The Determination of Polymyxin B in Critically Ill Patients by the HPLC-MS/MS Method

Polymyxin B (PB) is a dose-dependent drug used to treat multidrug-resistantgram-negative bacteria, for which a suitable method is needed to determine clinical samples. A simple, economical, and efficient high-performance liquid chromatography-mass spectrometry (HPLC-MS/MS) method was developed and validated for polymyxin B1 (PB1), polymyxin B1-Ile (PB1-I), polymyxin B2 (PB2), and polymyxin B3 (PB3) in human plasma. Chromatographic column was Waters BEH C18 column (2.1 × 50 mm, 1.7 μm). Phase A was water with 0.2% formic acid (FA), and phase B was acetonitrile containing 0.2% FA. The elution method is gradient elutio. The total analysis time was 5 min. The pretreatment method involved protein precipitation using acetonitrile containing 0.2% trifluoroacetic acid and 0.1% FA as the precipitant. The recovery rate was 92–99%. The total quantity of PB1 and PB1-I was measured in the linear range of 100–8000 ng/mL. Simultaneously, the total amounts of PB2 and PB3 were measured in the linear range of 11.9–948.5 ng/mL. This validated method was successfully applied to the pharmacokinetics of PB in critically ill patients.


Introduction
Polymyxin B (PB) is a lipopeptide antibiotic extracted from the fermentation products of Bacillus polymyxa [1]. In clinical practice, considered the "last line of defense," it is primarily used for infections caused by gram-negative bacteria with multidrug resistance, such as Pseudomonas aeruginosa, Acinetobacter baumannii, and Klebsiella pneumoniae [2,3]. PB is a dose-dependent drug discovered in the 1950s and has signifcant adverse efects on the kidney, which has impact on critically ill patients [3][4][5][6]. Terefore, it is important to maintain the drug concentration within the therapeutic window. Terefore, therapeutic drug monitoring (TDM) of PB is necessary for clinical practice.

Preparation of Stock and Working Solution.
Standard and IS stock solutions were prepared in Milli-Q water containing 1% FA (v/v) at 1 mg/mL (with all substances) and subpacked in EP tubes. Working solutions were diluted from the stock solution. Te concentrations of PB1 in the PB1-I's working solution were 160, 120, 100, 48, 24, 12, 6, and 2 μg/mL. Te quality control (QC) working solutions were 140, 80, 20, and 4 μg/mL. Te IS solution, polymyxin E2, was diluted in 1% FA water to 7.5 μg/mL. All solutions were stored at −80°C.

Selectivity and Matrix Efect.
Six blank matrices obtained from diferent individual sources, one high-fat matrix obtained from volunteers with abnormally high triglyceride levels, and the hemolytic matrix prepared by adding hemolytic whole blood (2%, v/v) to the blank matrix were selected to comprehensively evaluate the selectivity and matrix efect of this method. For selectivity, the lower limit of quantifcation (LLOQ) and blank-level samples were used for evaluation. Eight blank samples were prepared in the above matrices by adding 15 μL solvent and 200 μL precipitant to 95 μL of diferent matrices. LLOQ samples were prepared with working solutions of LLOQ, IS solution, and matrices. Te responses attributable to interfering components in the retention time should not be more than 20% of PB and not more than 5% of IS in the LLOQ sample of each matrix. Te matrix efect was evaluated by analyzing at least three replicates at low and high QC concentrations. Te QCL and QCH of plasma samples were prepared using their working solutions with the eight matrices in QC sample preparation. QCL and QCH of the solvent samples were prepared using 5 μL working solution, 95 μL solvent, 10 μL IS solution, and 200 μL precipitant. Te ratio of analyte and IS in the matrices and solvent, respectively, is calculated as the matrix factor (MF) of the analyte and IS. Te IS-normalized MF was then calculated to evaluate the matrix efect. Te coefcient of variation (CV) of the IS-normalized MF of the eight matrices should not be greater than 15%. (1)

Extraction Recovery.
Te extraction recovery was calculated by the peak area ratios of samples recovered from plasma, extracted blank plasma, and IS spiked with the same concentrations of PB. Samples at four concentrations were analyzed in triplicates.
extraction recovery � (peak area of the analyte added before extraction/peak area of IS) (peak area of the analyte added to the extracted supernatant/peak area of IS) * 100%. (2)

