D Sevillano

L Aguilar

L Alou

M J Giménez

N González

M Torrico

F Cafini

C Garcia-Rey

N Garcia-Escribano

J Prieto

Exposure-response analysis of tigecycline in pharmacodynamic simulations using

Keywords:

come

One meticillin-resistant vancomycin-heteroresistant Staphylococcus aureus, one Enterococcus faecium and one extended-spectrum -lactamase-producing Escherichia coli with equal tigecycline minimum inhibitory concentrations/minimum bactericidal concentrations (MICs/MBCs) (0.12/0.25 g/mL) were used. A computerised pharmacodynamic bicompartmental model simulated three tigecycline twice-daily dosing regimens over 48 h: 50 mg (100 mg loading dose); 100 mg; and 150 mg. Areas under bacterial growth curves were calculated, and differences between the growth curve used as control and the killing curve of bacteria exposed to tigecycline (ABBC) were determined.

With standard inocula [ca. 1  10 6 colony-forming units (CFU)/mL], linear increases in area under the concentration-time curve (AUC)/MIC (25.6 for 50 mg, 53.76 for 100 mg and 79.52 for 150 mg) produced linear increases in activity against Gram-positive organisms (mean ABBCs of 120.60, 143. 20 and 195.80 log CFU  h/mL for S. aureus and of 95.75, 172.55 and 216.90 log CFU  h/mL for E. faecium, respectively), with the activity of the 150 mg regimen being significantly higher (P < 0.01) than that of the other two regimens. ABBCs obtained with the 100 mg regimen using standard inocula were similar to those obtained with the 150 mg regimen when using high inocula (ca. 1  10 7 CFU/mL). Against E. coli, the highest dosing regimen was required to obtain significant antibacterial activity compared with control (mean ABBCs of 145.75 log CFU  h/mL with standard inocula and 63.33 log CFU  h/mL with high inocula). An increase in tigecycline dosing appears to be an interesting A c c e p t e d M a n u s c r i p t

Introduction

The emergence of metallo--lactamases (MBLs) and the increasing spread of extended-spectrum -lactamases (ESBLs) [START_REF] Ku | In vitro activity of tigecycline against clinical isolates of extended-spectrum -lactamase-producing Klebsiella pneumoniae, Serratia marcescens and Enterobacter cloacae[END_REF][START_REF] Woodford | Arrival of Klebsiella pneumoniae producing KPC carbapenemase in the United Kingdom[END_REF] among enterobacteria, together with vancomycin heteroresistance/tolerance linked to meticillin resistance in Staphylococcus aureus [START_REF] Jones | Microbiological features of vancomycin in the 21st century: minimum inhibitory concentration creep, bactericidal/static activity, and applied breakpoints to predict clinical outcomes or detect resistant strains[END_REF][START_REF] Tenover | The rationale for revising the Clinical and Laboratory Standards Institute vancomycin minimal inhibitory concentration interpretive criteria for Staphylococcus aureus[END_REF] and vancomycin resistance in enterococci [START_REF] Lentino | New antimicrobial agents as therapy for resistant Gram-positive cocci[END_REF][START_REF] Saribas | Vancomycin tolerance in enterococci[END_REF], implies the need for new antibiotics against different bacterial targets in a field where the available antibiotic armamentarium is rapidly deteriorating due to these resistance traits. Tigecycline is the first antibiotic of the glycylcycline class with a novel mechanism of action, preventing cross-resistance with antibiotics currently used against nosocomial Gram-positive organisms and ESBL-, AmpC-, carbapenemases or MBL-producing Gram-negative organisms [START_REF] Sorlózano | Activity of tigecycline against clinical isolates of Staphylococcus aureus and extended-spectrum -lactamase-producing Escherichia coli in Granada, Spain[END_REF], not exhibiting an inoculum effect against Enterobacteriaceae such as Klebsiella pneumoniae producing ESBLs and/or AmpC enzymes [START_REF] Conejo | Comparative activity of tigecycline, cefepime and imipenem against clinical isolates of Klebsiella pneumoniae producing extended spectrum -lactamases, plasmid-mediated AmpC-type -lactamases or both, associated or not with porin deficiency[END_REF]. Tigecycline is currently approved by the US Food and Drug Administration (FDA) for the treatment of complicated skin and skin-structure infections (SSSIs), complicated intra-abdominal infections (IAIs) and community-acquired bacterial infections.

Multidrug-resistant (MDR) Gram-positive pathogens such as meticillin-resistant S. aureus (MRSA) and vancomycin-resistant enterococci (VRE) are an increasing cause of nosocomial infections such as SSSIs (where high bacterial density is present) and bacteraemia [START_REF] Florescu | Efficacy and safety of tigecycline compared with vancomycin or linezolid for treatment of serious infections with methicillin-resistant Staphylococcus aureus or vancomycin-resistant enterococci: a Phase 3, multicentre, doubleblind, randomized study[END_REF]. Enterococci and Escherichia coli are the main facultative bacteria associated with secondary peritonitis (also with a high bacterial load) and secondary bacteraemia in severely ill patients [START_REF] Moellering | Enterococcus species, Streptococcus bovis, and Leuconostoc species[END_REF].

A c c e p t e d M a n u s c r i p t

The effectiveness of tigecycline in the treatment of severe infections by MDR bacteria (with borderline susceptibility) involving the bloodstream has not been clearly substantiated, and pharmacodynamic information may aid in further understanding the role of tigecycline [START_REF] Falagas | Clinical significance of the pharmacokinetic and pharmacodynamic characteristics of tigecycline[END_REF]. This study aimed to explore tigecycline exposure-bacterial responses (using different initial inocula sizes) in dose-ranging in vitro pharmacodynamic simulations, since owing to its linear pharmacokinetics, concentration-dependent effect and bacteriostatic effects, maximising the effect by increasing the dose appears as an appealing therapeutic option [START_REF] Falagas | Clinical significance of the pharmacokinetic and pharmacodynamic characteristics of tigecycline[END_REF].

Material and methods

Strains

Three clinical isolates chosen based on the same tigecycline minimum inhibitory concentrations/minimum bactericidal concentrations (MICs/MBCs) were used throughout the study: one MRSA showing heteroresistance to vancomycin determined as previously described [START_REF] Walsh | Evaluation of current methods for detection of staphylococci with reduced susceptibility to glycopeptides[END_REF] with two size inocula (see below), MICs were also determined using inocula of 10 7 colony-forming units (CFU)/mL.

In vitro kinetic model (Fig. 1)

A two-compartment dynamic model exposing bacteria to changing study drug concentrations and avoiding dilution of the bacterial inoculum together with the drug was used [START_REF] González | Influence of different resistance traits on the competitive growth of Haemophilus influenzae in antibiotic-free medium and selection of resistant populations by different -lactams: an in vitro pharmacodynamic approach[END_REF]. The central compartment consisted of a spinner flask, the lumina of the capillaries within the dialyser (FX50 class; Fresenius Medical Care S.A., Barcelona, Spain) and the tubing in between. The peripheral compartment (infection site) was represented by the extracapillary space of the dialyser unit combined with the intradialyser circulating tubing. The high surface-area-tovolume ratio of the dialysis unit (>200 cm 2 /mL) yields rapid equilibration of the concentration of the antimicrobial agent between the two compartments.

Before each experiment, the central compartment was filled with MHB. Decay of tigecycline concentrations in the central compartment was achieved by a continuous dilution-elimination process using computerised peristaltic pumps (Masterflex; Cole-Parmer Instrument Co. Ltd., Chicago, IL). Flow rates set in the peristaltic pumps were controlled using Win Lin software v.2 (Masterflex; Cole-Parmer Instrument Co. Ltd. ). In control drug-free simulations, the rate of peristaltic pumps was fixed to 0.12 mL/min. Additional pumps circulated the antimicrobial medium mixture at 50 mL/min between the central and peripheral compartments and at 20 mL/min within the extracapillary space through the external tubing. A computer-controlled syringe pump (402 Dilutor Dispenser; Gilson S.A, Villiers-le-Bel, France) allowed the simulation of 1-h infusion of A c c e p t e d M a n u s c r i p t tigecycline into the central compartment until a concentration similar to the target maximum concentration achieved in serum (C max ) was reached. Both compartments were maintained at 37 C over the entire simulation process. Target total concentrations were obtained by approximation of the biexponential decay of concentration-time curves of tigecycline to a sequence of 'pseudomonoexponential' profiles with different apparent elimination rate constants (Ke). Each segment in each time period was fitted using the expression:

Kinetic simulations

C t = A(exp -.t -exp -tstart ) + B(exp -.t -exp -tstart ) A = D/ti(V c ) . (K 21- )/(-). B = -D/ti(V c ) . (K 21- )/(-). K 21 = CL p /V p
C t = C o . exp -Ket
where C o is the residual concentration of previous periods.

