Covariate determinants of effective dosing regimens for time-dependent beta-lactam antibiotics for critically ill patients

Aims. Critically ill patients undergoing aggressive fluid resuscitation and treated empirically with hydrosoluble timedependent beta-lactam antibiotics are at risk for sub-therapeutic plasma concentrations. The aim of this study was to assess the impact of two covariates – creatinine clearance (Clcr) and cumulative fluid balance (CFB) on pharmacokinetics/pharmacodynamics (PK/PD) target attainment within a week of treatment with meropenem (ME) or piperacillin/ tazobactam (PIP/TZB). Methods. In this prospective observational pharmacokinetic (PK) study, 18 critically ill patients admitted to a surgical Intensive Care Unit (ICU) were enrolled. The primary PK/PD target was free antibiotic concentrations above MIC at 100% of the dosing interval (100%fT>MIC) to obtain maximum bactericidal activity. Drug concentration was measured using liquid chromatography-tandem mass spectrometry. Results. The treatment of both 8 septic patients with IV extended ME dosing 2 g/3 h q8 h and 10 polytraumatized patients with IV intermittent PIP/TZB dosing 4.0/0.5 g q8 h was monitored. 8/18 patients (44%) manifested augmented renal clearence (ARC) where Clcr ≥130 mL/min/1.73 m 2. Maximum changes were reported on days 2–3: the median positive CFB followed by the large median volume of distribution: Vdme=70.3 L (41.9–101.5), Vdpip = 46.8 L (39.7–60.0). 100%fTme>MIC was achieved in all patients on ME (aged ≥60 years), and only in two patients (non-ARC, aged ≥65 years) out of 10 on PIP/TZB. A mixed model analysis revealed positive relationship of CFBpip with Vdpip (P=0.021). Conclusion. Assuming that the positive correlation between CFB and Vd exists for piperacillin in the setting of the pathological state, then CFB should predict Vdpip across subjects at each and every time point.


INTRODUCTION
Critically ill patients undergoing aggressive fluid resuscitation and treated empirically with hydro-soluble β-lactams piperacillin/tazobactam (PIP/TZB) and meropenem (ME) may be at risk for sub-therapeutic plasma concentrations as a result of non-attainment of PK/PD targets considered crucial for appropriate bactericidal action.The bactericidal effect of these antibiotics is time-dependent, expressed as % of time in the dosing interval (T) when the plasma concentration of the free drug (f) is elevated above the minimum inhibitory concentration (MIC) for the suspected pathogen -(%f T > MIC).Ideally, this should be 100% of the dosing interval with maximal bacterial killing achieved at concentrations > one MIC or bacterial eradication achieved at four to five times the MIC (ref. 1 ).
Nevertheless, PK/PD target attainment (the desired %f T>MIC) is dependent on pathophysiological factors (covariates) generated by changes in organ function during the course of the disease in critically ill patients.Extravascular volume expansion with fluid loading and increased capillary permeability may alter the volume of distribution 2 , while changes in renal function can significantly influence drug renal clearance.This covariate might significantly influence hydrophilic drug Vd and could be a key factor for PK/PD target non-attainment.Therefore, its value could allow prediction of an individual loading dose compensating for extravascular fluid shift during the first days of therapy.
Another important value is the development of augmented renal clearance (ARC) -a phenomenon in which renal excretion of hydro-soluble beta-lactams is increased.ARC is defined by a creatinine clearance (Cl cr ) more than or equal to 130 mL/min while plasma creatinine concentrations remain normal 3 .For the assessment of ARC, a cut-off of Cl cr ≥130 mL/min normalized by the body surface area (BSA) calculated as weight (kg) 0.425 × height (cm) 0.725 × 71.84/10 000 (ref. 4 ) and was used based on previous data demonstrating an association with subtherapeutic ß-lactam concentrations, while using standard dosing 1,5,6 .6][7][8][9] ) depending on the population studied and the cut-off values used for its definition 8,10 .
Extravascular volume expansion assessed as positive cumulative fluid balance (CFB) was reported in ICU patients undergoing aggressive fluid resuscitation for prevention against hypotension and prolonged vasopressor use 11,12 .This covariate might significantly influence hydrophilic drug Vd and could be a key factor for PK/ PD target non-attainment.Therefore, its value could allow prediction of an individual loading dose compensating for extravascular fluid shift during the first days of therapy.
The primary aim of this study was to verify the impact of covariates, mainly CFB and Cl cr on the PK/PD target attainment (%fT>MIC).7-day monitoring was considered to be long enough to describe the two phases of IV fluid therapy namely Resuscitation and Optimisation aimed at correction of shock and maintenance of tissue perfusion, which are the most important for monitoring, as both intensity and treatment strategy should be individualized 11 .

