A highly sensitive three-dimensional excitation-emission fluorescence method was proposed to determine antihypertensives including valsartan and amlodipine besylate in human plasma with the aid of second-order calibration methods based on parallel factor analysis (PARAFAC) and alternating trilinear decomposition (ATLD) algorithms. Antihypertensives with weak fluorescent can be transformed into a strong fluorescent property by changing microenvironment in samples using micellar enhanced surfactant. Both the adopted algorithms with second-order advantage can improve the resolution and directly attain antihypertensives concentration even in the presence of potential strong intrinsic fluorescence from human plasma. The satisfactory results can be achieved for valsartan and amlodipine besylate in complicated human plasma. Furthermore, some statistical parameters and figures of merit were evaluated to investigate the performance of the proposed method, and the accuracy and precision of the proposed method were also validated by the elliptical joint confidence region (EJCR) test and repeatability analysis of intraday and interday assay. The proposed method could not only light a new avenue to directly determine valsartan or amlodipine besylate in human plasma, but also hold great potential to be extended as a promising alternative for more practical applications in the determination of weak fluorescent drugs.
Hypertension is considered as a chronical disease resulting in the elevation of arterial hypertension and increasing the risk of cardiac disease [
Based on the available literature, several analytical methods had been reported for the quantification of valsartan or amlodipine in biological matrixes. Liquid chromatography-tandem mass spectrometry using electrospray ionization mode [
Compared with the conventional fluorescence spectrometry, chemometric methodologies coupled with excitation-emission matrix (EEM) fluorescence can enhance the selectivity of analytical methods and reduce analytical cost. The predominant advantage of second-order calibration is that it allows concentration information of an individual component to be extracted even in the presence of uncalibrated interferences, and besides this method presented satisfactory results and had advantages over other conventional methods [
In this study, a simple, rapid, and effective method for the direct quantitative analysis of valsartan or amlodipine in human plasma by means of their strong fluorescence property after micellar enhanced microenvironment in samples was proposed by combining three-dimensional excitation-emission matrix fluorescence technology with second-order calibration strategies based on both PARAFAC [
The measurements of fluorescence were performed with a HITACHI F-7000 Fluorescence spectrophotometer fitted with a xenon lamp and interfaced to a Dell PowerEdge T420. In all cases, 1.00 cm quartz cell was used. The spectra data were imported to computer and analyzed in the Matlab environment. The programs of the PARAFAC and ATLD algorithms were homemade. The room temperature was controlled at 25°C.
Valsartan was purchased from TCI (Shanghai, China); Amlodipine Besylate was bought from National Institutes for Food and Drug Control. Phosphoric acid, sodium dihydrogen phosphate, acetic acid, sodium acetate, and sodium dodecyl sulfate (SDS) of analytical grade were obtained from Sinopharm Chemical Reagent Co., Ltd. The human plasma was obtained from Wuhan Institute of Biological Product Co., Ltd.
Stock solutions of 0.501 mg/mL valsartan and 0.402 mg/mL amlodipine besylate were prepared by dissolving appropriate amount in methanol. Working solutions were prepared by appropriate dilution. The concentration of valsartan and amlodipine besylate in working solution is 5.01
In the case of EEM fluorescence, a three-dimensional data array
The PARAFAC model proposed by Harshman, Carroll, and Chang is known as the canonical decomposition, which has been accepted owing to its consistency with Beers law in chemistry. This algorithm is based on a least-squares minimization. The second-order calibration algorithm based on PARAFAC, which is used widely in chemistry for its excellent performance, was adopted to resolve the overlapped spectroscopes and to give a satisfying result. However, the application of PARAFAC may be obstructed by the requirement of a precise estimation of the number of components in the mixtures and characteristic of slow convergence rate.
An improved algorithm, namely, alternating trilinear decomposition (ATLD), was proposed by Wu et al. to overcome the aforementioned disadvantages. It uses the alternating least-squares principle, Moore-Penrose generalized inverse based on singular value decomposition (SVD), and alternating iterative strategy to improve the performance of trilinear decomposition, making a loss function to reach a minimum. In general, ATLD shows a faster convergence than PARAFAC and eliminates the uncertainty associated with factor number estimation.
