR,AGS	615 (4.1)a	46.7 (9.9)a	159 (34.7)a
		329 (10.8)b	170 (10.5)b
Mean turnover time for hypothetical signal molecules (=1/kout,sig) (h)	MTTsig	1 (fixed)	1 (fixed)	0.087 (31.3)
Maximum inhibition by hypothetical signal molecules	Imax,sig12	0.997 (13.7)	0.996 (11.3)	0.881 (56.2)
Log10 hypothetical signal molecule concn at 50% max effect	Log10,IC50,Sig	10.2 (4.3)	9.63 (2.3)	8.95 (26)
Permeabilization of the outer membrane by AGS
Maximum fractional decrease of KC50,IPM by AGS via outer membrane disruption	Imax,OM,AGS	0.678c (31.8)	0.130c (11.1)	0.604c (126)
AGS concn causing 50% Imax,OM,AGS (mg/liter)	IC50,OM,AGS	5.55 (29.3)a	1.54 (17.5)a	4.29 (21.6)a
		1.13 (49.0)b	4.80 (14.2)b
Hill coefficient for bacterial killing
IPM	HillIPM	3.00 (13.8)	3.09 (14.2)	3.08 (27.4)
AGS	HillAGS	1.11 (5.5)	2.04 (10)	0.998 (11.9)a
SD of residual error on log10 scale	SDCFU	0.378 (6.0)	0.290 (5.2)	0.475 (10.4)

^aParameter estimates for tobramycin.

^bParameter estimates for amikacin.

^cThese estimates mean that the imipenem target site concentrations increased up to 3.11-fold for FADDI-PA088, 1.15-fold for FADDI-PA001, and 2.53-fold for FADDI-PA022 in the presence of high AGS concentrations (≫IC_50,OM,AGS).

We extended the MBM shown in Fig. 1 by simultaneously fitting the time courses of both the total population and the populations resistant to imipenem or the aminoglycoside (quantified on 3× MIC agar plates) for isolate FADDI-PA088. This extended MBM adequately captured the growth and killing of resistant bacteria, provided unbiased and reasonably precise curve fits (see Fig. S3 in the supplemental material), and thus supported the proposed structural model (Fig. 1).

In this extended MBM, the fraction of the aminoglycoside-resistant population that was quantifiable on aminoglycoside-containing agar plates increased with higher aminoglycoside concentrations. This fraction was previously defined as the subpopulation fraction by Ly et al. (17). The extended MBM suggested inducible aminoglycoside resistance for the aminoglycoside-resistant population (i.e., IR) (Fig. 1). For FADDI-PA088, an amikacin concentration of 1.08 mg/liter and a tobramycin concentration of 11.7 mg/liter yielded half-maximal induction of the subpopulation fraction for the aminoglycoside. The other populations (i.e., SS and RI) (Fig. 1) had constant, i.e., noninducible, subpopulation fractions for imipenem and the aminoglycosides, suggesting that there was no inducible resistance.

Monte Carlo simulations.

A continuous infusion of 5 g/day imipenem with a 1-g loading dose was predicted to achieve median (5th to 95th percentiles) unbound steady-state concentrations of 16.7 mg/liter (9.63 to 29.1 mg/liter) (see Fig. 5A). The 1-g imipenem loading dose was included in the simulation to achieve steady-state concentrations more rapidly. Following a 0.5-h infusion of 7 mg/kg of body weight tobramycin, the predicted concentrations (medians [5th to 95th percentiles]) were 17.7 mg/liter (12.8 to 23.8 mg/liter) at 0.5 h and 1.43 mg/liter (0.584 to 2.78 mg/liter) at 24 h. Against the double-resistant isolate (FADDI-PA088) (initial inoculum of 10^{7.53 ± 0.3} CFU/ml), the simulated imipenem monotherapies given as intermittent short-term infusions yielded 1.56-log₁₀ (1.1- to 2.4-log₁₀) bacterial killing, followed by rapid regrowth to ≥10^7.5 CFU/ml at 8 to 14 h (see Fig. 5B). A continuous infusion of imipenem at 5 g/day in monotherapy was predicted to achieve 3.3-log₁₀ (2.8- to 4.0-log₁₀) bacterial killing, followed by rapid regrowth to ≥10^7.5 CFU/ml for the majority of the simulated patients. Monotherapy with tobramycin at 7 mg/kg was predicted to achieve 3.1-log₁₀ (2.9- to 3.6-log₁₀) bacterial killing, followed by rapid and extensive regrowth to ≥10^7.5 CFU/ml at 8 to 14 h (see Fig. 5B).

