J. vet. Pharmacol. Therap. doi: 10.1111/jvp.12207

Pharmacokinetic/pharmacodynamic integration and modelling of amoxicillin for the calf pathogens Mannheimia haemolytica and Pasteurella multocida P. LEES*

Lees, P., Pelligand, L., Illambas, J., Potter, T., Lacroix, M., Rycroft, A., Toutain, P.-L. Pharmacokinetic/pharmacodynamic integration and modelling of amoxicillin for the calf pathogens Mannheimia haemolytica and Pasteurella multocida. J. vet. Pharmacol. Therap. doi: 10.1111/jvp.12207.

L. PELLIGAND* J. ILLAMBAS* , § T. POTTER* , ‡ M. LACROIX † A. RYCROFT* & P.-L. TOUTAIN † *The Royal Veterinary College, Hawkshead Campus, Hatfield, Herts, UK; †Ecole National Veterinaire de Toulouse, UMR 1331 Toxalim INRA, Toulouse Cedex 03, France

The antimicrobial properties of amoxicillin were determined for the bovine respiratory tract pathogens, Mannheima haemolytica and Pasteurella multocida. Minimum inhibitory concentration (MIC), minimum bactericidal concentration (MBC) and time-kill curves were established. Pharmacokinetic (PK)/pharmacodynamic (PD) modelling of the time-kill data, based on the sigmoidal Emax equation, generated parameters for three levels of efficacy, namely bacteriostatic, bactericidal (3log10 reduction) and 4log10 reduction in bacterial counts. For these levels, mean AUC(0–24 h)/MIC serum values for M. haemolytica were 29.1, 57.3 and 71.5 h, respectively, and corresponding values for P. multocida were 28.1, 44.9 and 59.5 h. Amoxicillin PK was determined in calf serum, inflamed (exudate) and noninflamed (transudate) tissue cage fluids, after intramuscular administration of a depot formulation at a dosage of 15 mg/kg. Mean residence times were 16.5 (serum), 29.6 (exudate) and 29.0 h (transudate). Based on serum MICs, integration of in vivo PK and in vitro PD data established maximum concentration (Cmax)/MIC ratios of 13.9:1 and 25.2:1, area under concentration–time curve (AUC0–∞)/MIC ratios of 179 and 325 h and T>MIC of 40.3 and 57.6 h for P. multocida and M. haemolytica, respectively. Monte Carlo simulations for a 90% target attainment rate predicted single dose to achieve bacteriostatic and bactericidal actions over 48 h of 17.7 and 28.3 mg/kg (M. haemolytica) and 17.7 and 34.9 mg/kg (P. multocida). (Paper received 10 March 2014; accepted for publication 7 January 2015) Pierre Louis Toutain, Ecole National Veterinaire de Toulouse, UMR 1331 Toxalim INRA, 23, Chemin des Capelles-BP 87614, 31076 Toulouse Cedex 03, France. E-mail: [email protected] ‡ Present address: Westpoint Veterinary Group, Dawes Farm, Bognor Road, Warnham, Sussex RH12 3SH, UK § Present address: Zoetis, Global Development & Operations, VMRD, Hoge Wei 10, B-1930 Zaventem, Belgium

INTRODUCTION The general formula used to determine dosage to achieve a given exposure (AUC) for systemically acting drugs is: Dose ¼

Cl  AUC F

ð1Þ

where Cl = body clearance, F = bioavailability (from 0 to 1) and AUC = area under serum/plasma concentration–time curve (Toutain & Bousquet-Melou, 2004a). © 2015 John Wiley & Sons Ltd

For those antimicrobial drugs (AMDs) for which the pharmacokinetic/pharmacodynamic (PK/PD) index that best predicts efficacy is AUC(0–24 h)/MIC, such as amoxicillin in the calf for the present investigation, this equation yielding the daily maintenance dose was adapted by Aliabadi and Lees (2001, 2002) and Toutain and Lees (2004) to: DoseðperdayÞ ¼

Cl 

AUCð024 hÞ MIC  MICdistribution fu  F

ð2Þ

where Cl = body clearance per h, AUC(0–24 h)/MIC (in h) = PK/PD index of the ratio of area under the serum concen1

2 P. Lees et al.

tration–time curve over 24 h to the minimum inhibitory concentration (MIC) of the test pathogen to achieve a given effect (bacteriostatic, bactericidal or eradication), MICdistribution = MICs (lg/mL) of amoxicillin, determined from an epidemiological survey, fu (from 0 to 1) = fraction of drug not bound to serum protein and F = bioavailability (from 0 to 1). From this, it is clear that selection of an optimal dose depends on (i) assessment of both PK (Cl, F, fu,) and PD (MIC) values and (ii) determination of an appropriate AUC(0–24 h)/MIC ratio. Ideally, these variables should be determined experimentally in vitro with the AMD in question (amoxicillin), the test organisms of interest (in this instance two calf respiratory pathogens, Pasteurella multocida and Manheimia haemolytica), and in biologically relevant matrices for the target species (calf serum). Equation (2) is appropriate for determining daily AMD dosage once steady-state has been reached. This situation corresponds to dose determination in human patients or in companion animals, when usually dosed once each day (maintenance dose for steady-state conditions). However, it does not apply to long-acting drug product formulations. For AMDs used in cattle, for example, the dosing situation differs, in that most commercial preparations are licensed for administration every 48 h or even as a single dose (single dose or also named in the present paper loading-dose calculation). In this study, both scenarios to compute dosage regimen have been compared. A further consideration is whether to use for each of the variables in equation (2): either mean/typical values or values based on their actual population distribution, thus allowing use of Monte Carlo simulations to estimate a population dose for a given target attainment rate (TAR), that is the dose encompassing appropriately a given percentile of the target population (generally 90% of animals). The first option will generate an average dose, which is most unlikely to be optimal, and the second option will generate a dose, which approximates to the optimal dose for a probabilistic (empirical) antimicrobial therapy, that is when the PK parameters and the MIC of the targeted pathogen are a priori unknown. The objectives of this investigation were (i) to compare the in vitro MIC and MBC of amoxicillin in two growth matrices, Mueller–Hinton Broth (MHB) and calf serum, of each of the two bacterial species, M. haemolytica and P. multocida; (ii) to determine time-kill profiles in MHB and serum and to model the data for three levels of bacterial growth inhibition, as a basis for breakpoint determination of the selected PK/PD index, which in this study is AUC(0–24 h)/MIC; (iii) to establish the serum concentration–time profile and to derive PK data for amoxicillin in calves after intramuscular administration of a depot formulation at the manufacturer’s recommended dosage (15 mg/kg); (iv) to determine the rate and extent of amoxicillin penetration into and elimination from carrageenan-inflamed (exudate) and noninflamed (transudate) fluids in a tissue cage model; (v) to integrate the in vivo PK and in vitro PD data for amoxicillin to determine breakpoint values for surrogates of clinical activity, Cmax/MIC, Cav/MIC, AUC0–24 h/MIC, AUC0–∞/MIC

