Pharmacokinetics of Polymyxin B in Hospitalized Adults with Cystic Fibrosis

ABSTRACT

The optimal polymyxin B dosage needed to achieve an efficacy target of 50 to 100 mg · h/liter when treating multidrug-resistant bacterial infections in adult cystic fibrosis (CF) patients is unclear. The pharmacokinetics of intravenous polymyxin B were evaluated to better inform dosing. This was a prospective, observational pharmacokinetic (PK) study of nine CF adults receiving intravenous polymyxin B as part of usual clinical care. Doses preceding PK sampling ranged from 50 to 100 mg every 12 h. Five PK samples were collected following the fourth or fifth dose and concentrations of polymyxin subcomponents B1 and B2 were quantified using liquid chromatography mass spectrometry (LC-MS). Population PK (NONMEM software) analysis was performed using pooled polymyxin B1+B2 concentrations. Participants were Caucasian, predominantly male, with mean age and weight of 31 years (range 21 to 57 years) and 58.0 kg (range 38.3 to 70.4 kg), respectively. A 1-compartment zero-order infusion and linear elimination model adequately described the data with estimated clearance and volume of distribution being 2.09 liters/h and 12.7 liters, respectively, corresponding to a 4.1 h mean half-life (t_1/2). Although body weight was observed to influence the volume of distribution, a fixed dose of 75 mg every 12 h was predicted to achieve the target steady-state exposure. Neurotoxicities were reported in all patients, with acute kidney injury events in two patients. These events resolved within 2 to 4 days after discontinuing polymyxin B. Fixed maintenance dosing of polymyxin B without loading is predicted to achieve the targeted therapeutic exposure in CF adults. Treatment-limiting neurotoxicities are very common in this population.

TEXT

Cystic fibrosis (CF) is a genetic disease affecting multiple organ systems; however, pulmonary disease is the primary cause of the majority of morbidity and mortality (1). CF lung disease is a chronic, progressive process punctuated by episodes of acute exacerbation that require antibiotic treatment. Pseudomonas aeruginosa is the predominant pathogen isolated in patients with acute exacerbations of CF, and guidelines from the Cystic Fibrosis Foundation recommend combination treatment when this pathogen is present (2). Such therapy traditionally consists of an antipseudomonal beta-lactam with either an antipseudomonal fluoroquinolone or an aminoglycoside. However, the improved survival of patients with CF has led to an increase in the prevalence of multidrug-resistant (MDR) P. aeruginosa in the adult population, with around 20% of adults aged >35 years colonized (1). The polymyxin antibiotics colistin and polymyxin B (PMB) are often necessary to treat patients with fluoroquinolone- and aminoglycloside-resistant isolates, or in cases where drug intolerances preclude the use of first-line agents.

The polymyxins are cyclic peptide antibiotics which are positively charged at physiologic pH and exert bactericidal activity through binding to the lipopolysaccharide component of Gram-negative bacterial membranes (3). Colistin, available as the prodrug colistimethate sodium, has historically been the most commonly used polymyxin in patients with and without CF (4, 5). However, population pharmacokinetic (PK) studies in critically ill patients have demonstrated high interpatient variability in the exposure of formed colistin and inadequate attainment of therapeutic levels in patients with adequate or augmented renal function (6, 7). This high interpatient variability in colistin exposure is due to variable conversion from colistimethate and the differential pathways of elimination for colistimethate, which is freely filtered and excreted in urine, and formed colistin, which is avidly reabsorbed in the kidney and eliminated by nonrenal mechanisms (8). Patients with CF generally exhibit augmented clearance of compounds eliminated by the kidney, which may place them at increased risk for underexposure of active colistin (9). In contrast to colistin, PMB is administered intravenously in its active drug form, has demonstrated more consistent PK in critically ill patients (10–12), and may provide more consistent exposure in the CF patient population.

The impact of intrinsic patient factors on the PK and dosing strategy of the polymyxins has been an area of active investigation in the non-CF patient population. As highlighted above, patient kidney function has a significant bearing on the PK of colistin, through its prodrug colistimethate sodium, but has negligible impact on PMB (10–12). Therefore, despite the fact that the PMB drug label includes dose adjustments for abnormal kidney function, this agent is often dosed without respect to patient kidney function in clinical practice (13). The other patient-specific factor that has traditionally informed the dosing of these agents is patient body weight; however, the most recent PK studies of PMB have failed to demonstrate an impact of patient body weight on the clearance of PMB. Despite these data, the majority of PMB dosing in clinical practice is still weight based, in line with historic practice (11, 12). Furthermore, dosing strategies extrapolated from PK data in non-CF patients may not be directly applicable to CF patients due to possible differences in drug elimination (9).