Ethical consideration
The study protocol was in accordance with the ethical standards laid down in the 2013 Declaration of Helsinki, and was approved by the Ethics Committee of the University Hospital Hradec Králové, Czech Republic in June 27, 2012.All patients or their relatives signed the informed consent before inclusion in the study.

Study patients
Enrolled in this prospective observational pharmacokinetic study were 18 critically ill patients admitted to the Surgical ICU of the University Hospital in Hradec Králové, Czech Republic.The inclusion criteria were a diagnosis of severe sepsis or septic shock or a systemic inflammatory response (SIRS), together with treatment with a broad-spectrum beta-lactam antibiotic meropenem (ME) respectively piperacillin-tazobactam (PIP/TAZ), provided that the patients signed the informed consent.Patients meeting any of the following criteria were excluded: age less than 18 years or more than 85 years, an expected ICU stay <24 h, allergy to any of the investigated antibiotics, any evidence of chronic kidney disease or renal replacement therapy, chronic liver disease (cirrhosis or ongoing liver dysfunction with hepatitis) (ref. 13,14).Participants were not allowed to receive any histamine-2-receptor antagonist due to interaction with tubular creatinine secretion 15 .
Patients were admitted to ICU on day 0. Administration of antibiotics was started on day 0 and plasma concentration monitoring was initiated on day 2 (after the fourth to fifth dose), except for patients who underwent some additional treatment (re-operation).In such a case, the start of monitoring was postponed to day 3-4.
The duration of antibiotic monitoring was related to ICU stay and was usually terminated on day 6-7 regardless of the duration of antibiotic treatment.

Dose adjustement
Antibiotic dosing was administered according to local guidelines for empiric antibiotic therapy.ME was used in the case of suspected colonization by extended spectrum beta-lactamase positive Gram-negative bacteria.Eight patients with peritonitis received an extended infusion dose of 2 g ME every 8 h given by 3 hours IV infusion using a syringe pump via a central venous catheter.Ten polytraumatized patients received empiric intermittent treatment with 4.0/0.5 g PIP/TAZ given by 1-h IV infusion every 8 h via the same way.
All patients were given IV fluid therapy with balanced crystalloids as early goal-directed therapy 12 .24 hours (daily) fluid balance (DFB) was recorded as the difference between daily fluid intake and output and the CFB was calculated as the total volume of fluid accumulated over a set period of time 11 .
In all study patients, demographic, pre-existing chronic disease, admission diagnosis and biological data were collected in institutional databases.The severity of illness of each patient was characterized using the Acute Physiology and Chronic Health Evaluation (APACHE II) or the Injury Severity Score (ISS) (ref. 16) and sequential organ failure assessment (SOFA) (ref. 17).Treatment of patients with catecholamines and mechanical ventilation was recorded, as was duration of ICU and hospital stay.Hemodynamic data were collected as baseline, and 8 and 24 h after the start of the protocol.

Laboratory analysis
Serial blood samples were collected over days 2 to 7 as follows: pre-dose, and at 1, 2.5, 4.5 and 6.5 h post-dose for PIP/TAZ (PIP); pre-dose and at 1, 2.5, and 4.5 h postdose for ME.Specimens were centrifuged at 3.000 rpm for 10 min within 30 min of sampling, and then frozen at -80 °C until analysis.Via an indwelling urinary catheter, urine samples were taken at 0-T (over the postdose interval, i.e. between the end of infusion to the next dose administration), and as 24-hour urine collection.The samples were analysed at the Central Laboratory of Clinical Chemistry Department, University Hospital in Hradec Králové using the previously validated method based on liquid chromatography-tandem mass spectrometry (LC-MS/MS) (ref. 18).The limits of detection of PIP and ME were 0.003 mg/L in plasma and urine.The calibration curves for both beta-lactam antibacterials were linear over the concentration range of 0.84-201 mg/L with correlation coefficient (r 2 ) = 0.999.The limit for quantification was 0.047 mg/L (for PIP) and 0.048 mg/L (for ME).Total plasma concentrations were measured.Correction for PIP protein binding (22%) was based on the published data 19 .Total plasma concentration of ME was not corrected as plasma protein binding is only 2% and considered not significant.

