Comparative polymyxin B pharmacokinetics in critically ill patients with renal insufficiency and in continuous veno-venous hemodialysis

The aim of this study was to assess polymyxin B pharmacokinetics (PK) in patients with varying degrees of renal dysfunction and in patients who require continuous veno-venous hemodialysis (CVVHD). The study enrolled 37 patients with sepsis, including 13 patients with glomerular filtration rate (GFR) below 80 mL/min and 11 patients on CVVHD. Each patient received a loading dose of polymyxin B (200–300 mg) and at least 3 subsequent doses of 100–150 mg every 12 h. For every patient, 6–8 blood samples were collected between doses. Polymyxin B (PMB) serum concentration was determined using enzyme-linked immunosorbent assay. In sepsis, patients with preserved renal function mean area under the curve over 24 h (AUC0–24 h) value reached 67.8 ± 9.8 mg*h/L, while in patients with GFR below 80 mL/min, mean AUC0–24 h was 87 ± 5.8 mg*h/L. PMB PK in patients with renal insufficiency was characterized by significantly lower clearance (CL) compared to the normal renal function group (2.1 ± 0.1 L/h vs 3.9 ± 0.4 L/h respectively). In patients on CVVHD, mean AUC0–24 h was 110.4 ± 10.3 mg*h/L, while CL reached 2 ± 0.23 L/h. The median recovery rate from dialysate constituted 22%. Simulation of different dosage regimens that indicate a fixed maintenance dose of 100 mg q12h with a loading dose of 200 mg is optimal for patients on CVVHD, and no dosage increase is required. This study demonstrates decreased clearance of PMB in patients with renal insufficiency, which puts them at risk of toxicity. Therefore, patients with extremes of renal function might benefit from therapeutic drug monitoring. For patients with anuria, who require CVVHD, we suggest a fixed dose of 100 mg q12h.


Introduction
Polymyxin B and polymyxin E (colistin) have become important treatment options in patients with infections caused by carbapenem-resistant bacteria, namely A. baumannii, P. aeruginosa, and K. pneumoniae [1,2]. These drugs have a relatively narrow therapeutic window [3]; therefore, it is critical to determine drug pharmacokinetics in different subsets of critically ill patients. Despite their similar molecular structure, polymyxin B and colistin have different pharmacokinetic properties. Colistin is administered as a prodrug colistin methanesulfonate, which is renally cleared [4,5], whereas polymyxin B is an active drug with predominantly non-renal mechanisms of clearance [6]. Unfortunately, most of the current data on polymyxin pharmacokinetics (PK) was derived from colistin studies and cannot be extrapolated to polymyxin B PK [7]. Acute kidney injury (AKI) is an important risk factor in sepsis with odds ratio for death around 1.5 [8,9]. Importantly, polymyxin therapy is itself a factor of nephrotoxicity which may reach 26% for colistin and 34% for polymyxin B [10], and the risk of nephrotoxicity is significantly higher at exposures (AUC 0-24 h ) above 100 mg*h/L [11]. Current consensus guidelines recommend against polymyxin B dosage adjustment in patients with renal impairment [3], as no association between polymyxin B clearance and renal function was observed in several studies [12][13][14]. In contrast, the largest study in patients with renal insufficiency completed so far demonstrated a significantly higher polymyxin B exposure (AUC 0-24 h 108.7 in patients with renal impairment versus 68.2 mg*h/L in patients without it) [15]. This implies that dosage correction might be necessary in extremes of renal function or in patients with AKI, who require renalreplacement therapy. Continuous renal-replacement therapy (CRRT) is frequently applied to substitute renal function in patients with AKI. This procedure might have a significant effect on drug clearance, as was previously demonstrated for colistin, which requires increased dosages during CRRT [16,17]. The primary determinants of the extracorporeal clearance are CRRT modality, protein binding, dialysis dose, and certain physicochemical characteristics, such as molecular size and lipophilicity [18]. Polymyxin B PK in continuous veno-venous hemofiltration (CVVH) was recently described in two studies, which demonstrated a significantly higher clearance and lower exposure on CVVH compared to offtherapy [19,20]. In contrast, in two patients receiving continuous veno-venous hemodialysis (CVVHD), no significant effect was demonstrated [21]. Given the scarcity of data and conflicting results in regard to polymyxin B PK in patients with renal dysfunction and patients, undergoing CRRT, additional studies are required to understand the necessity for dosage adjustments and potential applications for therapeutic drug monitoring.
The aim of this study was to extend current knowledge on polymyxin B pharmacokinetics in critically ill patients with or without renal insufficiency, as well as in patients, who require CVVHD. To the best of our knowledge, this study presents the largest cohort of patients who have received polymyxin B and CVVHD so far.

