Simultaneous Determination of Pethidine and Atropine in Rabbit Plasma by LC�CMS�CMS and Its Application to a Pharmacokinetic Study after Intramuscular Administration

A sensitive and selective liquid chromatography?Ctandem mass spectrometry method for the determination of pethidine and atropine in rabbit plasma was developed and validated. The analytes and internal standard (IS) are extracted from plasma by liquid?Cliquid extraction using ethyl acetate, and separated on a Zorbax SB-Aq column (2.1 × 150 mm, 3.5 ??m) using acetonitrile?C0.1% formic acid as mobile phase with gradient elution. Electrospray ionization source was applied and operated in positive ion mode, and multiple reaction monitoring mode was used for quantification using target fragment ions m/z 247.8 ?? 219.7 for pethidine, m/z 289.9 ?? 123.8 for atropine and m/z 295.0 ?? 266.8 for IS, respectively. The assay is linear over the range of 5?C1,000 ng mL^?1 for pethidine and atropine, with a lower limit of quantification of 3 ng mL^?1 for pethidine and 5 ng mL^?1 for atropine. Intra-day and inter-day precision are less than 11% and the accuracy are in the range of 90.4?C106.3%. Furthermore, the newly developed method is successfully used for the determination of pethidine and atropine in rabbit plasma for pharmacokinetic study.     

Determination of Rizatriptan in Human Plasma by Liquid Chromatography Stable Isotope Dilution Electrospray MS�CMS for Application in Bioequivalence Study

A simple, sensitive, selective, rapid, rugged, reproducible and specific liquid chromatography?Ctandem mass spectrometry (LC?CMS/MS) method was used for quantitative estimation of rizatriptan (RZ) in human plasma using rizatriptan-d ₆ (RZD6) as internal standard (IS). Chromatographic separation was performed on Ascentis Express RP Amide C18, 50 × 4.6 mm, 2.7 ??m column with isocratic mobile phase composed of 10 mM ammonium formate:acetonitrile (20:80 v/v) at flow rate of 0.5 mL min^?1. RZ and RZD6 were detected with proton adducts at m/z (amu) 270.2 ?? 201.2 and 276.1 ?? 207.1, respectively, in multiple reaction monitoring (MRM) positive mode. Liquid?Cliquid extraction was used and validated over a linear concentration range of 0.1?C100.0 ng mL^?1 with correlation coefficient r ² ?? 0.9981. The limit of quantification (LOQ) and limit of detection (LOD) were found to be 0.1 ng mL^?1 and 12.5 fg, respectively. Intra- and inter-day precision were within 1.7?C3.1% and 2.8?C3.7%, and accuracy within 96.0?C101.7% and 99.7?C101.4% for RZ. Drug was found to be stable throughout three freeze?Cthaw cycles. The method was successfully employed for analysis of plasma samples following oral administration of RZ (10 mg) in 25 healthy Indian male human volunteers under fasting conditions.     

Quantitative Determination of Anti-Inflammatory Columbianetin in Rat Plasma by LC-ESI-MS/MS for Pharmacokinetic Studies after Oral Administration of Duhuo Extract

Specific LC-ESI-MS/MS method or procedure was developed and validated for columbianetin quantification in rat plasma using epicatechin as an internal standard (IS). Chromatographic separation was performed on an Eclipse plus C18 (150 × 4.6 mm, 1.8 ??m) at a flow rate of 0.300 mL min^?1, and water-acetonitrile was used as mobile phase. The calibration curve of the method was linear in the concentration range of 5?C1,000 ng mL^?1. The lower limit of quantification (LLOQ) was 5 ng mL^?1. The intra- and inter-day precision of the quality control samples was within 15.0%, and the accuracy was within 90.0?C110%. The recoveries were more than 90.0% for columbianetin at concentrations of 10, 200 and 1,000 ng mL^?1, respectively. This method was successfully applied for evaluation of the pharmacokinetics of columbianetin after oral doses of 0.60 g kg^?1 Angelica pubescence extract in rats.     

