Advanced stability indicating chemometric methods for quantitation of amlodipine and atorvastatin in their quinary mixture with acidic degradation products

    Advanced stability indicating chemometric methods for quantitation of amlodipine and atorvastatin in their quinary mixture with acidic degradation products Hany W. Darwish, Said A. Hassan, Maissa Y. Salem, Badr A. El-Zeany PII: DOI: Reference:

S1386-1425(15)30254-7 doi: 10.1016/j.saa.2015.10.007 SAA 14109

To appear in: Received date: Revised date: Accepted date:

10 February 2015 2 June 2015 4 October 2015

Please cite this article as: Hany W. Darwish, Said A. Hassan, Maissa Y. Salem, Badr A. El-Zeany, Advanced stability indicating chemometric methods for quantitation of amlodipine and atorvastatin in their quinary mixture with acidic degradation products, (2015), doi: 10.1016/j.saa.2015.10.007

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ACCEPTED MANUSCRIPT Advanced stability indicating chemometric methods for quantitation of amlodipine and atorvastatin in their quinary mixture with acidic degradation products Hany W. Darwisha,b, Said A. Hassana*, Maissa Y. Salema and Badr A. El-Zeanya Department of Analytical Chemistry, Faculty of Pharmacy, Cairo University, Kasr El-Aini

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a

b

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Street, 11562, Cairo-Egypt.

Department of Pharmaceutical Chemistry, College of Pharmacy, King Saud University, P.O.

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Box 2457, Riyadh 11451, Saudi Arabia. Abstract

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Two advanced, accurate and precise chemometric methods are developed for the simultaneous determination of Amlodipine besylate (AML) and Atorvastatin calcium (ATV) in presence of their acidic degradation products in tablet dosage forms. The first method was

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Partial Least Squares (PLS-1) and the second was Artificial Neural Networks (ANN). PLS was compared to ANN models with and without variable selection procedure (Genetic Algorithm (GA)). For proper analysis, a 5-factor 5-level experimental design was established

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resulting in 25 mixtures containing different ratios of the interfering species. Fifteen mixtures

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were used as calibration set and the other ten mixtures were used as validation set to validate the prediction ability of the suggested models. The proposed methods were successfully

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applied to the analysis of pharmaceutical tablets containing AML and ATV. The methods indicated the ability of the mentioned multivariate calibration models to solve the highly overlapped UV spectra of the quinary mixture, yet using cheap and easy to handle

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instruments like the UV spectrophotometer. Key words: Amlodipine; Artificial Neural Networks; Atorvastatin; Genetic Algorithm; Partial Least Squares; Stability Indicating. *

Corresponding author:

e-mail: [email protected] [email protected] Tel. No. : +201000994542

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ACCEPTED MANUSCRIPT Introduction Amlodipine (AML) is 2-[(2-aminoethoxy)methyl]-4-(2-chlorophenyl)-1,4-dihydro-6methyl-3,5-pyridinedicarboxylic acid 3-ethyl 5-methyl ester [1]. AML is a dihydropyridine

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derivative with calcium antagonist activity, used in the management of hypertension, chronic

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stable angina pectoris and prinzmetal’s variant angina [2]. Atorvastatin (ATV) is [R-(R*,R*)]2-(4-Fluorophenyl)-β,δ-dihydroxy–5-(1–methylethyl)-3–phenyl–4-[(phenylamino)carbonyl]-

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1H-pyrrole–1–heptanoic acid [1]. ATV is a selective, competitive inhibitor of HMG-CoA reductase, the rate-limiting enzyme that converts 3-hydroxy-3-methylglutaryl-coenzyme A to mevalonate, a precursor of the sterols, including cholesterol. It is used to reduce LDL-

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cholesterol, apolipoprotein B, and triglycerides and to increase ATL-cholesterol in the treatment of hyperlipidaemias [3]. Caduet® is the first commercial product that has been

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launched by Pfizer Ltd. for the simultaneous treatment of hypertension and dyslipidaemia [4]. Caduet® contains both AML for the treatment of high blood pressure and ATV for the treatment of hypercholesterolaemia. Caduet® tablets are intended for oral administration and

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are available in several different strength combinations.