Ethics
The research was conducted in accordance with the Declaration of Helsinki and national and institutional standards. This study was approved by MEDSI Clinic Independent Ethical Committee, Moscow, Russia (Protocol #29 April 15, 2021). Informed consent form was signed by legal representatives of the patients.

Patients
The study conducted from May 2021 to February 2022 included in total of 37 patients with sepsis and varying degree of renal function, including 13 patients with preserved renal function (GFR > 80 mL/min), 13 patients with renal dysfunction (GFR 0-80 mL/min) and 11 patients on CVVHD. GFR was calculated on the sample collection day with the Cockcroft-Gault equation [22]. The value of 80 mL/min was selected because it was the median GFR value in patients without CVVHD; moreover, it is useful to relate our results with the largest polymyxin B PK study in patients with renal insufficiency [15]. Patients were included if they received over 48 h of polymyxin B therapy. Exclusion criteria included a low probability of survival in the next 24 h and concomitant extracorporeal membrane oxygenation. Demographic and clinical data is presented in Table 1.
All patients had secondary bacterial pneumonia or bloodstream infection, caused mostly by carbapenemresistant strains of K. pneumonia, A. baumannii, or P. aeruginosa (polymyxin B MIC < 0.5 mg/L). Polymyxin dose was selected by the treating physician. Patients received 100-150 mg (2.5-3 mg/kg/day) of polymyxin B twice daily as a 1-h infusion. In each group, patients received a loading dose of polymyxin B (200-300 mg). The loading and maintenance doses were selected by the treating physician. The dosage form of PMB was Vilimixin®, a product of Prebend Ltd (Moscow, Russia). Minimal inhibitory concentrations are provided based on automatic susceptibility testing with VITEK® 2 (bioMérieux, France). CRRT was performed on Fresenius Multifiltrate machines with Ultraflux® AV1000S filters (Fresenius, Germany); main dialysis parameters are presented in Table 1. Unfractionated heparin was used for anticoagulation in all patients.

Sample collection
For steady-state PK assessment, blood samples were collected after more than 48 h of therapy with polymyxin B, 6-8 blood samples (4 mL) were collected in EDTA tubes just before starting the polymyxin B infusion, 5 min, 30 min, 1, 2, 4, and 8 h after completion of the polymyxin B infusion and 11 h, just before starting the next polymyxin B infusion. Blood samples were centrifuged at 3470 g for 10 min, and the resultant 2 mL of sera was immediately frozen and stored at − 20 °C for 10-90 days until the analysis.

ELISA procedure
Polymyxin B concentration in tested samples was measured using a direct competitive ELISA described in detail previously [23]. The assay detection limit (IC 10 ) was 1.8 ng/mL, and the dynamic range (IC 20 -IC 80 ) constituted 5-200 ng/mL. The samples were diluted 100-fold before the analysis. The intra-and inter-assay coefficients of variation were below 11%. Briefly, serum samples were mixed with equal volume of 5% trichloroacetic acid to precipitate proteins. Next, 100 µL of study samples and 100 µL enzyme conjugate solution, containing polymyxin B conjugated to horseradish peroxidase, were added to 96-microwell Costar plates coated with anti-polymyxin B antibody. After incubation at room temperature for 1 h and wash step, bound enzyme tracer was detected using TMB/H 2 O 2 -substrate mixture (100 µL). Enzymatic reaction was terminated 30 min later with 0.5 M H 2 SO 4 (100 µL), and absorbance was measured at 450 nm using a LisaScan reader (Erba Manheim, Czech Republic).
To determine the analyte in the therapeutic concentration range, samples were diluted 100-fold with the assay buffer and then analyzed by ELISA.

