Spectrophotometric Determination of Ternary Mixtures of Thiamin

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Vitamins are essential compounds in living systems; they differ in their chemical structure and physiological action. Analytical methods have been developed for vitamin identification .... restriction supplied by Eq. (2) gives the definition of the.
ANALYTICAL SCIENCES NOVEMBER 2007, VOL. 23 2007 © The Japan Society for Analytical Chemistry

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Spectrophotometric Determination of Ternary Mixtures of Thiamin, Riboflavin and Pyridoxal in Pharmaceutical and Human Plasma by Least-Squares Support Vector Machines Ali NIAZI,*† Javad ZOLGHARNEIN,** and Somaie AFIUNI-ZADEH** *Chemistry Department, Faculty of Sciences, Azad University of Arak, Arak, Iran **Chemistry Department, Faculty of Sciences, University of Arak, Arak, Iran

Ternary mixtures of thiamin, riboflavin and pyridoxal have been simultaneously determined in synthetic and real samples by applications of spectrophotometric and least-squares support vector machines. The calibration graphs were linear in the ranges of 1.0 – 20.0, 1.0 – 10.0 and 1.0 – 20.0 μg ml–1 with detection limits of 0.6, 0.5 and 0.7 μg ml–1 for thiamin, riboflavin and pyridoxal, respectively. The experimental calibration matrix was designed with 21 mixtures of these chemicals. The concentrations were varied between calibration graph concentrations of vitamins. The simultaneous determination of these vitamin mixtures by using spectrophotometric methods is a difficult problem, due to spectral interferences. The partial least squares (PLS) modeling and least-squares support vector machines were used for the multivariate calibration of the spectrophotometric data. An excellent model was built using LS-SVM, with low prediction errors and superior performance in relation to PLS. The root mean square errors of prediction (RMSEP) for thiamin, riboflavin and pyridoxal with PLS and LS-SVM were 0.6926, 0.3755, 0.4322 and 0.0421, 0.0318, 0.0457, respectively. The proposed method was satisfactorily applied to the rapid simultaneous determination of thiamin, riboflavin and pyridoxal in commercial pharmaceutical preparations and human plasma samples. (Received January 15, 2007; Accepted June 14, 2007; Published November 10, 2007)

Vitamins are essential compounds in living systems; they differ in their chemical structure and physiological action. Analytical methods have been developed for vitamin identification and/or quantification, using a wide variety of strategies. Thus, the food and pharmaceutical industries have taken advantages of these reliable methods and used them for the estimation of vitamins from simple to complex matrices. Mixtures of vitamins such as vitamin B complex1,2 and multivitamins in tables and other pharmaceutical formulations are used in the treatment of several diseases. Therefore, the simultaneous determination of mixtures of vitamins is very useful in the pharmaceutical industry. Several methodologies have been developed for the determination of vitamins in different samples, such as liquid chromatography,3–5 high performance liquid chromatography,6 micellar electrokinetic capillary chromatography7 and spectrophotometry and derivative methods.8,9 The greatest difficulties with simultaneous spectrophotometric determination methods arise when the analytes to be determined give partly or fully overlapped spectra, as is the case with the ingredients of most pharmaceutical preparations. Nowadays, the combination of chemometrics methods with the computer controlled instruments to monitor the molecular absorption spectra creates powerful methods in multicomponent analysis.10 Partial least squares regression (PLSR) is the most commonly used multivariate calibration method. It is based on linear models and is used as a satisfactory solution in most cases where a linear relationship is present between the spectra and the property to be determined (concentration, for example).10 However, PLSR † To whom correspondence should be addressed. E-mail: [email protected]

is not always the best option, especially in situations where a nonlinear model is clearly required. Theory and application of PLS have been discussed by several workers.10–18 A support vector machine (SVM) is an algorithm from the machine learning community, developed by Cortes and coworker.19 Due to its remarkable generalization performance, SVM has attracted attention and gained extensive application in pattern recognition and regression problems.20 SVM maps input data into a high dimensional feature space where it may become linearly separable by a hyperplane. One reason that SVM often performs betters than other methods is that SVM was designed to minimize structural risk; such a design has been shown to be superior to the traditional empirical risk minimization principle employed by conventional neural networks. Especially, Suykens and coworker21,22 proposed a modified version of SVM called least-squares SVM (LS-SVM), which resulted in a set of linear equations instead of a quadratic programming problem, which can extend the applications of the SVM. There exist a number of excellent introductions of SVM.23–34 The theory of LS-SVM has also been described clearly by Suykens et al.21,22 Applications of LS-SVM in quantification and classification have been reported by some workers.35–39 So, we will only briefly describe the theory of LS-SVM.