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Literature survey revealed that AML is official in British Pharmacopoeia [5]. There are reported methods for the determination of AML or ATV in different drug combinations

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[6-10]. Also different methods have been reported for the simultaneous estimation of AML and ATV in their binary mixture [11-16], and stability indicating HPLC methods [17, 18] have been applied for the analysis of this mixture.

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Chemometrics is the art of processing data with various numerical techniques in order to extract useful information [19]. It is the application of mathematical and statistical methods to design optimum procedures and to provide maximum chemical information through the analysis of chemical data. Quantitative spectroscopy has been greatly improved by the use of a variety of multivariate statistical methods [20-24]. Multivariate calibrations are useful in spectral analysis because of the simultaneous inclusion of multiple spectral intensities which can greatly improve the precision and applicability of quantitative spectral analysis [25]. The rationales for this manuscript were the simultaneous determination of AML and ATV in presence of their acidic degradation products, after their separation and characterization, in laboratory prepared mixtures and tablets. To present a comparative study between Partial Least Squares (PLS-1) regression and Artificial Neural Networks (ANN) as multivariate calibrations, and to show the effect of variable selection procedure e.g. Genetic

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ACCEPTED MANUSCRIPT Algorithm (GA), when preceding these multivariate calibrations, on increasing the predictive power of them Material and Methods

SHIMADZU dual beam UV-visible spectrophotometer (Kyoto/ Japan), model 1650 UV-

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–

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Instruments

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PC, with matched 1-cm quartz cells. The bundled software, UV- Probe personal spectroscopy software version 2.21 (SHIMADZU) is used. The spectral bandwidth is 2.0 nm and wavelength scanning speed is 2800 nm/min with 0.1 nm interval. Gas chromatograph coupled to a mass spectrophotometer, Shimadzu Qp-2010 (Japan).

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IR Spectrophotometer: Shimadzu 435 (Kyoto, Japan), sampling was undertaken as

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potassium bromide discs and NaCl plates.

pH meter, Jenway, no. 924005-BO3-Q11C.

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Software

All chemometric methods were implemented in Matlab® 7.12.0.635 (R2011a). The t-

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test and F-test were performed using Microsoft® Excel 2010. All calculations were

Materials and reagents

Pure Amlodipine besylate; kindly supplied by Al-Hekma pharmaceutical Company,

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performed using a Dual CPU, 1.47 GHz, 2.00 GB of RAM under Microsoft Windows 7 TM.

Cairo, Egypt, its purity was certified to be 99.9 ± 0.7. –

Pure Atorvastatin calcium; kindly supplied by Al-Delta pharmaceutical Company, Cairo,

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Egypt, its purity was certified to be 99.8 ± 0.5. Caduet® 5mg/ 10mg tablets; labeled to contain 5 mg AML and 10 mg ATV, batch number 1030039 and Caduet® 10mg/ 10mg tablets; labeled to contain 10 mg AML and 10 mg ATV, batch number 0795049, manufactured by Pfizer Ltd., Cairo, Egypt. –

Methanol, Toluene, Chloroform, Acetic acid, Hydrochloric acid and Sodium hydroxide: analytical grade, purchased from El-NASR Pharmaceutical Chemicals Co., Cairo, Egypt.

Standard solutions –

AML and ATV standard stock solutions; 1.0 mg.mL-1 in methanol.

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AML and ATV standard working solutions; 80.0 μg.mL-1 in methanol.

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Amlodipine degradation product (AMdeg), Atorvastatin degradation product (ATdeg) and Aniline (ANL) standard solutions; 100.0 μg.mL-1 in methanol.

Procedures Preparation and separation of degradation products 3

ACCEPTED MANUSCRIPT Amlodipine degradation product HCl solution (50.0 mL, 1M) was added to pure AML (50.0 mg) in a flask and then the solution was refluxed for 2 hours and cooled. NaOH solution (1 M) was added to the

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degraded solution till pH about 7.00 and the solution was tested for complete degradation.