Data on tolerability of PMB is needed in the CF population. Although the polymyxins have been in use for over 50 years, they are reserved as last-line therapeutics due to their association with significant toxicities, namely nephrotoxicity and neurotoxicity. Nephrotoxicity is the primary dose-limiting toxicity in non-CF populations, with more recent studies suggesting an increased risk for acute kidney injury (AKI) with colistin relative to PMB (relative risk [RR] 1.55, 95% confidence interval [CI] 1.36 to 1.78) (14). Historical studies with colistin in pediatric patients with CF have demonstrated limited nephrotoxicity; however, neurotoxicities were reported with frequencies up to 97.3% (5). The most common manifestation of neurotoxicities with polymyxins is mild-moderate perioral paresthesias, followed by weakness, ataxia, and, in rare cases, respiratory compromise (5, 15, 16).

The objectives of this pilot study were to measure plasma concentrations of polymyxin B1 and B2 in adult CF patients receiving fixed intravenous dosing, develop a population pharmacokinetic model to describe these data, and predict individual exposure using this dosing approach to provide preliminary evidence for broader implementation of this strategy.

RESULTS

Patients and samples.

Patient characteristics for the 9 CF participants are shown in Table 1. All patients were Caucasian and all but one were male. The age (21 to 57 years) and weight (38.3 to 70.4 kg) were across an approximately 2-fold range, while estimated creatinine clearance (eCL_cr) (95 to 134 ml/min) values were in a narrower and normal range in the analysis population. Doses preceding PK sampling ranged from 50 to 100 mg every 12 h; each patient contributed the full set of 5 PK samples for a total of 45 PK samples included in the analysis. The lower limit of quantification (LLOQ) for polymyxin B1 was 50 ng/ml over a 50 to 5,000 ng/ml range of quantification, with a coefficient of correlation of >0.996. The LLOQ of polymyxin B2 was 25 ng/ml over a 25 to 5,000 ng/ml range of quantification, with a coefficient of correlation of >0.998. All samples, including quality control, were analyzed on a single day. Intraday accuracy ranges of 86.5 to 105.0% and 88.9 to 109.6% were observed for polymyxin B1 and polymyxin B2, respectively. The precision for both compounds was well within the 15% acceptable range. Observed individual and mean concentration-time profiles for polymyxin B1, polymyxin B2, and pooled polymyxin B1+B2 are illustrated in Fig. 1 (logarithmic y axis). The concentration-time profiles show limited variation between individuals, as well as consistency across the three analytes, supporting the use of pooled polymyxin B1+B2 as the dependent variable in model development. A single log-linear slope was evident in these plots.

TABLE 1.

Summary of characteristics of included patients^a

Patient no.	PMB doseb (mg)	Sex	Age range (yrs)	Ht (cm)	Wt (kg)	eCLcr (ml/min)	ppFEV1 (%)	MIC (μg/ml)
1	75	Male	55–60	174.0	70.2	95	27	1
2	50	Male	30–35	165.1	38.3	106	17	1
3	50	Male	20–25	167.6	58.7	113	36	≤0.25
4	60	Male	30–35	181.1	70.4	140	65	≤0.25
5	75	Male	20–25	171.5	51.8	95	32	2
6	50	Male	20–25	164.5	46.6	98	26	0.5
7	100	Female	40–45	167.0	68.0	109	72	0.5
8	60	Male	25–30	168.9	62.8	134	34	0.5
9	75	Male	20–25	170.2	55.2	117	70	1
Mean (SD)	66 (17)		31 (12.5)	170 (5.1)	58.0 (11.1)	112 (16)	42 (21)

^aPMB, polymyxin B; eCL_cr, estimated creatinine clearance at baseline using the Cockcroft-Gault equation; ppFEV₁, percent predicted forced expiratory volume in the first second; SD, standard deviation.

^bDose indicates the dose administered prior to the PK sampling interval.

FIG 1.

Observed polymyxin B1, B2, and B1+B2 concentration-time profiles.

Population PK model development.

Consistent with the observed concentration-time profiles, a 1-compartment model best described the data. Interindividual variability (IIV) could not be precisely estimated for either clearance (CL) or volume of distribution (V) (relative standard error [RSE] > 50%) due to the small sample size and homogeneity of the analysis population. Addition of a second disposition compartment did not improve model fit and only marginally decreased the OFV (−2.684, Table S1 in the supplemental material); therefore, the 1-compartment model was selected as the base structural model.