Pharmacokinetic and statistical analysis
Population pharmacokinetic analysis was conducted with a nonlinear mixed-effects modeling approach in Monolix version 2021R1 (Antony, France). Model parameters were estimated using the stochastic approximation expectation-maximization (SAEM) algorithm. Parameters were assumed to follow a lognormal distribution. One-and two-compartmental models were considered. The following parameters were assessed as potential covariates: age, total body weight (TBW), bilirubin level, albumin level, SOFA score, GFR, dialysis, and ultrafiltration  [3]. Additional statistical analysis was carried out with IBM SPSS Statistics version 28.0 (Chicago, SPSS Inc). Continuous variables were compared using Student's t-test and Mann-Whitney for normal and abnormal distribution, respectively. Categorical variables were compared with the χ 2 -test.
The individual PK parameters are presented in Table 2. In sepsis patients with preserved renal function, the median AUC 0-24 h value was 67.3 ± 9.8 mg*h/L (range 31.6-142.5), while in the renal impairment group, the median AUC 0-24 h reached 88 ± 5.8 mg*h/L (range 59.6-130). These groups were perhaps underpowered to detect significant differences between the groups (p = 0.08); however, significant distinctions were demonstrated for dose-normalized values of AUC 0-24 h (1 ± 0.14 versus 1.6 ± 0.1 mg*h/L, p < 0.01). Significant distinctions were observed for total CL, 3.9 ± 0.4 L/h in the preserved renal function group versus 2.1 ± 0.1 L/h in the renal dysfunction group (p < 0.001).
Polymyxin B concentrations versus time curves are presented in Fig. 1. The observed data was best described with a two-compartmental model with constant error model for residual variability. Among the tested covariates, log-transformed GFR and log-transformed albumin levels partly explained inter-individual variability of CL and V2, respectively, and led to model improvement in terms of ΔOFV. Other variables, such as weight, age, sex, total protein level, bilirubin level, and the SOFA score did not lead to model improvement. The resultant population PK model is described with the following equations, and additional data is presented in Table 3.
The RRT group included 11 critically ill adult patients who received CVVHD for AKI, complicating sepsis and  In patients receiving CRRT median AUC 0-24 h was 110.4 ± 10.3 mg*h/L (range 63.9-196.1). The value of AUC 0-24 h was above the recommended toxicity threshold in 7 out of 12 patients (58%). Polymyxin B CL was 2 ± 0.23 L/h (range 1-3.6). As patients in the CRRT group were more severely ill, direct comparison with other groups was not performed. In four patients dialysate was collected over period of 12 h, and total amount of polymyxin B was calculated. The mean amount of polymyxin B in dialysate was 27 mg (range 22.9-34.6), the corresponding mean recovery rate was 22% (range [18][19][20][21][22][23][24]. The corresponding extracorporeal clearance was 0.42 L/h (range 0.27-0.52).
The data was best described with a two-compartmental model with proportional error for residual variability. Among the tested covariates, log-transformed albumin level partly explained inter-individual variability of CL and V2, respectively, and led to model improvement in terms of ΔOFV. Other covariates, including dialysis and ultrafiltration dose, did not result in model improvement. The final population PK model is described with the following equations, and additional data is presented in Table 4.  The resultant population PK models were used to create a simulated dataset of polymyxin B exposure in patients without CVVHD with varying degrees of renal function and in patients on CVVHD with anuria. The range of GFR values simulated in patients without RRT was between 15 and 180 mL/min; the albumin level was fixed at 25 g/L. The simulated maintenance doses included 85, 100, 125, and 150 mg q12h. In patients on CVVHD, the albumin level was fixed at 25 g/L, while the simulated dosage regimes included 75, 85, 100, 125, and 150 mg q12h. The loading doses were simulated as twice the maintenance doses. The Monte-Carlo simulation results are presented in Table 5 together with the PTA analysis. The PTA graphs are presented for selected groups in Fig. 2.