FIG 5.

Simulated plasma concentrations and viable-count profiles of double-resistant (MIC_IPM of 16 mg/liter and MIC_TOB of 32 mg/liter) P. aeruginosa isolate FADDI-PA088 for monotherapies and combination dosage regimens with an initial inoculum of 10^7.5 CFU/ml. The Monte Carlo simulations included 10,000 critically ill virtual patients with bacteremia. These patients were assumed to have normal renal function and to completely lack any effect of the immune system. The success rate (Success), defined as ≤5.5 log₁₀ CFU/ml at 48 h, is indicated for each simulated dosage regimen. All imipenem infusions were given over 1 h (except for the continuous infusion). Tobramycin was infused over 0.5 h.

The intermittent-dosage regimens of imipenem (1 g every 8 h [q8h] and q6h as 1-h infusions) combined with 7 mg/kg tobramycin were predicted to lead to bacteriological failure with extensive regrowth of resistant bacteria at 48 h; only 7.0% to 11.2% of the simulated patients were predicted to succeed (see Fig. 5C). For a continuous infusion of imipenem at 4 g/day (with a 1-g loading dose) combined with 7 mg/kg tobramycin, the predicted probability of success was 80.9%. Excitingly, the combination of a continuous infusion of imipenem at 5 g/day (with a 1-g loading dose) plus 7 mg/kg tobramycin (0.5-h infusion) was predicted to achieve ≥2.0-log₁₀ bacterial killing without regrowth in 90.3% of the patients at 48 h and ≥3.5-log₁₀ bacterial killing in 75% of patients (see Fig. 5C). The 50th percentile for 10,000 hypothetical patients was predicted to achieve ≥2-log₁₀ killing over 7 days without regrowth for the regimen with 5 g/day imipenem plus tobramycin (data not shown).

DISCUSSION

This study presents the first systematic evaluation of synergy for carbapenem-plus-aminoglycoside combinations against carbapenem- and aminoglycoside-resistant clinical P. aeruginosa isolates using in vitro time-kill studies. Monte Carlo simulations based on the latest MBM were utilized to rationally optimize combination dosage regimens against a double-resistant isolate. Even at the highest clinically achievable unbound concentration, monotherapy with either imipenem or an aminoglycoside yielded limited bacterial killing, followed by rapid bacterial regrowth and emergence of resistance in a difficult-to-treat high bacterial inoculum.

Imipenem combined with either tobramycin or amikacin demonstrated substantially enhanced bacterial killing and suppression of resistance at clinically relevant concentrations. Against the double-resistant isolate FADDI-PA088, synergistic bacterial killing at 24 h occurred with aminoglycoside concentrations as low as 1/32 of the MIC (i.e., 1 mg/liter tobramycin with a tobramycin MIC [MIC_TOB] of 32 mg/liter) (Table 2 and Fig. 2). Resistance suppression at 48 h was achieved at 1/32 of the MIC for tobramycin and 1/8 of the MIC for amikacin (i.e., 0.5 mg/liter amikacin with an amikacin MIC [MIC_AMK] of 4 mg/liter) (Fig. 3). Our MBM indicated that the aminoglycoside enhanced the target site concentration of imipenem (Fig. 4). For our three isolates, we estimated that an aminoglycoside concentration (IC_50,OM,AGS) of 1.13 or 1.54 mg/liter half-maximally permeabilized the outer membrane of isolates with an aminoglycoside MIC of 4 mg/liter; ∼4.29 to 5.55 mg/liter aminoglycoside was needed for this synergistic effect in isolates with an aminoglycoside MIC of 8 or 32 mg/liter (Table 3). In agreement with our results, Loh et al. (18) found a correlation between the aminoglycoside MIC and the affinity of various aminoglycosides for binding to the outer membrane of P. aeruginosa; strain-to-strain variability in the outer membrane affinity was considerable. To our knowledge, this is the first mechanism-based time course model that quantified the aminoglycoside concentration required to enhance outer membrane permeability of P. aeruginosa (19). Overall, these MBM results demonstrated that clinically achievable aminoglycoside concentrations can achieve synergistic killing and prevent resistance in combination with imipenem against carbapenem-resistant and double-resistant P. aeruginosa isolates.