Simultaneous Determination of Escin Ia and Its Isomer Isoescin Ia by LC�CMS�CMS: Application to a Pharmacokinetic Study of Escin Ia in Rats

A rapid and sensitive LC?CMS?CMS method for the simultaneous determination of escin Ia and isoescin Ia in rat plasma, urine, feces and bile samples was developed and validated. Analytes and telmisartan [internal standard (IS)] were extracted by solid-phase extraction on C₁₈ cartridges. Components in the extract were separated on an HC-C₁₈ column (5 ??m, 150 × 4.6 mm i.d.) using 10 mM ammonium acetate?Cmethanol?Cacetonitrile (40:30:30, v/v/v) as the mobile phase. The method demonstrated good linearity from 5 ng mL^?1 (LLOQ) to 1,500 ng mL^?1 for both escin Ia and isoescin Ia. Intra- and inter-day precision measured as RSD was within ±15%. Recoveries and matrix effects of both escin Ia and isoescin Ia were satisfactory in all four matrices examined. The method was successfully applied to a pharmacokinetic study in Wistar rats after a single intravenous administration of escin Ia at the dose of 1.0 mg kg^?1.     

Determination of Quinine and Doxycycline in Rat Plasma by LC�CMS�CMS: Application to a Pharmacokinetic Study

A fast, sensitive, and specific LC?CMS?CMS method for determination of quinine (QN) and doxycycline (DOX) in rat plasma has been developed and validated. QN, DOX, and cimetidine (internal standard, IS) were extracted from the plasma by protein precipitation. The compounds were separated on a C₁₈ column with methanol?C0.1% aqueous formic acid 70:30 (v/v) as mobile phase at a flow rate of 0.5 mL min^?1 (split 1:3). Detection was by positive electrospray ionization (ESI+) in multiple reaction monitoring (MRM) mode, monitoring the transitions 325.0 ?? 307.0, 445.0 ?? 428.1, and 252.8 ?? 159.0, for QN, DOX, and IS, respectively. The analysis was carried out in 2.0 min and the method was linear in the plasma concentration range 5?C5,000 ng mL^?1. The mean extraction recoveries for QN, DOX, and IS from plasma were 89.4, 90.5, and 86.3%, respectively. The method was validated for linearity, precision, accuracy, specificity, and stability; the results obtained were within the acceptable range. The proposed method was successfully applied to the determination of QN and DOX in rat plasma samples to support pharmacokinetic studies.     

LC�CMS�CMS Method for Quantification of Hydralazine in BALB/C Mouse Plasma and Brain: Application to Pharmacokinetic Study

A rapid, sensitive and accurate high performance liquid chromatography method using tandem mass spectrometry detection for hydralazine in BALB/C mouse plasma and brain was developed and validated. The method involved a derivatization with 2,4-pentanedione at 50 °C for 1 h, and a step of solid phase extraction to purify and concentrate hydralazine derivative. Chromatographic separation was carried out on an Agilent ZORBAX SB-C18 column by elution with methanol?C0.01 mol L^?1 ammonium acetate (60:40, v/v). The multiple reaction monitoring transition used for quantification was m/z 225.2 ?? 129.5 in the electrospray positive ionization mode. Good linearity was obtained over the concentration range of 10?C200 ng mL^?1. The limits of detection were 0.49 and 1.05 ng mL^?1 for hydralazine in mouse plasma and brain, respectively. The limits of quantitation were 1.5 and 3.18 ng mL^?1 for hydralazine in mouse plasma and brain, respectively. Sample analysis time was 6 min including sample separation. The method was successfully applied to a pharmacokinetic study following intraperitoneal injection of hydralazine in BALB/C mice at the dose of 20 mg kg^?1.     

HPLC–MS Analysis of Isoniazid in Dog Plasma

A simple, rapid, and sensitive liquid chromatography–mass spectrometric (LC–MS) method was developed and validated for the determination of isoniazid in dog plasma. Plasma samples were deproteined with methanol and separated on a C₁₈ column interfaced with a single quadrupole mass spectrometer, using 0.1% formic acid–acetonitrile (91:9 v/v) as mobile phase. Detection was performed by positive electrospray ionization with selected ion monitoring at m/z 138 for isoniazid and 152 for entecavir maleate internal standard. Linearity was obtained over the range of 25–5,000 ng mL^?1, with a lower limit of quantification of 25 ng mL^?1. The intra- and inter-day precision was less than 2.7% in terms of relative standard deviation. Accuracy, expressed as relative error, ranged from ?2.0 to 8.0%. Plasma samples were analysed within 5 min. The method was successfully applied to the evaluation of the pharmacokinetics of isoniazid in dog plasma.     