Figures of merit (FOM) including SEN, SEL, LOD, and LOQ are frequently used to validate the results and compare the performance of various methods. In second-order calibration, the evaluations of FOM are closely related to the calculation of the net analyte signal (NAS), which is defined as the part of the signal that relates uniquely to the NAS. The SEN is estimated as the NAS at unit concentration, and the SEL is the ratio between the sensitivity and the total signal. The LOD of one method is the lowest quantity of a substance that can be distinguished from the absence of that substance (a background value) within a stated confidence limit. The LOQ is the limit at which we can reasonably tell the difference between two different values. Those formulas of FOM are estimated as
The root-mean-square error of prediction (RMSEP) can be calculated in terms of the formula as
As for valsartan, Twenty-seven samples including eleven calibration samples, six test samples, and ten prediction samples were prepared with concentrations within the range of 78.2–559.1 ng/mL. Calibration samples and test samples were made by appropriate dilution of the analyte working solution in methanol. Ten prediction samples contained ten different concentrations of valsartan, 0.01 mol L−1 of SDS, phosphoric acid/sodium dihydrogen phosphate buffer solution (PH = 2.0), and 10
The concentration of valsartan and amlodipine besylate in calibration, test, and prediction samples.
Analytes | Calibration samples | Test samples | Prediction samples | |||
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Number |
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Number |
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Number |
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Valsartan | 1 | 78.2 | 12 | 180.4 | 18 | 90.2 |
2 | 126.3 | 13 | 240.5 | 19 | 138.3 | |
3 | 174.3 | 14 | 300.6 | 20 | 186.4 | |
4 | 222.4 | 15 | 360.7 | 21 | 234.5 | |
5 | 270.5 | 16 | 420.8 | 22 | 282.6 | |
6 | 318.6 | 17 | 481.0 | 23 | 330.7 | |
7 | 366.7 | 24 | 378.8 | |||
8 | 414.8 | 25 | 426.9 | |||
9 | 462.9 | 26 | 474.9 | |||
10 | 511.0 | 27 | 523.0 | |||
11 | 559.1 | |||||
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Amlodipine besylate | 28 | 1.93 | 39 | 3.02 | 45 | 3.38 |
29 | 2.95 | 40 | 4.22 | 46 | 4.46 | |
30 | 3.98 | 41 | 5.43 | 47 | 5.55 | |
31 | 5.00 | 42 | 6.63 | 48 | 6.63 | |
32 | 6.03 | 43 | 7.84 | 49 | 7.72 | |
33 | 7.06 | 44 | 9.05 | 50 | 8.80 | |
34 | 8.08 | 51 | 9.89 | |||
35 | 9.11 | 52 | 10.97 | |||
36 | 10.13 | |||||
37 | 11.16 | |||||
38 | 12.06 |
As regards amlodipine besylate, twenty-five samples including eleven calibration samples, six test samples, and eight prediction samples were prepared with concentrations within the range of 1.93–12.06
As for valsartan, in order to avoid the Rayleigh and Raman scatterings, all the spectral surfaces were recorded at excitation wavelengths varying from 200 to 292 nm at a 2 nm step and emission wavelengths varying from 310 to 378 nm at a 2 nm step. For the same reason, all the spectral surfaces of amlodipine besylate were recorded at excitation wavelengths varying from 266 to 320 nm at a 2 nm step and emission wavelengths varying from 374 to 440 nm at a 2 nm step. The slit width was 10.0/10.0 nm and the scan rate was 2400 nm/min. Thus, a 47 × 35 × 27 (excitation wavelength × emission wavelength × samples) data array for valsartan and a 28 × 34 × 25 (excitation wavelength × emission wavelength × samples) data array for amlodipine besylate were assembled.