Theory The LS-SVM21 is capable of dealing with linear and nonlinear multivariate calibration and can resolve multivariate calibration problems in a relatively a fast way. In LS-SVM a linear estimation is done in kernel-induced feature space (y = wTφ(x) + b).

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As in SVM, it is necessary to minimize a cost function (C) containing a penalized regression error, as follows:

For a point yi to be evaluated it is: N

N

i=1

i=1

yi = ∑ αiφ(xi)Tφ(xj) + b = ∑ αi[(φ(xi),φ(xj)] + b

1 N 1 C = — wTw + — γ ∑ ei2 2 2 i=1

(1)

(9)

The α vector follows from solving a set of linear equation:

such that yi = wTφ(xi) + b + ei

(2)

for all, i = 1,..., N, where φ denotes the feature map. The first part of this cost function is a weight decay which is used to regularize weight sizes and penalize large weights. Due to this regularization, the weights converge to a similar value. Large weights deteriorate the generalization ability of the LSSVM because they can cause excessive variance. The second part of Eq. (1) is the regression error for all training data. The parameter γ, which has to be optimized by the user, gives the relative weight of this part as compared to the first part. The restriction supplied by Eq. (2) gives the definition of the regression error. Analyzing Eq. (1) and its restriction given by Eq. (2), one can conclude that we have a typical problem of convex optimization22 which can be solved by using the Lagrange multipliers method,40 as follow: N N 1 L = — ||w||2 + γ ∑ ei2 – ∑ α{wTφ(xi) + b + ei – yi} i=1 i=1 2







⎡ e1 ⎤⎥ ⎡α 1⎥⎤ ⎢ e2 ⎥ ⎢α ⎥ ⎢ ⎥ and α i = ⎢ 2⎥ . ⎢ ⎥ ⎢ ⎥ ⎢e ⎥ ⎢α ⎥ ⎣ N⎦ ⎣ N⎦

Obtaining the optimum, that is, carrying out ∂L(w,b,ei,αi)/∂w, ∂L(w,b,ei,αi)/∂b, ∂L(w,b,ei,αi)/∂ei, ∂L(w,b,ei,αi)/∂αi and setting all partial first derivatives to zero, the weights that are linear combinations of the training data are obtained:

∂L(w,b,e,α) ————— = w – ∑ αiφ(xi) = 0 ∴ w = ∑ αiφ(xi) i=1 i=1

(4)

∂L(w,b,e,α) ————— = ∑ γe – α = 0 i=1

(5)

N

N

∂w

(10)

where M is a square matrix given by: ⎡⎢ ⎤ K + γI 1N⎥⎥ M = ⎢⎢ ⎥⎥ ⎢⎢ ⎥ T 0 1 N ⎣ ⎦

(11)

where K denotes the kernel matrix with ijth element K(xi,xj) = φ(xi)Tφ(xj) and I denotes the identity matrix N × N, 1N = [1 1 ··· 1]T. Hence, the solution is given by: ⎡α ⎤ ⎡y⎤ ⎢ ⎥ = M–1 ⎢ ⎥ ⎣b ⎦ ⎣0⎦

(12)

(3)

where ⎡ y1 ⎤⎥ ⎢ y2 ⎥ yi = ⎢ ⎥ , e i = ⎢ ⎥ ⎢y ⎥ ⎣ N⎦

⎡α ⎤ ⎡ y ⎤ M⎢ ⎥=⎢ ⎥ ⎣b ⎦ ⎣ 0 ⎦

As one can see from Eqs. (11) and (12), usually all Lagrange multipliers (the support vectors) are nonzero, which means that all training objects contribute to the solution. In contrast with standard SVM, the LS-SVM solution is usually not sparse. However, as described by Suykens et al.,21 a sparse solution can be easily achieved via pruning or reduction techniques. Depending on the number of training data in the set, either direct solvers or iterative solving such as conjugate gradients methods (for large data sets) can be used, in both cases numerically reliable methods are available. In applications involving nonlinear regression, it is enough to change the inner product of Eq. (9) by a kernel function and the ijth element of matrix K equals Kij = φ(xi)Tφ(xj). If this kernel function meets Mercer’s condition,41 the kernel implicitly determines both a nonlinear mapping, x → φ(x) and the corresponding inner product φ(xi)Tφ(xj). This leads to the following nonlinear regression function:

N

∂e

N

y = ∑ αiK(xi,x) + b i=1

(13)

then for a point xj to be evaluated, it is: N

N

i=1

i=1

w = ∑ αiφ(xi) = ∑ γeiφ(xi)

(6)

N

yj = ∑ αiK(xi,xj) + b i=1

(14)

where a positive definite kernel is used as follows: K(xi,xj) = φ(xi)Tφ(xj)

(7)

An important result of this approach is that the weights (w) can be written as linear combinations of the Lagrange multipliers with the corresponding data training (xi). Putting the result of Eq. (6) into the original regression line (y = wTφ(x) + b), one can obtain the following result: N

N

i=1

i=1

y = ∑ αiφ(xi)Tφ(x) + b = ∑ αi[(φ(xi)T,φ(x)] + b

(8)

The attainment of the kernel function is cumbersome and it will depend on each case. However, the kernel function more often used is the radial basis function (RBF), exp(–(||xi – xj||2)/2σ2), a simple Gaussian function, and polynomial functions d, where σ2 is the width of the Gaussian function and d is the polynomial degree, which should be optimized by the user, to obtain the support vector. For α of the RBF kernel and d of the polynomial kernel, it should be stressed that it is very important to do a careful model selection of the tuning parameters, in combination with the regularization constant γ, in order to achieve a good generalization model. In the present work, we report on the results obtained in a

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1313 Table 1 Concentration data of the different mixtures used in the calibration set for the determination of thiamin (B1), riboflavin (B2) and pyridoxal (B6) (μg ml–1)

Fig. 1

Chemical structures of thiamin, riboflavin and pyridoxal.

study of simultaneous determination of thiamin, riboflavin and pyridoxal (Fig. 1) using spectrophotometric methods by application of LS-SVM. The aim of this work is to propose an LS-SVM method to resolve ternary mixtures of thiamin, riboflavin and pyridoxal in synthetic, pharmaceutical preparation and human plasma in trace levels. To our knowledge, this is the first application of LS-SVM in the direct spectrophotometric determination.

Experimental Reagents and standard solutions All reagents were of analytical reagent grade. The water utilized in all studies was double-distilled and deionized. Stock solutions of thiamin, riboflavin and pyridoxal (1000 μg ml–1) were prepared by direct weighting of the required amount of commercially available reagent, then by dissolving riboflavin in 0.01 M NaOH and each of the vitamins in doubly distilled water. These solutions were stored in the dark and were found stable for at least 4 weeks spectrophotometrically. Working solutions of each vitamin were prepared by the appropriate dilution to the stock solutions and were stored at room temperatures. A universal buffer solution (pH 8.0) was prepared by Lurie.42 Instrumentation and software A Hewlett-Packard 8453 diode array spectrophotometer controlled by a Hewlett-Packard computer and equipped with a 1-cm path length quartz cell was used for UV-Visible spectra acquisition. Data acquisition between 230 and 470 nm was performed with a UV-Visible ChemStation program (Agilent Technologies), running under Windows XP. A Metrohm 692 pH-meter furnished with a combined glass-saturated calomel electrode was calibrated with at least two buffer solutions at pH 3.00 and 9.00. The quantitative evaluations were carried out by using the PLS program from PLS-Toolbox version 2.0 for use with Matlab from Eigenvector Research Inc. The LS-SVM optimization and model results were obtained using the LSSVM lab toolbox (Matlab/C Toolbox for Least-Squares Support Vector Machines).22 All programs were run on an AMD 2000 XP and 512 MB RAM microcomputer. General procedure Known amounts of standard solutions were placed in a 10 ml volumetric flask and completed to the final volume with deionized water and universal buffer in pH 8.0. The final concentrations of these solutions varied between 1.0 – 20.0, 1.0 – 10.0 and 1.0 – 20.0 μg ml–1 for thiamin, riboflavin and pyridoxal, respectively. For constructing the individual

