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1.
This paper presents the development, optimization and validation of a methodology to determine nine key steroid hormones (viz. pregnenolone, progesterone, dehydroepiandrosterone, androstenedione, testosterone, dihydrotestosterone, estrone, 17α-estradiol and 17β-estradiol) expressed in the steroidogenesis in biological fluids. The analytical method allows for the determination of steroid hormones in blood plasma and serum down to 0.08–0.16 ng/mL for estrogens, 0.20–0.36 ng/mL for androgens and 0.36–0.43 ng/mL for progestagens. These limits of detection were obtainable using a two-step solid-phase clean-up for fractionation and elimination of interfering lipids (fatty acids, phospholipids, glycerides and sterols) from the steroid hormones. The accuracy of the method was 50–112% in the range 0.10 to 2.00 ng/mL.  相似文献   

2.
Steroid hormones play important roles in mammal at very low concentrations and are associated with numerous endocrinology and oncology diseases. Therefore, quantitative analysis of steroid hormones can provide crucial information for uncovering underlying mechanisms of steroid hormones related diseases. In the current study, we developed a sensitive method for the detection of steroid hormones (progesterone, dehydroepiandrosterone, testosterone, pregnenolone, 17-hydroxyprogesterone, androstenedione and 17α-hydroxypregnenolone) in body fluids by stable isotope labeling coupled with liquid chromatography-electrospray ionization-tandem mass spectrometry (LC-ESI-MS/MS) analysis. In this respect, a pair of isotopes labeling reagents, Girard reagent P (GP) and d5-Girard reagent P (d5-GP), were synthesized and utilized to label steroid hormones in follicular fluid samples and steroid hormone standards, respectively. The heavy labeled standards were used as internal standards for quantification to minimize quantitation deviation in MS analysis due to the matrix and ion suppression effects. The ionization efficiencies of steroid hormones were greatly improved by 4–504 folds through the introduction of a permanent charged moiety of quaternary ammonium from GP. Using the developed method, we successfully quantified steroid hormones in human follicular fluid. We found that the contents of testosterone and androstenedione exhibited significant increase while the content of pregnenolone had significant decrease in follicular fluid of polycystic ovarian syndrome (PCOS) patients compared with healthy controls, indicating that these steroid hormones with significant change may contribute to the pathogenesis of PCOS. Taken together, the developed stable isotope labeling coupled LC-ESI-MS/MS analysis demonstrated to be a promising method for the sensitive and accurate determination of steroid hormones, which may facilitate the in-depth investigation of steroid hormones related diseases.  相似文献   

3.
The chemiluminescent oxidation of sulphite by bromate was investigated and compared with that by cerium(IV). The reaction is sensitized by various steroid hormones which can thus be determined in the ranges 0.50–20.0μg ml 1 for cortisone; 0.50–5.00 μg ml?1 for hydrocortisone and progesterone and 0.50–6.00 μg ml?1 for testosterone and corticosterone.  相似文献   

4.
Steroid hormones play a critical role in maintaining the homeostasis of human metabolism. Urine as a noninvasive sample has been extensively used in clinical diagnosis for hormones homeostasis. In this study, the simultaneous characterization of fourteen hormones in urine was performed based on ultra‐high‐performance liquid chromatography/electrospray ionization tandem mass spectrometry (UPHLC/ESI(+)‐MS/MS) with multiple reaction monitoring in the positive ionization mode. The target hormones were cortisone, cortisol, 11‐deoxycortisol, aldosterone, corticosterone, 11‐deoxycorticosterone, progesterone, 17‐OH‐progesterone, pregnenolone, estrone, estradiol, estriol, testosterone and dehydreopiandrosterone. β‐Glucuronidase/sulfatase deconjugation and liquid–liquid extraction (LLE) were conducted for the determination of urinary hormones (free + conjugated forms). The limits of detection (LODs) ranged from 0.2 ng/mL (11‐deoxycortisol and testosterone) to 1 ng/mL (cortisone). The extraction recovery of the targeted compounds ranged from 87% to 127%, indicating sufficient extraction efficiency for the LLE process. Intraday precision was below 10% and the accuracy ranged from 84% to 122%. The profiling analysis of hormones in urine samples helps to understand the metabolic state of biological systems and can be employed as a diagnostic tool in diseases developed by endocrine‐disrupted systems.  相似文献   