Following identification of the base model, prespecified covariate effects were evaluated on CL (body weight, CrCL) and V (body weight) simultaneously following a full model approach. The full covariate model minimized successfully; however, the covariance step could not be completed as the estimate of IIV on V was near the boundary of zero with the inclusion of covariates. Removal of the IIV on V resulted in successful minimization and completion of the covariance step without impacting the objective function value (OFV); this model was deemed the working full model. The inclusion of the three covariate-parameter relationships only marginally reduced the OFV in the working full model compared to the base model (−8.041, Table S2 in the supplemental material). Of the three covariate-parameter relationships, only body weight on V was precisely estimated in the full model (RSE < 50%). In the backward elimination procedure, the effects of creatinine clearance (CrCL) on CL and body weight on CL did not meet the statistical selection criteria and were removed.

The final model consisted of a single disposition compartment with zero-order intravenous infusion and linear elimination and volume of the compartment dependent on body weight. Parameter estimates for the final model are summarized in Table 2 and the full NONMEM output file is included in the supplemental material. Estimates of IIV in CL (21.5% coefficient of variation [CV]) and residual variability (18.8%) were low, although IIV was not precisely estimated (RSE > 50%). Standard diagnostic plots, including concordance (predicted versus observed) plots, plots of residuals versus time and model-predicted concentration, Q-Q plots, typical value overlay plots, and individual overlay plots demonstrating the adequacy of the model are included in the supplemental material (Fig. S2 to S5). Additionally, pcVPCs with both linear and logarithmic axes are depicted in Fig. S6.

TABLE 2.

Final population pharmacokinetic model parameters^a

Theta / parameter	Estimateb	ASE	%RSE	95% CIb
1 CL (liters/h)	2.09	0.162	7.73	(1.77, 2.41)
2 V (liters)	12.7	0.802	6.33	(11.1, 14.2)
6 Wt on V (power)	0.784	0.305	39.0	(0.185, 1.38)
Residual Variability
3 Proportional Errorc	0.188 (18.8%)	0.0223	11.8	(14.5%, 23.2%)
Interindividual variability (IIV)b
ETA1–CL	0.0463 (21.5% CV)	0.0244	52.7	(0% CV, 30.7% CV)
Condition no.	2.3

^aASE, asymptotic standard error; RSE, relative standard error; CI, confidence interval; CL, systemic clearance; V, volume of the central compartment; IIV, interindividual variability; %CV, percent coefficient of variation.

^bUntransformed estimates from the model output are provided for random effects with transformed values in parentheses. Uncertainty in estimation (95% CIs) are presented as transformed values.

^cLog-additive error model with log-transformed concentration as the dependent variable approximates a proportional error model on the untransformed scale. Parameterized using fixed effects with SIGMA fixed to 1.

Individual post hoc empirical Bayesian estimates of PK parameters are summarized in Table 3. The mean PMB CL and V estimates were 2.14 liters/h and 12.3 liters, respectively, corresponding to a mean half-life (t_1/2) of 4.1 h.

TABLE 3.

Individual Bayesian post hoc predictions of PK parameters^a

Patient no.	CL (liters/h)	V (liters)	t1/2 (h)
1	2.78	14.3	3.58
2	1.51	8.92	4.10
3	2.04	12.5	4.23
4	2.83	14.4	3.52
5	2.14	11.3	3.66
6	2.41	10.4	2.99
7	1.63	14.0	5.96
8	2.07	13.1	4.39
9	1.83	11.9	4.50
Mean (SD)	2.14 (0.465)	12.3 (1.88)	4.10 (0.850)

^aCL, systemic clearance; V, volume of the central compartment; t_1/2, elimination half-life; SD, standard deviation.

Illustration of covariate effects.

Body weight was identified as the only statistically significant covariate (P < 0.05) in the analysis. The impact of body weight on steady-state PMB maximum concentration of drug in serum (C_max) was quantified using simulation with results illustrated in Fig. 2. Uncertainty in model parameter estimates was incorporated to generate 1,000 sets of parameter values and simulated 1,000 typical predicted (PRED) concentration-time profiles for subjects with the test (40, 50, 70, and 80 kg) and reference (60 kg) body weight values. The ratio (90% CI) of steady-state exposure for each test condition to the reference condition was calculated and the 5^th, 50^th, and 95^th percentiles of the resulting distribution of ratios were plotted.

FIG 2.

Forest plot of the impact of body weight on predicted steady-state exposure. C_max, peak (maximum) concentration; AUC_0–24, area under the concentration-time curve (AUC) over 24 h. Note: circles show the ratio of the median exposure metric under the test conditions compared to the reference. The line segments represent the corresponding 90% CI. The reference condition was a cystic fibrosis patient receiving polymyxin B at 75 mg every 12 h with a body weight of 60 kg. Test conditions were body weights of 40 to 80 kg in 5 kg increments. Vertical dashed lines indicate the reference interval of 0.8 to 1.25.