Mixture

B1

B2

B6

Mixture

B1

B2

B6

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11

1.0 4.8 8.6 12.4 16.2 20.0 16.2 12.4 8.6 4.8 1.0

1.0 1.0 1.0 1.0 1.0 1.0 2.8 4.6 6.4 8.2 10.0

20.0 16.2 12.4 8.6 4.8 1.0 1.0 1.0 1.0 1.0 1.0

M12 M13 M14 M15 M16 M17 M18 M19 M20 M21

1.0 1.0 1.0 1.0 4.8 8.6 12.4 4.8 8.6 4.8

8.2 6.4 4.6 2.8 2.8 2.8 2.8 4.6 4.6 6.4

4.8 8.6 12.4 16.2 12.4 8.6 4.8 8.6 4.8 4.8

calibration lines, the absorbances were measured at 269, 242 and 326 nm against a blank for thiamin, riboflavin and pyridoxal, respectively. Multivariate calibration A mixture design was used to maximize statistically the information content in the spectra.43 A training set of 21 samples was taken (Table 1). The concentrations of thiamin (vitamin B1), riboflavin (vitamin B2) and pyridoxal (vitamin B6) were between 1.0 – 20.0, 1.0 – 10.0 and 1.0 – 20.0 μg ml–1 varied, respectively. Each standard, prediction and synthetic mixture was prepared according to procedures explained in the general procedure section. The absorption spectra were recorded between 230 and 470 nm with scan rate of 600 nm min–1 against a blank. The spectral region between 230 and 470 nm, which implies working with 240 experimental points per spectra (as the spectra are digitized each 1.0 nm), was selected for analysis, because this is the zone with the maximum spectral information from the mixture components of interest. Real samples The analyses of pharmaceutical preparations were carried out by triplicate, weighing homogeneous portions of the multivitamin sample in powder (about 1 g) and dissolving them with pure water in volumetric flasks. Then each solution was maintained in an ultrasonic bath for a period of 15 min. In order to remove suspended particles, a fraction of the solution was centrifuged at 3000 rpm for 10 min. Finally, each aliquot of the supernatant was analyzed by using the procedure described above. Plasma spiked with thiamin, riboflavin and pyridoxal were obtained by diluting aliquots of the stock standard of thiamin, riboflavin and pyridoxal mixtures with the human plasma. A 1 ml aliquot of this spiked solution was diluted to 5 ml with ethanol in a 10 ml centrifuge tube. The precipitated protein was separated by centrifugation for 10 min at 3000 rpm. The clear supernatant layer was filtered by a Whatman filter to produce protein free-spiked human plasma,44 and then it was added into a 10 ml volumetric flask and diluted to the mark by a universal buffer (pH 8.0). Statistical parameters For the evaluation of the predictive ability of a multivariate calibration model, the root mean square error of prediction (RMSEP) and relative standard error of prediction (RSEP) can be used:

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Table 2

Composition of synthetic mixtures and predicted values for thiamin (B1), riboflavin (B2) and pyridoxal (B6)

Added/μg ml–1

Found (PLS)/μg ml–1

B1

B6

B1

B2

B6

19.0 9.0 19.0 2.0 4.0 2.0 10.0 1.0 5.5 3.0 10.0 5.0 4.0 7.0 18.0 11.0 3.0 1.0 3.0 10.0 10.5 7.0 7.0 7.0

17.48 1.88 11.02 3.14 3.79 10.45 2.78 6.76

9.68 3.78 1.06 9.88 6.84 3.21 10.71 7.16

18.24 2.11 5.11 4.89 18.67 0.91 10.98 7.23

B2

NPCa PRESS γ σ2 RMSEP RSEP, %

8 0.4602

0.6926 7.5737

8 0.1803

0.3755 5.2780

Found (LS-SVM)/μg ml–1

Error, % B1

B2

B6

8.0 6.0 –10.2 –4.7 5.3 5.0 7.3 3.4

–7.6 5.5 –6.0 1.2 2.3 –7.0 –7.1 –2.3

4.0 –5.5 7.1 2.2 –3.7 9.0 –4.6 –3.3

B1 18.97 2.01 10.06 3.01 3.97 10.93 2.99 6.94

B2

B6

9.03 3.98 1.00 9.97 7.03 3.01 10.07 7.00

19.08 2.01 5.48 5.02 18.09 1.00 10.52 7.03

Error, % B1

B2

B6

0.2 –0.5 –0.6 –0.3 0.7 0.6 0.3 0.9

–0.3 0.5 0.0 0.3 –0.4 –0.3 –0.7 0.0

–0.4 –0.5 0.4 –0.4 –0.5 0.0 –0.2 –0.4

8 0.8319 50 40 60 20 10 20 0.0421 0.0318 0.0457 0.4607 0.4472 0.4297

0.4322 4.0644

a. Number of factors.