While monotherapies failed with limited bacterial killing followed by extensive regrowth, combinations containing ≥0.88× MIC of imipenem were much more likely to prevent resistance over 48 h than were combinations with lower imipenem concentrations (Table 2 and Fig. 2 and 3). The extent of synergy (measured as viable counts that were ≥2 log₁₀ CFU/ml lower than those of the most active monotherapy) tended to be greater at 24 and 48 h than at 6 h (Table 2). For combinations in the lower range of clinically relevant concentrations, resistance emergence after 24 h was most likely due to the amplification of preexisting resistant mutants, as we found in our clinical isolates (Fig. 3; see also Fig. S2 in the supplemental material).

Our findings substantially extend the results from previous studies on β-lactams in combination with aminoglycosides against P. aeruginosa. In the past, studies that used checkerboard methods showed that carbapenem-plus-aminoglycoside combinations were synergistic against P. aeruginosa; however, limited or no information on suppression of resistance and the type of synergy was provided (20–26). A few SCTK combination studies demonstrated that combinations (a β-lactam plus an aminoglycoside) are beneficial (14, 27, 28) but also reported extensive regrowth at 24 h (28). Synergistic bacterial killing, suppression of resistance, or both were found for the combination of meropenem plus an aminoglycoside in the hollow-fiber infection model and in murine pneumonia and septicemia models (8, 15, 29). Louie et al. evaluated the combination of meropenem plus tobramycin in a murine pneumonia model against a double-susceptible (meropenem MIC of 0.5 to 1 mg/liter and tobramycin MIC of 1 mg/liter) P. aeruginosa isolate (8). None of these studies evaluated or optimized dosage regimens against P. aeruginosa isolates that were resistant to carbapenems, aminoglycosides, or both. Furthermore, the mechanism of synergy has not been characterized based on a mathematical PK/pharmacodynamic (PD) model that incorporates bacterial killing, regrowth, and resistance.

Our MBM for the time course of synergistic bacterial killing and prevention of resistance had the same model structure and yielded consistent parameter estimates across three clinical P. aeruginosa isolates (Fig. 1 and Table 3). Mechanistic synergy (19, 30) was successfully incorporated with the aminoglycoside disrupting the outer membrane, thereby enhancing penetration and the concentrations of imipenem at its target site. This was expressed as a considerable decrease in the KC_50,IPM against the relevant bacterial populations of all three isolates (Fig. 4). This mechanism of synergy is in close agreement with data from studies that showed outer membrane disruption of P. aeruginosa by albumin-conjugated aminoglycosides (31, 32). The outer membrane of P. aeruginosa presents a major penetration barrier (33, 34), and its disruption is likely to enhance the target site penetration of imipenem (19, 35).

We performed Monte Carlo simulations against a high inoculum of a double-resistant clinical isolate of P. aeruginosa, FADDI-PA088, which represented the 98th percentile of the MIC distribution of both antibiotics according to the EUCAST database. The targeted critically ill patients were assumed to lack any effect of the immune system and to have normal renal function and bacteremia. The predicted between-patient variability of the unbound plasma concentrations in critically ill patients was large (Fig. 5) due to the large variability in clearance (34% coefficient of variation [CV] for imipenem and 31% CV for tobramycin) and in the volume of distribution of the central compartment for imipenem (81% CV) (36, 37). All monotherapies failed to prevent regrowth over 48 h (Fig. 5B).

The rationally optimized combination of imipenem at 5 g/day as a continuous infusion (with a 1-g loading dose) plus tobramycin at 7 mg/kg every 24 h was predicted to achieve ≥2-log₁₀ killing at 24 h and 48 h without regrowth in 90.3% of patients (i.e., regrowth in only 9.7% of patients) (Fig. 5C). The success rate for a continuous infusion of 4 g/day imipenem (with a 1-g loading dose) plus 7 mg/kg tobramycin every 24 h was 80.9%. These simulations were performed with a high inoculum of 10^7.5 CFU/ml of an extremely difficult-to-treat (double-resistant) isolate, and most of the regimens provided a benefit over 24 to 48 h. While our Monte Carlo simulations for bacteremia used a relatively high initial inoculum, which harbored preexisting resistant mutants, the predicted success rates are conservative and would have been higher for lower initial inocula.

