Simultaneous spectrophotometric determination of drugs lacking peak maxima in their zero-order profiles by graphical or statistical representation of data European Journal of Chemistry 9 (3) (2018) 194-201 European Journal of Chemistry View Journal Online View Article Online Simultaneous spectrophotometric determination of drugs lacking peak maxima in their zero-order profiles by graphical or statistical representation of data Ragaa Magdy 1, Ahmed Hemdan 1,*, Nermine Victor Fares 2 and Maha Farouk 2 1 Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Ahram Canadian University, 6th October, 12566, Egypt dr.ragaa.magdy@hotmail.co.uk (R.M.), hemmdan@yahoo.com (A.H.) 2 Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Ain Shams University, Cairo, 11566, Egypt nermine.victor@yahoo.com (N.V.F.), drmahafarouk@yahoo.com (M.F.) * Corresponding author at: Pharmaceutical Analytical Chemistry Department, Faculty of Pharmacy, Ahram Canadian University, 6th October, 12566, Egypt. Tel: +2.012.21620730 Fax: +2.023.8334379 e-mail: hemmdan@yahoo.com (A. Hemdan). 10.5155/eurjchem.9.3.194-201.1727 Received: 29 April 2018 Received in revised form: 02 June 2018 Accepted: 04 June 2018 Published online: 30 September 2018 Printed: 30 September 2018 Trandolapril has no sharp peak in its zero-order spectrum, therefore it is difficult to be measured by direct spectrophotometry. In this study, direct univariate spectrophotometric methods were developed and validated for determination of Trandolapril and Verapamil combination in pure and tablet dosage forms. The first method for measuring both Trandolapril and Verapamil is Absorbance Subtraction (AS), this method depends on the presence of iso-absorptive point in the zero-order curve at 217 nm. It has the advantage of measuring the concentration of both Trandolapril and Verapamil from unified regression equation at the iso-absorptive point. The second, third and fourth methods were applied on the first order spectra of the studied drugs. Second method is Derivative Subtraction (DS) for Trandolapril and Derivative subtraction followed by spectrum subtraction (DS-SS) for Verapamil. The third and fourth methods are constant value and concentration value methods. In the concentration value method, the concentration of the drugs is determined from the graphical representation without the use of regression equations. All the developed methods were validated as per International Conference on Harmonization guidelines and the results proved that the developed methods are simple, accurate, and selective. Moreover, a statistical comparison between the developed methods and a reference method was done. Also, One-way ANOVA statistical test was done between all the proposed spectrophoto- metric methods and results showed no significant differences. Verapamil Trandolapril Constant value Concentration value Derivative subtraction Absorbance subtraction Cite this: Eur. J. Chem. 2018, 9(3), 194-201 Journal website: www.eurjchem.com 1. Introduction Trandolapril (TR) is used for patients with left ventricular systolic dysfunction as it is classified as an angiotensin conver- ting enzyme (ACE) inhibitor [1,2]. Trandolaprilat is the active form, where trandolapril, as a prodrug, is converted to its active metabolite in the liver by esterase enzymes [3]. It has the longest duration of action among the anti-hypertensive drugs developed so far [3,4]. Trandolapril has been approved by the FDA 1996 and is available as a single drug or in combination with verapamil (Tarka®, Abbott Laboratories) which is an immediate release formulation of Trandolapril and a slow release formulation of verapamil [5]. Verapamil (VER) is categorized as calcium channel blocker. It regulates the movement of calcium across the cell membrane of the arterial smooth muscle and in contractile myocardial cells [6,7]. Combination of Trandolapril and Verapamil demonstrated better compliance and more effect- tiveness than monotherapy [8,9]. Many methods were reported for the analysis of this combination or one of its components in pharmaceuticals or body fluids. These include spectrophotometry [10], HPLC with spectrophotometric detection [11,12], high performance thin layer chromatography [13,14] and LC-MS/MS [15,16]. In 2014, Vijayalakshmi et al. suggested a colorimetric method for deter- mination of Trandolapril and Flucloxacillin in pharmaceutical formulation, where the Trandolapril color complex was measured at 430 nm [17]. Amir et al. suggested a colorimetric method in 2016 using Bromothymol Blue and bromocresol green for determination of Trandolapril [18]. The main problem is that, Trandolapril has no sharp peak in zero order spectrum. So, the key challenge was the determination of Trandolapril by direct spectrophotometry without the use of coloring reagents. The aim of the present study was to develop and validate direct univariate spectrophotometric methods for determination of Trandolapril and Verapamil combination without the aid of external reagents as chromogens. 