5.
In this study, a sensitive and multiclass method has been developed for analysis of three families of steroid hormones, i.e. progestins, oestrogens, androgens, by SPE-HPLC-ESI-MS/MS. The extraction efficiency of thermally condensed humic acids onto silica sorbent (HA-C@silica), here for the first time studied for multiclass enrichment of these sex hormones, was tested in different environmental waters (tap and river water, urban wastewater treatment plant effluent) spiked at the nanograms per litre levels (5–1000 ng L−1). Quantitative adsorption was achieved using 200 mg sorbent for preconcentration of 250–1000 mL sample, at the native pH (pH = 6.5–7.7). Elution was performed by two sequential fractions (methanol followed by acetonitrile), obtaining in all the matrices investigated satisfactory recoveries (71% to 124% for river waters and 71–113% for urban wastewater treatment plant effluent) and RSDs below 15% (n = 3). The high enrichment factors (up to 4000) coupled with high-performance liquid chromatography tandem mass spectrometry quantification (MRM mode) provided low limits of detection and quantification (a few ng L−1), that are suitable for environmental monitoring. Most of the analytes were detected in river water and in wastewater effluent samples (in the ng L−1 concentration range), attesting their environmental diffusion. The proposed method was extended to a fourth class, Glucocorticoids, achieving good results in river samples, by the same SPE cartridge and chromatographic run.  相似文献   

6.
A sensitive and selective liquid chromatography–tandem mass spectrometry method for the determination of pethidine in human plasma was developed and validated over the concentration range of 4–2000 ng/mL. After addition of ketamine as internal standard, liquid–liquid extraction was used to produce a protein‐free extract. Chromatographic separation was achieved on a 100 × 2.1 mm, 5 µm particle, AllureTM PFP propyl column, with 45:40:15 (v/v/v) acetonitrile–methanol–water containing 0.2% formic acid as mobile phase. The MS data acquisition was accomplished by multiple reactions monitoring mode with positive electrospray ionization interface. The lower limit of quantification was 4 ng/mL; for inter‐day and intra‐day tests, the precision (RSD) for the entire validation was less than 7%, and the accuracy was within 95.9–106.5%. The method is sensitive and simple, and was successfully applied to analysis of samples of clinical intoxication. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
A simple sensitive LC–MS/MS method has been developed for the simultaneous determination of giraldoid A and giraldoid B in rat plasma. The method was applied to pharmacokinetics studies of the two compounds from Daphne giraldii Nitsche. Chromatographic separation was accomplished on an Acquity UPLC™ BEH C18 column (100 × 2.1 mm, 1.7 mm) by gradient elution with a flow rate of 0.2 mL min−1. The method was linear over the concentration range of 1.0–1000 ng mL−1, and the lower limits of quantification were 1.04 ± 0.10 and 1.04 ± 0.09 ng mL−1, respectively. The intra‐ and inter‐day precisions (RSD) were <10.14 and 9.96%. The extraction recovery of the analytes was acceptable. Stability studies demonstrated that the two compounds were stable in the preparation and analytical process. The maximum plasma concentration was 687.78 ± 243.62 ng mL−1 for giraldoid A and 952.38 ± 131.99 ng mL−1 for giraldoid B. The time to reach the maximum plasma concentration was 0.50 ± 0.37 h for giraldoid A and 0.50 ± 0.66 h for giraldoid B. The validated method was successfully applied to investigate the concentration–time profiles of giraldoid A and giraldoid B.  相似文献   