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Complete degradation was tested by TLC using chloroform: methanol: acetic acid (15.0: 2.0: 0.4 by volume) as developing solvent. Then the solution was evaporated slowly in rotavapor

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just to dryness. The degradation product was extracted from solid NaCl with methanol and then the methanol was evaporated. The extraction was repeated three times to ensure complete extraction of the degradation products from NaCl. The purity of the degradation

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product was tested by dissolving a small portion in methanol, applying onto TLC plates and developing using the previously mentioned solvent system. The structure of the isolated

Atorvastatin degradation products

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degradation product was elucidated using IR and mass spectrometry.

ATV (50.0 mg) was dissolved in least volume of methanol in a flask, then 50.0 mL of

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6 M HCl solution was added and the solution was refluxed for 3 hours and cooled. NaOH

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solution (6 M) was added to the degraded solution till pH about 7.00 and the solution was tested for complete degradation. Complete degradation was tested by TLC using toluene:

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methanol (7.0: 3.0 v/v) as developing solvent. Then the solution was evaporated slowly in rotavapor just to dryness to obtain the first degradation product (ATdeg). The collected evaporated liquid was heated to get rid of solvents and the second degradation product (ANL)

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was obtained. The degradation product (ATdeg) was extracted from solid NaCl with methanol and then the methanol was evaporated. The extraction was repeated three times to guarantee complete extraction of the degradation products from NaCl. The purity of the degradation product was tested by dissolving a small portion in methanol, applying onto TLC plates and developing using the previously mentioned solvent system. The structure of the isolated degradation products was elucidated using IR and mass spectrometry. Spectral characteristics of AML, ATV and degradation products The zero-order (D0) absorption spectra of 12 μg.mL-1 AML, ATV, AMdeg, ATdeg and ANL are recorded against methanol as a blank over the range of 200-400 nm. Experimental design A 5-level, 5-factor calibration design was performed using 5 concentration levels coded from +2 to −2 for each of the 5 components to be analyzed, including the 2 main drugs and the 3 degradates. The design aims to span the mixture space fairly well; where 4

ACCEPTED MANUSCRIPT there are 5 mixtures for each compound at each concentration level, resulting in 25 mixtures [26]. The central level of the design is 10 μg.mL-1 for AML and 16 μg.mL-1 for ATV. The concentration levels for each component were based on the linearity range, the

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ratio of AML and ATV in the pharmaceutical product and the fact that the degradation

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products were involved in levels up to about 30% of the corresponding drugs to cover a wide range of possibilities in future analysis. Table 1 represents the concentration design matrix.

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The 2D scores plot for the first two PCs of the concentration matrix was obtained to confirm well position of the mixtures in space, orthogonality, symmetry and rotatability [26], (Supp. Mat. Fig. S1). The regions from 200- 215 nm were rejected. Fifteen mixtures of this design

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were used as a calibration set and the other ten mixtures were used as a validation set to test the predictive ability of the developed multivariate models.

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Application of the PLS-1, GA-PLS and ANN for the simultaneous determination of AML and ATV in Caduet® tablets

Ten tablets of both Caduet® 5(AML)/10(ATV) mg, 10(AML)/10(ATV) mg were

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accurately weighed and finely powdered. An amount of the powder equivalent to 2 mg ATV

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was weighed, dissolved in methanol by shaking in ultrasonic bath for about 30 minutes. The solutions were filtered and transferred quantitatively into two separate 100-mL volumetric

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flasks. The volume was then completed to the mark with methanol. Necessary dilutions were made to reach concentrations of linear range. Solutions obtained were analyzed by the proposed chemometric methods. Results and discussion