Fig. 2 Absorption spectra of thiamin (B1) (15 μg ml–1), riboflavin (B2) (8 μg ml–1) and pyridoxal (B6) (15 μg ml–1).

RMSEP =

∑ (ypred – yobs)2 n n i=1

RSEP(%) = 100 ×

∑ ni=1(ypred – yobs)2 ∑(yobs)2

(15)

(16)

where ypred is the predicted concentration in the sample, yobs is the observed value of the concentration in the sample and n is the number of samples in the validation set.

Results and Discussion Absorption spectra The electronic absorption spectra of thiamin, riboflavin and pyridoxal in water at pH 8.0 at 230 – 470 nm intervals were recorded. Sample spectra of thiamin, riboflavin and pyridoxal at pH 8.0 in water are shown in Fig. 2. As can be appreciated in Fig. 2, absorption spectra of thiamin, riboflavin and pyridoxal overlap too much with each other. Due to this similarity, the absorption spectra of thiamin, riboflavin and pyridoxal also are similar and analysis of these vitamins is not simply possible with conventional methods. This problem was overcome by the

Fig. 3 Plots of PRESS versus number of factors by partial least squares.

use of chemometrics methods such as LS-SVM. The influences of the pH of the medium on the absorption spectra of thiamin, riboflavin and pyridoxal were studied over the pH range 2.0 – 10.0. A universal buffer solution of pH 8.0 was selected, in order to select the optimum pH value at which the minimum overlap occurs. To ensure linear behavior of each vitamin and to obtain the linear dynamic range for each vitamin we constructed an individual calibration curve with several points at λmax of each vitamin (269 nm for thiamin, 242 nm for riboflavin and 326 nm for pyridoxal) as absorbance value versus vitamin concentration. The linear ranges are 1.0 – 20.0, 1.0 – 10.0 and 1.0 – 20.0 μg ml–1 with detection limits of 0.6, 0.5 and 0.7 μg ml–1 for thiamin, riboflavin and pyridoxal, respectively. Partial least squares (PLS) The determination of the thiamin, riboflavin and pyridoxal in mixtures by spectrophotometric mean using multivariate calibration involved constructing a calibration and prediction set. According to the procedure section, the calibration matrix was designed. In Table 1 the compositions of the ternary mixtures used in the calibration matrices are summarized. For the prediction set, 8 mixtures were prepared according to procedure section (see Table 2). To ensure that the prediction and real samples are in the subspace of the training set, we sketched the score plot of the first principal component versus

ANALYTICAL SCIENCES NOVEMBER 2007, VOL. 23

Fig. 4

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Plots of predicted concentration versus actual concentration for thiamin (B1), riboflavin (B2) and pyridoxal (B6).

the second; all the samples are spanned with the training set scores. In order to determine the optimum number of factors (latent variables) for the partial least squares calibration model, we applied the cross validation procedure. There are several cross validation routines and “leave one sample out” was used in our experiments. As the calibration set was performed with 21 spectra, the calibration was performed on 20 of them. The process was repeated 21 times and predicted and known concentrations were compared. The predictive residual error sum of squares (PRESS) was computed, which is defined as follows: PRESS = ∑(yi – yˆ i)2

(17)