8.
The detection of the markers of Cannabis consumption in biological specimens is an important task for drug testing laboratories in varous contexts. A simple assay combining salting-out assisted liquid–liquid extraction sample preparation and LC–MS/MS analysis was applied to the measurement of Δ9-tetrahydrocannabinol, 11-nor-9-carboxy-Δ9-tetrahydrocannabinol (THC-COOH), 11-hydroxy-Δ9-tetrahydrocannabinol, cannabinol and cannabidiol concentrations in 100 μl plasma specimens. The assay had linearity of 1–100 ng ml−1 for THC-COOH and 0.5–50 ng ml−1 for the other tested cannabinoids. Assay validation criteria were fulfilled. Extraction yields (88.7–97.3%) and internal-standard correct matrix effects (−9.6 to +5.4%) were acceptable. The assay was applied to 238 clinical specimens from trauma patients, with 19 samples presenting quantifiable concentrations of at least one of the target compounds. The developed assay is a simple and efficient strategy for simultaneous measurement of Δ9-tetrahydrocannabinol, THC-COOH, 11-hydroxy-Δ9-tetrahydrocannabinol, cannabinol and cannabidiol concentrations in plasma specimens.  相似文献   

9.
Xiao‐Ai‐Ping injection (XAPI) is a traditional Chinese medicine that has been widely used to treat cancer. Modern pharmacological studies have demonstrated that C21 steroids are the main active compounds in XAPI. In this study, a sensitive and specific liquid chromatography tandem mass spectrometry (LC‐MS/MS) method was developed and validated the first time for simultanenous determination of three isomeric pregnane genins (17β‐tenacigenin B, tenacigenin B and tenacigenin A) and their corresponding glycosides (tenacigenoside A, tenacissoside F and marsdenoside I) from XAPI in rat plasma. A simple liquid–liquid extraction technique was used after the addition of dexamethasone acetate as internal standard. The chromatography separation of analytes was achieved on an Agilent Zorbax Eclipse XDB‐C18 column (3.5 µm, 150 × 3 mm i.d.) using methanol–water as mobile phase in a gradient elution program. Detection was performed in multiple reaction monitoring mode using electrospray ionization in the negative ion mode. The method showed satisfactory linearity over a concentration range 5.00–2000.00 ng/mL for tenacigenin B, tenacigenin A, marsdenoside I and tenacissoside F (r2 > 0.99), 10.00–4000.00 ng/mL for 17β‐tenacigenin B and tenacigenoside A (r2 > 0.99). Intra‐ and inter‐day precisions (valued as relative standard deviation) were <9.00% and accuracies (as relative error) in the range ?6.31 to 7.23%. Finally, this validated method was successfully applied to the pharmacokinetic study of XAPI after intravenous administration to rats. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

10.
A highly sensitive and specific LC‐MS/MS method has been developed for simultaneous estimation of nortriptyline (NTP) and 10‐hydroxynortriptyline (OH‐NTP) in human plasma (250 µL) using carbamazepine as an internal standard (IS). LC‐MS/MS was operated under the multiple reaction‐monitoring mode using the electrospray ionization technique. A simple liquid–liquid extraction process was used to extract NTP, OH‐NTP and IS from human plasma. The total run time was 2.5 min and the elution of NTP, OH‐NTP and IS occurred at 1.44, 1.28 and 1.39 min, respectively; this was achieved with a mobile phase consisting of 20 mm ammonium acetate : acetonitrile (20:80, v/v) at a flow rate of 0.50 mL/min on a HyPURITY C18 column. The developed method was validated in human plasma with a lower limit of quantitation of 1.09 ng/mL for both NTP and OH‐NTP. A linear response function was established for the range of concentrations 1.09–30.0 ng/mL (r > 0.998) for both NTP and OH‐NTP. The intra‐ and inter‐day precision values for NTP and OH‐NTP met the acceptance as per FDA guidelines. NTP and OH‐NTP were stable in a battery of stability studies, i.e. bench‐top, auto‐sampler and freeze–thaw cycles. The developed assay was applied to a pharmacokinetic study in humans. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

11.
A reliable, high‐throughput and sensitive LC–MS/MS procedure was developed and validated for the determination of five tyrosine kinase inhibitors in human plasma. Following their extraction from human plasma, samples were eluted on a RP Luna®‐PFP 100 Å column using a mobile phase system composed of acetonitrile and 0.01 m ammonium formate in water (pH ~4.1) with a ratio of (50:50, v /v) flowing at 0.3 mL min−1. The mass spectrometer was operating with electrospray ionization in the positive ion multiple reaction monitoring mode. The proposed methodology resulted in linear calibration plots with correlation coefficients values of r 2 = 0.9995–0.9999 from concentration ranges of 2.5–100 ng mL−1 for imatinib, 5.0–100 ng mL−1 for sorafenib, tofacitinib and afatinib, and 1.0–100 ng mL−1 for cabozantinib. The procedure was validated in terms of its specificity, limit of detection (0.32–1.71 ng mL−1), lower limit of quantification (0.97–5.07 ng mL−1), intra‐ and inter assay accuracy (−3.83 to +2.40%) and precision (<3.37%), matrix effect and recovery and stability. Our results demonstrated that the proposed method is highly reliable for routine quantification of the investigated tyrosine kinase inhibitors in human plasma and can be efficiently applied in the rapid and sensitive analysis of their clinical samples.  相似文献   