and T>MIC; and (vi) to use data from (a) the in vitro time-kill curves, (b) the in vivo PK study and (c) scientific literature epidemiological MIC distributions to calculate, using Monte Carlo simulations, dosages of amoxicillin for an empirical (probabilistic) therapeutic response for (a) each bacterial species, (b) three levels of growth inhibition and (c) three duration periods in steady-state conditions and after a single-dose administration. MATERIALS AND METHODS In vitro phase Origin, storage and selection of bacterial isolates. Twenty isolates of each of two calf pneumonia pathogens, M. haemolytica and P. multocida, were collected at postmortem from field cases of calf pneumonia. Each was supplied on swabs by the Veterinary Laboratories Agency (VLA, Addlestone, Surrey, UK) and stored at 70 °C in a fluid of composition, glycerol:milk: water, 20:10:70. From the 20 isolates of each species, two criteria were used to select six per species for further study. First, each isolate was investigated for ability to grow logarithmically in four fluids, MHB and calf serum, exudate and transudate. Second, using CLSI methods (2008), each isolate was evaluated for sensitivity to amoxicillin in an initial screen (disc diffusion), then confirmed by determination of MICs, using doubling dilutions, based on CLSI methodology (2004, 2008). Culture methods and bacterial counts. Bacterial isolates were cultured in MHB (Oxoid, Loughborough, UK) or on 7% sheep blood agar [defibrinated sheep blood (TCS Biosciences, Buckingham, Bucks, UK) and blood agar base No. 2 (Oxoid)]. Agar cultures were incubated statically in a CO2 incubator (Thermo Scientific, Heraeus, MA, USA), and MHB cultures were incubated with shaking at 150 rpm in a C25 incubating shaker (New Brunswick Scientific, Edison, NJ, USA) both at 37 °C. Bacterial viability counts were determined by serial dilution and spot-plate counts. Ten or 100-fold dilutions were prepared in phosphate-buffered saline (PBS), and three 10 lL drops of each dilution were transferred to the agar surface and allowed to dry for 10 min before incubating at 37 °C. Determination of minimum inhibitory and minimum bactericidal concentrations. MICs and MBCs for six isolates each of M. haemolytica and P. multocida were established in accordance with CLSI methods (CLSI, 2004) by broth microdilution, except that five overlapping sets of doubling dilutions of amoxicillin were prepared in MHB. Serial dilutions were prepared (1 9 108), and a volume of 97.5 lL of each dilution was aliquoted into a well of an U-shaped 96-well plate. Four mL of MHB was inoculated with a few colonies of the strain to be tested and incubated at 37 °C until growth reached approximately 1 9 108 cfu/ mL, judged by visual comparison with 0.5 McFarland Standard. A volume of 2.5 lL of a 1:10 dilution of the © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 3

culture in PBS was inoculated into each well. The plate was incubated statically at 37 °C for 16–20 h. For each 10 lL, the bacterial count (cfu/mL) was determined after incubation for 18 h. The original inoculum count was calculated by taking the mean count for each 10 lL volume and multiplying by 100 to give the cfu/mL. MIC determinations for the six isolates of both bacterial species were repeated, as described above for MHB, using five sets of overlapping dilutions of amoxicillin prepared in bovine serum (Gibco, Paisley, Scotland, UK). Minimum bactericidal concentrations in both matrices, MHB and serum, were determined according to CLSI methods (2004), using a single set of doubling dilutions. After each MIC determination, the wells were examined for growth and the three subsequent concentrations greater than the MIC were noted. MBC was determined on these samples using the spotplate technique to establish a 3log10 decrease in the inoculum count. Effect of inoculum size on MIC determination. Further MIC measurements in MHB were undertaken, as described above for five overlapping sets of doubling dilutions, for two isolates each of M. haemolytica and P. multocida, to compare MICs for low, intermediate and high initial inoculum counts. The culture was grown to 1.0 McFarland Standard and diluted to final counts of 2.5–2.9 9 104, 2.5–2.9 9 106 and 2.5– 2.9 9 108 cfu/mL, respectively. In vitro antimicrobial growth (time-kill) curves. For four isolates each of M. haemolytica and P. multocida, inoculating cultures were prepared by adding 3–4 colonies of the isolate to be tested to 4 mL MHB, followed by incubation overnight. Fifty microlitre of this culture was diluted 1:50 in prewarmed, freshly prepared MHB and incubated statically at 37 °C for one h. The culture was then centrifuged at 31 000 g for 2 min. The supernatant was discarded and the cells resuspended in 50 lL PBS. The viable cell counts (cfu/mL) were determined by serial dilution and spot-plate counts. Amoxicillin concentrations corresponding to 0 (growth control), 0.25, 0.5, 1, 2 and 49 multiples of MIC for each isolate were prepared in prewarmed MHB or calf serum. Four microlitre of the prepared culture was used to inoculate the dilutions to provide a 400-lL final volume. The cultures were placed in an orbital shaking incubator at 37 °C for 24 h. Forty lL of each culture was sampled and the viable count (cfu/mL) determined by serial dilution and spot-plate counts after incubation for 1, 2, 4, 8 and 24 h. The lowest detectable count was 33 cfu/mL. PK/PD modelling of in vitro time-kill data. Ratios of AUC(0–24 h)/ MIC were calculated for each of the four isolates of the two organisms at each of the five amoxicillin concentrations tested (0.25 to 4xMIC). The data were modelled to the sigmoidal Emax equation (equation 3) by nonlinear regression in WinNonlin version 5.2 (Pharsight Corporation, Mountain View, CA, USA): © 2015 John Wiley & Sons Ltd

E ¼ E0 þ

Emax  X N ECN50 þ X N

ð3Þ

where E0 is the bacterial growth after 24-h incubation in the absence of drug, expressed as log10 cfu/mL subtracted from the initial inoculum log10 cfu/mL; Emax is the maximum growth inhibition determined as the change from the initial count in log10 cfu/mL over 24-h incubation with amoxicillin; X is the independent variable (expressed as AUC(0–24 h)/MIC in h), and N is the Hill coefficient, which describes the slope of the AUC(0 –24 h)/MIC-effect curve; EC50 is the AUC(0–24 h)/MIC value providing 50% of the maximum antibacterial effect. Bacteriostatic (E = 0, no change form initial inoculum count), bactericidal (E = 3, a 3log10 reduction) and virtual eradication (E = 4, a 4log10 reduction from initial inoculum count) AUC(0–24 h)/ MIC values in h were determined for each isolate of each organism in MHB and serum (Aliabadi & Lees, 2001; Sidhu et al., 2010). The calculated AUC(0–24 h)/MIC values should be regarded as proportionality factors between the MIC of the test pathogen and the average MHB or average serum amoxicillin concentration required to achieve each of the three levels of growth inhibition. From the AUC(0–24 h)/MIC values in h, the average concentrations corresponding to the three levels of kill in each matrix over 24 h were calculated and expressed as multiples of MIC by dividing each value by 24 h (Toutain et al., 2007). In vivo phase Animals and surgical procedures. A study was conducted in 10 healthy female Aberdeen Angus calves. At the time of dosing, weights were in the range 145–204 kg (mean = 179 kg, SD = 16.7) and ages ranged from 79 to 131 days. Tissue cages were implanted subcutaneously in the paralumbar fossa, under general anaesthesia, as described by Sidhu et al. (2003). Thirty-five days was allowed after surgery for wound healing and to permit the growth of granulation tissue into the cages. Amoxicillin (Betamox LAâ, Norbrook Laboratories Ltd., Newry, Co. Down, N. Ireland) was injected intramuscularly into gluteal muscles (two equal volumes into right and left thighs) at a dosage of 15 mg/kg at zero time. Also at zero time, 0.5 mL of 1% w/v sterile lambda carrageenan solution in saline (Viscarin, Marine Colloids, Springfield, USA) was injected into a single tissue cage. This tissue cages was subsequently used to harvest exudate. A second, unstimulated cage was used to collect noninflammatory fluid (transudate). Sampling procedures. Blood samples (10 mL) were collected, protected from light, from a jugular vein, into vacutainers without anticoagulant (Becton, Dickinson and Company, Oxford, Oxon, UK) before and at times of 15, 30 and 45 min and then regularly up to 120 h after injection of amoxicillin. Exudate and transudate samples (1.5 mL) were collected, protected from light, before and at predetermined times from 1 to 120 h. All samples were centrifuged (2000 g for 10 min at