Pharmacokinetic analysis
Plasma and urine drug concentrations were used to estimate PK variables using the non-compartmental analysis as follows: the elimination rate constant (k e ) was calculated by least-squares linear regression of the loglinear portion of the plasma concentration-time curves, and elimination half-life (t 1/2 ) was calculated as 0.693/k e .The area under the plasma concentration-time curve (AUC 0-T ) was obtained using the linear trapezoidal rule.Total (plasma, systemic) clearance (Cl tot ) was estimated as dose/AUC 0-T and renal clearance (Cl ren ) as Au 0-T /AUC 0-T , where Au 0-T is the amount of the antibiotic excreted in urine over the postdose interval.Volume of distribution (Vd) = Cl tot /k e (ref. 20).
The 24-hour creatinine clearance (Cl cr ) was measured every study day 5 .Cl cr = U v x U cr / (1.440 x S cr ) x 1.73m 2 / BSA, where U v is urinary volume, U cr the urinary creatinine concentration (µmol/L), S cr is the serum creatinine concentration in the middle of a sampling period (µmol/L) (ref. 5), and BSA is body surface area.

Pharmacodynamic analysis
The PK/PD target was free drug concentration maintained above the MIC of the suspected pathogen for 100 % of the dosing interval (100%fT > MIC target), where MIC is a hypothetical target (minimum inhibitory concentration) for the susceptibility breakpoint of the least susceptible microorganisms (wild-type Pseudomonas spp.) for which these antibiotics were used (according to EUCAST) (ref. 21) in accordance with previous studies 5,9 .

PK/PD target attainment
The percentage time of the free fraction above the MIC (%f T>MIC) was evaluated by a graphical method 22 or calculated using a mathematical expression 23 .
This was defined as %f T pip >MIC (16 mg/L) for PIP and %f T me > MIC (2 mg/L) for ME.

Clinical response testing during the clinical study
a) Definition of treatment outcome: a/ Positive treatment outcome was completion of the treatment course without change or addition of antibiotic therapy or commencement or additional antibiotics within 48 h of discontinuation of the antibiotic therapy.
b) The disappearance of all signs related to aseptic or septic SIRS, or improvement in the form of marked or moderate reduction in their severity and number of signs.Clinical parameters of SIRS were evaluated according to SOFA main symptoms: respiratory parameters (FiO 2 , PaO 2 , and ventilation style), blood parameters (platelets), liver function (bilirubin), central nervous system condition (GCS), cardiovascular parameters (MAP), vasopressors administration, kidney functions (serum and urine creatinine, urine output) -all at the start and on the end of the study.c) Hemodynamic monitoring and testing the organ functions and return to the normal tissue perfusion: physical examination and review of observations such as peripheral perfusion, oedema, oxygen saturation, and ECG.A daily fluid balance that could be in equilibrium or even negative by the study end (day 7).Fluid balance was considered the essential biomarker of critical illness.

Statistical analysis
Continuous data are presented as the median (interquartile range).Statistical software package -Sigma Plot 13 SPSS, Inc. Chicago, IL, USA was used for comparison of data between groups and intra-patient data by means of non-paired and paired t-test.

Identification of covariates
Statistical analysis was performed using the NCSS 9 software -Hintze, J. (2013) NCSS 9. NCSS, LLC.Kaysville, Utah, USA, www.ncss.com(ref. 24).To evaluate changes in both %fT and Vd during antibiotic treatment and the impact of CFB and Cl cr , we used mixed effect models -a general procedure, which allows for repeated measurements.For MER, the day of treatment was entered as a categorical fixed effect, with CFB and Cl cr as covariates.The variable patient was entered as a random effect.
For PIP, the variable day of treatment was entered as a possible covariate together with CFB.The distribution of Cl cr values enabled us to divide them into two categories: below 130 mL/min/1.73m 2 and above this valueand enter Cl cr as a factor.The patient x time interaction represented the random model.The significance of the fixed components was tested with an F-test adjusted by Kenward -Roger correction.The significance level was P>0.05.If appropriate, Bonferroni adjustment for multiple tests was used.M-male, F-female, + data given as mean (±SD), *data given as median (range)