As depicted in Fig. 2, the impact of body weight on steady-state exposure is not predicted to be clinically meaningful over the range of values relevant to adults with CF (40 to 80 kg). PMB steady-state C_max is predicted to be 1.20-fold (90% CI,1.06 to 1.35) higher at a body weight of 40 kg and 0.89-fold (90% CI,0.84 to 0.96) lower at a body weight of 80 kg compared to the approximate median value of 60 kg in the analysis population. There is no predicted effect of body weight on steady-state area under the concentration-time curve (AUC).

Individual exposure predictions.

Individual patient exposure predictions were generated on day 1 and day 8 under different fixed dosing conditions using individual post hoc empirical Bayesian estimates of PK parameters. Results are summarized in Table 4. With the lowest dosing regimen of 50 mg every 12 h, the mean steady-state AUC₂₄ was predicted to be 48.8 mg · h/liter, which approximates the lower end of the efficacy target of approximately 50 to 100 mg · h/liter (C_avg,ss ∼2 to 4 mg/liter) (17), with 3 of 9 patients in this target range on this dosing. At the protocol recommended dosing of 75 mg every 12 h, all 9 subjects were predicted to achieve exposure in the therapeutic range. Under all dosing conditions, accumulation from day 1 to day 8 was minimal, with a mean accumulation ratio of 1.10.

TABLE 4.

Individual Bayesian post hoc predictions of polymyxin B exposure with fixed dosing^a

Dose	Patient no.	Day 1		Day 8		AR
		Cmax (mg/liter)	AUC24 (mg · h/liter)	Cmax (mg/liter)	AUC24 (mg · h/liter)
50 mg q12h	1	3.17	33.7	3.21	36.0	1.07
	2	5.38	60.4	5.48	66.3	1.10
	3	3.90	44.3	3.98	49.0	1.10
	4	3.15	33.1	3.17	35.3	1.07
	5	4.06	43.5	4.10	46.7	1.07
	6	4.08	39.7	4.10	41.4	1.04
	7	3.98	50.8	4.24	61.5	1.21
	8	3.76	43.3	3.84	48.3	1.11
	9	4.19	48.8	4.30	54.6	1.12
	Mean (SD)	3.96 (0.654)	44.2 (8.54)	4.05 (0.677)	48.8 (10.6)	1.10 (0.0483)
75 mg q12h	1	4.76	50.5	4.81	54.0	1.07
	2	8.07	90.6	8.21	99.4	1.10
	3	5.85	66.5	5.97	73.5	1.10
	4	4.72	49.6	4.76	53.0	1.07
	5	6.09	65.2	6.16	70.0	1.07
	6	6.12	59.5	6.15	62.1	1.04
	7	5.97	76.2	6.36	92.2	1.21
	8	5.63	65.0	5.76	72.4	1.11
	9	6.29	73.2	6.45	82.0	1.12
	Mean (SD)	5.95 (0.981)	66.3 (12.8)	6.07 (73.2)	73.2 (16.0)	1.10 (0.048)
100 mg q12h	1	6.35	67.3	6.41	72.1	1.07
	2	10.8	121	11.0	133	1.10
	3	7.80	88.7	7.96	97.9	1.10
	4	6.29	66.2	6.35	70.6	1.07
	5	8.12	86.9	8.21	93.4	1.07
	6	8.17	79.4	8.20	82.8	1.04
	7	7.96	101.6	8.48	123	1.21
	8	7.51	86.7	7.69	96.5	1.11
	9	8.39	97.6	8.60	109	1.12
	Mean (SD)	7.93 (1.31)	88.4 (17.1)	8.09 (1.35)	97.6 (21.3)	1.10 (0.048)

^aC_max, peak (maximum) polymyxin B1+B2 concentration; AUC₂₄, area under the polymyxin B1+B2 concentration-time curve over 24 h; AR, accumulation ratio calculated as the ratio of AUC₂₄ on day 8 to AUC₂₄ on day 1; SD, standard deviation.

Adverse reactions.

Adverse reactions are summarized in Table 5. Acute kidney injury (AKI), as defined by the Kidney Disease Improving Global Outcomes (KDIGO) criteria, occurred in two of nine patients, though the majority of patients were exposed to concomitant nephrotoxins (18). Subject 2 has historically had fluctuating creatinine clearance throughout hospitalizations, with AKI not far from his baseline at his peak serum creatinine, while subject 5 clearly experienced AKI either due to PMB or a combination of nephrotoxins during the hospitalization. All episodes of nephrotoxicity resolved with conservative treatment within 4 days of onset.

TABLE 5.