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To the best of our knowledge, the stability indicating methods that have been reported for determination of AML and ATV mixture did not separate or identify their degradation products, so the first goal of this paper was to develop a stability indicating methods for determination of AML and ATV after separation and elucidation of the structures of the degradates. The second goal was to represent a comparative study between PLS-1 models and ANN as multivariate calibrations, and finally the paper shows the effect of variable selection procedure (GA), when preceding these multivariate calibrations, on increasing the predictive power of them. Degradation of AML and ATV AML has been reported to degrade by photolysis, oxidation, acidic and basic hydrolysis [27], while ATV has been reported to degrade by acidic hydrolysis [17]. The combination of AML and ATV was subjected to many stability studies for their simultaneous 5

ACCEPTED MANUSCRIPT determination [17, 18, 28], but no method of them separated or characterized the degradation products. In this study, AML was degraded by refluxing with 1 N HCl and the degradation

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process was monitored by spotting on TLC plates using chloroform: methanol: acetic acid

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(15.0: 2.0: 0.4 by volume) as developing solvent. Only one spot different from that of AML was observed (Supp. Mat. Fig. S2).

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It was found that complete degradation of AML occurs after 2 hours of reflux with 1 N HCl and the suggested degradation pathway is shown in Fig. 1, which indicates hydrolysis of the ester linkages and release of the free alcohols. The degradation product was separated

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and its structure confirmed by mass and IR spectrometry. The mass spectrum in Fig. 2 showed a peak at m/z 368 corresponding to the main degradation product (AMdeg)

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represented in Fig. 1. The IR spectra of intact AML and AMdeg (Fig. 3) showed that the characteristic band at 1682 cm-1, corresponding to carbonyl group, was shifted in the spectrum of AMdeg to lower frequency 1579 cm-1 which indicates that the first one is a

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carbonyl of an ester and the second is a carbonyl of acid [29] and this confirms the suggested

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mechanism of degradation.

ATV was degraded by refluxing with 6 N HCl, this resulted in cleavage of the amide

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bond producing the main degradation product (ATdeg) with free carboxylic acid group and aniline (ANL) as shown in Fig. 4. The degradation process was monitored by spotting on TLC plates using toluene: methanol (7.0: 3.0 v/v) as developing solvent, and it was found that ATV degrades completely after 3 hours. Two spots different from that of ATV were observed

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(Supp. Mat. Fig. S3). The solid ATdeg was extracted from NaCl, after neutralization and evaporation of the solution, by methanol; while ANL was collected with the evaporated solution and extracted after heating at 100oC to expel water. The structures of the degradation products were elucidated by mass and IR spectrometry. The mass spectrum (Fig. 5) showed a peak at m/z 483 corresponding to ATdeg, and the mass spectrum (Fig. 5) showed the peak of ANL at m/z 93. The IR spectra of intact ATV, ATdeg and ANL (Fig. 6) showed that the characteristic band at 3421 cm-1 in ATV spectrum, corresponding to NH group, disappeared in the IR spectrum of ATdeg, and a forked peak at 3431 and 3356 cm-1 appeared in the ANL spectrum corresponding to NH2 group which confirmed the hydrolysis of the amide bond as mechanism of degradation. Chemometric methods The UV absorption spectra of AML, ATV, and their degradation products (Fig. 7) showed severe overlap that prevents resolution of the mixture by direct and derivative 6

ACCEPTED MANUSCRIPT spectrophotometric measurements. The higher the number of compounds in a mixture, the more difficult the analysis and the lower the ability of traditional approaches of handling UV spectroscopic techniques to find robust and precise solutions especially when the degradation

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products show serious overlap with the two main drugs AML and ATV.

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The quality of multicomponent analysis is dependent on the wavelength range and spectral mode used [30]. The wavelengths used were in range 215–400 nm in AML and 215-

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330 nm in ATV. Wavelengths less than 215 nm were rejected due to the noisy content and wavelengths more than 330 nm for ATV were not used because of its zero absorbance in

Variable selection (Genetic Algorithm)

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these regions.

Genetic algorithms (GA) maintain and manipulate a family, or population, of

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solutions and implement a ‘survival of fittest’ strategy in their search for better solutions. GA can be used successfully for wavelength selection. GA consists of five steps: Initiation, evaluation, exploitation, exploration and mutation [31-35].