4 P. Lees et al.

4 °C) and supernatant serum was aliquoted into three polypropylene tubes. The aliquots were stored at 70 °C until assayed for amoxicillin or used for measurement of ex vivo antibacterial activity. Analysis of amoxicillin in serum, exudate and transudate. Working standards were prepared by serial dilution of amoxicillin (1 mg/mL) in water to obtain final concentrations of 100, 10 and 1 lg/mL. Standard and quality control (QC) solutions were obtained by adding appropriate volumes of these solutions to drug-free matrix, to provide concentrations from 20 to 5000 ng/mL for the calibration line and of 60, 300, 3000 ng/mL for QC samples for serum and from 20 to 1000 ng/mL for the calibration line and of 60, 300, 750 ng/mL for QC samples for exudate and transudate. These solutions were stored at 80 °C. Ampicillin was used as internal standard (IS). Amoxicillin and ampicillin were extracted from each matrix with protein precipitation. Samples (100 lL) were added to 10 lL of IS and 400 lL of methanol. Samples were mixed for 30 sec and centrifuged at 20,000 g at 4 °C for 15 min. The supernatant was collected and dried under nitrogen at 40 °C. The extracted sample was reconstituted in 100 lL of water. This solution was vortexed then centrifuged at 20 000 g for 5 min at 4 °C. The supernatant (50 lL) was collected, and 10 lL was injected into the chromatographic system. Chromatographic analyses were performed on a Thermofinnigan Surveyor HPLC system with a LCQ Deca XP Max ion trap mass spectrometer (Thermo Electron Corporation, Waltham, MA, USA). Separation was achieved with a Hypersil-BDS C18 column (100 9 2.1 mm; 3 lm, Thermo Electron Corporation) and a C18 guard column (10 9 2.1 mm, Thermo Electron Corporation) at 40 °C. A gradient elution was performed at a flow rate of 200 lL/min with a mobile phase of methanol, 0.1% formic acid (A) and water, 0.1% formic acid (B) under the following conditions: 0 min, 10% A; 0–3 min, 90% A; 3–5.5 min, 90% A; 5.5–6 min, 10% A and 6–12 min, 10% A. The retention times were 4.1 and 5.3 min for amoxicillin and ampicillin, respectively. Molecules were detected by selected reaction monitoring (SRM) with the following MS/MS transitions: m/z 366 ->349 and m/z 350 ->160 for amoxicillin and ampicillin, respectively. Chromatographic data were monitored by Xcalibur 1.4 software (Thermo Electron Corporation). Pharmacokinetic analyses. Amoxicillin concentration–time data in serum, exudate and transudate in individual calves were analysed in WinNonlin by noncompartmental analysis using the statistical moment approach described by Yamaoka et al. (1978). The linear trapezoidal rule was used to calculate AUC values and area under the first moment curve (AUMC). The mean residence time (MRT) was determined as AUMC/AUC. Pharmacokinetic/pharmacodynamic integration. The surrogate indices Cmax/MIC, AUC(0–24 h)/MIC, AUC(0–48 h)/MIC, AUC0 –∞/MIC and T>MIC were calculated for each fluid (serum,

exudate and transudate) harvested in the tissue cage study from 10 calves. Results were expressed as mean  SD (n = 10 calves) and based on arithmetic mean MICs (n = 6). In addition, the ratios of average serum concentration (Cav)/MIC, for four consecutive 24-h periods after administration of amoxicillin, were calculated. Dosage determination using a steady-state approach (after multiple doses given every 48 h) In equation (2), the term AUC(0–24 h)/MIC (h) is the experimentally determined PK/PD index to achieve, expressed as the ratio of area under the serum concentration–time curve over 24 h to MIC, determined using a test pathogen for a given bacteriological effect (bacteriostatic, bactericidal or virtual eradication). For greater clarity, we replaced the AUC(0–24 h)/MIC ratio (that is traditionally expressed, implicitly or explicitly, in h in the human literature) by a more readily understood dimensionless equivalent PD factor: jPD (Toutain et al., 2007). jPD is determined by dividing AUC(0–24 h)/MIC in h by 24 h, but this requires, for consistency, the plasma clearance to be expressed per day (Clday where Clday = 24 h 9 Cl expressed per hour as for equation (2)) when the computed dose is a daily dose. Hence, jPD represents the scaling factor by which the clinical MIC (or any MIC from the MIC distribution) should be multiplied to obtain the appropriate plasma concentration to be achieved for a given PD effect (bacteriostatic, bactericidal or virtual eradication). When jPD is substituted in equation (2), it yields: Doseðmaintenance per dayÞ ¼

Clday  KPD  MICdistribution F  fu

ð4Þ

where Dose(maintenance per day) should be viewed as a daily maintenance dose in steady-state equilibrium conditions; the expression can now be extended to time intervals longer than 24 h (Toutain et al., 2007). For the long-acting formulation of amoxicillin used in this study, with a recommended interval of 48 h between first and second doses, Clday is substituted in equation (5) by Cl48 h (where Cl48 h = 48 h 9 Cl expressed per hour as for equation (2)). The maintenance dose calculated from equation (5) is equal to twice the dose computed with equation (4). Doseðmaintenance per 48 hÞ ¼ Clð48 hÞ 

KPD  MICdistribution F  fu

ð5Þ

Dosage determination using a single-dose approach (one-off longacting treatment lasting 48 h) It is also relevant for a so-called long-acting (LA) formulation to estimate the single dose required to achieve bacteriostatic, bactericidal and 4log10 reductions in count over the first dosage interval (here 48 h), that is before reaching steady-state conditions. This first dose should be viewed as a loading dose, whilst the dose computed by equation (5) is a maintenance dose. The ratio between the loading dose and the maintenance © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 5

R¼

AUCðloading doseÞ AUCðmaintenance doseÞ

ð6Þ

Assuming that administration of the dose n + 1 occurs at a time after which the distribution of the previous dose n is complete (pseudo-steady-state), the accumulation ratio can be simplified as per equation (7): R¼

1 ; 1  expðK10  sÞ

ð7Þ

with k(10) expressed in h1 and s is the dosing interval in h. Therefore, R is dimensionless. Combining equations (6) and (7) and assuming pharmacokinetic linearity (clearance identical with two dose levels), the loading dose for 48-h effect for the ith calf Dosei (loading dose) is calculated from equation (8): 1  Dosemaintenance per 48h 1  expðK10  sÞ 1  Clð48hÞ ¼ 1  expðK10  48Þ KPD  MICdistribution  F  fu ð8Þ