RESULTS
18 patients were enrolled after admission to the Surgical ICU of the University Hospital in Hradec Králové, Czech Republic.The reason for admission was abdominal sepsis (n=8) or polytrauma manifesting SIRS (n=10) (Table 1).Patients suffering from abdominal sepsis were treated with ME and polytraumatized patients were given PIP.Prospective data collection was conducted on study days (over 2-7) dependent on therapeutic procedures (re-operation, special examination).Finally, the study days were stratified into 3 groups including day 2-3, 4-5, and 6-7, respectively.
Blood samples were taken as follows: one predose and three postdose blood samples (for ME detection) were taken during 3 study days from 8 ICU patients.One predose and four postdose samples (for PIP detection) were taken during 3 study days in 5 ICU patients, and during 2 study days in 5 patients.In total 221 samples were analysed.Urine samples: single concentrations were obtained for each patient from urine collected over the postdose interval and a 24h -urine collection per study day.In total 104 urine samples were obtained and analysed.Eight/18 patients (44%) manifested ARC (Cl cr >130 mL/min/1.73m 2 ) -seven polytrauma subjects, one with sepsis.Three/8 patients manifested ARC on one occasion during the 7-study days, 5/8 patients on more than one occasion of Cl cr measurements.

The impact of two covariates -Cl cr and CFB on %fT and antibiotic Vd
The mixed model analysis of PIP data revealed a statistically significant difference in %fT pip for two categories of Cl cr (Cl cr >130 mL/min and Cl cr <130 mL/min) (P= 0.0018) (Table 2).Also, the analysis of ME data showed a significant inverse relationship between %fT me and Cl cr : %fT me declined with elevated value of Cl cr (P=0.012)(Table 3).There was non-significant relationship between CFB me and Vd me (P=0.10)(Table 3), while Vd pip became much larger with a higher value of CFB (P=0.021)(Table 2).
Clinical response to treatment a.During patients ICU stay (terminated by day 7-10), there was no modification of antibiotic therapy.b.The initial clinical or laboratory data describing the patient states are given in Table 1.By the end of 7-day monitoring the score value of SOFA -median (range) in patients suffering from polytrauma dropped as follows 7.5 (3-14) to 2 (2-9), P<0.001 and in abdominal peritonitis 8 (3-16) to 2.5 (0-8), P<0.001.
No patient died within the stay in the ICU so as later.

DISCUSSION
This study demonstrates significant higher values of the Vd of both betalactam antibiotics given to the ICU patients if compared with data reported for healthy volunteers or less seriously ill patients [25][26][27][28] .The impact of age and decreasing Cl cr (ref. 29) was noticed in renal clearance estimation.Values of the median Cl tot,me and that of Cl tot,pip were higher than that estimated in healthy volunteers 30 , and compatible with patients´data 31 in the septic patients > 60 year old, Cl ren,me reached only 44.5% of Cl tot,me and indicated the augmented extrarenal clearance in critically ill older patients also reported by others 25 .This outcome is considered a consequence of increased exposure to dehydropeptidase 1, causing nonspecific hydrolysis in tissue to an inactive metabolite 27 .The primary PK/PD target were free antibiotic concentrations above the MIC at 100% of the dosing interval (100%fT > MIC).As demonstrated above, 7-study day monitoring revealed that intermittent dosing 4.0/0.5 g q8h of PIP, and extended infusion dosing 2.0 g/3 h q8h of ME was sufficient for obtaining this predefined exposure in non-ARC patients aged ≥ 60 year, approximately, but was not achieved in younger ARC patients in accordance with previous reports 5,27 .If fourfold the MIC is the target of intervention, then %fT me ranges 40-100 % with low values within 40-70% attributed to 3 patients with normal or augmented renal clearance.Accordingly, %fT pip is within 8-26%.
This failure after conventional dosing is considered a result of sub-therapeutic plasma concentration-time profiles and changes in PK parameters (Vd and Cl), affected by two main covariates: Cl cr and positive CFB.Positive CFB (reflecting extravascular volume expansion) results from increased capillary permeability and IV fluid loading which is widely regarded as the first step in the resuscitation of critically ill and injured patients who have evidence of impaired organ perfusion.The present study shows a rapid increase in CFB during days 0-1 culminating on days 2-3, that is followed by a large value of Vd of ME and PIP.A normal value of Vd reflecting both the dose and extracellular distribution usually ranges 0.2-0.4L/ kg.In a pathological setting this value can exceed the real extracellular fluid volume as a result of higher penetration into intraabdominal and pulmonary tissues, skin or peritoneal fluids, or may reflect higher tissue binding 25,32 .Thus positive CFB underlines the importance of individual dosing that would compensate an intravascular drug deficit due to extravascular volume expansion.
This study also denotes the impact of two pathological models -polytrauma and sepsis -on kinetic variables mediated via the covariates.CFB correlated with Vd pip (in polytraumatized patients) , while not with Vd me (in sepsis).This difference can be attributable to the patient (age, renal function), to the properties of a drug and especially to the pathological setting.It seems that positive correlation between CFB and Vd does not develop in the pathological state suppressing renal functions as shown via Cl cr.The influence of Cl cr may be bidirectional: high Cl cr predicts non-achievement of the predefined %f T (ref. 5,22) and failure of antibiotic therapy as shown in patients treated with conventional dosing of piperacillin.Reduced Cl cr and consequent low antibiotic Cl ren can result in drug accumulation 22,30 and elevated %f T. Unfortunately, Cl cr was shown to be a covariate not predictive of variations in drug PK/PD target attainment in such setting 33 .Is CFB next covariate that should be taken into consideration as the predictor of the first (loading) doses and that presented by Cl cr as the predictor of next dosing adaptation?