These simulations represent a near-worst-case scenario with a highly tobramycin-resistant isolate (MIC of 32 mg/liter). Against FADDI-PA088, the combination of amikacin plus imipenem is expected to be more efficacious than that of tobramycin plus imipenem (Fig. 2A2), since this isolate had an amikacin MIC of 4 mg/liter and a tobramycin MIC of 32 mg/liter. The selected target endpoint for successful therapy (≥2 log₁₀ units at 24 h and 48 h) was based on data from a study by Drusano et al. (38). This study suggested that achieving a target of ≥2-log₁₀ bacterial killing at 24 h allows the granulocytes to contribute a few additional log₁₀ CFU/ml of bacterial killing in an immunocompetent murine pneumonia model and minimizes the emergence of resistance.

Studies by Kumar et al. (39, 40) found that rapid and early antibiotic treatment significantly increases survival in an immunocompetent murine infection model of septic shock. These studies and our simulations suggest that a continuous infusion of imipenem at 5 g/day (with a loading dose) plus tobramycin at 7 mg/kg every 24 h may provide a beneficial effect in reducing the bacterial burden to an extent where the immune system in immunocompetent patients can achieve bacterial clearance. Therefore, prospective validation of this optimized combination dosage regimen in dynamic infection models is warranted.

Our results demonstrate the importance of evaluating the robustness of combination dosage regimens for effective early therapy via Monte Carlo simulations in the presence of the high between-patient variability in PK that is typically observed in critically ill patients (41–43). Our most robust regimen, which contained imipenem at 5 g/day as a continuous infusion, was promising with regard to success rate of therapy; however, this dose may slightly increase the risk of seizures compared to that with 2 to 4 g imipenem per day (44, 45). Following imipenem treatment, nausea and vomiting were observed in one patient (out of 45 patients in the study); these symptoms were considered to be probably due to rapid infusion, as they disappeared after the duration of infusion was increased (46). Several studies demonstrated that therapeutic drug monitoring (TDM) may be a valuable strategy to optimize antibiotic exposure and minimize toxicity in critically ill patients (42, 47, 48). This approach may help to attain effective imipenem concentrations using 2 or 4 g imipenem per day.

In summary, clinically relevant concentrations of imipenem plus an aminoglycoside provided synergistic bacterial killing and suppression of resistance against a high inoculum of clinical isolates resistant to a carbapenem or to both a carbapenem and an aminoglycoside. Approximately 1.34 mg/liter aminoglycoside was sufficient to enhance the imipenem target site concentration half-maximally if the aminoglycoside MIC was 4 mg/liter; ∼4.88 mg/liter aminoglycoside was required if the aminoglycoside MIC was 8 or 32 mg/liter. Mechanism-based modeling suggested that disruption of the outer membrane by an aminoglycoside contributed to the synergy of combinations of imipenem plus an aminoglycoside. Against a double-resistant isolate of P. aeruginosa, Monte Carlo simulations predicted a 90.3% success rate in achieving ≥2-log₁₀ killing at 24 h and 48 h for a clinically relevant imipenem-plus-tobramycin combination dosage regimen. Thus, future evaluation of this promising combination dosage regimen in dynamic infection models is warranted to provide guidance on effective early therapy against infections caused by extremely difficult-to-treat double-resistant P. aeruginosa isolates.

MATERIALS AND METHODS

Bacterial isolates and susceptibility testing.