Doseloadingdose48h ¼

Monte Carlo simulation for the two approaches to dose estimation Dosages were computed using Monte Carlo simulations in Oracle Crystal Ball (Oracle Corporation, Redwood Shores, CA, USA). Maintenance dose (per 48 h) was calculated using equation (5), and loading dose (for 48-h effect) was calculated using equation (8). Loading and maintenance doses were determined to achieve bacteriostatic and bactericidal responses and a 4log10 reduction in count for 48 h. The probabilistic approach took into account distributions embedded in equations (5) and (8). The average point estimate of the serum jPD was calculated from the data obtained with four isolates of each species, but variability in jPD was not included in the MC simulation. The distribution of individual plasma clearances within the sample population (10 calves in this study) was included for calculation of the maintenance dose (equation 5). The observed statistical distribution of products of individual plasma clearance by individual accumulation ratio for a 48-h dosing interval (determined by individual k(10)) was incorporated for calculations of the loading dose (equation 8). The distribution of field MIC values for M. haemolytica and P. multocida (considered separately) was included in the simulation. The distribution of MICs from the scientific literature (Guyonnet, personal communication, mean data accessible on http:// www.vmd.defra.gov.uk/productinformationdatabase/SPC_Documents/SPC_429850.doc) is represented in Fig. 1. For the MIC distributions, values were corrected by the published value of © 2015 John Wiley & Sons Ltd

fu (Villa et al., 1994) to correct for amoxicillin protein binding in serum, as the reported MIC literature values were determined in broth. The probabilities of distribution for each dosage estimation were run for 50 000 simulated trials. Statistical analyses Pharmacokinetic variables are presented as geometric, harmonic or arithmetic means, as appropriate, and SD or pseudo SD. MIC and MBC data are presented as geometric means and SD. Differences in MIC and MBC values between MHB and serum were compared with the paired t-test or the nonparametric Wilcoxon test, depending on whether the data passed a normality test. Mean differences in AUC(0–24 h)/MIC ratios determined in MHB compared with those determined in serum for bacteriostatic, bactericidal and 4log10 reductions in count were compared by ANOVA. RESULTS Selection of isolates From the initial 20 isolates of each organism, six were selected after initial studies to satisfy two criteria. First, percentages of the isolates growing logarithmically in the four fluids were 65, 65, 40 and 55 (M. haemolytica) and 90, 75, 65 and 65 (P. multocida), respectively, for MHB and calf serum, exudate and transudate. Second, all isolates of both species were classified as susceptible to amoxicillin, based on CLSI zone diameter of inhibited growth in disc diffusion susceptibility tests (data not shown). Initial MIC studies conducted in MHB using doubling dilutions confirmed that all selected isolates were sensitive to amoxicillin (data not shown). Six isolates of each species were then selected for further study, comprising highest, lowest and four intermediate MICs.

70.0

Percentage of total

dose is equal by definition to the accumulation ratio and for the present LA formulation as shown in equation (6) (Toutain & Bousquet-Melou, 2004b):

60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0312 0.0625 0.125

0.25

0.5

1

2

4

8

MIC (µg mL–1) M. haemolytica (n = 59)

P. multocida (n = 76)

Fig. 1. MIC distribution for P. multocida (59 strains) and M. haemolytica (76 strains). The MIC data were obtained from a commercial company (J. Guyonnet, personal communication). All specimens were collected from infected cattle from seven different EU countries (Czech republic, Denmark, France, Germany, Spain, United Kingdom) during the time period 2009–2012.

6 P. Lees et al.

Minimum inhibitory and minimum bactericidal concentrations In all experiments, except those comparing low, intermediate and high starting counts (vide infra), the initial inoculum count ranged from 5 9 105 to 5 9 106 cfu/mL. MIC and MBC values in MHB and serum for individual isolates are illustrated in Fig. 2. Table 1 presents data as geometric mean MIC and MBC and as ratios MBC:MIC and also serum:broth ratios for both MIC and MBC. For both organisms, geometric mean MICs were virtually identical in serum and MHB, whereas MBCs were

1.8- to 3.1-fold greater than MICs. MBCs were 1.5- to 1.6-fold greater in serum than in MHB. Amoxicillin MICs were additionally determined for two strains each of M. haemolytica and P. multocida using low, medium and high initial inoculum counts. For M. haemolytica, initial counts were 2.5 9 104, 2.5 9 106 and 2.5 9 108 cfu/mL, respectively. Corresponding initial counts for P. multocida were 2.9 9 104, 2.9 9 106 and 2.9 9 108 cfu/mL. For M. haemolytica, mean MICs were 0.5 lg/mL (low), 1.0 lg/mL (intermediate) and 2.5 lg/mL (high). Corresponding values for P. multocida were 0.29, 0.29 and 0.88 lg/mL. Time-kill curves

0.8

Broth

MIC (µg mL–1)

MIC MBC

0.6

0.4

0.2

12 50 19 78 10 56 39 59 41 21 37 22 43 23 40 96 40 72

20 08

26 53

20 59

0.0

Amoxicillin time-kill curves, using multiples of MIC in the range 0.25 to 4.0, are illustrated in Fig. 3 (M. haemolytica) and Fig. 4 (P. multocida). For both organisms, 0.25 and 0.5 multiples of MIC produced very limited growth inhibition. For M. haemolytica, killing patterns were similar in MHB and serum, except for a somewhat more rapid and greater reduction in count at 2xMIC in MHB than in serum. However, at 4xMIC after 8-h exposure, the initial count was reduced by 4log10 cfu/mL in serum and 5log10 cfu/mL in MHB. For P. multocida, growth inhibition patterns were similar in

Serum MIC MBC

(a)

Amoxicillin in broth for M.haemolytica

1010 109

0.6

CFU mL–1

MIC (µg mL–1)

0.8

0.4

0.2

Table 1. Geometric mean (SD) MIC and MBC in MHB and serum for amoxicillin and MIC:MBC and MHB:serum ratios (n = 6) Matrix M. haemolytica MHB Serum Serum:MHB ratio P. multocida MHB Serum Serum:MHB ratio

MIC (lg/mL)

MBC (lg/mL)

MBC:MIC ratio

0.25

106

0.5

105

1

104

2

103

4

102

LOD 0

4

8

12

16

20

24

Time (h) Amoxicillin in serum for M.haemolytica

(b) 10 10

CFU mL–1

Fig. 2. MICs and MBCs for amoxicillin against 12 strains (first six, left to right, M. haemolytica, second six, left to right, P. multocida) in MHB and serum.

0

107

10 1

12 50 19 78 10 56 39 59 41 21 37 22 43 23 40 96 40 72

20 08

26 53

20 59

0.0

108

10 9

0

10 8

0.25

10 7

0.5

10 6

1

10 5

2

10 4

4

10 3

0.10 (0.01) 0.10 (0.01) 1.1:1

0.20 (0.07) 0.31 (0.08) 1.6:1*

2.1:1 3.1:1

0.18 (0.05) 0.18 (0.03) 1.1:1

0.33 (0.08) 0.49 (0.12) 1.5:1*

1.8:1 2.7:1

*0.05 < P < 0.10, difference for serum:MHB ratios.