Finally, the flow of the in vitro system was calculated using Ke according to the expression F = Ke . V d , where F is the flow and V d is the volume of distribution (450 mL). Table 1 summarises the process-dependent pharmacokinetic parameters introduced in the computerised pharmacodynamic device.

Pharmacokinetic analysis

For measurement of simulated antimicrobial concentrations, aliquots (0.5 mL) were taken from the peripheral compartment at 0, [START_REF] Ku | In vitro activity of tigecycline against clinical isolates of extended-spectrum -lactamase-producing Klebsiella pneumoniae, Serratia marcescens and Enterobacter cloacae[END_REF][START_REF] Woodford | Arrival of Klebsiella pneumoniae producing KPC carbapenemase in the United Kingdom[END_REF][START_REF] Tenover | The rationale for revising the Clinical and Laboratory Standards Institute vancomycin minimal inhibitory concentration interpretive criteria for Staphylococcus aureus[END_REF][START_REF] Saribas | Vancomycin tolerance in enterococci[END_REF][START_REF] Conejo | Comparative activity of tigecycline, cefepime and imipenem against clinical isolates of Klebsiella pneumoniae producing extended spectrum -lactamases, plasmid-mediated AmpC-type -lactamases or both, associated or not with porin deficiency[END_REF][START_REF] Moellering | Enterococcus species, Streptococcus bovis, and Leuconostoc species[END_REF][START_REF] Walsh | Evaluation of current methods for detection of staphylococci with reduced susceptibility to glycopeptides[END_REF]13,[START_REF] Rangel-Frausto | The natural history of the systemic inflammatory response syndrome (SIRS). A prospective study[END_REF][START_REF] Brun-Buisson | Incidence, risk factors, and outcome of severe sepsis and septic shock in adults. A multicenter prospective study in intensive care units. French ICU Group for Severe Sepsis[END_REF][START_REF] Doan | Tigecycline: a glycylcycline antimicrobial agent[END_REF][START_REF] Kresken | Susceptibility of clinical isolates of frequently encountered bacterial species to tigecycline one year after the introduction of this new class of antibiotics: results of the second multicentre surveillance trial in Germany (G-TEST II, 2007)[END_REF][START_REF]TYGACIL ® prescribing information[END_REF][START_REF] Meagher | Pharmacokinetic/pharmacodynamic profile for tigecycline-a new glycylcycline antimicrobial agent[END_REF][START_REF] Meagher | Exposure-response analyses of tigecycline efficacy in patients with complicated skin and skin-structure infections[END_REF][START_REF] Passarell | Exposure-response analyses of tigecycline efficacy in patients with complicated intra-abdominal infections[END_REF][START_REF] Alou | In vitro effect of the presence of human albumin physiological concentrations on tigecycline antibacterial activity against Gram-positive and Gram-negative bacteria[END_REF] and 48 h in all simulations. All samples were stored at -50 C until use. Concentrations were determined by bioassay [START_REF] Andrews | Microbiological assays[END_REF] A c c e p t e d M a n u s c r i p t using Bacillus cereus ATCC 11778 as the indicator organism (linear concentrations from 0.03 g/mL to 2 g/mL; limit of quantitation 0.06 g/mL).

Standards were prepared in the same broth employed in the pharmacokinetic simulation and were added to wells in the plates with the indicator organism.

Plates were incubated for 18-24 h at 37 C. Interday and intraday coefficients of variations were 5.28% and 2.22%, respectively, for a tigecycline concentration of 0.75 g/mL. Pharmacokinetic analysis was performed by a non-compartmental approach (model 200) using WinNonlin Professional program version 5.2. C max and time to C max (T max ) were obtained directly from observed data. The area under the concentration-time curve from time 0 to 12 h (AUC) was calculated by the linear-log trapezoidal rule.

Measurement of antibacterial effect

Colonies from an overnight culture were allowed to grow in MHB to a density ranging from 1  10 8 to 2  10 8 CFU/mL as measured by an ultraviolet spectrophotometer (Hitachi U-1100; Hitachi, Tokyo, Japan). To obtain two different inocula sizes in simulations with the 100 mg and 150 mg tigecycline regimens, 6 mL of this bacterial suspension (for high inocula) or of a 1:10 dilution of the bacterial suspension (for standard inocula) were added into the peripheral compartment and incubated for 1 h to allow the microorganism to adapt to the medium. Samples (0.5 mL) were collected at 0, 2, 4, 6, 8, 10, 12, 24, 26, 28, 30, 32, 34, 36 and 48 h and were serially diluted in 0.9% sodium chloride. At least four dilutions of each sample (20 L) were spread onto

A c c e p t e d M a n u s c r i p t

Mueller-Hinton agar and overnight incubated for colony counting. The limit of detection was 50 CFU/mL. Each experiment was performed in triplicate.

Measurement of antibacterial activity and pharmacodynamic analysis

Percentage reductions in initial inocula were calculated: [(CFU/mL at time 0 -CFU/mL at each sampling time)  100]/CFU/mL at time 0. Antibacterial activity was also analysed as in previous studies [START_REF] González | Influence of different resistance traits on the competitive growth of Haemophilus influenzae in antibiotic-free medium and selection of resistant populations by different -lactams: an in vitro pharmacodynamic approach[END_REF][START_REF] Firsov | Predictors of effect of ampicillin-sulbactam against TEM-1 -lactamaseproducing Escherichia coli in an in vitro dynamic model: enzyme activity versus MIC[END_REF][START_REF] White | Comparative in vitro pharmacodynamics of imipenem and meropenem against Pseudomonas aeruginosa[END_REF] by determining the area under the bacterial count-time curve (AUBC) (log CFU  h/mL) as a measure of global killing along the experimental time (AUBC 0-48 ). AUBCs were calculated by the trapezoidal rule using the program GraphPad Prism 5.02 (GraphPad Software, San Diego, CA). Bacterial growth curves of the three strains in antibiotic-free simulations were used as controls. Differences between the growth curve used as control and the killing curve of bacteria exposed to tigecycline (ABBC) (log CFU  h/mL) were determined.

The percentage of the dosing interval that simulated antibiotic concentrations exceeded the MIC (T>MIC) was calculated by a non-compartmental approach for pharmacodynamic data using model 220 of WinNonlin program version 5.2. AUC 0-24 /MIC (Table 2) were calculated using AUC 0-24 calculated as follows: (a) for 100 mg and 150 mg tigecycline regimens, by the expression 2  AUC 0-12 , where AUC 0-12 is the AUC from 0 to 12 h (Day 1) or the AUC from 24 h to 36 h (Day 2); and (b) for the 50 mg tigecycline regimen (with a 100 mg loading dose), AUC 0-24 for Day 1 was calculated by adding the AUC 0-12 (after the 100 mg loading dose) and the AUC from 24 h to 36 h (after the 50 mg dose), and for Day 2 by the expression 2  AUC 0-12 (from 24 h to 36 h).

A c c e p t e d M a n u s c r i p t

Statistical analysis

Per-strain comparisons of ABBCs obtained with each of the three antibiotic regimens were performed by analysis of variance (ANOVA). Owing to multiple comparisons, a P-value of <0.01 was considered significant.

Results

MICs determined with the high inocula (10 7 CFU/mL) increased four-fold from 0.12 g/mL (determined with standard inocula) to 0.5 g/mL for the two Grampositive organisms (S. aureus and E. faecium) and two-fold to 0.25 g/mL for E. coli. Fig. 2 shows concentration profiles (population-based serum profile, target and experimentally obtained), with near identity between the three curves for all tigecycline regimens tested. Table 2 shows pharmacokinetic and pharmacodynamic parameters of the three tigecycline regimens. With the 100 mg and 150 mg regimens, the serum trough concentration (C min ) increased from Day 1 to Day 2 up to >0.12 g/mL (value of tigecycline MIC determined with standard inocula for the three strains tested), thus increasing T>MIC to 100%. This did not occur with the 50 mg regimen where, owing to the 100 mg loading dose, similar C min and AUC values were obtained on Days 1 and 2. In a similar way, AUC 0-24 /MIC values increased from Day 1 to Day 2 from 32.16 to 53.76 (67.16% increase) for the 100 mg regimen and from 50.56 to 79.52 (57.28%

A c c e p t e d M a n u s c r i p t increase) for the 150 mg regimen, with a slight decrease for the 50 mg regimen (from 27.76 to 25.60; 7.78% decrease). Fig. 3 shows bacterial counts (log CFU/mL) over time for the three target bacteria obtained with the three tigecycline regimens using both inocula. Mean initial inocula (CFU/mL) were 1.2  10 6 , 3.8 10 6 and 3.7 10 6 (standard inocula) and 8.5 10 6 , 2.5  10 7 and 2.8  10 7 (high inocula) for S. aureus, E.

faecium and E. coli, respectively. Initial inocula increased in control curves up to mean values (CFU/mL) of ≥1  10 8 at 12 h, ≥3.2 10 8 at 24 h and ≥1 10 9 at 48 h for both Gram-positives, and up to 6.3 10 7 at 12 h, 1.3 10 8 at 24 h and 8.7  10 7 at 48 h for the E. coli strain.