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The GA was run for 186 variables (in the range 215–400 nm) and 116 variables (in the

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range 215–330 nm) for AML and ATV, respectively. A critical issue of successful GA performance is the adjustment of GA parameters. The fitness values were used as response

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variables. Mutation rate was 0.005 in all cases as when it increased above this value, no convergence occurred between average fitness and best fitness values and model stop. The adjusted GA parameters are shown in Table 2.

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The GA was run for spectral datasets using a PLS with maximum number of factors allowed is the optimal number of components determined by cross-validation on the model containing all the variables, and the selected variables were used for running of PLS model and as input data for ANN. GA reduced absorbance matrix to about 40% of the original matrix (76 wavelength for AML and 52 wavelength for ATV). PLS-1 method Multivariate calibration models aim to establish a relation between the spectra in a data matrix X of size I×J, and the concentrations in a data vector C. Various methods have been developed for building a multivariate calibration model. The most common methods are Principal Component Regression (PCR) and Partial Least Squares (PLS). PLS can be seen as a further development of PCR, because the C data contribute to the construction of the scores as well [36]. Full description of PLS can be found in the literature [37-39]. Two different approaches can be used in Partial Least Squares called PLS-1 and PLS-2. PLS-2 uses the 7

ACCEPTED MANUSCRIPT whole information about the concentration of all components to form latent variables (LVs), while PLS-1 uses only the information about concentration of one component to create the LVs used by the model [40].

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PLS-1 method was run on the calibration data of absorption spectra. Mean centering

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of the data proved to be the best preprocessing method for getting the optimum results and leave one out cross validation was applied.

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To select the number of factors in the PLS-1 algorithm, a cross-validation method leaving out one sample at a time [41] was employed using calibration set of 15 calibration spectra.

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The RMSECV was used as a diagnostic test for examining the errors in the predicted concentrations. It indicates both of the precision and accuracy of predictions. It was

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recalculated upon addition of each new factor to the PLS-1. The method developed by Haaland and Thomas [42] was used for selecting the optimum number of factors, which involves selecting that model including the smallest number of factors that results in an

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insignificant difference between the corresponding RMSECV and the minimum RMSECV

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(Fig. 8). Number of factors used for each drug is shown in Table 3. GA did not reduce the optimal number of factors for the analytes as shown in Fig. 8

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and Table 3, but RMSEP and RSD % were greatly decreased indicating an increase in prediction power of GA-PLS model than PLS-1 model. The comparison of results obtained from GA-PLS with those obtained from PLS-1 showed that GA-PLS is more suitable for simultaneous determination of these two analytes in their quinary mixture with degradates.

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This result may be attributed to the fact that GA introduces the most relevant wavelengths, to the drug concentration, to the PLS model. ANN Artificial neural network (ANN) is a type of artificial intelligence method that resembles biological nervous system in having the ability to find the relationship between inputs and outputs. A network is made up of a number of interconnected nodes (called neurons) arranged into three basic layers (input, hidden and output) that are interconnected by connections called weights. The type of ANN used in this manuscript is feed-forward network trained with the back propagation of errors learning algorithm. The input nodes in this representation perform no computation but are used to distribute inputs into the network. It is called feed-forward ANN as information passes one way through the network from the input layer, through the hidden layer and finally to the output layer. The outputs (predicted 8

ACCEPTED MANUSCRIPT concentrations) are compared with targets (actual concentrations), and the difference between them is called error [43]. ANN parameters to be optimized are transfer functions, Hidden neurons number (HNN), Number of neurons, learning coefficient (Lc), learning coefficient

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decrease (Lcd) and learning coefficient increase (Lci) [44-46]. For optimization of the ANN

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parameters, many experiments have to be done through which we can improve the model performance.

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We used in our work four networks, two for prediction of AML and ATV concentrations from raw data and two for prediction of the drug concentrations from genetic algorithm model. For proper modeling of ANN, different parameters were optimized (Table

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4, Supp. Mat. Fig. S4 and S5).