where yi is the reference concentration for the ith sample and yˆ i represents the estimated concentration. The Haaland and Thomas criterion45 was applied to determine the optimum number of factors. The optimum number of factors was determined rather than the selection of the model, which yields a minimum in prediction error variance or PRESS, the model selected is the one with the fewest number of factors such that PRESS for that model is not significantly greater than the minimum PRESS. In our case, 11 factors (half the standards + 1) were used as the maximum number of initial factors. A plot of the PRESS against the number of factors for each individual component indicates a minimum value for an optimal number of factors. For finding the fewest number of factors, the Fstatistics was used to carry out the significance determination.45 Table 2 shows the optimum number of factor and PRESS values for each vitamin. In Fig. 3, the PRESS obtained by optimizing the calibration matrix of the absorbance data with PLS model is shown. Least-squares support vector machines (LS-SVM) LS-SVM was performed with RBF as a kernel function. In the model development using LS-SVM and RBF kernel, γ and σ2 parameters were a manageable task, similar to the process employed to select the number of factors for PLS models, but in this case for a two-dimensional problem. For each combination of γ and σ2 parameters, root mean square error of crossvalidation (RMSECV) was calculated and the optimum parameters were selected so as to produce the smaller RMSECV. In Table 2 are shown the optimum γ and σ2 parameters for the LS-SVM and RBF kernel, using the spectra calibration sets for ternary mixtures. These parameters were optimized generating models with values of γ in the range of 1 – 100 and values of σ2 in the range of 1 – 100 with adequate increments. Table 2 shows the optimum γ and σ2 values for each vitamin. Table 2 also shows RMSEP and RSEP.

Determination of thiamin, riboflavin and pyridoxal in synthetic mixtures The predictive ability of the method was determined using 8 three-component thiamin, riboflavin and pyridoxal mixtures (their compositions are given in Table 2). The results obtained from simultaneous analysis of vitamins by PLS and LS-SVM methods are listed in Table 2. Table 2 also shows RMSEP, RSEP and the percentage error for prediction series of thiamin, riboflavin and pyridoxal mixtures. When one compares the results for PLS and LS-SVM models, it is possible to observe that RMSEP and RSEP values for the three vitamins using the LS-SVM are better than PLS, with smaller errors. Good results were achieved in LS-SVM model with percentage error ranges from –0.6 to 0.9, –0.7 to 0.5 and –0.5 to 0.4 for thiamin, riboflavin and pyridoxal, respectively. As can be seen, the percentage error was also quite acceptable. The plots of the predicted concentration versus actual values are shown in Fig. 4 for each vitamin (linear equations and R2 values are also shown). For all three vitamins, the correlation coefficients (R2) for LS-SVM model were better than PLS and close to one. Also, we see that LS-SVM presents excellent prediction abilities when compared with PLS regression. Determination of thiamin, riboflavin and pyridoxal in pharmaceutical preparation and human plasma In order to show the analytical applicability of the proposed method, we applied LS-SVM to simultaneous determination of thiamin, riboflavin and pyridoxal in real samples (pharmaceutical formulations) and complex matrices, i.e. human plasma. Table 3 shows that satisfactory recovery values were obtained for the samples assayed. The precision of the method was investigated by the analysis of the real samples three times each. The result showed that the relative standard deviation (RSD) obtained was acceptable. Therefore, the LSSVM model is able to predict the concentrations of each thiamin, riboflavin and pyridoxal in the real matrix samples.

Conclusion A new method for the simultaneous determination of thiamin, riboflavin and pyridoxal using spectrophotometric and leastsquares support vector machines method is proposed. A simple, safe, sensitive, inexpensive and non-polluting scheme for simultaneous determination of thiamin, riboflavin and pyridoxal was developed and optimized. The thiamin, riboflavin and pyridoxal mixture is an extremely difficult complex system due to the high spectral overlapping observed between the absorption spectra for their components. For overcoming the drawback of spectral interferences, LS-SVM multivariate

1316 Table 3

ANALYTICAL SCIENCES NOVEMBER 2007, VOL. 23 LS-SVM results applied on the real samples

Multivitamin tablet (diluted) Human plasma

Thiamin (B1)

Riboflavin (B2)

Added Found RSD Recovery, %

Added Found RSD Recovery, %

— 3.0 1.0 3.0

3.45 6.39 0.91 2.89

0.18 0.21 0.11 0.19

— 98.0 91.0 96.3

— 3.0 1.5 3.0

calibration approaches are applied. The results of this study clearly show the potential and versatility of this method, which could be applied to simultaneous determination of thiamin, riboflavin and pyridoxal spectrophotometrically in synthetic and real samples.

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4.05 7.11 1.42 3.05

0.24 0.28 0.16 0.20

Pyridoxal (B6)

— 102.0 94.7 101.7

Added Found RSD Recovery, % — 3.0 3.0 3.5

2.19 5.21 2.93 3.44

0.12 0.19 0.21 0.26

— 100.7 97.7 98.3

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