Determination of SYUIQ-F5, a Novel Telomerase Inhibitor and Anti-tumor Lead-Compound, in Tissues and Plasma Samples by LC�CMS�CMS: Application to a Tissue Distribution Study in Rat

A sensitive assay for determining SYUIQ-F5, a novel telomerase inhibitor and anti-tumor drug, in rat tissues and plasma was developed and validated by using liquid chromatography/tandem mass spectrometry (LC?CMS?CMS). After a single step liquid?Cliquid extraction with ethyl acetate-dichloromethane, SYUIQ-F5 and SUCL (internal standard) were subjected to LC?CMS?CMS analysis using positive electro-spray ionization under selected reaction monitoring mode. Chromatographic separation of SYUIQ-F5 and SUCL was achieved on a Zorbax Eclipse Plus C18 column (I.D. 4.6 mm × 150 mm, 3.5 ??m) with a mobile phase consisting of acetonitrile-2 mM ammonium formate (90:10, v/v) at a flow rate of 0.6 mL min^?1. The intra- and inter-batch precision of the method were <12.2 and 8.7%, respectively. The intra- and inter-batch accuracies ranged from 100.2 to 107.3%. The lowest limit of quantification for SYUIQ-F5 was 0.5 ng mL^?1. The method was applied to a SYUIQ-F5 tissue distribution study after an oral dose of 30 mg kg^?1 to rats. SYUIQ-F5 tissue concentrations decreased in the order of small intestine> liver> lung> spleen> stomach> kidneys> heart> brain> muscle> fat> testes> plasma. SYUIQ-F5 could still be detected in most of the tissues at 48-h post-dosing. These results indicated that the LC?CMS?CMS method was sensitive, reliable, and specific to quantify SYUIQ-F5 in different rat tissues.     

Simultaneous Determination of Hydrocodone, and Its Two Metabolites in Human Plasma by HPLC�CMS�CMS

A rapid, sensitive and specific assay method has been developed to simultaneously determine human plasma concentrations of hydrocodone and its metabolites, norhydrocodone, hydromorphone, using high-performance liquid chromatography with an electrospray ionization (ESI) tandem mass spectrometry (HPLC?CMS?CMS). Hydrocodone, its metabolites, and internal standard, hydrocodone-d ₃, norhydrocodone-d ₃, hydromorphone-d ₃, were separated from human plasma using solid-phase extraction (Empore MPC-SD Solid Phase Extraction Disk). The eluate was dried, reconstituted and injected into the LC?CMS?CMS system. Chromatographic separation was performed on a Kromasil 100-5SIL-Dimensions C₁₈ column (100 × 2.1 mm, 5.0 ??m, Thermo Hypersil-Keystone, USA) using a gradient mobile phase with 20 mmol L^?1 ammonium formate in water with 0.2% formic acid and 0.1% formic acid in acetonitrile. Detection and quantitation were performed by MS/MS using electrospray ionization and multiple reactions monitoring in the positive ion mode. The calibration curves were linear over the concentration ranges 0.05?C50 ng mL^?1 for hydrocodone (r ² = 0.9991) and norhydrocodone (r ² = 0.9990), and 0.01?C10 ng mL^?1 for hydromorphone (r ² = 0.9990). The limit of quantification was 0.05 ng mL^?1 for hydrocodone and norhydrocodone, and 0.01 ng mL^?1 for hydromorphone. The extraction recovery was above 64.36, 68.51 and 71.78% for hydrocodone, norhydrocodone and hydromorphone. The accuracy was higher than 99.06, 97.70 and 100.07% for hydrocodone, norhydrocodone and hydromorphone. The intra- and inter-day precisions were <5.80, 5.90 and 3.02% for hydrocodone, norhydrocodone and hydromorphone. The method was accurate, sensitive and simple and was successfully applied to a pharmacokinetic study after a single oral administration of hydrocodone bitartrate at a dose of 5 mg in 12 healthy Chinese volunteers.     