LOD

10 2 10 1

0

4

8

12

16

20

24

Time (h) Fig. 3. In vitro inhibition of growth of M. haemolytica over 24 h exposure to five MIC multiples of amoxicillin in (a) MHB and (b) serum (mean, n = 4). SEM bars not included for clarity. © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 7

(a) 10 10

counts were reduced by 5–6log10 cfu/mL after 24-h incubation at 4xMIC.

Amoxicillin in MHB for P.multocida

10 9

0

CFU mL–1

10 8

0.25

10 7

0.5

10 6

1

10 5

2

10 4 10 3

4

10 2

LOD

10 1

0

4

8

12

16

20

24

Time (h) (b)

Amoxicillin in serum for P.multocida

CFU mL–1

10 10 10 9

0

10 8

0.25

10 7

0.5

10 6

1

10 5

2

10 4

4

10 3

LOD

10 2 10 1

0

4

8

12

16

20

24

Time (h) Fig. 4. In vitro inhibition of growth of P. multocida over 24 h exposure to five MIC multiples of amoxicillin in (a) MHB and (b) serum (mean, n = 4). SEM bars not included for clarity.

serum and MHB at MIC multiples of 0.25, 0.5, 1 and 2, but at 4xMIC, killing was more rapid in serum than in broth. For both organisms and both matrices, bacterial

PK/PD modelling For both serum and MHB and for both organisms, the in vitro time-kill data were used to estimate typical values of AUC(0– 24 h)/MIC ratio required to produce, after 24-h exposure, three levels of growth inhibition: no change in bacterial count (bacteriostasis), 3log10 reduction in count (bactericidal action) and 4log10 reduction in count. AUC(0–24 h)/MIC values are presented in Tables 2 (M. haemolytica) and 3 (P. multocida). The maximum mean decrease from the initial count, 4.98log10 in MHB and 5.92log10 in serum, indicated a strong bactericidal action for M. haemolytica. For each level of kill, AUC(0–24 h)/MIC values were somewhat lower in MHB than in serum. For serum, interisolate variability in AUC(0–24 h)/MIC was moderate; for the three levels of kill, CV% values were 24, 36 and 47. Mean AUC(0–24 h)/MIC serum values for M. haemolytica were 29.1 (bacteriostatic), 57.3 (bactericidal) and 71.5 h (eradication), corresponding to average concentrations over 24 h of 1.2, 2.4 and 3.0 multiples of the corresponding MIC, also defined as the jPD scaling factor from equation (4) (Toutain et al., 2007). The range of AUC(0–24 h)/MIC values required to inhibit growth at the three levels was greater for P. multocida than for M. haemolytica, with MHB as the matrix. Values of AUC(0–24 h)/ MIC required to inhibit growth of P. multocida were slightly but not significantly greater in serum than in MHB. For serum, interisolate variability in AUC(0–24 h)/MIC was moderate; for the three levels of kill, CV% values were 35, 25 and 33. Mean AUC(0–24 h)/MIC serum values for P. multocida for the three levels of kill were 28.1, 44.9 and 59.5 h, corresponding to average concentrations of 1.2, 1.9 and 2.5 multiples of the corresponding MIC (defined as jPD).

Table 2. Growth inhibition data (mean, SD, n = 4 unless stated) required for three levels of growth inhibition of M. haemolytica by amoxicillin in MHB and serum Isolate Variable Mueller–Hinton Broth Log Emax (cfu/mL) Log E0 (cfu/mL) Log Emax-log E0 (cfu/mL) Bacteriostatic AUC(0–24 h)/MIC (h) Bactericidal AUC(0–24 h)/MIC (h) 4log10 reduction in AUC(0–24 h)/MIC(h) Serum Log Emax (cfu/mL) Log E0 (cfu/mL) Log Emax-log E0 (cfu/mL) Bacteriostatic AUC(0–24 h)/MIC (h) Bactericidal AUC(0–24 h)/MIC (h) 4log10 reduction in AUC(0–24 h)/MIC(h) *P < 0.05, comparison of MHB and serum. © 2015 John Wiley & Sons Ltd

1250

2008

2059

2653

5.28 0.13 5.41 8.81 11.91 12.71

4.68 2.75 7.43 23.52 25.63 27.03

5.57 0.16 5.73 9.81 14.61 15.92

4.48 1.68 6.05 22.12 28.83 34.53

5.62 0.12 5.73 30.33 61.06 79.88

4.45 1.83 6.28 20.22 29.93 34.63

8.04 2.29 10.3 28.43 55.76 

5.60 1.45 7.07 37.24 82.28 100.0

Mean

SD

4.98 1.18 6.16 16.07 20.25* 22.55*

0.54 1.27 0.89 7.83 8.24 10.07

5.92 1.14 7.35 29.05 57.25* 71.50* (n = 3)

1.51 0.93 2.06 7.00 21.52 33.48

8 P. Lees et al. Table 3. Growth inhibition data, including AUC24 h/MIC ratios (mean, SD, n = 4, unless stated), required for three levels of growth inhibition of P. multocida by amoxicillin in MHB and serum Isolate Variable Mueller–Hinton Broth Log Emax (cfu/mL) Log E0 (cfu/mL) Log Emax-log E0 (cfu/mL) Bacteriostatic AUC(0–24 h)/MIC (h) Bactericidal AUC(0–24 h)/MIC (h) 4log10 reduction in AUC(0–24 h)/MIC(h) Serum Log Emax (cfu/mL) Log E0 (cfu/mL) Log Emax-log E0 (cfu/mL) Bacteriostatic AUC(0–24 h)/MIC (h) Bactericidal AUC(0–24 h)/MIC (h) 4log10, reduction in AUC(0–24 h)/MIC(h)

1250

2008

2059

2653

Mean

SD

3.71 3.95 7.66 20.32 33.63 

5.47 3.32 8.80 23.82 47.75 65.97

5.36 1.72 7.07 6.51 17.22 25.43

4.08 3.58 7.66 19.42 30.23 56.46

4.66 3.14 7.80 17.52 32.21 49.29 (n = 3)

0.89 0.98 0.72 7.58 12.54 21.20

5.00 2.72 7.72 38.44 48.15 53.95

5.20 2.37 7.57 22.22 36.24 45.45

4.48 3.48 7.96 34.13 59.06 88.49

5.38 2.92 8.30 17.62 36.04 50.25

5.02 2.87 7.89 28.10 44.87 59.53

0.39 0.46 0.32 9.79 11.03 19.61

No significant differences between MHB and serum for AUC(0–24

h)/MIC.