Against S. aureus in simulations with standard inocula, reductions in initial inocula >90% were obtained up to 12 h with the 50 mg regimen, up to 28 h with the 100 mg and up to 48 h with the 150 mg tigecycline regimen. A similar picture was obtained against E. faecium, but with reductions >99% from 12 h to 28 h with the 100 mg regimen and from 6 h to 36 h with the 150 mg regimen. In simulations carried out with high inocula, reductions >90% were obtained up to 26 h for S. aureus and up to 12 h for E. faecium with the 100 mg tigecycline twice-daily regimen. When increasing the dose to 150 mg, the killing period was extended up to 36 h for both Gram-positives.

Against E. coli, the activity provided by the 50 mg regimen was negligible, whilst with the 100 mg regimen reduction rates up to 70% (for short time periods) were obtained regardless of the inoculum size. With the 150 mg regimen, reductions A c c e p t e d M a n u s c r i p t >99% were obtained from 24 h on in simulations using standard inocula and >90% from 6 h to 34 h in simulations using high inocula. Fig. 4 shows the effect of increasing doses of tigecycline regimens on the area under the bactericidal count-time curve (AUBC 0-48 ). As shown in Fig. 4, for Gram-positives in simulations using standard inocula, AUBC 0-48 of controls (antibiotic-free) decreased ca. 35% with the 50 mg regimen, ca. 50% with the 100 mg regimen and ca. 65% with the 150 mg regimen. When high inocula were used, AUBC 0-48 of controls (antibiotic-free) decreased ca. 25% with the 100 mg regimen and ca. 50% with the 150 mg regimen. In the case of E. coli, a reduction of control AUBC 0-48 was only obtained with the 150 mg regimen (ca. 50% with standard inocula and ca. 22% with high inocula simulations).

Finally, when measuring antibacterial activity as the difference between the growth curve in antibiotic-free simulations (controls) and the curve for each bacteria exposed to antibiotic (i.e. ABBC) (Table 3), significantly (P < 0.01) greater activity (i.e. significantly higher ABBC) was obtained with the 150 mg regimen versus the 100 mg regimen (and also versus the 50 mg regimen) for the three study strains, regardless of the inocula size, whilst the ABBC of the 100 mg regimen was only significantly higher than that of the 50 mg regimen for E. faecium.

Discussion

Bacteraemia is usually of low-grade and transient, even in the absence of antimicrobial chemotherapy, provided that reseeding of blood does not occur A c c e p t e d M a n u s c r i p t [START_REF] Munford | Sepsis, severe sepsis, and septic shock[END_REF]. Secondary bacteraemia from an infected tissue (where a high bacterial load is present) is more likely to have a fatal outcome than bacteraemia from a vascular catheter [START_REF] Renaud | Outcomes of primary and catheter-related bacteremia. A cohort and case-control study in critically ill patients[END_REF]. In this sense, the risk of development of severe sepsis is ten times higher for IAIs than for urinary tract infections [START_REF] Brun-Buisson | Bacteremia and severe sepsis in adults: a multicenter prospective survey in ICUs and wards of 24 hospitals. French Bacteremia-Sepsis Study Group[END_REF], and blood cultures are more commonly positive in patients with severe sepsis (and even more with septic shock) than in those with sepsis [START_REF] Rangel-Frausto | The natural history of the systemic inflammatory response syndrome (SIRS). A prospective study[END_REF], with bacteraemia in this situation associated with mortality [START_REF] Brun-Buisson | Incidence, risk factors, and outcome of severe sepsis and septic shock in adults. A multicenter prospective study in intensive care units. French ICU Group for Severe Sepsis[END_REF]. In addition, bloodstream infections with certain microorganisms such as MRSA or VRE (bacteria commonly isolated from deep wounds or debrided tissue in diabetic patients and also from nosocomial IAIs in the case of VRE) have been often used as an imperfect surrogate outcome for severe sepsis/septic shock [START_REF] Munford | Sepsis, severe sepsis, and septic shock[END_REF].

The broad antimicrobial spectrum and the large volume of distribution of tigecycline are usually employed as the rationale for its clinical use [START_REF] Doan | Tigecycline: a glycylcycline antimicrobial agent[END_REF].

Tigecycline is currently approved for the treatment of complicated SSSIs, complicated IAIs and community-acquired bacterial infections; other possible indications under discussion, facing the multidrug resistance field, involve bloodstream primary and secondary infections [START_REF] Munford | Sepsis, severe sepsis, and septic shock[END_REF].

In this study, we explored the effect of different size inocula on the killing kinetic profile of the tigecycline standard dose (50 mg twice daily with a 100 mg loading dose) and whether this effect can be overcome by increasing the dose in the dosing regimen, an opportunity provided by the linear pharmacokinetics of tigecycline and the reported safety profile and tolerability with doses ranging from 12.5 mg to 300 mg [START_REF] Muralidharan | Pharmacokinetics of tigecycline after single and multiple doses in healthy subjects[END_REF]. For this purpose, three target bacteria as coli, E. faecium and S. aureus. MICs of tigecycline determined with standard inocula (0.125 g/mL for the three isolates) were similar to MIC 90 values (MIC for 90% of the organisms) for the three species in recently published surveillance studies [START_REF] Kresken | Susceptibility of clinical isolates of frequently encountered bacterial species to tigecycline one year after the introduction of this new class of antibiotics: results of the second multicentre surveillance trial in Germany (G-TEST II, 2007)[END_REF][START_REF] Nørskov-Lauritsen | Antimicrobial susceptibility of tigecycline and comparators against bacterial isolates collected as part of the TEST study in Europe (2004-2007)[END_REF]. According to FDA breakpoints (≤0.5 g/mL for S. aureus and ≤2 g/mL for E. coli) [START_REF]TYGACIL ® prescribing information[END_REF] or British Society for Antimicrobial Chemotherapy breakpoints (≤0.5 g/mL for S. aureus and ≤1 g/mL for E. coli) [START_REF]BSAC methods for antimicrobial susceptibility testing[END_REF], the S. aureus and E. coli isolates used in this study were susceptible to tigecycline (no breakpoints are available for E. faecium).

Previous in vitro and mouse models have suggested that tigecycline exhibits time-dependent action as well as a prolonged post-antibiotic effect [START_REF] Meagher | Pharmacokinetic/pharmacodynamic profile for tigecycline-a new glycylcycline antimicrobial agent[END_REF]. In the present pharmacodynamic model, the increase in tigecycline dose increased the T>MIC (considering the MIC determined with standard inocula) from 30% for the 50 mg regimen to 100% for the 100 mg and 150 mg regimens, but the 150 mg regimen exhibited significantly higher activity [when measured as AUBC (Fig. 4) or ABBC (Table 3)] than the 100 mg regimen. If T>MIC was calculated with MICs determined with high inocula (0.5 g/mL for Gram-positives), values of T>MIC were 12.5% and 22.5% for the 100 mg and 150 mg regimens, respectively, and despite these low values significant ABBCs were found (higher with the 150 mg regimen). Thus, in this in vitro model T>MIC appears not to be a good predictor of activity.

In a previous in vivo study, a relative reduction of bacterial E. coli density was found with subinhibitory concentrations (T>MIC = 0%) [START_REF] Nicasio | In vivo pharmacodynamic profile of tigecycline against phenotypically diverse Escherichia coli and Klebsiella pneumoniae[END_REF]. In the present in A c c e p t e d M a n u s c r i p t vitro study, the situation for E. coli was different since despite T>MIC values (30.4% and 63.9% for the 100 mg and 150 mg regimens, respectively) higher than those obtained for the Gram-positives (MIC of 0.25 g/mL for E. coli, high inocula), tigecycline activity against E. coli was significantly lower (lower ABBCs) and was negligible with the 100 mg regimen in comparison with the activity depicted against Gram-positives (Table 3). Again, it appears that T>MIC is not the best predictor for all target bacteria. This model simulates human pharmacokinetics of three increasing dose regimens based on the linear pharmacokinetics of tigecycline. This characteristic, together with its prolonged post-antibiotic effect, long half-life and high volume of distribution (implying that serum concentrations do not exactly predict concentrations at the infectious foci), are the basis to consider AUC/MIC as the most suitable pharmacodynamic parameter for prediction of microbiological and subsequent clinical efficacy with tigecycline [START_REF] Muralidharan | Pharmacokinetics of tigecycline after single and multiple doses in healthy subjects[END_REF][START_REF] Nicasio | In vivo pharmacodynamic profile of tigecycline against phenotypically diverse Escherichia coli and Klebsiella pneumoniae[END_REF]. In this sense, dose increases (from 50 mg to 150 mg) produced linear increases in AUC/MIC (MIC using standard inocula) at Day 2 (from 25.6 to 79.52) and subsequent linear increases in antibacterial activity (ABBCs) against Grampositives (mean values increasing from 120.60 to 195.80 log CFU  h/mL for S. aureus and from 97.75 to 216.90 log CFU  h/mL for E. faecium) (Table 3).