Since the large number of nodes in the input layer of the network (i.e. the number of

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wavelength readings for each solution) increases the CPU time for ANN modeling, the absorbance matrix was reduced from 186 into 76 nm and from 116 into 52 nm for AML and ATV, respectively, before introducing into the network using genetic algorithm, and then

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ANN model was run. The output layer is the concentration matrix of one component. The

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hidden layer consists of just single layer which has been considered sufficient to solve similar or more complex problems. Moreover, more hidden layers may cause overfitting [46].

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After optimization of parameters and architectures of the ANN (Table 4), the training step was done. We trained ANN by different training functions and there is no difference in performance (i.e. there is no decrease in Mean Square Error of prediction (MSE)). Levenberg-Marquardt backpropagation (TRAINLM) was thus preferred as it is time saving.

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Transfer function pair found to give best results in our work is purelin-purelin between input and hidden layer; and between hidden layer and outer layer. This is logic because the relationship between absorbance and concentration in our work is linear relationship. To avoid overfitting of our model, the validation set was encountered in training step and ANN stops when MSE of calibration set decreased and that of validation set increased. The comparison of GA-ANN results with ANN shows that GA-ANN is more suitable for simultaneous determination of the two drugs. GA allowed the use of less number of neurons (so shorter training time) for ATV than those used in the networks utilized raw data and gave almost the same results. While for AML, GA did not show any improvement in number of neurons. The comparison between PLS-1 and ANN shows that ANN has more predictive power than PLS-1 as indicated by RMSEP. This may be due to the fact that ANN is a type of 9

ACCEPTED MANUSCRIPT artificial intelligence and that in ANN there is no chance for overfitting that may occur in PLS calibrations. The proposed chemometric methods were run on the calibration data using optimal

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parameters. The concentrations of the two drugs in the calibration set (15 mixtures) were

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calculated. By plotting predicted concentrations of each component versus actual concentrations, a straight line was obtained. The data of the straight line for each component

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including slope, intercept and correlation coefficient was collected in Table 3. In order to validate the proposed methods, the validation set (10 mixtures) was analyzed with the proposed methods Table 5, where GA-PLS, ANN and GA-ANN gave best

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results.

The proposed GA-PLS, ANN and GA-ANN methods were successfully used for the

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determination of AML and ATV in Caduet® tablets, Table 6. The validity of the proposed methods was further assessed by applying the standard addition technique (Supp. Mat. Table S1).

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The results obtained for the analysis of AML and ATV in Caduet® tablets by the

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suggested methods were statistically compared with those obtained by applying the reported first derivative method [11] and no significant difference between the results was obtained as

Conclusion

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shown in Table 7.

Two advanced stability indicating chemometric methods (GA-PLS and ANN) have been presented as powerful alternatives for traditional chemometrics to resolve the binary

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mixture of AML and ATV in presence of more than 30 % of their degradation products. GA greatly increased the prediction power of PLS-1 and ANN for the presented dataset. ANN showed better results compared to PLS regressions. The results in this paper suggest the use of the proposed methods (GA-PLS and ANN) in quality control analysis of AML and ATV mixtures without interference of degradates. This gives hopes for using smart chemometrics for the stability indicating analysis of pharmaceutical products using cheap and simple instruments like UV spectrophotometer even if the number of interfering components is high and

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Table 1. The 5-level, 5-factor experimental design shown as concentrations

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MA

of the mixture components in μg.mL-1.

13

AML

ATV

AMdeg

ATdeg

ANL

1.

10

16

1.5

1.5

1.5

6

8

2

1

2.5

3.

10

8

1

2.5

T

1

4.

14

12

2

1.5

1

5.

6

24

1.25

2.5

1.5

6.

14

16

1.25

1

2

7.

8

24

1.5

1

1

8.

8

12

1.75

2.5

2

9.

10

12

1.25

2

2.5

10.

8

20

2

2

1.5

11.

14

20

1.5

2.5

2.5

12.

12

24

1.75

1.5

2.5

13.

12

16

2

2.5

0.5

14.