To investigate the fluorescent properties of the valsartan and amlodipine besylate, the pure valsartan and amlodipine besylate were prepared and measured via fluorescence spectrophotometer at the given parameters; Figures
Three-dimensional plots of the excitation-emission matrix fluorescence spectra: (a) 318.6 ng/mL pure valsartan; (b) 318.6 ng/mL valsartan and 50
Three-dimensional plots of the excitation-emission matrix fluorescence spectra: (a) 9.11
However, a serious profile overlapping between the valsartan and human plasma together with amlodipine besylate and human plasma was experimentally observed, which consequently made the quantitative analysis of the two analytes using traditional fluorescent methodologies impossible; one can resort to the second-order calibration methods which allow for unique decomposition of trilinear data and only require that the species of interest in both calibration samples and the prediction samples are the same, so with the aid of chemometrics the interference of human plasma can be mathematically separated and accomplish reliable resolution of spectra and accurate quantification of valsartan and amlodipine besylate in complicated biological matrix.
Accurate and reliable calibration models are the key for direct determination of either valsartan or amlodipine besylate with the interference of human plasma; the reliability of the two calibration models for valsartan samples and amlodipine besylate was validated by average recovery and different statistical parameters. The results were shown in Table
Determination of valsartan and amlodipine besylate in test samples using two algorithms.
Analytes | Test samples | 12 | 13 | 14 | 15 | 16 | 17 |
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Valsartan | Recovery (%) | 97.8 | 100.6 | 101.4 | 100.9 | 100.9 | 100.2 |
Average recovery | 100.3 |
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RMSEP (ng/mL) | 3.64 | ||||||
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Test samples | 39 | 40 | 41 | 42 | 43 | 44 | |
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Amlodipine besylate | Recovery (%) | 99.5 | 103.4 | 99.4 | 102.1 | 97.2 | 94.3 |
Average recovery | 99.3 |
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RMSEP (ng/mL) | 0.27 | ||||||
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The correct analytical results can hardly be obtained when the number of components is either big or small; hence it is crucial that the estimation of component numbers is close to the actual one for the purpose of the accurate resolution and validation result; therefore, the core consistency diagnostic (CORCONDIA) as a classical estimation method is applied for solving such a frustrating problem. CORCONDIA was proposed by Bro and Kiers and used to estimate the correct component numbers before the concentration prediction of valsartan or amlodipine besylate in human plasma. The definition of function is as follows:
When the selected number is bigger than the correct factor number, the core consistency is close to zero, even negative. Only when the selected number is equal to or smaller than the correct number, the core consistency is close to one. It is generally acknowledged that the number is equal to or smaller than the correct number when the value is bigger than 0.5. The values of core consistency at different numbers of factors for valsartan and amlodipine besylate are shown in Figure
The core consistency value about valsartan (a) and amlodipine besylate (b) in human plasma.
The algorithms of PARAFAC and ATLD were employed for the resolution of three-dimensional fluorescent data of both valsartan and amlodipine besylate in human plasma with the optimal factor number of two (
Actual and resolved excitation spectra (a1) and emission spectra (b1) of valsartan in human plasma using PARAFAC, and actual and resolved excitation spectra (a2) and emission spectra (b2) of valsartan in human plasma using ATLD. The solid lines, dotted solid lines, and dotted lines represented the loadings of valsartan, the loadings for an inherent interference from the human plasma, and the actual spectral profiles of valsartan, respectively.
Actual and resolved excitation spectra (a1) and emission spectra (b1) of 78 amlodipine besylate in human plasma using PARAFAC, and actual and resolved excitation spectra (a2) and emission spectra (b2) of valsartan in human plasma using ATLD. The solid lines, dotted solid lines, and dotted lines represented the loadings of amlodipine besylate, loadings for an inherent interference from the human plasma, and the actual spectral profiles of amlodipine besylate, respectively.
The prediction results about valsartan and amlodipine besylate in human plasma using both PARAFAC and ATLD algorithms were listed in Tables
Determination of valsartan in human plasma using PARAFAC and ATLD.
Prediction samples | Actual concentration (ng/mL) | Recovery (%) | |
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PARAFAC | ATLD | ||
18 | 90.2 | 99.3 | 96.8 |
19 | 138.3 | 100.8 | 101.7 |
20 | 186.4 | 100.6 | 102.2 |
21 | 234.5 | 102.1 | 103.7 |
22 | 282.6 | 99.2 | 101.5 |
23 | 330.7 | 98.1 | 100.9 |
24 | 378.8 | 100.4 | 103.3 |
25 | 426.9 | 98.9 | 102.2 |
26 | 474.9 | 97.7 | 101.8 |
27 | 523.0 | 97.5 | 101.2 |
Correlation coefficient | 0.9996 | 0.9996 | |
Regression equation |
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Average recovery (%) |
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RMSEP (ng/mL) | 6.55 | 7.37 | |
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Determination of amlodipine besylate in human plasma using PARAFAC and ATLD.