When using MIC determined with high inocula (0.5 g/mL for Gram-positives) for AUC/MIC calculation, the increase in AUC/MIC from 13.44 (100 mg regimen) to 19.88 (150 mg regimen) produced an increase in ABBCs from 67.92-91.05 log CFU  h/mL to ca. 155 log CFU  h/mL. These data are in accordance with previous clinical studies suggesting that AUC/MIC values of A c c e p t e d M a n u s c r i p t 17.9 predict efficacy against S. aureus producing complicated skin and softtissue infections [START_REF] Meagher | Exposure-response analyses of tigecycline efficacy in patients with complicated skin and skin-structure infections[END_REF] and support the proposed value of 0.25-0.5 g/mL as the clinical breakpoint for susceptibility for S. aureus, pharmacodynamically based on the AUC/MIC identified by Classification and regression tree (CART) analysis and subsequently used in Monte Carlo simulations [START_REF] Macgowan | Tigecycline pharmacokinetic/pharmacodynamic update[END_REF].

As a general finding, against Gram-positives the activity (ABBCs) provided by the 150 mg regimen in simulations using high inocula was similar to the activity observed with the 100 mg regimen when using standard inocula.

The situation was completely different for E. coli since, in the current study, the proposed value of 0.25-0.5 g/mL as the clinical breakpoint for susceptibility [START_REF] Macgowan | Tigecycline pharmacokinetic/pharmacodynamic update[END_REF] did not correlate with antibacterial activity (measured as AUBC or ABBC), which was only obtained when the tigecycline dose was increased to 150 mg. It has been suggested that AUC/MIC values of 6.96 are needed for bacteriological efficacy against E. coli in IAIs [START_REF] Passarell | Exposure-response analyses of tigecycline efficacy in patients with complicated intra-abdominal infections[END_REF], but in the present study higher values (obtained with the 100 mg regimen) did not correlate with pharmacodynamically significant ABBCs. Regardless of the inocula, significant ABBCs were only obtained when the tigecycline dose was increased to 150 mg. From the results obtained in this study testing only one E. coli strain, it appears that higher AUC/MIC values are needed for bacteriological efficacy against this target bacterium (in contrast to Gram-positives). However, it should be taken into account that in vitro pharmacodynamic simulations do not include factors such as immunity or surgical drainage that have a clear influence in the in vivo situation. In this sense, it has been postulated that while data generated in A c c e p t e d M a n u s c r i p t neutropenic animals define the pharmacodynamic parameter, the magnitude of the parameter relative to human pharmacodynamic targets is best defined in immunocompetent models [START_REF] Nicasio | In vivo pharmacodynamic profile of tigecycline against phenotypically diverse Escherichia coli and Klebsiella pneumoniae[END_REF].

One limitation of this study is that it does not take into account protein binding (80%) [START_REF] Van Wart | Population pharmacokinetics of tigecycline in healthy volunteers[END_REF] for tigecycline. The use of human albumin is technically and economically not feasible in two-compartmental systems that are more suitable than one-compartmental systems to simulate serum profiles (such as that of tigecycline) with a pronounced clearance in the first period, since twocompartmental systems prevent massive elimination of microorganisms during initial periods (with high clearance). However, protein binding was addressed in a recently published study by our group which showed that the presence of human albumin at physiological concentrations in broth did not significantly alter the antibacterial activity of tigecycline concentrations in killing curves against the same isolates [START_REF] Alou | In vitro effect of the presence of human albumin physiological concentrations on tigecycline antibacterial activity against Gram-positive and Gram-negative bacteria[END_REF].

Other limitations of this study are the limited 48 h duration of the experiments, the fact that only three selected strains were tested (one per species) and the simulation of serum concentrations. Study strains were selected (same tigecycline MIC and MBC values) in order to explore, on a species basis, the effect of the linear increase in tigecycline pharmacokinetic/pharmacodynamics. The MBC/MIC ratio of 2 for all species in this study correlates with MBC 90 and MIC 90 values reported in a previous A c c e p t e d M a n u s c r i p t surveillance study [START_REF] Zhang | In vitro activities of tigecycline against clinical isolates from Shanghai, China[END_REF] in the case of MRSA but not for E. coli since the MBC 90 /MIC 90 ratio in the abovementioned study was 8.

Simulation of tigecycline serum concentrations is a limitation of the study because serum concentrations of tigecycline do not exactly predict concentrations at the infectious foci owing to its high volume of distribution. AUC 0-24 values in bile, gallbladder, colon and lungs are 573-, 23-, 2.6-and 2times higher than the AUC 0-24 in serum [START_REF] Rodvold | Serum, tissue and body fluid concentrations of tigecycline after a single 100 mg dose[END_REF]. Therefore, pharmacodynamics based on serum concentrations may predict the bacterial load decrease over time in bacteraemia where inocula are expected to be lower than in tissue infections (or infectious foci) where a higher bacterial density is present but also higher tigecycline concentrations are achieved. None the less, the results of this study showed that the increase in the tigecycline dose in regimens to maximise effectiveness in severe infections appears an interesting therapeutic option owing to its linear pharmacokinetics and pharmacodynamics against Grampositives in the present study, especially when infections with high bacterial load are suspected.

A

  c c e p t e d M a n u s c r i p t E-mail address: laguilar@med.ucm.es (L. Aguilar). A c c e p t e d M a n u s c r i p t ABSTRACT This study explored tigecycline exposure-bacterial responses in pharmacodynamic simulations (in vitro kinetic model) using different inocula.

A

  c c e p t e d M a n u s c r i p t therapeutic option to maximise antibacterial activity owing to its linear pharmacokinetics and pharmacodynamics, especially when severe infections with high bacterial load are suspected.

  ; one Enterococcus faecium; and one ESBL-producing E. coli (inhibitor-resistant TEM-34: IRT-6) characterised by lactamase polymerase chain reaction (PCR) amplification and direct sequencing as described previously [13]. Modal tigecycline MIC/MBC values (five determinations) were 0.12/0.25 g/mL as determined by microdilution in Mueller-Hinton broth (Difco Laboratories, Detroit, MI) supplemented with calcium and magnesium (MHB) following Clinical and Laboratory Standards Institute recommendations [14,15]. In addition, since simulations were plannedA c c e p t e d M a n u s c r i p t

  Serum total concentrations corresponding to three regimens of tigecycline administered by 1-h infusion were simulated over 48 h: (a) 50 mg twice daily (with 100 mg loading dose); (b) 100 mg twice daily; and (c) 150 mg twice daily. Mean population pharmacokinetic parameters of tigecycline described in a previous study using a two-compartmental model for multiple doses were used to determine the concentration-time profile of each regimen (c = central; p = peripheral): clearance CL c = 16.3 L/h; volume V c = 57.7 L; CL p = 74.7 L/h; and V p = 1030 L [17]. Mean values of pharmacokinetic parameters were introduced into a two-compartment model with an order 0 kinetic in the administration phase and a first-order kinetic in the elimination phase (see equation below) of the WinNonlin Professional program version 5.2 (Pharsight Corp., Mountain View, CA) and the concentration-time data over 48 h were obtained:

A

  c c e p t e d M a n u s c r i p t where C t is the plasma concentration at time t after the start of infusion, ti is the length of the infusion, tstart = t-ti, , , A and B are constants, K 21 is the transfer rate constant from the peripheral to the central compartment, and D is the dose.

A

  c c e p t e d M a n u s c r i p t representatives of isolates implicated in IAIs and SSSIs were used, namely E.

Fig. 1 .

 1 Fig. 1. Diagram of the in vitro computerised device.

Fig. 2 .

 2 Fig. 2. Concentration profiles of the tigecycline regimens tested: serum

Fig. 3 .

 3 Fig. 3. Bacterial counts [log 10 colony-forming units (CFU/mL)] over time for the

Fig. 4 .

 4 Fig. 4. Area under the bacterial count-time curve from 0-48 h (AUBC 0-48 ) [log

1 .