Calibration Curve and Carry-Over.
Eight calibrationlevel samples, a blank sample, and a zero sample were used to establish the curve. Te preparation was the same as that described in Section 2.6. Te upper limit of quantifcation (ULOQ) and LLOQ are shown in the curve. Te LLOQ is the lowest point of the curve, whereas the ULOQ is the highest. Fitting the curve by the least square regression analysis, the accuracy of the LLOQ should be within ±20%; other calibration samples should be within ±15%. Carry-over was assessed using blank samples after calibration at the ULOQ. Compared with the LLOQ, the area of the analyte should not be greater than 20 or 5% for the IS.

Accuracy and Precision.
Accuracy and precision were determined using fve QCs: LLOQ, QCL, QCM1, QCM2, and QCH. Five replicates at each concentration level were paralleled for each run. Te between-run accuracy and precision were evaluated in three runs over two days. Te accuracy of the LLOQ should be within ±20% and that of other QCs should be within ±15% overall. Te precision of the LLOQ should not exceed 20%; the other QCs should not exceed 15% overall.

Dilution Integrity.
During the investigation of dilution integrity, the dilution QC concentration was 10000 ng/mL, which was diluted with blank plasma. Te two dilution factors investigated were two and four, respectively. Tere were fve replicates for each dilution factor. Te mean accuracy of the dilution QC samples should be within ±15%; the precision should not exceed 15%.

LC-MS/MS Method Development.
PB standards include PB1, PB1-I, PB2, and PB3. In this method, PB1 and PB1-I were not separated by chromatography, similar to PB2 and PB3. PB's structural formula is shown in Figure 1. PB1 and PB1-I are isomers, and the quantitative ion pair was the same at 602.7/101.1. Based on previous reports [19,20], it was considered that they could be determinated as one peak. Similarly, PB2 and PB3 were isomers. Te quantitative ion pair was 595.7/101.1, suggesting that they could be determinated as one peak too. Te PB content is the sum of the four components. Te precursor ion of PB1/PB1-I was [M+2H] 2+ 602.7. Te iron product is shown in Figure 2. Iron 101.0 was selected, which was common to PB1 and PB1-I, and had the highest response. Te precursor ion of PB2/ PB3 was 595.7, a form of [M+2H] 2+ . Te product scan of iron is shown in Figure 2; 101.0 was selected for the same reasons. Te product scan of IS is shown in Figure 2; the iron pair was 578.7/101.1. Te typical peak shapes of the blank, plasma standard of LLOQ and ULOQ, IS, and clinical samples are shown in Figure 3. Overall, it is feasible to measure the PB components of the same mass together as the peak shape of each concentration is good, meeting the quantitative requirements. For the measurement of clinical samples, PPE is simple, more convenient, and more economical than SPE. Terefore, PPE was adopted in this method. Comparing the extraction recovery and the peak area of ACN, ACNe containing 0.1% FA, ACN with 0.2% TFA and 0.1% FA, and ACN with 0.1-2% TFA, we found that the addition of TFA can increase the response of polymyxin, which was consistent with what has been reported [19]. When the extraction solution was pure ACN, the response and extraction recovery were low, which did not meet the quantitative requirements. Considering that TFA has ionic inhibition on MS and corrosivity, it should only be added to the extraction, and the concentration should not be high. After comparison and screening, ACN containing 0.2% TFA and 0.1% FA was selected as the extraction solution. Te response and extraction recovery of PB met the analytical requirements. Te extraction recovery rate was 92-99%; CV <5% (Table 1). Te TFA concentration in the fnal analysis sample was 1.3%. TFA was only added to the sample and not to the mobile phase, which had no impact on the MS.
During the experiment, the Waters HSS T3 column (2.1 × 100 mm, 3.5 μm) [20], Agilent poroshell 120 SB-C18  0-0.5 min, the aqueous phase was the main phase for keeping PB on the column and eluting substances with large polarity in the sample. In the frst minute, they were almost salt. Terefore, no MS was conducted. Subsequently, the organic phase ratio was increased to elute analytes. A high organic phase (90% phase B) was used to elute impurities with low polarity. Ten, returned to the initial proportion and postrun for 1.8 min to stabilize the pressure.