Limitation
This study has a number of limitations.First, only a small number of patients were eligible, even if these subjects were monitored 2-3times a 7-day treatment.Secondly, %fT was based on 1-week empirical treatment with broad spectrum beta-lactams and MIC obtained from EUCAST, but de-escalation does not seem to resolve the problem of under-dosing.The probability that therapeutic exposure of critically ill patients would be achieved was shown even lower for narrower-spectrum antibiotics with conventional dosing than that for the broad-spectrum drugs 34 .Thirdly, the target attainment defined as 100%fT >MIC and/or 100%fT >4 MIC should be analysed since the first 24 h of treatment.
This aside, we believe that a more detailed analysis of the relationship between Vd a CFB and its practical use is worth studying next.Fluid balance as a predictor of drug Vd available at the bedside would help critically ill ICU patients, who require adequate dosing within 24 h after the start of treatment and /or next dose adaptation 35 .

CONCLUSION
Assuming that the positive correlation between CFB and Vd exists for piperacillin in the pathological setting, then CFB should predict Vd across subjects at each and every time point.The authors recommend to use two times higher starting dose of piperacilin/tazobactam and 100%f T > 4 MIC for PK/PD target attainment in critically ill patient undergoing aggressive fluid resuscitation than in standard type of patient.

ABBREVIATIONS
%fT, the percentage time during the dosing interval (T) where the free (unbound) drug concentration (f) remained above the MIC of the suspected pathogen; APACHE II, Acute physiology and chronic health evaluation II; ARC, Augmented renal clearance; AUC, Area under the curve; BSA, Body surface area; Cl ren , Renal clearance; Cl cr , Creatinine clearance; Cl tot , Total (plasma) body clearance; CFB, Cumulative fluid balance; DFB,

Fig. 1 .
Fig. 1.Cumulative fluid balance (CFB) in a/ septic patients treated with meropenem (CFB me ) and b/ polytraumatized patients treated with piperacillin/tazobactam (CFB pip ) during 7 days.CFB [L] measured as the difference between fluid input and loss results from increased vascular permeability and fluid loading.The extreme values in CFB me were noticed in the patient with the initial Cl cr = 9 mL/min.The median CFB me and CFB pip reached a maximum on day 2-3 and slowly declined afterwards if fluid therapy was stopped and enhanced vascular permeability returned to a normal state.

Fig. 2 .
Fig. 2. Meropenem a/ volume of distribution (Vd me ) and b/ total clearance (Cl tot.me ) estimated in septic patients treated with meropenem at extended infusion dosing 2 g over 3 h every 8 h for 7 days.

Table 1 .
Baseline demographic characteristics and prognostics scoring systems and systemic therapies.

Table 2 .
Piperacillin.Description of fixed effects in models for %fT pip and Vd pip .

Table 3 .
Meropenem.Description of fixed effects in models for %fT me and Vd me .Therefore, we cannot exclude a significant relationship between CFB me and Vd me that could be registered in a study conducted with numerous patients who experience normal or augmented renal clearance.