Magnetic Nanoparticle-Based Micro-Solid Phase Extraction and GC�CMS Determination of Oxadiargyl in Aqueous Samples

A new facile, rapid, inexpensive, and sensitive method based on magnetic micro-solid phase extraction (M-??-SPE) coupled to gas chromatography?Cmass spectrometry (GC?CMS) was developed for determination of the herbicide oxadiargyl in environmental water samples. The feasibility of employing non-modified magnetic nanoparticles (MNPs) as sorbent was examined and applied to perform the extraction process. Influential parameters affecting the extraction efficiency along with desorption conditions were investigated and optimized. The limit of detection (LOD, S/N = 3) and limit of quantification (LOQ, S/N = 10) of the method under optimized conditions were 0.005 and 0.030 ng mL^?1, respectively. The relative standard deviations (RSD) (n = 3) at a concentration of 0.10 ng mL^?1 was 11%. The calibration curve of oxadiargyl showed linearity in the range of 0.050?C0.50 ng mL^?1. The developed method was successfully applied to the extraction of oxadiargyl from spiked tap water and Zayande-Rood River water samples and the relative recoveries of 98 and 94% were obtained, respectively.     

Simultaneous LC–MS–MS Analysis of Danshensu, Salvianolic Acid B, and Hydroxysafflor Yellow A in Beagle Dog Plasma, and Application of the Method to a Pharmacokinetic Study of Danhong Lyophilized Powder for Injection

A reliable and sensitive liquid chromatographic–tandem mass spectrometric method, with rutin as internal standard, has been developed and validated for simultaneous determination of danshensu, salvianolic acid B (SAB), and hydroxysafflor yellow A (HSYA) in beagle dog plasma. Plasma samples spiked with the analytes were extracted by solid-phase extraction and the analytes were separated on a 250 × 4.6 mm i.d., 5-μm particle, C₁₈ column with methanol–acetonitrile–0.5% formic acid 20:25:55 (v/v) as mobile phase at a flow rate of 1 mL min^?1. LC–MS–MS analysis was performed with a Finnigan TSQ triple-quadrupole tandem mass spectrometer operated in negative-ion selected-reaction-monitoring mode, using electrospray ionization. The accuracy and precision of the method were acceptable and linearity was good over the range 20–4,000 ng mL^?1 for danshensu, 50–10,000 ng mL^?1 for SAB, and 10–2,000 ng mL^?1 for HSYA. The method was successfully applied to a pharmacokinetic study of a traditional Chinese medicinal preparation, Danhong lyophilized powder for injection.     

Rapid and Simultaneous Determination of Efavirenz, 8-Hydroxyefavirenz, and 8,14-Dihydroxyefavirenz Using LC�CMS�CMS in Human Plasma and Application to Pharmacokinetics in Healthy Volunteers

We developed a rapid and sensitive method for determining efavirenz, 8-hydroxyefavirenz, and 8,14-dihydroxyefavirenz in human plasma simultaneously using liquid chromatography?Ctandem mass spectrometry (LC?CMS?CMS). Three compounds and ritonavir, an internal standard, were extracted from plasma using ethyl acetate in the presence of 0.1 M sodium carbonate after incubation of ??-glucuronidase (500 U). After drying the organic layer, the residue was reconstituted in mobile phase (acetonitrile:20 mM ammonium acetate, 90:10, v/v) and injected onto a reversed-phase C₁₈ column. The isocratic mobile phase was eluted at 0.2 mL min^?1. The ion transitions monitored in multiple reaction-monitoring mode were m/z 314 ?? 244, 330 ?? 258, 346 ?? 262, and 721 ?? 296 for efavirenz, 8-hydroxyefavirenz, 8,14-dihydroxyefavirenz, and ritonavir, respectively. The retention time is 1.93, 1.70, 1.52, and 1.82 min for efavirenz, 8-hydroxyefavirenz, 8,14-dihydroxyefavirenz, and ritonavir, respectively. The coefficients of variation of the assay precision were less than 10.7%, and the accuracy was 90?C111%. The lower limits of quantification (LLOQ) were 5 ng mL^?1 for efavirenz and 8-hydroxyefavirenz. This method was used to measure the plasma concentrations of efavirenz and its metabolites from healthy volunteers after a single 600 mg oral dose of efavirenz. This analytical method is a very rapid, sensitive, and accurate to determine the pharmacokinetic profiles of efavirenz including its metabolites.     