 1 Central compartment (spinner flask, tubing and lumen of capillary), 2. Fresh broth reservoir, 3. Elimination, 4. Peristaltic pumps, 5. Syringe pump, 6. PTFE tubing, 7. Silicone tubing, 8. Infection compartment (Extracapillary space), 9. Inoculation port, 10. Sample port, 11. RS-232 connection, 12. GSIOC connection, 13. Temperature probe, 14. Air filter y

Table 1

 1 Process-dependent pharmacokinetic parameters introduced in the

	computerised pharmacodynamic device
	Process	Time period (h) Ke (h -1 ) CL (L/h)
	Dose 1
	Order 0 infusion	0-1	0.00	0.00
	Monoexponential decay 1-3	1.13	0.51
	Monoexponential decay 3-4	0.32	0.15
	Monoexponential decay 4-12	0.02	0.01
	Dose 2
	Order 0 infusion	12-13	0.00	0.00
	Monoexponential decay 13-15	0.93	0.42
	Monoexponential decay 15-16	0.20	0.09
	Monoexponential decay 16-24	0.02	0.01
	Dose 3
	Order 0 infusion	24-25	0.00	0.00
	Monoexponential decay 25-27	0.82	0.37
	Monoexponential decay 27-28	0.15	0.07
	Monoexponential decay 28-36	0.02	0.01
	Dose 4
	Order 0 infusion	36-37	0.00	0.00
	Monoexponential decay 37-39	0.75	0.34
	Monoexponential decay 39-40	0.12	0.05
	Monoexponential decay 40-41	0.02	0.01
	Ke, apparent elimination rate constant; CL, clearance.

Table 2

 2 Pharmacokinetic/pharmacodynamic parameters of the three tigecycline twice-daily regimens

		Day 1			Day 2
	Pharmacokinetic parameters
	Regimen (mg twice daily)	50 a	100	150	50 a	100	150
	C max (g/mL)	0.88  0.12 0.88  0.11 1.38  0.10 0.45  0.03 1.00  0.12 1.53  0.16
	C min (g/mL)	0.06  0.00 0.07  0.02 0.12  0.02 0.06  0.01 0.15  0.04 0.21  0.04
	AUC 42
	AUC 0-24 (g h/mL) (mean)	3.47	4.02	6.32	3.20	6.72	9.94
	Pharmacodynamic parameters
	Staphylococcus aureus, Enterococcus faecium and Escherichia coli: MICs/MBCs = 0.125/0.25 g/mL
	C max /MIC	7.04	7.04	11.04	3.60	8.00	12.24
	AUC 0-24 /MIC	27.76	32.16	50.56	25.60	53.76	79.52
	T>MIC (% dosing interval)	26.9	29.5	86.5	30.0	100	100
	C max , maximum serum concentration; C min , trough serum concentration; AUC 0-x , area under the concentration-time curve from 0 to x h (see
	Section 2.6); MIC, minimum inhibitory concentration; MBC, minimum bactericidal concentration; T>MIC, percentage of the dosing interval that
	simulated antibiotic concentrations exceeded the MIC; S.D., standard deviation.
	a 100 mg as loading dose followed by 50 mg twice daily.

0-12 (g h/mL) (mean  S.D.) 1.87  0.25 2.01  0.36 3.16  0.47 1.60  0.10 3.36  0.56 4.97  0.

Table 3

 3 Antibacterial activity of the different tigecycline regimens in terms of ABBC (log CFU  h/mL) a ABBC = difference between the area under the growth control curve and the area under the bactericidal curve (AUBC) for each regimen (area under the growth control curve: 315.80  11.46 log CFU  h/mL for S. aureus, 328.15  13.22 log CFU  h/mL for E. faecium and 294.55  4.45 log CFU  h/mL for E.

	Organism	Inoculum Tigecycline regimen (mg twice daily)
			50 b	100	150
	Staphylococcus	Standard 120.60 	143.20 	195.80 
	aureus		10.89	15.70	20.65
		High	N/D	91.05  7.00 156.35 
					20.01
	Enterococcus	Standard 95.75  4.88 172.55 	216.90 
	faecium			1.93	70.01
		High	N/D	67.92 	155.90 
				18.69	0.71
	Escherichia coli	Standard 29.80  4.81 11.15  4.13 145.75 
					0.35
		High	N/D	-3.42  5.04 63.33  8.39
	CFU, colony-forming units; N/D, not determined.
	coli).

a b 100 mg as loading dose followed by 50 mg twice daily.

Acknowledgment

The authors thank A. Perez for continuous scientific support.

Funding

This study was supported in part by an unrestricted grant from Wyeth Farma S.A. (San Sebastian de los Reyes, Madrid, Spain).

Competing interests

NG-E is an employee of Wyeth Farma S.A. (Madrid, Spain), not owning stock or options in the company. CG-R was an employee of Wyeth Farma S.A. at the time of the study, not owning stock or options in the company. All other authors declare no competing interests.

Ethical approval

Not required.


Carmen Betriu
email: cbetriu.hcsc@salud.madrid.org

Esther Culebras

María Gómez

Fátima López-Fabal

Iciar Rodríguez-Avial

Juan J Picazo

Comparative in vitro activity of ceftobiprole against Gram

Keywords:

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. irrespective of their susceptibility to other agents such as oxacillin, linezolid or glycopeptides. Ceftobiprole was also highly active against penicillin-resistant S. pneumoniae and macrolide-resistant -haemolytic streptococci, inhibiting 99.6% of all streptococci tested at ≤0.5 g/mL. Based on these results, ceftobiprole appears to be a promising agent for the treatment of infections caused by multidrug-resistant Gram-positive pathogens.

A c c e p t e d M a n u s c r i p t

Introduction

The rising incidence of infections caused by multidrug-resistant Gram-positive bacteria, such as meticillin-resistant staphylococci or penicillin-resistant pneumococci, underscores the need for novel agents with activity against these pathogens. Ceftobiprole is an expanded-spectrum pyrrolidinone-3-ylidenemethyl cephalosporin with documented in vitro activity against a wide range of Gram-positive cocci, including meticillin-resistant staphylococci and penicillinresistant Streptococcus pneumoniae. Ceftobiprole is also active against Gramnegative bacilli, including Pseudomonas aeruginosa. It is active against meticillin-resistant Staphylococcus aureus (MRSA) because of its high affinity for penicillin-binding protein 2a (PBP2a) and its stability against class A lactamases. It also binds to PBP2X, which mediates penicillin resistance in S.

pneumoniae. The bactericidal activity of ceftobiprole against MRSA has been demonstrated by several authors [START_REF] Lin | Activity of ceftobiprole compared with those of other agents against Staphylococcus aureus strains with different resistotypes by time-kill analysis[END_REF][START_REF] Rouse | In vitro activity of ceftobiprole, daptomycin, linezolid, and vancomycin against methicillin-resistant staphylococci associated with endocarditis and bone and joint infection[END_REF][START_REF] Zhanel | Pharmacodynamic activity of ceftobiprole compared with vancomycin versus methicillin-resistant Staphylococcus aureus (MRSA), vancomycinintermediate Staphylococcus aureus (VISA) and vancomycin-resistant Staphylococcus aureus (VRSA) using an in vitro model[END_REF]. Ceftobiprole has been reported to have low potential for selection of resistance in multiple-passage studies [START_REF] Bogdanovich | Antistaphylococcal activity of ceftobiprole, a new broad-spectrum cephalosporin[END_REF][START_REF] Kosowska | Antipneumococcal activity of ceftobiprole, a novel broad-spectrum cephalosporin[END_REF].

The objective of this study was to assess the activity of ceftobiprole and several comparator agents against a variety of Gram-positive cocci.

Materials and methods

The activity of ceftobiprole and comparator agents was analysed against a collection of 880 isolates, comprising 200 meticillin-susceptible S. aureus The sources of the isolates were blood (77.5%), respiratory tract (11.2%), skin and soft-tissues (6.5%), urine ( Antimicrobial susceptibility testing was performed using the reference broth microdilution method described by the Clinical and Laboratory Standards Institute (CLSI) [START_REF]Methods for dilution antimicrobial susceptibility tests for bacteria that grow aerobically[END_REF]. Cation-adjusted Mueller-Hinton broth was supplemented with 5% lysed horse blood for streptococci. A calcium supplement (up to 50 g/mL) was used for testing daptomycin. Sensititre microdilution panels (Trek Diagnostic Systems, East Grinstead, UK) were used for all the drugs except ceftobiprole. The microdilution trays for ceftobiprole were prepared in house using fresh broth and following the recommendations of the CLSI [START_REF]Methods for dilution antimicrobial susceptibility tests for bacteria that grow aerobically[END_REF].

Ceftobiprole standard powder was provided by Johnson & Johnson

Pharmaceutical Research and Development (Raritan, NJ). Stock solution of ceftobiprole was prepared and dissolved according to the CLSI method [START_REF]Performance standards for antimicrobial susceptibility testing. Nineteenth informational supplement[END_REF]. The A c c e p t e d M a n u s c r i p t group of antimicrobial agents tested varied according to the bacterial species and are listed in Table 1.