We studied three carbapenem-resistant P. aeruginosa isolates (FADDI-PA088, FADDI-PA022, and FADDI-PA001) from the collection at Monash University (Table 1). These isolates were resistant to tobramycin, amikacin, or both aminoglycosides. All susceptibility testing and SCTK experiments were performed with cation-adjusted Mueller-Hinton II broth (CAMHB; BBL, BD, Sparks, MD). Counting of viable bacteria was conducted on cation-adjusted Mueller-Hinton II agar (CAMHA; Medium Preparation Unit, The University of Melbourne). Stock solutions of imipenem (Merck Sharp & Dohme Pty., NSW, Australia), tobramycin (AK Scientific, Inc., Union City, CA), and amikacin (Sigma-Aldrich, St. Louis, MO) were prepared in sterile, distilled water and filter sterilized with a Millex-GV 0.22-μm polyvinylidene difluoride (PVDF) syringe filter (Merck Millipore Ltd., Cork, Ireland). The MICs were determined in triplicate according to Clinical and Laboratory Standards Institute guidelines (49). EUCAST breakpoints were used to define resistance to carbapenem and the aminoglycosides (50).

Static-concentration time-kill experiments.

Clinically relevant imipenem concentrations ranging from 8 to 36 mg/liter were studied as monotherapies and in combination with an aminoglycoside. The evaluated aminoglycosides were tobramycin (1 to 32 mg/liter) and amikacin (0.5 to 64 mg/liter). The selected antibiotic concentrations included the highest clinically achievable average unbound plasma concentrations at steady state (19, 36, 51). Higher and lower antibiotic concentrations were included to explore the range of synergistic concentrations and to consider the MICs for the isolates.

As previously described (30, 52, 53), the SCTK experiments were performed with a clinically relevant high initial inoculum (10^7.5 CFU/ml) to mirror more severe infections (54–59). Serial broth samples were taken within 5 to 10 min before dosing (i.e., at 0 h) and at 1, 3, 6, 24, 29, and 48 h. At 24 h, bacterial suspensions were centrifuged, the supernatant was carefully removed, and bacteria were resuspended in fresh, prewarmed broth with the targeted antibiotic concentration(s). Informed by our imipenem stability data using CAMHB at 35°C, an imipenem amount corresponding to 50% of the original dose was supplemented at 6 and 30 h to further offset the thermal degradation of imipenem, as previously described (19, 60). All bacterial samples were washed twice in sterile saline. Viable counts were determined by manual plating of 100 μl of an undiluted or an appropriately diluted suspension in saline onto CAMHA plates (19, 30, 52, 53). Serial dilution (1:10) was performed via the addition of 100 μl of an undiluted bacterial suspension to 900 μl of sterile saline. Aliquots of the undiluted or diluted sample were plated onto agar plates supplemented with imipenem, tobramycin, or amikacin at 3× MIC to quantify the resistant subpopulations.

Mechanism-based modeling of combinations of imipenem and an aminoglycoside.

An MBM was developed to describe and predict the time course of bacterial growth, killing, and resistance; to characterize the synergy for the studied carbapenem-plus-aminoglycoside combinations (19, 61–63); and to enable mechanism-based Monte Carlo simulations based on previously reported population PK models (36, 37).

Life cycle growth model.

The developed PD model contained a life cycle growth model that describes bacterial replication via two states (61, 64, 65): bacterial cells that are growing and preparing for replication are in state 1, and bacteria immediately before replication reside in state 2. The first-order growth rate constant (k₁₂) determines the mean generation time (MGT). Bacterial replication was assumed to be rapid, with the replication rate constant k₂₁ being fixed at 50 h⁻¹ (64).

Model for combinations of imipenem and an aminoglycoside.

The model for the combinations of imipenem and an aminoglycoside includes three preexisting bacterial populations: population 1 was susceptible to both antibiotics (CFU_SS), population 2 was imipenem resistant and aminoglycoside intermediate (CFU_RI), and population 3 was imipenem intermediate and aminoglycoside resistant (CFU_IR) (Fig. 1). Each population was described by the two states (i.e., compartments) of the life cycle growth model. Thus, the composite model contained six bacterial compartments. The total concentration of all viable bacteria (CFU_all) was

$${\text{CFU}}_{\text{all}}={\text{CFU}}_{\text{SS}1}+{\text{CFU}}_{\text{SS}2}+{\text{CFU}}_{\text{RI}1}+{\text{CFU}}_{\text{RI}2}+{\text{CFU}}_{\text{IR}1}+{\text{CFU}}_{\text{IR}2}$$ (1)

CFU_NNx denotes the concentration of viable bacteria of population NN in state x. At high bacterial densities, high concentrations of hypothetical signal molecules (C_sig) were assumed to inhibit the bacterial growth rate via the inhibition term Inh_k12, as defined below and described previously (61):

$${\text{Inh}}_{\text{k}12}=\left(\frac{I_{\max ,\text{sig}12}\cdot C_{\text{sig}}}{C_{\text{sig}}+{\text{IC}}_{50,\text{sig}}}\right)$$ (2)

I_max,sig12 is the maximum extent of inhibition of the rate of replication at high C_sig, and IC_50,sig is the signal molecule concentration associated with 50% I_max,sig12.