14

24

1

2

0.5

15.

10

24

2

0.5

2

14

8

1.75

0.5

1.5

12

8

1.5

2

2

6

20

1

1.5

2

6

16

1.75

2

1

20.

12

12

1

1

1.5

21.

10

20

1.75

1

0.5

22.

12

20

1.25

0.5

1

23.

8

8

1.25

1.5

0.5

24.

6

12

1.5

0.5

0.5

25.

8

16

1

0.5

2.5

16. 17. 18. 19.

a

SC R NU

MA D TE

a

AC

2.

IP

Mix. No.

CE P

ACCEPTED MANUSCRIPT

The shaded rows represent the validation set

14

ACCEPTED MANUSCRIPT Table 2. Parameters of the genetic algorithms. Value

Population size

20

T

Parameter

50

Mutation rate The number of variables in a window (window width)

MA

% wavelengths used at initiation

NU

Per cent of population the same at convergence

SC R

IP

Maximum generations

Crossover type

2 100 50 Single AML (4) - ATV (2) Random

TE

Cross validation

D

Maximum number of latent variables

0.005

4

Number of iterations for cross validation at each generation

2

AC

CE P

Number of subsets to divide data into for cross validation

15

ACCEPTED MANUSCRIPT

GA-PLS method

AML

ATV

AML

4-14

8-24

4-14

No. of factors

4

2

4

RMSEC a

0.2126

0.2799

RMSEP b

0.2291

0.2743

RMSECV c

0.1601

0.6813

Intercept d

0.0903

0.0771

Slope d

0.9892 0.9959

CR

interest

PLS-1 method

ATV

ATV

AML

ATV

8-24

4-14

8-24

4-14

8-24

2

---

---

---

---

0.1268

0.1735

0.1075

0.1471

0.1012

0.1436

0.1521

0.1593

0.1158

0.1406

0.0953

0.1327

0.1321

0.5904

---

---

---

---

0.0066

0.0270

-0.0314

-0.0238

-0.0435

-0.0574

0.9972

0.9998

0.9991

1.0031

1.0012

1.0050

1.0032

0.9987

0.9985

0.9995

0.9990

0.9996

0.9991

0.9996

coefficient (r) d

AC

US

MA N

CE P

(µg.mL-1)

Correlation

GA-ANN Method

AML

Concentration range

ANN Method

TE D

Parameter of

IP

T

Table 3. Statistical parameter values for simultaneous determination of AML and ATV using optimized chemometric methods.

a

Root Mean Square Error of Calibration Root Mean Square Error of Prediction c Root Mean Squares Error of Cross-Validation d Data of the straight line plotted between predicted concentrations of each component versus actual concentrations. b

16

ACCEPTED MANUSCRIPT

Hidden neurons number

AML

IP

AML

ATV

186-10-1

116-20-1

76-10-1

52-9-1

10

20

9

CR

Architecture

GA-ANN

10

MA N

Drug

ANN

US

Method

T

Table 4. Optimized parameters of ANNs.

ATV

Purelin–Purelin

Transfer functions 0.001

0.001

Learning coefficient decrease

0.001

0.001

Learning coefficient increase

100

100

AC

CE P

TE D

Learning coefficient

17

0.001

0.001

0.001

0.001

100

100

ACCEPTED MANUSCRIPT Table 5. Determination of AML and ATV in validation set by the proposed chemometric methods. PCRa method

PLS-2a method

PLS-1 method

(µg.mL-1)