Results

The activities of ceftobiprole and comparator agents against all staphylococci and streptococci tested are shown in Table 1. Based on the MIC 50 /MIC 90 values (minimum inhibitory concentrations for 50% and 90% of the organisms, respectively), the activity of ceftobiprole (0.5/1 g/mL) against all S. aureus tested was comparable with that of vancomycin (1/1 g/mL), teicoplanin (0.5/1 g/mL) and daptomycin (0.25/0.5 g/mL). Six MRSA isolates were resistant to linezolid (MICs ≥ 8 g/mL) and one MRSA isolate showed intermediate susceptibility to vancomycin (MIC = 4 g/L). Among CoNS, three isolates were resistant to linezolid and four were resistant to teicoplanin (MICs ≥ 32 g/mL).

Daptomycin was active against all the staphylococci tested. Ceftobiprole MICs were ≤4 g/mL against all staphylococci, with MIC 50 and MIC 90 values four-fold lower for MSSA isolates than for MRSA isolates.

According to the CLSI cefotaxime breakpoints for non-meningeal isolates [START_REF]Performance standards for antimicrobial susceptibility testing. Nineteenth informational supplement[END_REF], 14% of the S. pneumoniae isolates tested were not susceptible to cefotaxime (MICs ≥ 2 g/mL). All of these isolates were inhibited by ceftobiprole at MICs of ≤1 g/mL. For macrolide-resistant S. pyogenes, resistance rates to clindamycin and tetracycline were 10% and 14%, respectively. The MIC 50 and MIC 90 values for ceftobiprole were ≤0.008 g/mL and 0.015 g/mL, respectively. More than one-half (54%) of the macrolide-resistant S. agalactiae were resistant to A c c e p t e d M a n u s c r i p t clindamycin and 84% were resistant to tetracycline. Among the 100 macrolideresistant S. agalactiae isolates, the MIC 50 and MIC 90 values for ceftobiprole were 0.015 g/mL and 0.03 g/mL, respectively. Table 2 presents the distribution of ceftobiprole MICs for each group of organisms tested. The percentages of S. pneumoniae isolates inhibited at 0.25 g/mL and 0.5 g/mL ceftobiprole were 94% and 99%, respectively. The S. pyogenes and S. agalactiae isolates tested were inhibited at ≤0.015 g/mL and ≤0.25 g/mL, respectively. Among staphylococci, meticillin-susceptible isolates were more susceptible to ceftobiprole than meticillin-resistant isolates (Table 2).

CLSI interpretative breakpoints

are not yet available for ceftobiprole. By applying the ceftobiprole susceptibility breakpoint interpretations used in a previous study [START_REF] Jones | In vitro evaluation of BAL9141, a novel parenteral cephalosporin active against oxacillinresistant staphylococci[END_REF] (MIC ≤4 g/mL for staphylococci and MIC ≤1 g/mL for streptococci), all the isolates included in the present study were susceptible to ceftobiprole.

Discussion

Unlike other studies [START_REF] Rouse | In vitro activity of ceftobiprole, daptomycin, linezolid, and vancomycin against methicillin-resistant staphylococci associated with endocarditis and bone and joint infection[END_REF][START_REF] Bogdanovich | Antistaphylococcal activity of ceftobiprole, a new broad-spectrum cephalosporin[END_REF][START_REF] Pillar | In vitro activity profile of ceftobiprole, an anti-MRSA cephalosporin, against recent Gram-positive and Gram-negative isolates of European origin[END_REF] in which the staphylococci tested were all susceptible to linezolid, the present study included some staphylococcal isolates that were not susceptible to this antibiotic. Ceftobiprole showed excellent activity against staphylococci irrespective of their susceptibility to other agents such as oxacillin, linezolid or glycopeptides. Our results are similar to those previously reported by Fritsche et al. [START_REF] Fritsche | Antimicrobial activity of ceftobiprole, a novel anti-methicillin-resistant Staphylococcus aureus cephalosporin, tested against contemporary pathogens: results from the SENTRY Antimicrobial Surveillance Program (2005-2006)[END_REF]. Ceftobiprole was also highly active against penicillin-resistant S. pneumoniae and macrolide-resistant -



  These data were presented at the 49th Interscience Conference on Antimicrobial Agents and Chemotherapy (ICAAC), 12-15 September 2009, San Francisco, CA (E-191).

A

  c c e p t e d M a n u s c r i p t ABSTRACT The activity of ceftobiprole and comparator agents was evaluated against a collection of 880 isolates, comprising 200 meticillin-susceptible Staphylococcus aureus, 200 meticillin-resistant S. aureus, 180 coagulase-negative staphylococci blood isolates, 100 Streptococcus pneumoniae and 200 macrolide-resistant -haemolytic streptococci (100 Streptococcus pyogenes and 100 Streptococcus agalactiae). Ceftobiprole showed excellent activity against staphylococci (minimum inhibitory concentrations ≤4 g/mL),

(

  MSSA), 200 MRSA, 180 coagulase-negative staphylococci (CoNS) blood isolates, 100 S. pneumoniae and 200 macrolide-resistant -haemolytic A c c e p t e d M a n u s c r i p t streptococci (100 Streptococcus pyogenes and 100 Streptococcus agalactiae).

  In vitro activity of ceftobiprole and comparator agents against staphylococci and streptococci Organism (no. of isolates)/antimicrobial agent MIC (µg/mL)RangeMIC 50 MIC 90Staphylococcus aureus oxacillin-susceptible (n inhibitory concentration; MIC 50/90 , MIC for 50% and 90% of the organisms, respectively; CoNS, coagulase-negative staphylococci.

  Staphylococcus intermedius; and 1 Staphylococcus warneri. The quality control strains S. aureus ATCC 29213 and S. pneumoniae ATCC 49619 were included in each testing run.

	2.9%), genital tract (1.2%) and abdominal tract
	(0.6%). Organisms were identified by standard methods including latex
	agglutination (Slidex Staph, Slidex Pneumo, Slidex Strepto A and Slidex Strepto
	B Kits; bioMérieux, Marcy l'Etoile, France). CoNS were identified using the Vitek
	2 Gram-positive identification card (bioMérieux) and species were distributed as
	follows: 113 Staphylococcus epidermidis; 42 Staphylococcus hominis; 20
	Staphylococcus haemolyticus; 3 Staphylococcus lugdunensis; 1

Funding

None.

A c c e p t e d M a n u s c r i p t haemolytic streptococci, inhibiting 99.7% of all streptococci tested at ≤0.5 g/mL. In agreement with the data reported by Jones et al. [START_REF] Jones | In vitro evaluation of BAL9141, a novel parenteral cephalosporin active against oxacillinresistant staphylococci[END_REF], all pneumococci were inhibited by ceftobiprole at MICs ≤1 g/mL. Ceftobiprole MIC 50 and MIC 90 values against S. pneumoniae (≤0.008 g/mL and 0.25 g/mL respectively) were similar to those reported by Pillar et al. [START_REF] Pillar | In vitro activity profile of ceftobiprole, an anti-MRSA cephalosporin, against recent Gram-positive and Gram-negative isolates of European origin[END_REF]. To our knowledge, only three published studies [START_REF] Jones | In vitro evaluation of BAL9141, a novel parenteral cephalosporin active against oxacillinresistant staphylococci[END_REF][START_REF] Fritsche | Antimicrobial activity of ceftobiprole, a novel anti-methicillin-resistant Staphylococcus aureus cephalosporin, tested against contemporary pathogens: results from the SENTRY Antimicrobial Surveillance Program (2005-2006)[END_REF][START_REF] Amsler | In vitro activity of ceftobiprole against pathogens from two phase 3 clinical trials of complicated skin and skin structure infections[END_REF] have reported ceftobiprole activity against haemolytic streptococci. Two of them [START_REF] Jones | In vitro evaluation of BAL9141, a novel parenteral cephalosporin active against oxacillinresistant staphylococci[END_REF][START_REF] Fritsche | Antimicrobial activity of ceftobiprole, a novel anti-methicillin-resistant Staphylococcus aureus cephalosporin, tested against contemporary pathogens: results from the SENTRY Antimicrobial Surveillance Program (2005-2006)[END_REF] presented results for these organisms as a group without differentiating between species. In the third study [START_REF] Amsler | In vitro activity of ceftobiprole against pathogens from two phase 3 clinical trials of complicated skin and skin structure infections[END_REF], as in ours, the results for S. pyogenes and S. agalactiae are presented separately. However, the authors studied a smaller number of isolates (n = 71 and n = 42, respectively) than we did and included macrolide-susceptible andresistant isolates. We found that ceftobiprole was slightly more active against erythromycin-resistant S. pyogenes isolates than against erythromycin-resistant S. agalactiae isolates. This new cephalosporin inhibited 100% of S. pyogenes and S. agalactiae isolates tested at 0.015 µg/mL and 0.25 g/mL, respectively.