Calf in vivo study Amoxicillin method validation. The analytical method for amoxicillin was fully validated in bovine serum samples, and a partial validation was applied for exudate and transudate samples. Selectivity was verified for each matrix on six blank samples from a matrix pool obtained from untreated calves. This method was linear over the calibration range 20– 5000 ng/mL with a linear regression model weighted by 1/X². Intraday and interday precisions were less than 12% and accuracy ranged from 88 to 111%. The lower limit of quantification (LLOQ) was 20 ng/mL with a precision of 10% and accuracy of 93%. Spiked amoxicillin serum samples were stable after three freeze–thaw cycles, and the processed extracts were stable in the auto sampler at 15 °C for at least 24 h. Amoxicillin concentrations in serum, exudate and transudate. The mean (+SEM) concentrations of amoxicillin are presented in Fig. 5 (serum, 0–24 h) and Fig. 6 (serum, exudate and transudate, 0–120 h). PK parameters are summarized in Table 4. Scrutiny of the serum concentration–time data for individual calves revealed two or three concentration peaks in 6 of 10 animals. These occurred at 1–1.5 h (peak 1) and at 2, 6 or 10 h (second/third peaks). Amoxicillin penetration into carrageenan-induced exudate and transudate was similar. From 8 h, up to 96 h amoxicillin concentrations in tissue cage fluids were higher than serum concentrations. Similar concentrations were attained in transudate compared to exudate; Cmax values were 1.45 and 1.29 lg/mL, respectively. Slightly higher AUC values than in serum were obtained in exudate and transudate, 46.0 and 53.7 lg h/mL, respectively, compared to 34.6 lg.h/mL in serum. The rate of elimination of amoxicillin from tissue cage fluids was somewhat longer than the terminal half-life of serum,

Fig. 5. Mean  SEM (n = 10) amoxicillin concentration in serum in the first 24 h after intramuscular injection at a dose rate of 15 mg/kg.

Fig. 6. Mean  SEM (n = 10) amoxicillin concentrations in serum, exudate and transudate after intramuscular injection at a dose rate of 15 mg/kg. © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 9 Table 4. Pharmacokinetic parameters for amoxicillin in serum, exudate and transudate (geometric mean and SD, n = 10) Serum Variable (units) Cmax (lg/mL) Tmax (h)* T½ (h)† AUC0–last (lg h/mL) AUC0–∞ (lg h/mL) AUC0–24 (lg h/mL) AUC0–48 (lg h/mL) MRT(0–last) (h)* CI/F (mL/kg/h)

Exudate

Transudate

Mean

SD

Mean

SD

Mean

SD

2.91 1.30 12.9 35.2 36.3 25.8 31.9 17.65 428.4

0.93 0.35 10.9 6.88 6.66 5.33 6.53 6.261 92.3

1.29 10.6 17.2 46.0 46.8 21.9 36.5 31.7 NA

0.16 5.17 3.71 20.67 21.07 8.87 14.66 4.65 –

1.45 14.5 17.9 53.7 55.0 25.8 43.4 31.7 NA

0.49 9.03 6.10 14.83 14.88 8.44 13.12 3.59 –

*Arithmetic mean. † Harmonic mean. Tmax, Time following dosing at which the maximum concentration (Cmax) occurred. T½: Half-life; AUC0–last, Area under the concentration–time graph from 0 to the last sample; AUC0-∞, Area under the concentration–time graph from 0 to infinity; AUC0–24, Area under the concentration–time graph from 0 to 24 h; AUC0–48, Area under the concentration–time graph from 0 to 48 h; MRT, Mean residence time; CI/F, Clearance scaled by bioavailability.

indicated by mean T½ values of 17.9 h for exudate and 19.8 h for transudate, compared to 12.9 h for serum. Longer overall persistency of amoxicillin in exudate and transudate was indicated by higher MRTs, 29.6 and 29.0 h compared to 16.5 h in serum (P < 0.01). Pharmacokinetic/pharmacodynamic integration. Pharmacokinetic (PK)/pharmacodynamic (PD) integration established the values of Cmax/MIC, T>MIC, AUC0–24 h/MIC and AUC0–∞/MIC for amoxicillin, derived from in vivo concentrations in the PK study (10 animals) and in vitro arithmetic mean MICs (six isolates) measured in serum of 0.11 lg/mL for M. haemolytica and 0.20 lg/mL for P. multocida (Table 5). Cmax/MIC and AUC0–24 h/MIC ratios and T>MIC indicated that serum concentrations of amoxicillin would be predicted to have a high level of activity against the six isolates of P. multocida and M. haemolytica investigated. Average amoxicillin concentrations (Cave) in serum in the PK study, over four successive 24-h time periods, from 0–24 to 72–96 h, were determined relative to the mean serum MICs for the two test organisms (Table 6). The ratios were >1:1 up to 48 h. Ratios of Cave/MIC in exudate and transudate exceeded 1:1 for at least 72 h (data not shown).

Table 5. PK/PD integration for amoxicillin in calf serum (mean and SEM, n = 10 calves)

Variable (units) Cmax/MIC AUC0–24/MIC (h) AUC0-∞/MIC (h) T>MIC (h)

P. multocida (mean MIC = 0.20 lg/mL) 13.9 128.9 178.8 40.3

© 2015 John Wiley & Sons Ltd

(0.29) (2.17) (2.11) (3.38)

M. haemolytica (mean MIC = 0.11 lg/mL) 25.2 234.3 325.0 57.6

(0.29) (2.17) (2.11) (4.55)

Table 6. Average serum amoxicillin concentration/MIC ratios for four 24-h periods following IM dosing at 15 mg/kg (n = 10) Cave/MIC Time period after dosing (h)

0–24

24–48

48–72

72–96

P. multocida

5.37

1.28

0.49

0.13

9.76

2.33

0.89

0.24

M. haemolytica

Based on serum mean MIC (0.20 lg/mL) Based on serum mean MIC (0.11 lg/mL)

Dosage determination by Monte Carlo simulation using a steadystate approach (as would be obtained after multiple doses given every 48 h) Predicted doses for the three levels of growth inhibition are presented in Table 7. The relationships between dose and TAR for (i) both organisms, (ii) three levels of growth inhibition and (iii) for both single-dose and steady-state approaches are shown in Fig. 7. The Monte Carlo simulations indicated that 90% TAR for P. multocida would be achieved in steady-state conditions (i.e. approximately after 4 half-lives, after the second administration) with maintenance daily doses of 15.5 mg/kg (bacteriostasis), 24.7 mg/kg (bactericidal action) and 32.8 mg/kg (4log10 reduction in bacterial count). Comparative values for M. haemolytica were 13.7, 27.1 and 33.8 mg/kg, respectively. Dosage determination by Monte Carlo simulation using the singledose calculation Predicted dosages are presented in Table 7. The doses predicted for bacteriostatic and bactericidal effects over 48 h for P. multocida were 8.96 and 14.32 mg/kg for 50% TAR.

10 P. Lees et al. Table 7. Predicted dosage based on PK/PD modelling and Monte Carlo simulation of amoxicillin data in serum using the steady-state or the singledose calculation (long-acting veterinary drugs) for computation Computed dose to guarantee average serum concentration of кPD-fold MIC for a duration of 48 h Predicted doses for P. multocida Bacteriostatic Bactericidal 4log10 reduction in count Predicted doses for M. haemolytica Bacteriostatic Bactericidal 4log10 reduction in count

Steady-state approach

Single-dose approach

TAR 50%

TAR 90%

TAR 50%

TAR 90%

8.13 13.00 17.24

15.49 24.75 32.82

8.96 14.32 18.99

17.68 28.26 37.47

7.56 14.93 18.62

13.73 27.12 33.81

8.98 17.73 22.1

17.69 34.93 43.56

TAR = target attainment rate (probability for the plasma concentration to exceed the PD endpoint for efficacy). Dosages were computed by Monte Carlo simulation using equations (5) and (7) for the steady-state and loading-dose approaches, respectively, with (i) MICliterature distributions ranging from 0.0312 to 4 lg/mL (n = 76) for P. multocida and 0.125 to 0.5 lg/mL (n = 59) for M. haemolytica (Guyonnet personal communication, 2013), (ii) average AUC(0–24 h/MICe)/24 h = кPD calculated for experimentally obtained bacteriostatic, bactericidal action or 4log10 reduction in count (data from three or four strains); (iii) individual clearance and elimination constant (K10) empirical distributions obtained for 10 healthy calves (this study) receiving the dose recommended by the manufacturer (15 mg/kg); fu the amoxicillin free fraction as per Villa et al., 1994.