Adverse reactions and outcomes^a

Patient no.	Baseline CrCl (ml/min)	Min CrCl (ml/min)	KDIGO AKI stage	Concomitant nephrotoxins	Neurotoxicity
1	95	95	0	i.v. vancomycin	paresthesiab
2	106	58	1	i.v. vancomycin	altered mentation, ataxiab
3	113	102	0	p.o. sulfamethoxazole-trimethoprim	ataxia, euphoria, visual disturbance
4	140	140	0	none	akathisia, altered mentation, ataxia, paresthesia
5	95	46	2	i.v. piperacillin-tazobactam, p.o. sulfamethoxazole-trimethoprim	ataxia, paresthesia
6	98	91	0	i.v. piperacillin-tazobactam, i.v. tobramycin	ataxia, paresthesia
7	109	90	0	none	ataxia, paresthesia
8	134	127	0	none	paresthesia
9	117	92	0	i.v. ketorolac, p.o. sulfamethoxazole-trimethoprim	Paresthesia

^aeCl_cr, baseline creatinine clearance as estimated using the Cockcroft-Gault equation; KDIGO, Kidney Disease Improving Global Outcomes; AKI, acute kidney injury; i.v., intravenous; p.o., by mouth; SD, standard deviation.

^bData collected retrospectively, all other data prospective.

Neurotoxic adverse reactions were reported by all patients within the first few doses of PMB treatment, and tended to be the reason patients declined future courses of PMB. Neurotoxicities reported included perioral, facial, and extremity paresthesias, ataxia, euphoria, and altered mental status. The description of subjective neurotoxicities varied among patients and did not correlate with timing, duration, or dose of infusion. All neurotoxicities resolved within 2 days of last PMB exposure.

DISCUSSION

The demographics of patients with CF have shifted to an older population, with important implications for antimicrobial therapy. The shrinking antipseudomonal armamentarium due to growing antibiotic resistance with recurrent courses of therapies has renewed interest in the use of polymyxin antibiotics. However, the posology of these agents is uncertain in special populations, such as those with CF. Extrapolation of results from PK studies conducted in critically ill adults suggests that therapeutic exposures of colistin are unlikely to be achieved in patients with good renal function, such as adults with CF, due to rapid clearance of the inactive colistimethate prodrug (3). PMB, which is administered directly as an active drug and does not appear to undergo significant renal elimination, may be better able to achieve therapeutic exposure with less variability in this patient population, but needs prospective validation of PK in the CF patient population (3, 10–12).

The only PK study of PMB in patients with CF retrospectively included 9 patients with a median of 2 samples analyzed per patient (31 samples total) collected for therapeutic drug monitoring (TDM) as a part of clinical care (19). The final population PK model in this analysis consisted of two disposition compartments; however, the reduction in Akaike’s Information Criterion (AIC) for the 2-compartment model was only 0.48 points, implying that selecting a 1-compartment model would also have been acceptable. This prior study also modeled a sigmoidal relationship between PMB CL and eCL_cr. However, the uncertainty of that model is high (very large confidence bands) because the asymptote (maximum clearance) is leveraged against a single data point from a patient with an eCL_cr of approximately 180 ml/min.

Target enrollment was 16 adults. Institutional restrictions on clinical research during the COVID-19 pandemic prevented this enrollment target from being achieved. The current use of highly effective modulator therapy has also decreased hospitalization rates for acute pulmonary exacerbations. Despite these setbacks, these analyses respond to reproducibility and rigor considerations of PMB PK and tolerability data in this specific population.

The present analysis used data obtained from prospective sampling over a full dosing interval at steady-state. A 1-compartment disposition model with IIV only included on CL was identified as the most parsimonious compartmental model structure, and only body weight on volume of distribution (V) was identified as a statistically significant covariate effect following backward elimination. The estimate of IIV on V approached the lower bound of zero after the inclusion of body weight as a covariate; therefore, IIV on V was removed from the model. The eCL_cr was not identified as a significant covariate of PMB clearance; however, the range of values among included subjects was very narrow, affording low power to detect an effect if present.

Body weight is not predicted to result in clinically meaningful differences in steady-state PMB exposure over a range of values likely among adults with CF (i.e., 50 to 80 kg). Steady-state C_max is predicted to differ by 20% or less with no impact on AUC. This finding supports the use of fixed dosing of PMB in adults with CF who are at least 50 kg, and the low magnitude of interindividual and residual variability (<25%) quantified in this analysis suggests that TDM is not required in this patient population. Steady-state C_max is predicted to increase by more than 20% at 40 kg; therefore, use of a reduced dose in extremely low body weight patients (<50 kg) may improve safety.