12.
Senkyunolide I is one of the major bioactive components in the herbal medicine Ligusticum chuanxiong. The aim of this study was to develop and validate a fast, simple and sensitive LC‐MS/MS method for the determination of senkyunolide I in dog plasma. The plasma samples were processed with acetonitrile and separated on a Waters Acquity UPLC BEH C18 column (50 × 2.1 mm, 1.7 μm). The mobile phase consisted of 0.1% formic acid aqueous and acetonitrile was delivered at a flow rate of 0.3 mL min−1. The detection was achieved in the positive selected reaction monitoring mode with precursor‐to‐product transitions at m/z 225.1 → 161.1 for senkyunolide I and at m/z 349.1 → 305.1 for an internal standard. The assay was linear over the tested concentration range, from 0.5 ng mL−1 to 1000 ng mL−1, with a correlation coefficient >0.9992. The mean extraction recovery from dog plasma was within the range of 85.78–93.25%, while the matrix effect of the analyte was within the range of 98.23–108.89%. The intra‐ and inter‐day precisions (RSD) were <12.12% and the accuracy (RR) ranged from 98.89% to 104.24%. The validated assay was successfully applied to pharmacokinetic and bioavailability studies of senkyunolide I in dogs. The results demonstrated that (a) senkyunolide I showed short elimination half‐life (<1 h) in dog, (b) its oral bioavailability was >40% and (c) senkyunolide I showed dose‐independent pharmacokinetic profiles in dog plasma over the dose range of 1–50 mg kg−1.  相似文献   

13.
Anabolic and androgenic steroids (AASs) are synthetic substances related to the primary male sex hormone, testosterone. AASs can be abused in both human and equine sports and, thus, are banned by the International Olympic Committee and the Association of Racing Commissioners International (ARCI). Enforcement of the ban on the use of AASs in racehorses during competition requires a defensible and robust method of analysis. To address this requirement, a high‐throughput ultra high‐performance liquid chromatography–mass spectrometric (UHPLC–MS) method was developed for the detection, quantification and confirmation of 55 AASs in equine plasma. AASs were recovered from equine plasma samples by liquid–liquid extraction with methyl tert‐butyl ether (MTBE). Analytes were chromatographically separated on a sub‐2 µm particle size C18 column with a mobile phase gradient elution and detected by selected‐reaction monitoring (SRM) on a triple quadrupole mass spectrometer. AASs with isobaric precursor ions were either chromatographically resolved or mass spectrometrically differentiated by unique precursor‐to‐product ion transitions. A few of them that could not be resolved by both approaches were differentiated by intensity ratios of three major product ions. All the epimer pairs, testosterone and epitestosterone, boldenone and epiboldenone, nandrolone and epinandrolone, were chromatographically base‐line separated. The limit of detection and that of quantification was 50 pg/ml for most of the AASs, and the limit of confirmation was 100–500 pg/ml. Full product ion spectra of AASs at concentrations as low as 100–500 pg/ml in equine plasma were obtained using the triple quadrupole instrument, to provide complementary evidentiary data for confirmation. The method is sensitive and selective for the detection, quantification and confirmation of multiple AASs in a single analysis and will be useful in the fight against doping of racehorses with AASs. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