Simultaneous Estimation of Vinpocetine and Its Metabolite, Apovincaminic Acid, in Beagle Plasma by LC-MS-MS

A method was developed to determine vinpocetine and its metabolite, apovincaminic acid, in beagle plasma by LC-MS-MS. After protein precipitation with methanol, the supernatant of the sample was concentrated and injected into an Agilent Zorbax XDB-C₁₈ column. The sample was separated by a mobile phase consisting of acetonitrile and 0.2% formic acid solution, and the reading was determined on an Agilent 6410 Triple Quad Tandem mass spectrometer in multiple reaction monitoring mode with the following transitions: m/z 351.5 ?? 280.2/266.3 for vinpocetine, 323.2 ?? 236.1/280.2 for apovincaminic acid, and 411.2 ?? 191.1 for the internal standard. The intra- and inter-day variances were less than 15% (RSD%), and average recoveries were higher than 80%. The linearity ranges (LR) between 0.1 and 20.0 ng mL^?1 for vinpocetine (r ² = 0.9980) and between 1.0 and 200.0 ng mL^?1 for apovincaminic acid (r ² = 0.9995) were established. In summary, this method is sensitive, specific, and appropriate for in vivo study of various dosage forms of vinpocetine.     

Simultaneous Determination of Buprenorphine, Norbuprenorphine and Naloxone in Human Plasma by LC-MS-MS

A novel sensitive and selective liquid chromatography-tandem mass spectrometry (LC-MS-MS) method simultaneously determined buprenorphine (BUP) and its active metabolite, norbuprenorphine (NBUP), and a coformulant, naloxone was developed, validated and applied successfully in humans. Buprenorphine-d ₄ and norbuprenorphine-d ₃ were used as the internal standard. The analysis was performed on a silica column, and the mobile phase was isocratic and composed of acetonitrile:2 mM ammonium formate in H2O (82:18, v/v). Mass spectrometry employed multiple reaction monitoring modes with transitions of m/z 468.1?C55.2 for BUP, 414.2?C101.2 for NBUP, 328.3?C310.3 for naloxone, 472.1?C59.2 for buprenorphine-d ₄ and 417.2?C101.2 for norbuprenorphine-d ₃. Lower limit of quantification (LLOQ) of the analytical method was 0.05 ng mL^?1 for BUP, 0.1 ng mL^?1 for NBUP and 0.025 ng mL^?1 for naloxone, respectively. The standard calibration curves of BUP, NBUP and naloxone were linear over the concentration range of 0.05?C20 ng mL^?1, 0.1?C20 ng mL^?1 and 0.025?C20 ng mL^?1, respectively. The precisions (RSD) and accuracies (RE) of LLOQ and other QC samples were in acceptable range, with RSD < 20% and RE ± 20% for LLOQ and RSD < 15% and RE within ±15% for QC samples. The method was accurate, precise and specific, and was applied to the pharmacokinetic study of buprenorphine in healthy volunteers.     

Rapid and Selective LC�CMS�CMS Method for the Determination of cyclo-trans-4-l-Hydroxyprolyl-l-serine (JBP485) in Rat Plasma

A rapid and selective liquid chromatographic/tandem mass spectrometric method for the determination of JBP485 was developed and validated. Following protein precipitation, the analyte and internal standard (JBP923) were separated from human plasma using an isocratic mobile phase on an Elite Kromasil C18 column. An API 3200 tandem mass spectrometer equipped with a Turbo ionSpray ionization source was used as the detector and operated in the positive ion mode. Multiple reaction monitoring using the precursor to product ion combinations of m/z 201.2 ?? 86.2 and m/z 219.2 ?? 86.2 was performed to quantify JBP485 and JBP923, respectively. The method was linear in the concentration range of 0.10?C50.00 ??g mL^?1 using 100 ??L of plasma. The lower limit of quantification was 0.10 ??g mL^?1. The intra- and inter-day relative standard deviations over the entire concentration range were less than 6.65%. Accuracy determined at three concentrations (0.25, 4.00 and 25.00 ??g mL^?1 for JBP485) ranged from ?0.78 to 2.74% in terms of relative error. Each plasma sample was chromatographed within 2.0 min. The method was successfully applied to characterize the pharmacokinetic profiles of JBP485 in rats after an intravenous injection of 6.25 mg kg^?1 JBP485.     