Individual post hoc exposure predictions suggest that the dosing protocol used led to optimal attainment of efficacious exposure (i.e., AUC₂₄ 50 to 100 mg · h/liter). All patients were predicted to achieve target exposure at a dose of 75 mg every 12 h, and the patient with a body weight of <40 kg was predicted to achieve target exposure at the reduced dose of 50 mg every 12 h. Additionally, the predicted mean t_1/2 was around 4 h, indicating that steady-state exposure is achieved by the second day of therapy. Correspondingly, the mean accumulation ratio from day 1 to day 8 was only 1.10, suggesting that loading doses are not likely to improve response in this patient population.

AKI occurred in two (22.2%) study patients during their hospitalizations, though a majority of patients were exposed to concomitant nephrotoxins. Only two studies assessing nephrotoxicity of colistin or PMB have included patients with CF. Phe and colleagues included 38 patients with CF and found that CF was actually protective against colistin-associated AKI (aOR 0.03, 95% CI 0.001 to 0.79) in multivariable analysis (20). Unfortunately, no CF patients in this study received PMB, so the relative rates of kidney injury between the two agents in this population could not be assessed. A 2017 study investigated the association between polymyxin treatment and kidney injury in 220 adult CF patients, 29 treated with PMB and 191 treated with colistin (21). The study found no difference in rates of AKI between PMB and colistin (34.5% versus 29.8%, P = 0.77) in patients, nor in the rates of renal recovery by hospital discharge (90.0% versus 91.2%, P = 1.00). The high rates of AKI observed in this retrospective study were not reproduced in the present analysis.

A critically important finding of this analysis is the high rate of neurotoxicity reported by study patients. Neurotoxicities with the polymyxins have been poorly characterized in the literature, both in patients with and without CF, especially with PMB. Studies of colistin in pediatric patients with CF have document rates of neurotoxicity ranging from 0 to 97.3% (5). The most common manifestation of neurotoxicity reported with polymyxins is mild-moderate perioral paresthesias followed by weakness, ataxia, and, in rare cases, respiratory compromise (5, 15, 16). Consistent with this, mild-to-moderate paresthesias were reported most commonly; however, ataxia, euphoria, and altered mental status were also reported. There was no discernible relationship between neurotoxicity and the time since previous dose, the duration of infusion, or the total dose of PMB, suggesting a limited exposure-response and precluding management with prolongation of infusion duration or dose modifications. Based on these findings, neurotoxicity appears to be the primary use-limiting toxicity of PMB.

There are a few implications from this analysis for the posology and clinical use of PMB in adults with CF. First, fixed dosing of PMB is likely to be appropriate for the majority of CF adults (50 to 80 kg) given the limited impact of body weight on steady-state C_max, no impact on AUC, and low magnitude of interindividual variability; however, a dose reduction for extremely low body weight (<50 kg) subjects may improve tolerability. Protocolized dosing of 75 mg every 12 h for patients weighing at least 40 kg, and 50 mg every 12 h for those less than 40 kg, was predicted to achieve therapeutic exposure in 100% of study participants. Furthermore, loading doses are not necessary in this patient population given the short half-life of PMB and limited accumulation from day 1 to steady state, based on simulations. Therapeutic drug monitoring is not likely to improve dose individualization in adults with CF due to limited interindividual variability and the lack of a clear exposure-response relationship for adverse events. The finding of limited IIV in PMB PK may be a feature of this patient sample, and greater interindividual variation may be present in other CF patient populations, particularly those with critical illness. Precision dosing approaches, including therapeutic drug monitoring, may have some benefit among higher variability populations. Finally, neurotoxicity was frequent in the study population at therapeutic exposure, suggesting a minimal therapeutic index for PMB in this population. Despite complete resolution of neurotoxicity symptoms with completion of therapy, there was patient and provider reluctance to utilize PMB for the duration of the antibiotic course due to this side effect. Formulary decisions related to use of colistin versus PMB in this population will need to balance the potential for subtherapeutic exposure to colistin in this patient population with the risk for neurotoxocity with PMB. It is hypothesized that matched exposures to colistin and PMB are likely to result in similar incidence of neurotoxicity in this population; however, this needs to be confirmed in future studies.

In conclusion, polymyxin B1 and B2 plasma concentrations were quantified in 9 adult patients with CF receiving fixed-dose intravenous PMB. These data were best fit using a 1-compartment population PK model with zero-order infusion and first-order elimination. Of the covariates evaluated, body weight was found to be a statistically significant covariate of volume of distribution; however, the magnitude of effect is not predicted to be clinically meaningful over the weight range of 50 to 80 kg. Fixed maintenance dosing of PMB without loading is predicted to achieve therapeutic exposure in this sample of adult CF patients. AKI was observed in two patients, both of whom were receiving concomitant nephrotoxins. Neurotoxicities occurred in all nine patients and are likely to be the primary dose-limiting toxicity of PMB in this population.