Based on our findings and those of other authors [START_REF] Jones | In vitro evaluation of BAL9141, a novel parenteral cephalosporin active against oxacillinresistant staphylococci[END_REF][START_REF] Pillar | In vitro activity profile of ceftobiprole, an anti-MRSA cephalosporin, against recent Gram-positive and Gram-negative isolates of European origin[END_REF][START_REF] Fritsche | Antimicrobial activity of ceftobiprole, a novel anti-methicillin-resistant Staphylococcus aureus cephalosporin, tested against contemporary pathogens: results from the SENTRY Antimicrobial Surveillance Program (2005-2006)[END_REF][START_REF] Amsler | In vitro activity of ceftobiprole against pathogens from two phase 3 clinical trials of complicated skin and skin structure infections[END_REF][START_REF] Yun | Activity of ceftobiprole against community-associated methicillin-resistant Staphylococcus aureus isolates recently recovered from US military trainees[END_REF], together with the drug's excellent pharmacokinetic and safety profiles [START_REF] Deresinski | The efficacy and safety of ceftobiprole in the treatment of complicated skin and skin structure infections: evidence from 2 clinical trials[END_REF][START_REF] Lodise | Pharmacokinetic and pharmacodynamic profile of ceftobiprole[END_REF], ceftobiprole appears to be a promising agent for the treatment of infections caused by multidrug-resistant Gram-positive pathogens.

Competing interests


Romain Tavenard

Hervé Jégou

Laurent Amsaleg

Balancing clusters to reduce response time variability in large scale image search

Many algorithms for approximate nearest neighbor search in high-dimensional spaces partition the data into clusters. At query time, for efficiency, an index selects the few (or a single) clusters nearest to the query point. Clusters are often produced by the well-known k-means approach since it has several desirable properties. On the downside, it tends to produce clusters having quite different cardinalities. Imbalanced clusters negatively impact both the variance and the expectation of query response times. This paper proposes to modify k-means centroids to produce clusters with more comparable sizes without sacrificing the desirable properties. Experiments with a large scale collection of image descriptors show that our algorithm significantly reduces the variance of response times without severely impacting the search quality.

Introduction

Finding the nearest neighbors of high-dimensional query points still receives a lot of research attention as this fundamental process is central to many content-based applications. Most approaches rely on some different kinds of partitioning of the data collection into clusters of descriptors. At query time, an indexing structure selects the few (or a single) clusters nearest to the query point. Each candidate cluster is probed, actual distances to its points are computed and the query result is built based on these distances.

There are various options for clustering points, the most popular being the k-means approach. Its popularity is caused by its nice properties: it is a simple algorithm, surprisingly effective and easy to implement ; it nicely deals with the true distribution of data in space by minimizing the mean square error over the clustered data collection. On the downside, it tends to produce clusters having quite different cardinalities. This, in turn, impacts the performance of the retrieval algorithm: scanning heavily filled clusters is costly as the distances to many points must be computed. In contrast, under-filled clusters are cheap to process, but they are selected less often as the query descriptor is also less likely to be associated with these less populated clusters. Overall, having imbalanced clusters impacts both the variance and the expectation of query response times. This is very detrimental to contexts in which performance is paramount, such as high-throughput settings since the true resource consumption can no more be accurately predicted by costs models. This phenomenon has an even more detrimental impact at large scale. In this case, clusters must be stored on disks and the performance severely suffer when fetching large clusters due to the large I/Os. Furthermore, k-means is known to fail clustering at very large scale, and hierarchical or approximate k-means must be used, which, in turn, tend to increase the imbalance between clusters [START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF]. This paper proposes an extension of the traditional k-means algorithm to produce clusters of much more even size. This is beneficial to performances since it reduces the variance and the expectation of query response times. Balancing is obtained by slightly distorting the boundaries of clusters. This, in turn, impacts the quality of results since clusters do not match the initial optimization criterion anymore. This paper is organized as follows. Section 2 defines the problem we are addressing and introduces the key metrics later used in the evaluation. Section 3 details the proposed balancing strategy. Section 4 evaluates the impact of balancing on the response times when using large collections of descriptors extracted from 1 million Flickr images. It also shows result quality remains satisfactory compared to regular k-means. Section 5 concludes the paper.

Problem statement 2.1 Base Clustering and Searching Methods

Without loss of generality, we partition a collection of N high-dimensional feature vectors into clusters defining Voronoi regions. We typically use a k-means algorithm quantizing the data into k clusters. This process intends to minimize the mean-squared-error (MSE) criterion, that is:

k i=1 x∈Ci x -c i 2 , (1)
where C i is the i-th cluster and c i is its associated centroid. Each cluster stores a list of its associated data points. This approach is widely adopted in the context of image searches, where clustering is applied to local [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF][START_REF] Nistér | Scalable recognition with a vocabulary tree[END_REF] or global descriptors [START_REF] Douze | Evaluation of gist descriptors for web-scale image search[END_REF][START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF]. A search strategy exploiting this partitioning is usually approximate: only one or a few clusters are probed at query time. The quality of results is typically increased when multiple clusters are probed during the search as in [START_REF] Lv | Multi-probe LSH: Efficient indexing for high-dimensional similarity search[END_REF][START_REF] Joly | A posteriori multi-probe locality sensitive hashing[END_REF][START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF][START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF].

The actual distances between the query point and the features stored in each such cluster are subsequently computed [START_REF] Datar | Localitysensitive hashing scheme based on p-stable distributions[END_REF][START_REF] Muja | Fast approximate nearest neighbors with automatic algorithm configuration[END_REF]. Therefore, the response time of a query is directly related to (i) the strategy used to identify the clusters to probe, (ii) the total number of vectors used in distance computations.

The cost for (i) is fixed and mainly corresponds to finding the m p centroids that are the closest to the query point (L 2 ). In contrast, the cost for (ii) heavily depends on the cardinality of each cluster to process. It is of course linked to m p . Note that (i) is often negligible compared to (ii).

Metrics: Selectivity and Recall

Probing m p clusters results in a list of vector candidates for which distance to the query vector must be computed. The trade-off between result quality and retrieval time is measured by recall and selectivity, respectively. Selectivity is the fraction of the data collection that is used in the distance calculations. Obviously, the larger selectivity, the higher the cost of the retrieval process. Recall is the average rate of nearest neighbors returned for a query, with respect to a given ground truth. In other words, recall is equal to the number of true results returned among the total set of true results. Observe that if the true nearest neighbor is found within any of the selected clusters, then it is re-ranked first if exact distance computation is performed in a subsequent stage [START_REF] Datar | Localitysensitive hashing scheme based on p-stable distributions[END_REF][START_REF] Muja | Fast approximate nearest neighbors with automatic algorithm configuration[END_REF].

Imbalance Factor

As in [START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF], we empirically measure the imbalance between the cardinalities of the clusters resulting from a kmeans using an imbalance factor γ defined as:

γ = k k i=1 p i 2 (2)
where p i is the probability that a given vector is stored in the list associated with the i th cluster.

As shown in [START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF], for a given k and m p = 1, γ is directly related to the search cost: γ = 3 means that the expectation of the search time is three times higher than the one associated with perfectly balanced clusters. This is the reason why imbalance factor is, to our opinion, more appropriate to assess balancing than entropy, even if both metrics reach an extremum in the case of perfectly balanced clusters.

Optimal balancing (γ = 1) is obtained when |C i | = N/k for all i. In that case, the variance of query time is zero, as any given cluster contains exactly the same number of elements, as shown by the analytical expression of the variance of the number of elements in a cluster list:

Var = N 2 k i=1 p i p i - 1 k 2 . ( 3
)
3 Balancing Clusters

The Balancing Process

Balancing clusters is an iterative post-processing step performed on the final output of a k-means type-of algorithm. The idea is to artificially enlarge the distances between the data points and the centroids of the heavily filled clusters so as to shrink and slightly drain loaded clusters. Penalties applied to distances depend on the population of clusters. Hence, the contents of clusters and thus their population can be recomputed accordingly. This balancing process eventually converges to equally filled clusters. The penalties are called penalization terms and are computed as follows:

∀i,

b 0 i = 1 ∀l ≤ r, b l+1 i = b l i n l i nopt α (4)
where α controls the convergence speed and r is the number of iterations performed. A small value for α ensures that balancing will be done in a smooth way, while it implies to have greater r in order to get cluster of even population. Note that, at each iteration l, the populations |C l i | are updated so as to take these penalization terms into account. More precisely, distances from any point x to the i th centroid are set to The initial value for b 0 i is explained by Equation 5, as it assigns an energy to balance factors that is comparable to the one of other dimensions of the data, under the assumption that vectors are normalized.

d l bal (x, c i ) 2 = d(x, c i ) 2 + b l i . (5)

Geometrical Interpretation

A geometrical interpretation of the balancing process described above is possible. Assume the balancing process first embeds the k-means clustered d-dimensional vectors into a (d + 1)-dimensional space. In this space, the d first components of all vectors are the ones they had in their initial space, while component d + 1 is set to zero. Centroids are embedded similarly, except for their last component that is set to b 0 i . Then, along iterations, it is set to the appropriate b l i value. The intuition is that centroids are elevated in an iterative way from the hyperplane where vectors lie. The more vectors in a cluster, the more elevation its centroid gets. This is illustrated in Figure 1, where the z-axis corresponds to the added dimension. While iterating, updated assignments for vectors are computed with respect to the coordinates of the points lying in the augmented space. The artificial elevation of centroids tends to shrink the most populated clusters, dispatching some of its points in neighboring clusters. Figure 2 exhibits the influence of the (d + 1) th coordinate of the centroids on the position of the borders.