14.
This study described a fully automated method using on‐line solid phase extraction of large volume injections coupled with high performance liquid chromatography (HPLC) and tandem mass spectrometry (MS/MS) to simultaneously detect a group of recalcitrant microconstituents (pharmaceuticals and personal care products, steroid hormones and sterols) in aqueous matrices. Samples (1 mL to 20 mL) were loaded to the preconcentration column at 1 mL/min, and the column was washed with 1000 μL of 25% methanol in LC/MS water to remove polar and ionic interferences before LC‐MS/MS analysis. Three different atmospheric pressure ionization (API) techniques, including photoionization (APPI) with four different dopants (acetone, anisole, chlorobenzene and toluene), heated electrospray ionization (HESI) and atmospheric pressure chemical ionization (APCI), were evaluated on the basis of method detection limits (MDLs) and recoveries from different aqueous matrixes. Results indicated that APPI with toluene as dopant was the most sensitive ionization method for the majority of the analytes. When using 5 mL of sample, MDLs for pharmaceuticals and personal care products, including carbamazepine, DEET, caffeine, naproxen, acetaminophen and primidone, were between 0.3 ng/L and 15 ng/L. MDLs of hormones, including testosterone, equilenin, progesterone, equilin, 17β‐estradiol, 17α‐ethynylestradiol, estrone, androsterone, mestranol and estriol, were between 1.2 ng/L and 37 ng/L. The combination of APPI with dopant allowed the detection of two difficult to ionize fecal related sterols, such as coprostan‐3‐ol and coprostan‐3‐one with MDLs of 5.4 ng/L and 11 ng/L, respectively. Calculated MDLs are more than adequate for analysis of wastewater using 1 to 5 mL sample size and for surface waters using up to 20 mL sample size. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

15.
We developed and validated a high‐performance liquid chromatography–tandem mass spectrometry analytical method to measure E‐3810, a novel dual inhibitor of fibroblast growth factor receptor 1 and vascular endothelial growth factor receptor 1–3 in tissues and determined the drug concentration in a biopsy of human breast cancer for the first time. The method is a modification of our previous one in plasma to study the clinical pharmacokinetics of the drug during the phase I/II trial. In view of the changes in matrix, we applied a partial validation protocol to determine recovery, sensitivity, range of linearity, precision, accuracy and stability of the method over three runs in a mouse tumor tissue and liver. The recovery of E‐3810 from liver or tumor homogenate was >69%, and the lower limit of quantification was 5 ng/ml. The method was linear in the concentration range 5.0–500.0 ng/ml, as demonstrated by a determination coefficient R2 ≥ 0.9955. The range of the calibration curve was appropriate for the analysis, as demonstrated by the accuracy, which was between 91.4% and 106.7%. Interday precision and accuracy on quality control samples at 9, 30 and 300 ng/ml were 3.1‐11.2% and 98.3–111.4%, respectively. The assay was applied successfully to determine the intratumor concentration of E‐3810 in different mouse xenograft tumor models and in a biopsy of a patient with breast cancer included in the phase I/II trial of the drug. In mouse tumors, the concentrations of E‐3810 were higher than necessary to exert antitumor activity in vitro (1 µM). Even more of interest was the result obtained in a human biopsy of few milligrams, where E‐3810 reached 4.9 µg/g (11 µM). Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

16.
An ultra‐high‐performance liquid chromatography–tandem mass spectrometry (UHPLC‐MS/MS) method for the analysis of cefazolin and cefalothin in human plasma (total and unbound), urine and peritoneal dialysate has been developed and validated. Total plasma concentrations are measured following protein precipitation and are suitable for the concentration range of 1–500 µg/mL. Unbound concentrations are measured from ultra‐filtered plasma acquired using Centrifree® devices and are suitable for the concentration range of 0.1–500 µg/mL for cefazolin and 1–500 µg/mL for cefalothin. The urine method is suitable for a concentration range of 0.1–20 mg/mL for cefazolin and 0.2–20 mg/mL for cefalothin. Peritoneal dialysate concentrations are measured using direct injection, and are suitable for the concentration range of 0.2–100 µg/mL for both cefazolin and cefalothin. The cefazolin and cefalothin plasma (total and unbound), urine and peritoneal dialysate results are reported for recovery, inter‐assay precision and accuracy, and the lower limit of quantification, linearity, stability and matrix effects, with all results meeting acceptance criteria. The method was used successfully in a pilot pharmacokinetic study with patients with peritoneal dialysis‐associated peritonitis, receiving either intraperitoneal cefazolin or cefalothin. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