Discussion
Polymyxin B is increasingly used to treat MDR infections; however, the results of PK studies are somewhat controversial. Given the high probability of death in critically ill patients who develop AKI [8,9] and high incidence of polymyxin B-induced nephropathy [10], it is crucial to describe polymyxin B PK in patients with renal insufficiency and in patients who require CRRT. Although polymyxin B clearance is predominantly dependent on non-renal mechanisms and dosage adjustment is not recommended by the current guidelines [3], a weak but significant correlation between polymyxin B CL and creatinine clearance was demonstrated in the study by Manchandani et al. [6], and higher polymyxin B exposure was demonstrated in the largest PK study in patients with renal insufficiency [15]. This study enrolled 37 patients with sepsis, among whom 13 patients with decreased renal function (GFR < 80 mL/ min) and 11 patients receiving CVVHD. The head-to-head PK comparison was performed for patients with preserved renal function and patients with renal insufficiency, while the PK data for the CVVHD group is presented separately. The reason for this is the higher severity of disease in the CVVHD group and the variety of non-renal factors which may account for PK changes.
Overall, compared to the normal renal function group, a significantly higher PMB exposure (dose-normalized AUC 0-24 h ) was demonstrated in patients with renal impairment, 1.6 versus 1 mg*h/L (p < 0.01) respectively. This may be explained by the significant decrease of CL in patients with renal insufficiency, which constituted 2.1 L/h compared to 3.9 L/h in patients with preserved renal function (p < 0.001). These distinctions between the two groups in terms of clearance and exposure support data were presented previously [15], although the observed clearance values were generally higher in our study. The PTA analysis suggests that in patients with GFR of 15 mL/min, all dosages above 85 mg q12h lead to PTA above 90% at MIC ≤ 1, while in patients with preserved and increased renal clearance, higher doses might be required to avoid therapeutic failure.
The CVVHD group demonstrated high exposure values with a mean AUC 0-24 h reaching 110.6 mg*h/L, while the recommended toxicity threshold was exceeded in 58% of patients. This contrasts with the recent study on polymyxin B PK in CVVH [20], in which a threefold lower exposure was shown in patients on RRT compared to the same patients after RRT withdrawal (AUC 0-24 h normalized to dose 1 mg/ kg daily 14.9 vs. 42.8 mg*h/L). Mean AUC 0-24 h normalized the same way (44.5 mg*h/L) in the current study was much closer to the latter value. These differences seem logical, given the different drug clearance mechanisms in CVVH and CVVHD. The observed CL values were similar to those in the renal impairment group (2 L/h), though no formal statistical analysis was carried out. Therefore, high exposures in the CVVHD group should probably be attributed to decreased distribution due to hypoperfusion or decreased renal uptake. The dialysate recovery rate calculated in only 4 out of 11 patients lies between 18 and 24%, which was a little higher than previously reported [21]. The extracorporeal clearance was within the range of 0.27-0.52 L/h.
The results of PTA analysis in patients with anuria, undergoing CVVHD, indicate that at MIC, 1 mg/L maintenance doses of 85 mg q12h are sufficient to reach the predefined efficacy threshold in > 90%. However, given higher mortality at doses below 200 mg/day in patients on RRT in observational studies [24], a fixed dose of 100 mg q12h might be a reasonable approach. This study has several limitations. First, drug PK was described for only one dosage interval in each patient. The dialysis clearance was calculated only in 4 out of 11 patients, which precludes formal statistical analysis. Finally, no follow-up data was available, and therefore, relations between polymyxin B exposure and important patient outcomes could not be investigated.

Conclusion
In summary, the renal function might be an important factor contributing to polymyxin B clearance, and patients with renal dysfunction and on CVVHD are at increased risk of toxicity. Given the high risk of toxicity in patients with severe renal impairment and treatment failure in patients with high creatinine clearance, TDM might be of a great value in these groups. No dosage increase is required in patients undergoing CVVHD, and the fixed regime of 100 mg q12h is proposed.