Note that new Voronoi region boundaries are parallel to initial ones at each step, which can be shown as follows. Updated boundary between clusters i and j is defined as

H i,j = x, f (x) + b l i -b l j = 0
using f (x) = d(x, c i ) 2 -d(x, c j ) 2
where b l i and b l j are constant with respect to x. This implies that the vector ∂f ∂x1 ,

• • • , ∂f ∂x d is normal to H i,j .
As it is also normal to the initial boundary, both boundaries are parallel.

Partial Balancing

The proposed balancing strategy empirically converges towards clusters having the same cardinalities. Several stopping criteria can be applied, the most simple being a maximum number of iterations. It is also possible to target a particular value for γ, either fixed or possibly in proportion to the initial imbalance factor. Early stopping the balancing process reduces the overall distortion of the initial Voronoi regions.

Experiments

Datasets and Imbalance Factors Analysis

Our analysis has been performed on descriptors extracted from a large set of real-world images. We downloaded one million images from Flickr to build the database and another one thousand images for the queries. Several description schemes were applied to these images, namely SIFT local descriptors [START_REF] Lowe | Distinctive image features from scale-invariant keypoints[END_REF], Bag-of-features [START_REF] Sivic | Video Google: A text retrieval approach to object matching in videos[END_REF] (BOF), GIST [START_REF] Oliva | Modeling the shape of the scene: a holistic representation of the spatial envelope[END_REF] and VLAD descriptors [START_REF] Jégou | Aggregating local descriptors into a compact image representation[END_REF]. SIFT were extracted from Hessian-Affine regions [START_REF] Mikolajczyk | Scale and affine invariant interest point detectors[END_REF] using the software of [START_REF] Mikolajczyk | Binaries for affine covariant region descriptors[END_REF]. BOF vectors have been generated from these local descriptors, using a codebook obtained by regular k-means clustering with 1000 visual words. The VLAD descriptors were generated using a codebook of 64 visual words applied to the same SIFT descriptors, leading to vectors of dimension 64 × 128 = 8192. For GIST, we have used the most common setup (colors and 3 scales), leading to 960dimensional descriptors. Global descriptors (BOF, GIST and VLAD) produce exactly one descriptor per image, leading to one million vectors for each type of descriptor. We have randomly sampled the SIFT local descriptors to keep 1 million vectors, so as to allow fair comparison between γ values for all types of descriptors.

In all cases, we assume a closed-world setup, i.e., the dataset to be indexed is fixed, which is valid for most applications. A more thorough study of open-world case can be found later in this section.

Table 1 reports imbalance factors obtained for each type of descriptors after performing a standard k-means clustering on our database. It can be observed that higher dimensional vectors tend to produce higher imbalance factors. BOF descriptors have an imbalance factor which is lower than GIST for a comparable dimension, which might be due to their higher sparsity. The number k of clusters has a significant impact on γ: larger values for k lead to higher γ. The low values for k we have considered here explains why γ measured for the SIFT descriptors in Table 1 are lower than those reported in the literature: [START_REF] Jégou | Improving bag-offeatures for large scale image search[END_REF] reports 1.21 and 1.34 for codebooks of size k=20 000 and k=200 000, respectively. Note that, in the case of hierarchical clustering, observed imbalance factor are much higher since balancing issues are present at every level of the clustering tree.

Evaluation of the proposed method

We analyze here the impact of our method on selectivity, recall and variability of the response time. So as to better study the impact of clustering in the feature space, we use a ground truth based on actual feature space distances rather than on semantic image similarity. We also analyze the convergence properties of our method. α is set to 0.01 in all our experiments. Note that our balancing strategy is especially interesting for global descriptors where having perfectly balanced clusters leads to constant query time. Therefore we performed our experimental validation on the well known BOF vectors. In the following, we use m p = 1 in order to better show the impact of balancing. Note however that significantly better recall performances could be achieved by using larger m p .

Selectivity/recall performance

Figure 3 shows the compromise between accuracy and complexity for different values of k. First note that the tradeoff between selectivity and recall can be adjusted using the number k of clusters and the number m p of probes. Our method exhibits comparable performance with that of the k-means clustering in terms of selectivity and recall. For example, using k = 512, performing a k-means without balancing (γ = 1.77) leads to a selectivity of 0.0035 for a recall of 0.34, while performing only 4 iterations of our balancing strategy (γ = 1.53) allows one to achieve a selectivity of 0.0030 (-14%) for a recall of 0.33 (-3%). Note however that with our method a given selectivity/recall point is obtained with a much better (lower) variability of the response time, as shown later in this section.

Impact of the number of iterations

The number r of iterations in Equation 4is an important parameter of our method, as it controls to which extent complete balancing is enforced or not. Figure 3 shows that selectivity is reduced in the first iterations with a reasonable loss in recall, i.e., comparable to what we would obtain by modifying the number of clusters. Following iterations are comparatively less profitable, as the gain in selectivity is obtained at a relatively high cost in recall. Modifying the stopping criterion allows our method to attain a target imbalance factor which is competitive with respect to the selectivity/recall trade-off.

Convergence speed

Figure 4 shows that even a small number of iterations can lead to reasonably balanced clusters. Full balancing is almost achieved after 64 iterations, which leads to a computational cost that is negligible in the experiments we conducted compared to that of the clustering. Higher values of k for the initial k-means do not require more balancing iterations, which is somewhat surprising as more penalization terms have to be learned. Note that convergence of our algorithm is not guaranteed, though it has been observed in our experiments.

Variance of the query response time

The impact of our balancing strategy on the variability of the response time is illustrated by Figure 5, which gives the distribution of the number of vectors returned by the indexing structure. The tight distribution obtained by our method shows that the objective of reducing the variability of the query time resulting from unbalanced clusters is fulfilled: the response time is almost constant with full balancing, while its variance is significantly lower with partial balancing than with the original clustering.

Is closed-world setup mandatory ?

Previous section presented results obtained in a closedworld setup as it allows to achieve quasi-constant query time in all cases. However, Figure 6 shows that, as soon as the distribution of the learning set is reasonably close to the one of the database, comparable selectivity-versusrecall compromise can be achieved in the open-world case. In this example, the database is the same as the one used in the previous experiments. For both closed-world and semiclosed-world setups, another 1 million images from Flickr are used as a learning set to train k-means. The difference between both setups is that in the semi closed-world one, balancing is learned on the database itself while in the openworld setup, it is optimized on the learning set, which could lead to unbalanced database clusters. Note nevertheless that quality of the balancing in semi closed and open-world setups strongly depends on the learning set having comparable distribution to the one of the database. Therefore, their usage should be restricted to cases where this assumption is likely to be verified, as for example in cases where the learning set is a subset of the entire database.

Conclusion

Many high-dimensional indexing schemes partition the feature space into clusters, typically using k-means clustering. These schemes are efficient because they process a small proportion of clusters at query time. In this paper, we address an issue of these methods: having to process clusters with very different cardinalities causes important variations in the response time to queries. We propose an algorithm that iteratively balances clusters such that they become more equal in size, reducing the response time variance without significantly impacting the search quality.

Figure 1 .

 1 Figure 1. Data points and centroids embedded in a 3-d example. Data points are plotted as triangles while centroids are represented as dots, with a non-null z-axis value after some iterations. Initial Voronoi region boundaries and their shifted version are respectively plotted as solid and dashed lines.

Figure 2 .

 2 Figure 2. Voronoi region boundaries shifted after some iterations. Along iterations, clusters of large population get their centroids moved away while other centroids stay close to the z = 0 plane where data points lie. New boundaries, plotted as dashed lines, shrink the left-hand-side cluster because of its large population.

Figure 3 .

 3 Figure 3. Impact of varying balancing on the trade-off selectivity/recall. Top to bottom: the points of a given curve correspond to 0, 4, 16 and 64 iterations. Observe that first iterations of our algorithm tend to significantly lower selectivity without severely impacting recall.

Figure 4 .

 4 Figure 4. Convergence speed in terms of the number r of iterations.

Figure 5 .

 5 Figure 5. Histograms of the number of vectors returned, computed over our 1000 queries, for the original k-means and our algorithm with three number of iterations (k = 1024 in all cases). Observe the tightness of the distribution in the case of our method, which reflects a very low variability in response time.

Acknowledgements

This work was partly realized as part of the Quaero Project, funded by OSEO, French State agency for innovation.