MATERIALS AND METHODS

Patients and ethics.

This study was approved by the institutional review board at the University of Michigan. Adult (≥18 years) CF patients receiving intravenous PMB for treatment of suspected or confirmed infection as part of routine clinical care were eligible for inclusion. Patients who were pregnant or receiving extracorporeal organ support that would alter drug distribution (e.g., renal replacement or extracorporeal membrane oxygenation) were excluded. Informed consent was obtained from all patients.

Study design.

This was a prospective, single-center, open-label, observational pharmacokinetic study of intravenous PMB in adult CF patients. PMB dosing was at the discretion of the treating physician. Local guidelines for the use of polymyxins in adult CF patients were in place during the study period; these recommended a fixed dose of 75 mg every 12 h for patients ≥40 kg and 50 mg every 12 h for patients <40 kg. Doses were recommended to be infused over 1 to 2 h. Prolongation of the infusion time or reduction in dose could be performed at the discretion of the treating physician for management of adverse reactions. Pharmacokinetic sampling was planned following the fourth or fifth doses, which should approximate steady state. Samples were collected at the following time points in prelabeled and chilled plasma EDTA sampling tubes: predose, end of infusion (EOI), 1 h after EOI, 3 h after EOI, and 8 h after EOI. Samples were immediately centrifuged, separated into two plasma aliquots, and stored at −80 C until analysis.

Bioanalytical method.

A rapid and sensitive ultra-performance liquid chromatography-high resolution mass spectrometry (UPLC-HRMS) method was developed to measure the concentration of polymyxin B1 and polymyxin B2 in human plasma samples. In brief, the human plasma proteins were precipitated by mixing 50 μl plasma, 50 μl water, and 100 μl acetonitrile with an internal standard in EP tubes. Then the tube was vortexed for 2 min to completely mix. After centrifugation at 13,000 rpm for 10 min, 10 μl of supernatant was injected for UPLC-HRMS analysis. To make calibration standard solutions, two sets (for calibration curve and QCs) of analyte stock solutions and one set of internal standard (Polymyxin E2, Sigma-Aldrich, St. Louis, MO, USA) were prepared individually in dimethyl sulfoxide (DMSO) at a 2 mg/ml concentration. Then, both 2 mg/ml stock solutions of polymyxin B1 and polymyxin B2 (Toku-E, Tokyo, Japan) were mixed together to make the 1 mg/ml stock solution mixture. The mixture was diluted with acetonitrile to prepare the calibration working solution mixtures of polymyxin B1 and B2 (0.5, 1, 2, 5, 10, 20, 50, and 100 μg/ml). Quality controls (0.5, 10, and 50 μg/ml) were prepared by the same dilution method. The working solution of internal standard (0.5 μg/ml) was prepared in acetonitrile directly for plasma sample precipitation. An aliquot of 475 μl of K₂ EDTA human plasma was spiked with 25 μl of mixture working solution of polymyxin B1 and B2 to obtain the required concentrations in the plasma. The plasma calibration curve standards were prepared at concentrations of 25, 50, 100, 250, 500, 1,000, 2,500, and 5,000 ng/ml for both polymyxin B1 and B2. Similarly, quality control samples were made at 25 (LQC), 500 (MQC), and 2,500 (HQC) ng/ml. All spiked plasma samples were used freshly or stored at −80°C until their use. Quantitative analysis was performed using a Shimadzu LC-20AD (Kyoto, Japan) chromatographic system coupled to Sciex X500R QT of high resolution mass spectrometer (Toronto, Canada) and operated in positive electrospray ionization through time of flight mass spectrometry (TOFMS) monitoring. The data collecting and processing was executed using Sciex OS (version 2.0). Chromatographic separation of polymyxin B1 and B2, along with its internal standard polymyxin E2, was achieved on an Agilent Poroshell 120 ec-C₁₈ column (50 mm × 2.1 mm ID, 2.7 μm) with a gradient mobile phase consisting of 0.1% formic acid in acetonitrile (B) and 0.1% formic acid in water (A) at a flow rate of 0.5 ml/min. The gradient (B) was held at 2% (0 to 1 min), increased to 50% at 1.5 min, then stayed at isocratic 50% B for 1.0 min, and increased to 70% at 2.3 min, stayed at isocratic 70% B for 1.2 min, then immediately stepped back down to 2% for 2 min of reequilibration. The temperature of the column oven was set at 50°C. A mass spectrometer with a Turbo ion spray interface at 550°C was operated to quantify the separated components. The ions were monitored from 400 to 700 Da in the TOFMS positive ion mode with electrospray ionization (ESI) source. The ion spray voltage set was 5,000 V. The source-dependent parameters maintained were (source gas 1): 50 lb/in², (source gas 2): 70 lb/in², curtain gas: 30 lb/in², and CAD gas: 7 lb/in². The compound parameters maintained for the analytes and internal standard, including declustering potential: 80 V; collision energy: 5 eV. Separation of analytes was obtained within 5.5 min. Analysis was performed from full scan mode using a 5 ppm mass window. Ions monitored for targeted full scan mode data analysis were 602.382 m/z for polymyxin B1 and 595.374 m/z for polymyxin B2 and 578.382 m/z for polymyxin E2.