Corresponding values for M. haemolytica were similar, 9.0 and 17.7 mg/kg. For 90% TAR over 48 h, predicted doses for bacteriostatic action were 17.7 mg/kg (P. multocida) and 17.7 mg/kg (M. haemolytica). Higher dosages were estimated for a bactericidal action over 48 h and 90% TAR, 28.3 mg/kg (P. multocida) and 34.9 mg/kg (M. haemolytica). The simulations further indicated that, after a single administration and for a bactericidal effect, the recommended dosage of 15 mg/kg would have a TAR of 60 to 65% for P. multocida and only 35% for M. haemolytica. The predicted single dose exceeded the steady-state dose by 10–30% across the range of TARs as shown in Fig. 7(e). DISCUSSION Pharmacodynamics In this study, for clinical isolates of the calf respiratory pathogens, M. haemolytica and P. multocida, MICs were, on average, slightly (1.1-fold) but not significantly greater in serum than in the artificial growth medium, MHB. In comparing MICs generated in these two matrices, it should be noted that total protein and albumin concentrations in the calf serum used in this study were 60.9 and 37.6 g/L, respectively. Corresponding concentrations in MHB were much lower, 3.78 and 0.08 g/L (Brentnall et al., 2012). In vivo, most AMDs bind to serum proteins, mainly to albumin, to varying degrees, and for amoxicillin, the reported percentage protein binding in the calf was 32  3 (Villa et al., 1994). Assuming a similar level of binding to serum proteins in this in vitro study and no protein binding in MHB, an increase in MIC of approximately 50% (fu = 0.68 and 1/fu = 1.47) for serum compared to MHB would be predicted. The differences in MIC between MHB and serum actually obtained were slightly less and nonsignificant, thus indicating

no major impact of growth matrix composition on MIC. In contrast to these moderate differences between matrices for amoxicillin, for drugs of the tetracycline (oxytetracycline) and triamilide (tulathromycin) classes, matrix had a very marked impact on MIC and MBC values (Illambas et al., 2009; Potter et al., 2009). The principal MIC and MBC data in this study were established for an intermediate starting bacterial count. However, additional data for high compared to low initial inoculum counts were generated; M. haemolytica MIC was 5-fold greater and P. multocida MIC was 3-fold higher with the high starting inoculum count. For these organisms, pathogen load in clinical disease is therefore likely to be a crucially important factor in determining an optimal dosage regimen, which ideally is one that eradicates bacteria. The importance of pathogen load for the fluoroquinolone, marbofloxacin, was demonstrated by Kesteman et al. (2009). In a rat lung Klebsiella pneumoniae infection model, the AUC/MIC ratio required to prevent the emergence of resistance was fourfold higher with a high compared to a low pathogen load. The development of resistance to marbofloxacin was further shown to be greater in an Escherichia coli infection mouse thigh model, when animals were infected with a high, compared to a low, initial inoculum (Ferran et al., 2009). Therefore, it will be appropriate to undertake further time-kill studies with a heavy initial inoculum to determine AUC(0–24 h)/MIC values of amoxicillin (vide infra) and therefore dosages required for each predetermined level of bacterial kill. Type of bacterial kill profile The scientific literature has, almost invariably, classified amoxicillin together with other penicillins as time dependent in killing actions (Craig, 1998; Frimodt-Moller, 2002; McNab & Bui, 2002; Martinez & Silley, 2010). However, whether the killing action is time, concentration or codependent can vary between © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 11

TAR M. haemo. (steady state calculation) 100 80 60 40

Bacteriostatic M. heamo Bactericidal M. heamo Eradication M. heamo

20 0 0

10

20

30

TAR P. multo. (steady state calculation)

(c)

40

Taget attainment rate (%)

Taget attainment rate (%)

(a)

100 80 60

Bacteriostatic P. multocida Bactericidal P. multocida Eradication P. multocida

40 20 0

50

0

10

–1

60

Bacteriostatic M. heamo Bactericidal M. heamo Eradication M. heamo

0 10

20

30

40

Taget attainment rate (%)

Taget attainment rate (%)

80

0

100 80 60

Bacteriostatic P. multocida Bactericidal P. multocida Eradication P. multocida

40 20 0

50

0

10

–1

20

30

40

50

–1

Dose (mg kg )

Dose (mg kg ) Single dose/Steady state dose ratio for both species

(e)

Taget attainment rate (%)

50

TAR P. multo. (single dose calculation)

(d)

100

20

40

Dose (mg kg )

TAR M. haemo. (single dose calculation)

40

30 –1

Dose (mg kg ) (b)

20

100 80 60

M. heamolytica P. multocida

40 20 0 90

100

110

120

130

140

150

Dose ratio (%) Fig. 7. Relationship between dose and Target Attainment Rate (TAR) for M. haemolytica (blue curves) and P. multocida (green curves) using the steady state calculation (Fig. 7a and c, corresponding to administration every 48 h, see eqn 2) or the single dose calculation (Fig. 7b and d, corresponding the use of long acting formulation in large animals, see eqn 8). Fig. 7e represents the ratio (as percentages) of the two doses. See legends of Table 7 for the definition of the distributions considered in and the parameters of the Monte Carlo simulation.

bacterial species for many AMDs. This is well illustrated in the present study by the time-kill data for each of four strains of the pneumonia pathogens, M. haemolytica and P. multocida. © 2015 John Wiley & Sons Ltd

The killing pattern suggests a concentration-dependent action for M. haemolytica in both MHB and serum, as well as for P. multocida in serum. In broth, the killing action against

12 P. Lees et al.

P. multocida was, from the shape and time course of the timekill curves, probably best described as codependent. The concentration-dependent killing profile of amoxicillin in serum in vitro was confirmed in ex vivo studies. Therefore, the modelling of AUC/MIC data as a surrogate for/predictor of efficacy is clearly justified for both bacterial species (Thomas et al., 1998; Schentag, 2000). In addition, it was shown that for drugs like the b-lactams, where efficacy has been found to be correlated to T>MIC, the best PK/PD index shifts towards AUC/MIC dependence as half-life increases (Nielsen & Friberg, 2013). Moreover, similar data have been reported for amoxicillin against single isolates of M. haemolytica and P. multocida obtained from sheep (Delis et al., 2010). These authors reported 2–3log10 decreases in bacterial count, within 8 h of exposure, at only 1xMIC and at least 4log10 decrease in count at 2xMIC, with no regrowth up to 24 h, in the three fluids, MHB, sheep serum and sheep tissue cage fluid. The present data for four isolates of each species, harvested from calf cases of pneumonia, likewise reduced bacterial count by 2– 6log10 cfu/mL at 2xMIC after only 8-h exposure. At 4xMIC, bacterial count was reduced by 5–6log10 cfu/mL after 24-h exposure. Furthermore, Lauritzen et al. (2005) evaluated in pigs single versus divided dosage regimens, with the same total dose of amoxicillin, in an Actinobacillus pleuropneumoniae disease model. With the divided dosage regimen, plasma amoxicillin concentrations exceeded MIC for twice as long as with single-dose treatment, whereas AUC values were similar, as also were clinical efficacy and hematological and biochemical markers. Their data suggested that the activity of amoxicillin was not time dependent in their whole animal disease model. Pharmacokinetic/pharmacodynamic modelling Despite the fact that MICs for amoxicillin were almost identical for MHB and serum matrices, modelling of the time-kill data confirmed that higher amoxicillin concentrations (as multiples of MIC in each matrix) were required to inhibit growth when serum was used as the growth medium compared to MHB. The artificial growth media used (in this study MHB) are formulated to achieve optimal growth of bacteria in vitro, whereas biological fluids, such as serum, interstitial fluid and pulmonary epithelial lining fluids, are not so formulated, yet they comprise the fluids in which organisms grow in causing clinical disease. Differences in composition between artificial growth media and body fluids, such as protein concentration, concentrations of cations and pH, can lead to marked differences in MIC, as demonstrated by data from our laboratory for oxytetracycline (Potter et al., 2009) and tulathromycin (Illambas et al., 2009). Consequently, for both organisms, but especially for M. haemolytica, the findings point to the importance of basing dosage prediction for clinical use on time-kill data generated in serum rather than MHB, as the former is a more relevant physiological fluid. These results show that it is important to generate comparative matrix data of this kind, even when differences