17.
Major depressive disorder is a severe, life‐threatening and highly prevalent psychiatric disorder. A high percentage of people suffering from depression are characterized by hyperactivity of the hypothalamic–pituitary–adrenal axis, resulting in plasma glucocorticoid (cortisol in human and corticosterone in rodent) elevations. Glucocorticoid is a critical molecule in the onset of pathology of depression. A simple, highly sensitive and specific method based on ultra‐fast liquid chromatography–tandem mass spectrometry method has been developed for the quantitation of corticosterone in mouse plasma for the first time, which provides technical support for the high‐throughput measurement for clinical determination of corticosterone in biological samples. Samples were spiked with methanol to precipitate the protein, and then chromatographed on an Agilent Zorbax Eclipse Plus C18 (100 × 2.1 mm,1.8 µm) column by linear gradient elution with methanol and 0.1% formic acid as the mobile phase within 5 min. The detection of corticosterone was performed on ultra‐fast liquid chromatography–triple quadrupole tandem mass spectrometry in the positive ion. The ions [M + H]+ m/z 347.2 → m/z 311.1 for corticosterone and [M + H]+ m/z 363.2 → m/z 327.2 for hydrocortisone (internal standard) were used for quantitative determination. The lower quantification limit for corticosterone was 1 ng/mL. The validated method was successfully applied to the quantitation of corticosterone in mouse plasma. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

18.
A highly sensitive derivatization method for liquid chromatography (LC)-electrospray ionization (ESI) tandem mass spectrometry of dehydroepiandrosterone (DHEA), testosterone (T), pregnenolone (P5), and 17α-OH-pregnenolone (17-OHP5) was developed based on the use of fusaric acid as a reagent. DHEA, P5, and 17-OHP5 were rapidly and quantitatively converted to the 3-fusarate esters by treatment with fusaric acid and 2-methyl-6-nitrobenzoic anhydride. The positive ESI-mass spectra of the fusarate esters of each steroid were dominated by the appearance of [M + H]+ as base peaks. The fusarate derivatization of these steroids showed 17.6-fold (DHEA), 11.9-fold (P5), 3.3-fold (17-OHP5), and 1.8-fold (T) higher sensitivity to those of the corresponding picolinate derivatives in LC-selected reaction monitoring.  相似文献   

19.
A rapid, sensitive and specific liquid chromatography tandem mass spectrometry (LC/MS/MS) method was developed and validated for the quantification of heteroclitin D in rat plasma after using gambogic acid as internal standard (IS). Chromatographic separation was done on a Thermo Hypersil GOLD column (30 × 2.1 mm, 3 µm) using a mobile phase consisting of methanol–water–formic acid (80:20:0.1, v/v/v). The mass spectrometer worked with positive electrospray ionization in multiple reaction monitoring mode, using target ions at [M + H]+ m/z 483.3 for heteroclitin D and [M + H]+ m/z 629.3 for the IS. The standard curve was linear (R2 ≥0.995) over the concentration range 9.98–2080 ng/mL and had good back‐calculated accuracy and precision. The intra‐ and interday precision and accuracy determined on three quality control samples (29.94, 166.4 and 1872 ng/mL) were ≤12.8 and –8.9–3.6%, respectively. The extraction recovery was ≥88.2% and the lower limit of quantification was 9.98 ng/mL. The method was successfully applied to evaluate pharmacokinetics of heteroclitin D in Sprague–Dawley rats following a single intravenous bolus injection of 2.0 mg/kg heteroclitin. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

20.
A simple and rapid high‐performance liquid chromatography–tandem mass spectrometric assay for determination of paclitaxel on rat dried blood spots was developed and validated. The extracted sample was chromatographed without further treatment using a reverse‐phase Oyster ODS3, 4.6 × 50 mm, 3 µm column with mass spectrometry detection. The mobile phase comprised of acetonitrile–water, 60:40 v/v, with a flow rate of 0.4 mL/min was used. The calibration was linear over the range 0.2–20 ng/mL. The limits of detection and quantification were 0.08 and 0.2 ng/mL, respectively. The intra‐ and inter‐day precision (CV%) and accuracy (relative error %) were less than 10 and 12%, respectively. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

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