Prediction samples | Actual concentration (ng/mL) | Recovery (%) | |
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PARAFAC | ATLD | ||
45 | 3.38 | 98.8 | 104.5 |
46 | 4.46 | 107.3 | 102.2 |
47 | 5.55 | 104.8 | 100.6 |
48 | 6.63 | 102.7 | 98.2 |
49 | 7.72 | 108.1 | 103.9 |
50 | 8.80 | 109.1 | 105.6 |
51 | 9.89 | 103.1 | 99.7 |
52 | 10.97 | 98.8 | 96.6 |
Correlation coefficient | 0.9976 | 0.9971 | |
Regression equation |
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Average recovery (%) |
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RMSEP (ug/mL) | 0.44 | 0.24 | |
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Due to the fact that the chosen algorithms have different performance, it is vital to set up a criteria such as FOM for the validation of results and the comparison of various algorithms. In this work, FOM including SEN, SEL, LOD, and LOQ were calculated to compare the performance of two algorithms; the results were shown in Table
Figures of merit of valsartan and amlodipine besylate in human plasma using two algorithms.
Figures of merit | Valsartan | Amlodipine besylate | ||
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PARAFAC | ATLD | PARAFAC | ATLD | |
SEN (mL/ng) | 3.23 | 3.23 | 0.022 | 0.066 |
SEL | 0.44 | 0.44 | 0.05 | 0.15 |
LOD (ng/mL) | 0.052 | 0.11 | 0.044 | 0.046 |
LOQ (ng/mL) | 0.61 | 0.34 | 0.13 | 0.14 |
For the sake of a further investigation into the accuracy of these algorithms, the actual concentrations were linearly regressed against the predicted concentrations. The calculated intercept and slope were compared with their ideal values of 0 and 1, based on the elliptical joint confidence region (EJCR) test. Figure
EJCRs for valsartan (a) and amlodipine besylate (b) by applying PARAFAC and ATLD with
In order to validate the accuracy and precision of the proposed method for two analytes, our group randomly selected Number 22 (valsartan) and Number 48 (amlodipine besylate) prediction sample, which was prepared in triplicate, and each of them was repetitively measured three times in a day and lasted for three consecutive days; the corresponding results were listed in Table
Intra- and interaccuracy and precision of valsartan and amlodipine besylate using two algorithms.
Analytes | Algorithms | Intraday | Interday | ||
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Mean ± SD |
RSD |
Mean ± SD |
RSD |
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Valsartan | PARAFAC |
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ATLD |
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Amlodipine besylate | PARAFAC |
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ATLD |
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In this paper, excitation-emission (EEM) fluorescence data matrix was processed by PARAFAC and ATLD algorithms for the determination of valsartan and amlodipine besylate in human plasma with intense intrinsic fluorescence. Herein, the second-order advantage was adequately exploited in the data mining, which would help obtain quantitative information of two antihypertensives in the presence of uncalibrated interferences, namely, human plasma. Furthermore, after the evaluation of a series of indexes, including the FOM, the EJCR tests, and the accuracy and precision of the proposed method, it can be further confirmed that both algorithms could give accurate results for two analytes; however, the performance of ATLD was proved to be better than that of PARAFAC in the cases suffering from matrix effects. This proposed scheme with aid of second-order calibration algorithm could not only provide a novel, rapid, and reliable reference method for the analysis of biological samples, but also possess great potential to be further tailored as a general and promising alternative for the determination of weak fluorescent drugs.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was financially supported by the National Natural Science Foundation of China (nos. 21205145, 21476270, and 21276006), The Open Funds of State Key Laboratory of Chemo/Biosensing and Chemometrics of Hunan University (no. 201111), and the “Five-twelfth” National Science and Technology Support Program (2012BAI27B00).