In most cases, the rates of bacterial killing by high concentrations of imipenem or the aminoglycoside or by their synergistic combinations were higher than the bacterial growth rate. Thus, we applied a direct-killing process with a Hill function to describe killing by each antibiotic. The time course of bacterial killing and, where applicable, regrowth (if it occurred) during treatment with imipenem, tobramycin, amikacin, or combinations thereof was fitted simultaneously for all three isolates. The differential equation for the concentration of bacteria belonging to population 1 (IPM^S/AGS^S) in state 1 (CFU_SS1) comprised killing by imipenem (concentration of IPM [C_IPM]) and an aminoglycoside (concentration of the aminoglycoside [C_AGS]) (initial conditions are described below):

$$\frac{d({\text{CFU}}_{\text{SS}1})}{dt}=2\cdot \text{PLAT}\cdot k_{21}\cdot {\text{CFU}}_{\text{SS}2}-k_{12\text{S}}\cdot (1-{\text{Inh}}_{\text{k}12})\cdot {\text{CFU}}_{\text{SS}1}-(\frac{K_{\text{max},\text{IPM}}\cdot {C_{\text{IPM}}}^{{\text{Hill}}_{\text{IPM}}}}{{C_{\text{IPM}}}^{{\text{Hill}}_{\text{IPM}}}+{(\text{OM}\_\text{effect}\cdot {\text{KC}}_{50,\text{SS},\text{IPM}})}^{{\text{Hill}}_{\text{IPM}}}}+\frac{K_{\text{max},\text{SS},\text{AGS}}\cdot {C_{\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}}{{C_{\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}+{{\text{KC}}_{50,\text{SS},\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}})\cdot {\text{CFU}}_{\text{SS}1}$$ (3)

The plateau factor (PLAT) is defined as 1 − [CFU_all/(CFU_all + CFU_max)], with CFU_max being the maximum population size. The factor 2 represents the doubling of bacteria during replication (61). The maximum killing rate constant for imipenem (K_max,IPM), the imipenem concentration causing 50% K_max for the double-susceptible population (KC_50,SS,IPM), and the Hill coefficient for IPM (Hill_IPM) affected both states 1 and 2 of the population. The maximum killing rate constant for the aminoglycoside was denoted K_max,SS,AGS, and the aminoglycoside concentration causing 50% K_max was denoted KC_50,SS,AGS. The ability of the aminoglycosides to permeabilize the outer membrane (OM_effect) (i.e., the synergy term) is described in equation 5 below. The differential equation for state 2 of population 1 (CFU_SS2) was

$$\frac{d({\text{CFU}}_{\text{SS}2})}{dt}=-k_{21}\cdot {\text{CFU}}_{\text{SS}2}+k_{12\text{S}}\cdot (1-{\text{Inh}}_{\text{k}12})\cdot {\text{CFU}}_{\text{SS}1}-(\frac{K_{\text{max},\text{IPM}}\cdot {C_{\text{IPM}}}^{{\text{Hill}}_{\text{IPM}}}}{{C_{\text{IPM}}}^{{\text{Hill}}_{\text{IPM}}}+{(\text{OM}\_\text{effect}\cdot {\text{KC}}_{50,\text{SS},\text{IPM}})}^{{\text{Hill}}_{\text{IPM}}}}+\frac{K_{\text{max},\text{SS},\text{AGS}}\cdot {C_{\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}}{{C_{\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}+{{\text{KC}}_{50,\text{SS},\text{AGS}}}^{{\text{Hill}}_{\text{AGS}}}})\cdot {\text{CFU}}_{\text{SS}2}$$ (4)

The differential equations for population 2 (i.e., CFU_RI) and population 3 (i.e., CFU_IR) used the same structure as the one for double-susceptible population 1 but different parameters for KC_50,IPM, k₁₂, K_max,AGS, and KC_50,AGS, as described previously (19, 30).