Simple, Sensitive, High-Throughput Method for the Quantification of Mitragynine in Rat Plasma Using UPLC-MS and Its Application to an Intravenous Pharmacokinetic Study

A simple, sensitive and rapid ultra-performance liquid chromatography-mass spectrometry (UPLC-MS) method was developed and validated for the quantification of mitragynine in rat plasma using amitriptyline hydrochloride as an internal standard. Sample preparation involved a one-step liquid?Cliquid extraction using methyl t-butyl ether. Mitragynine was separated on an Acquity UPLC^? BEH HILIC column using isocratic elution with a mobile phase of 10 mM ammonium formate buffer containing 0.1% formic acid:acetonitrile (15:85, v/v). At a flow rate of 0.2 mL min^?1, the retention time of mitragynine was found to be 1.3 min. Ionization was performed in the positive ion electrospray mode. The selected mass-to-charge (m/z) ratio transition of mitragynine ion [M + H]⁺ used in the selected ion recording (SIR) was 399.1. The calibration curve was found to be linear over a concentration range of 1?C5,000 ng mL^?1 (r = 0.999) with a lower limit of quantification (LLOQ) of 1 ng mL^?1. Intra- and inter-day assay variations were found to be less than 15%. The extraction recoveries ranged from 85?C93% at the three concentrations (2, 400 and 4,000 ng mL^?1) in rat plasma. This method was successfully used to quantify mitragynine in rat plasma following intravenous administration of the compound.     

HILIC-MS-MS for the Quantification of Pidotimod in Human Plasma

A method for fast, sensitive, and specific hydrophilic interaction chromatography combined with tandem mass spectrometry (HILIC-MS/MS) was developed for the first time to determine the level of pidotimod in human plasma. With rosiglitazone as internal standard, analysis was carried out on a HILIC column (150 mm × 2.1 mm, 3.5 ??m) using a mobile phase consisting of methanol:0.2% formic acid (60:40, v/v). Detection was carried out by tandem mass spectrometry using electrospray ionization (ESI). Linear calibration curves were obtained in the concentration range of 11.2?C1.12 × 10⁴ ng mL^?1 for pidotimod, with a lower limit of quantification of 11.2 ng mL^?1. The intra- and inter-day precision values were high, with standard deviations lower than 15%, and the accuracy, in terms of relative error, ranged from ?10.5 to 9.4% at all quality control (QC) levels.     

LC�CMS Method for Determination of Amphotericin B in Rabbit Tears and Its Application to Ocular Pharmacokinetic Study

A rapid and sensitive LC?CMS?CMS method was developed for the quantification of amphotericin B in rabbit tears using natamycin as internal standard. The analyte and internal standard were extracted from the tear sample using a solid phase extraction method. Chromatographic separation was achieved on a Phenomenex Luna 3 ??m CN column (100 × 2 mm, 3 ??m) using 3.5 mM ammonium acetate (pH 4):methanol (10:90) as mobile phase. The assay was validated with a linear range of 0.1?C3.2 ??g mL^?1 for amphotericin B using 10 ??L of tear sample. The intra- and inter-day assay precision ranged from 2.49 to 4.37 and 2.17 to 5.59%, respectively, and intra- and inter-day assay accuracy was between from 0.27 to 3.32 and ?0.51 to 3.72%, respectively. The method was successfully applied to the pharmacokinetic studies of amphotericin B eye drops in rabbit tears.     

LC�CMS Analysis of Sertraline and Its Active Metabolite in Human Serum Using a Silica Column with a Non-Aqueous Polar Mobile Phase

A sensitive liquid chromatography?Cmass spectrometry method for the simultaneous determination of sertraline (SER) and its major metabolite norsertraline (NOR) from serum was developed and validated in the context of a pharmacokinetic study in pregnant women. The separations were achieved on a silica column with a non-aqueous polar mobile phase consisting of acetonitrile, methanol and ammonium acetate at a flow rate of 0.5 mL min^?1. The concentrations were measured using a single quadruple mass spectroscopic detector supplied with atmospheric pressure ionization electrospray. Sample preparation consisted of a simple liquid?Cliquid procedure. The detector was set in selective ion mode for each compound of interest, 306 m/z for SER and 275 m/z for NOR. Calibration curves were generated by least square linear regression for concentration of 5?C160 ng mL^?1 for SER and from 10 to 320 ng mL^?1 for NOR. The curves for both compounds of interest were linear, with correlation coefficients r ² ?? 0.999.