are moderate in magnitude and regardless of cause, when the objective is to correlate PK and PD data for the purpose of dosage prediction (Nightingale & Murakawa, 2002). Pharmacokinetics It was necessary to use a mass spectrometry-based detection analytical method for amoxicillin in this investigation. Ultraviolet detection methodology does not guarantee specificity for amoxicillin, as it is metabolized in vivo. Whilst there are no published data in calves, Reyns and co-workers (Reyns et al., 2008a,b, 2009) have reported formation of two interfering metabolites (amoxicilloic acid and, in smaller amounts, amoxicillin diketopiperazine-20 ,50 -dione) in pigs after both oral and intravenous dosing of amoxicillin. Amoxicillin has a short elimination half-life in all species investigated; it is actively secreted by proximal renal tubular cells and also in some species secreted into bile. Previously reported half-life values after intravenous administration were 1.7 h in calves (Ziv et al., 1977) and 1.3 h in cows (Rutgers et al., 1980). The much longer terminal half-life of 13 h obtained in this study is due to incorporation of amoxicillin in a depot formulation, with prolonged absorption leading to one, two or three peaks in the serum concentration–time profile and assumed flip-flop PK, explaining the long terminal half-life, which is actually an absorption half-life. Pharmacokinetic/pharmacodynamic integration Pharmacokinetic/pharmacodynamic integration may be regarded as a complimentary approach to PK/PD modelling for predicting the adequacy of a dosage regimen in clinical subjects. For the six strains each of the two pathogens used in this study, PK parameters were integrated with the MIC data to derive the three commonly used PK/PD surrogates, Cmax/MIC, AUC/MIC and T>MIC, required to inhibit growth. All of these are dose dependent and all were predictive, from the present data, of a high level of bacterial kill for this product against the 12 isolates of the two pathogens investigated. Thus, for M. haemolytica and P. multocida, serum values of Cmax/MIC exceeded 10:1 and 20:1, AUC0–24/MIC exceeded 100 and 200 h, and T>MIC was greater than 40 and 55 h, respectively. Of course, these PK/PD variables should also be integrated with field derived MIC50 and/or MIC90 or using MIC distribution values from field isolates, as predictors of efficacy under field conditions, as outlined below. Monte Carlo simulations to estimate dosage As noted above, lower amoxicillin concentrations were required for bacterial kill when time-kill data were determined in broth; therefore, had the following simulations been based on the latter data, lower dosages would have been predicted, especially for M. haemolytica. However, we suggest that serum is a more clinically relevant fluid than broth for generating PD data to predict clinically relevant dosage schedules. © 2015 John Wiley & Sons Ltd

Amoxicillin and calf pathogens 13

Monte Carlo simulations predicted the single doses providing bactericidal concentrations for both pathogens throughout a 48-h period for a 50% TAR; for both species, these were similar to the recommended dosage of 15 mg/kg. However, they further predicted that single doses similar to 15 mg/kg would provide bacteriostatic concentrations for only 30 to 65% TAR over 48 h. Doses predicted to achieve eradication over 48-h exposure at 90% TAR were much higher than the licensed dose, 37.5 mg/kg (P. multocida) and 43.6 mg/kg (M. haemolytica). It should stressed that the eradication endpoint under in vivo conditions may differ from predictions based on in vitro data; the natural body mechanisms of defence are likely to be a major factor for eradication, especially if the inoculum size has been previously reduced by the first 24/48 h of drug exposure (vide infra). Target achievement rates of 90% are thus very conservative, as they also include resistant bacterial isolates with MICs at the far right of the distribution curve. The majority of reported Monte Carlo simulations for probabilistic determination rely on steady-state calculations and the AUC0–24 h/MIC ratio (Nielsen & Friberg, 2013), which is not relevant for the long-acting formulations that are usually administered once only and do not achieve a steady-state condition. The present paper proposes a solution for rational dosage determination for long-acting veterinary formulations, with a single injection (the most likely clinical scenario) or with injections repeated every 48 h. Comparison of the predicted dosages confirms that the doses determined by the steady-state approach for a dosage interval of 48 h were marginally lower than when using the single-dose approach in calves. Experimental versus field conditions Under field conditions, there are many factors that will determine the dosage required to achieve the gold standard of AMD therapy, namely a bacteriological cure, with no emergence of resistant strains for the target pathogen. It is therefore necessary to make the following cautionary statements. Our dosage calculations are based on: (i) a moderate to severe bacterial load in the time-kill studies (starting inoculum count in the range 106 to 107 cfu/mL in both in vitro and ex vivo studies); (ii) PK data generated in only 10 healthy calves rather than population PK from a larger number of animals with clinical disease whose Cl/F may differ; (iii) data for MIC field distributions were limited and obtained from one source (76 isolates of P. multocida and 59 isolates of M. haemolytica) and therefore are not guaranteed to be wholly representative of field isolates; ideally a larger number of the order of 400 isolates would be used; and (iv) a value of amoxicillin for binding to serum proteins in vivo, based on a single study in healthy animals and not from calves with natural disease. Moreover, the calculations do not and cannot take account of any contribution to outcome provided by each animal’s own defence mechanisms, recognizing that BRD calves may/may not be immune competent. Nevertheless, we propose that these PK/PD integration and modelling approaches, combined with Monte Carlo simulations, provide a novel and rational basis for dose determination © 2015 John Wiley & Sons Ltd

to be evaluated subsequently in clinical trials. Moreover, our approach avoids many of the problems associated with (and will be generally superior to) traditional dose titration studies as discussed by Lees et al. (2004). Such studies are limited, at best, to an attempt to determine an effective rather than an optimal dosage regimen; as such, they offer very little to the problem of avoiding the emergence of AMD resistance.

ACKNOWLEDGMENTS This study was supported by a generous grant from the Department for the Environment, Food and Rural Affairs (DEFRA, United Kingdom). Amoxicillin was supplied by Norbrook Laboratories Ltd.

SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article: Data S1. Additional data on in vitro findings.

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