GA-PLS method

ANN method

GA-ANN method

T

Recovery % b

ATV

AML

ATV

AML

ATV

96.75

98.33

99.25

99.12

99.80

99.50

99.80

98.79

98.00

98.79

99.11

99.50

99.36

99.86

99.36

98.13

96.14

98.21

98.86

98.85

99.57

99.00

99.79

99.00

94.38

95.42

94.71

95.84

98.73

99.58

98.66

99.63

99.13

98.79

97.51

97.88

97.15

97.88

97.95

98.75

99.22

99.48

99.25

99.75

99.22

96.94

99.25

96.94

99.17

96.96

99.31

98.93

99.31

98.56

99.30

98.92

99.31

24

96.88

97.96

96.56

97.99

96.93

98.17

99.21

98.83

99.21

98.83

99.28

99.08

14

8

103.36

105.15

103.57

105.00

103.34

103.75

102.12

101.03

101.64

100.05

101.45

100.50

6

20

95.15

97.99

95.08

98.03

TE D

ATV

AML

ATV

AML

ATV

AML

ATV

6

8

95.67

96.78

95.67

96.75

96.02

14

12

98.56

97.61

98.57

97.69

14

16

96.53

98.15

96.43

8

12

94.73

95.90

8

20

97.24

12

24

14

95.83

98.50

97.67

98.75

98.33

99.48

98.62

98.98

12

12

95.06

95.83

95.00

95.83

95.75

96.08

99.18

99.68

99.43

99.78

99.25

99.77

Mean

97.01

98.21

97.01

98.12

97.23

98.26

99.06

99.36

99.35

99.45

99.55

99.38

RMSEP c

0.3942

0.3977

0.4066

0.4123

0.3803

0.3530

0.1521

0.1593

0.1158

0.1327

0.0953

0.1406

RSD%

2.600

2.700

2.734

2.718

2.508

2.259

1.176

0.666

0.922

0.380

0.779

0.515

CE P

MA N

US

CR

AML

AC

AML

IP

Concentration

a

The PCR and PLS algorithms described in literature [39].

b

average of three determinations

c

Root Mean Square Error of Prediction

18

ACCEPTED MANUSCRIPT Table 6. Determination of AML and ATV in Caduet® tablets by the proposed chemometric methods. Drug

GA-PLS Method

ANN Method

GA-ANN Method

Recovery % ± RSD a

IP

T

Product

100.54±1.131

99.75±1.005

ATV

100.33±0.890

100.39±0.806

100.17±0.906

Caduet® AML

100.58±1.260

99.75±0.958

99.84±0.887

99.98±0.839

100.03±0.840

100.11±0.845

5/10

10/10

CE P

TE

D

MA

NU

average of three determination.

AC

a

ATV

SC R

100.36±0.838

Caduet® AML

19

ACCEPTED MANUSCRIPT Table 7. Statistical comparison for the results obtained by the proposed chemometric methods and the reported method [11] for the analysis of

N

Variance

AML

100.47

0.965

6

0.940

ATV

100.16

0.798

6

AML

100.02

1.015

6

ATV

100.11

0.702

6

AML

99.99

0.771

ATV

100.08

0.850

Reported

AML

100.10

0.838

Method b

ATV

100.41

0.756

ANN

GA-ANN

F value a

(2.228)

(5.05)

0.701

1.335

0.639

0.559

1.109

1.069

0.086

1.518

0.583

0.447

1.011

6

0.719

0.623

1.020

6

0.616

0.590

1.069

-----

-----

NU

GA-PLS

IP

RSD%

Student's t test a

SC R

Mean

MA

Value

T

AML and ATV in Caduet® tablets.

6

0.704

6

0.576

The values in the parenthesis are the corresponding theoretical values of t and F at P= 0.05.

b

first derivative spectrophotometry at 340 and 295 nm for AML and ATV respectively.

AC

CE P

TE

D

a

20

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

21

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

22

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

23

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

24

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

25

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

26

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

27

AC

CE P

TE

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

28

D

MA

NU

SC R

IP

T

ACCEPTED MANUSCRIPT

AC

CE P

TE

Graphical abstract

29

ACCEPTED MANUSCRIPT

T

IP

SC R

NU MA D

–

TE

–

CE P

–

AC

– –

Highlights Smart & advanced chemometric approaches for stability indicating analysis Comparative study between PLS models and ANN as multivariate calibrations Effect of GA, preceding multivariate calibration, on increasing the predictive power The first isolation & structure elucidation of Amlodipine & Atorvastatin degradates Cheap & simple spectrophotometer can be used despite the high number of interferents

30