Mechanism-based modeling of synergy.

The presence of mechanistic synergy (i.e., antibiotic A enhancing killing by antibiotic B of one or multiple bacterial populations) was evaluated previously (30). Mechanistic synergy was incorporated by assuming that disruption and, thus, permeabilization of the bacterial outer membrane by aminoglycosides (31, 32, 35) enhance the target site penetration of imipenem. This effect was implemented in the model via the term OM_effect by the aminoglycoside decreasing the KC_50,IPM in a concentration-dependent manner. The effect of aminoglycosides on the outer membrane was described as follows (parameters are described in Table 3):

$$\text{OM}\_\text{effect}=1-\left(\frac{I_{\text{max},\text{OM},\text{AGS}}\cdot C_{\text{AGS}}}{C_{\text{AGS}}+{\text{IC}}_{50,\text{OM},\text{AGS}}}\right)$$ (5)

Initial conditions.

The total inoculum (log CFU₀) and the log₁₀ mutation frequencies for population 2 (RI) and population 3 (IR) were estimated (Fig. 1). Initial conditions were implemented as described previously (19, 61).

Observation model.

An additive residual-error model on a log₁₀ scale was used to fit the log₁₀ viable counts. For observations of viable counts below 100 CFU/ml (equivalent to <10 colonies per plate), a previously developed residual-error model was utilized to fit the number of colonies per plate (52). Observed viable counts below the limit of counting (i.e., 1 log₁₀ CFU/ml, equivalent to 1 colony per agar plate) were plotted as zero.

Estimation.

The importance sampling algorithm (S-ADAPT setting, pmethod = 4) was used for the simultaneous estimation of all PD parameters in the parallelized S-ADAPT software (version 1.57) (66) facilitated by the SADAPT-TRAN tool (67, 68). The between-curve variability of the PD parameters was fixed to a final, small coefficient of variation (52). Competing models were evaluated by the objective function (−1 × log likelihood in S-ADAPT), the biological plausibility of the parameter estimates, standard diagnostic plots, and visual predictive checks, as described previously (69–72).

Monte Carlo simulations.

For each dosage regimen, we performed Monte Carlo simulations for 10,000 adult critically ill patients with normal renal function. We combined the final MBM with previously reported human population PK models for imipenem (37) and tobramycin (36) in critically ill patients using Berkeley Madonna software (version 8.3.18). Tobramycin and imipenem population PK models, parameter estimates, and between-subject variability were implemented as reported previously (19).

The simulated patients were assumed to have bacteremia caused by a multidrug-resistant (MDR) P. aeruginosa isolate (FADDI-PA088) and lacked any aspect of the immune system. This isolate had an imipenem MIC of 16 mg/liter and a tobramycin MIC of 32 mg/liter, which reflect the 98th percentiles of the EUCAST MIC distributions of both antibiotics for P. aeruginosa (last accessed 22 April 2016) (50).

Unbound plasma concentrations were simulated by assuming unbound fractions of 0.91 for imipenem and 1.0 for tobramycin (36, 37). Viable-count profiles were predicted for imipenem and tobramycin in monotherapy and in combination by using the combined MBM. The dosage regimens simulated included 1 g imipenem given every 6 or 8 h as a 1-h infusion and 4 or 5 g imipenem given as a continuous infusion with a 1-g loading dose (dosed as a 1-h infusion). The simulated tobramycin regimen was 7 mg/kg given as a 0.5-h infusion every 24 h. A successful therapeutic outcome was defined as ≥2-log₁₀ bacterial killing compared to the initial inoculum, i.e., viable counts of the total population of 10^5.5 CFU/ml or lower, at both 24 and 48 h (38–40, 73). We chose the 48-h time point for our double-resistant isolates and assumed that the immune system (38, 73) can clear the bacteria remaining at 48 h, if antibiotic combination therapy achieves at least 2-log₁₀ killing without regrowth over 48 h. The success rate was calculated as the fraction of all simulated patients who were predicted to achieve this target.