Linearity and Carry-Over.
Each validation or sample measurement was performed simultaneously using a standard curve. Eight points were selected to construct the standard curve, and 1/X 2 was the weight factor. Te correlation coefcient R 2 was greater than 0.99. For PB1/PB1-I, the linearity was y � 1.2477x − 0.0214; for PB2/PB3, the linearity was y � 2.0285x + 0.0050 (Table 2). Te linear range was determined by referring to the reported range of PB, the residual efect, and the actual sample concentration distribution. Te concentrations of 35 samples from fve patients were 100-5000 ng/mL. Terefore, the LLOQ was set at 100 ng/ml; the ULOQ was increased to 8000 ng/mL. Compared with previous methods [12,19,21,22], the number of diluted clinical samples can be reduced.

Precision and Accuracy.
Te intrabatch and interbatch accuracy and precision of the three batches were verifed within two days. Five QC samples were selected (LLOQ, QCL, QCM1, QCM2, and QCH). Te accuracy of the three intrabatch analyses was within ±15%; the CV was within 10% (Table 3). Te interassay accuracy was within ±15%; the CV was within 10%, as shown in Table 3. Tis implies that the method is accurate and precise.

Selectivity and Matrix Efect.
Te area of the analyte at the retention time in the blank sample was lower than 20% in the LLOQ. Te IS area was lower than 5%, indicating high selectivity. As showed in Table 1, the matrix efect was investigated using QCH and QCL. For PB1/PB1-I, the ISnormalized MF of QCL was 1.03 and of QCH was 1.10. For PB2/PB3, it was 1.03 and 1.05. Te CV did not exceed 15% of each level, which implies that there was no matrix efect among six diferent batches of the normal, hemolytic, and high-fat matrix.

Integrity of Dilution.
Te investigation of the two dilution factors, two and four, is presented in Table 4. Te accuracy was within ±15%; the precision was within 5%. For PB1/PB1-I, the mean accuracies were 109.1 and 108.2%; the 5      CV was 2.0 and 3.7%, respectively. For PB2/PB3, the mean accuracies were 100.6 and 101.2%; CV was 1.0 and 2.3%, respectively. Terefore, samples higher than 8000 ng/mL can be determined using dilution. Te highest concentration that can be measured by this method is 32000 ng/mL.

Stability.
Stability was investigated for short-term, freeze-thaw, and long-term stability. Table 5 shows that the sample was stable at room temperature for 4 h, at 4°C for 24 h, at −20°C, and at −80°C for three freeze-thaw cycles. Te extracted supernatant was stable in an automatic sampler for     International Journal of Analytical Chemistry

Clinical Application.
Te established HPLC-MS/MS method was used to measure more than 300 samples collected clinically. A steady-state metabolic curve of polymyxin B was obtained, as shown in Figure 4. Tis also suggests that the method can be applied to TDM and PPK.

Conclusions
In this study, a precise, accurate, and convenient method for the determination of PB was developed and validated with a linearity range of 100-8000 ng/mL for PB1/PB1-I and 11.9-948.5 ng/mL for PB2/PB3 within 5 min. To our knowledge, this is the frst study to measure PB1, PB1-I, PB2, and PB3 together, which is convenient. Te method was successfully applied to a PPK study of 350 samples. Terefore, it was also suitable for TDM.

Data Availability
Te data used to support the fndings of this study are included within the article.

Consent
Written informed consent was obtained from each patient or their legal representatives.

Conflicts of Interest
Te authors declare that there are no conficts of interest.

Authors' Contributions
Yirong Wang, Jingchun Chen, and Jinpan Du contributed equally to this work. XPW and CBC equally contributed to the design of the research and interpretation of the data. YRW, JCC, and JPD contributed to the conception and design of the research, as well as interpretation of the data, and critically revised the manuscript. YRW, JCC, and JPD performed the research and collected data. YRW experimented and analyzed the data. All authors contributed to the acquisition and analysis of the data, drafted the manuscript, and agreed to be fully accountable for ensuring the integrity and accuracy of the work. All authors read and approved the fnal manuscript.