Population pharmacokinetic model development.

Analyses were performed using the nonlinear mixed effects modeling methodology as implemented in NONMEM (version 7.3) using the first-order condition estimation method with interaction (FOCE-I) (22). Data postprocessing and graphical analysis of the data or output from the models was performed using R (Version 3.6.3) software (23). Natural logarithm-transformed polymyxin B1+B2 concentration was used as the dependent variable. Discrimination between candidate models was based on successful minimization and completion of the covariance step in NONMEM, reductions in the NONMEM objective function value (OFV) for hierarchical models, and assessment of standard diagnostic and goodness-of-fit plots. Model stability was also considered using the condition number (the ratio of largest to smallest eigenvalues of the correlation matrix) with values >1,000 indicating ill conditioning (24).

Base structural model development commenced with a 1-compartment model with zero-order intravenous infusion and first-order elimination parameterized in terms of clearance (CL) and volume of distribution (V). Interindividual random effects were assumed to be lognormally distributed and were initially included on both CL and V. A single residual random effect was included, parameterized as a fixed effect using a log-additive model, which approximates the proportional residual error model on the untransformed scale. Inclusion of a second distribution compartment was also evaluated at this stage.

Following identification of the base structural model, including assessment of random effects, a full covariate model was developed by including all covariates of interest simultaneously. Given the limited sample size, only covariates of body weight and estimated creatinine clearance (eCL_cr) were considered. The effect of body weight was evaluated on CL and V, while the effect of eCL_cr was evaluated only on CL. Both continuous covariate effects were parameterized using power forms centered on the approximate median covariate values in the study population.

A stepwise backward elimination procedure was used to identify the final PK model. In each round, the covariate-parameter relationship which had the lowest change in OFV and did not meet the inclusion criteria ΔOFV >3.84 (P < 0.05) was eliminated and the stepwise backward elimination procedure was repeated until all covariate parameters met the inclusion criteria. The preliminary final model identified following the backward elimination procedure was evaluated using prediction-corrected visual predictive checks (pcVPCs) (25). Parameter estimates were fixed to the estimates from the final model and used to generate 1,000 data sets, which replicated the dosing, sampling times, and individual covariate vectors from the observed data set. The observed 5^th, 50^th, and 95^th percentiles of polymyxin B1+B2 concentration were binned by time and compared visually to the 5^th and 95^th percentiles (90% confidence interval) of the 1,000 simulated summary measures at the corresponding percentiles (5^th, 50^th, and 95^th) of the simulated data in order to provide a visual assessment of the predictive performance of the PK model.

Population pharmacokinetic model applications.

The impact of predictive covariates from the final population PK model on steady-state polymyxin B1+B2 exposure was presented using forest plots. The multivariate normal distribution was used as an approximate posterior distribution to generate 1,000 sets of population parameters using a smoothed parametric bootstrap procedure. The mean vector of the multivariate normal distribution was set to the population parameter estimates and the covariance matrix set to the covariance matrix of the estimates from the final model. A simulation data set was created with individual subjects differing in only body weight (40 to 80 kg) from the reference subject (60 kg). One thousand (1,000) data sets were generated by simulation, one for each unique set of parameter values, containing steady-state concentration-time profiles for individual subjects following dosing of PMB at 75 mg administered every 12 h for 1 week. For each simulation, steady-state peak concentration (C_max) and daily area under the concentration-time curve (AUC₂₄) values were calculated for each subject, and the mean values and ratios (test/reference) were calculated for each weight group. The 5^th, 50^th, and 95^th percentiles from the 1,000 ratios were calculated and presented in in forest plots.

The final population PK model was also used to generate individual subject empirical Bayesian estimates of PK parameters and exposure predictions over 24-h intervals on day 1 and day 8 (steady state) under various fixed dosing regimens: 50 mg every 12 h, 75 mg every 12 h, and 100 mg every 12 h. A descriptive post hoc individual empirical Bayesian prediction approach was used in place of simulation due to the small sample size and imprecise estimation of interindividual random effects.