1.1. Theoretical background 1.1.1. Constant value (CV) ABSTRACT RESEARCH ARTICLE KEYWORDS European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2018 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. http://dx.doi.org/10.5155/eurjchem.9.3.194-201.1727 http://dx.doi.org/10.5155/eurjchem.9.3.194-201.1727 https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.9.3.194-201.1727&domain=pdf&date_stamp=2018-09-30 http://www.eurjchem.com/ http://dx.doi.org/10.5155/eurjchem.9.3.194-201.1727 mailto:dr.ragaa.magdy@hotmail.co.uk mailto:hemmdan@yahoo.com mailto:nermine.victor@yahoo.com mailto:drmahafarouk@yahoo.com mailto:hemmdan@yahoo.com http://www.eurjchem.com/ https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.9.3.194-201.1727&domain=pdf&date_stamp=2018-09-30� Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 195 Constant value is a simple method used for resolving overlapped binary mixtures, so in a mixture of X+Y, where Y is more extended than X, by dividing the zero order spectrum of the mixture by zero order normalized spectrum of a divisor of the more extended compound Y; which obtained by dividing certain spectrum of Y component by its concentration (1 µg/mL concentration); therefore the constant obtained from the plateau region at the extended part is related only to the concentration of the extended compound, and by the same way for getting the concentration of the less extended compound X, after resolving from Y, its concentration could be obtained by dividing its spectra by the normalized spectrum of a divisor of X (1 µg/mL concentration), therefore, the constant obtained from the plateau region is related to the concent- ration of X. The calibration curve is constructed between the concentration and constant obtained by dividing each spectrum by its normalized one [19] 1.1.2. Concentration value Concentration value is a new spectrophotometric app- roach depending upon graphical representation of the spectra, where the concentration value of the drug is obtained directly from the spectral chart and represents the actual concent- ration of the drug without the need of regression equations. It is conducted by dividing the zero order absorption spectrum of the mixture by zero order normalized spectrum of the divisor of the more extended component (1 µg concentration); therefore the constant obtained from the plateau region represents the concentration of the more extended component without the need of any equation or calculation steps, therefore the recoveries calculated directly from the values of the constant as it is considered to be equal to the concent- ration of the drug in the mixture. The less extended compo- nent can be also obtained by resolving it first from the more extended one by any resolution technique, and then dividing the obtained spectra by zero order of the normalized spectrum of the divisor of the less extended component (1 µg concentration); so plateau region represents the concentration of the less extended component [20,21]. 1.1.3. Absorbance subtraction method This method is utilized for the analysis of a binary mixture with severe overlapping, and intersects at iso-absorptive point, and one spectrum is extended than the other. At iso- absorptive point (λiso) the absorbance (Aiso) is equal for both X and Y and the absorbance (A2) at another selected wavelength (λ2) in the extended part is only for the extended component Y. So, the absorbance factor which is a constant representing the ratio of the absorbance values at λiso (Aiso): to those at λ2 (A2) at the extended part [F = Aiso/A2] is calculated, and then the factor is multiplied by the Absorbance at λ2 (A2) to get the absorption of the extended component alone at the iso- absorbtive point, after that the absorption of the less extended drug at iso-absorptive point can be obtained easily by subtraction of the absorption of the more extended one at λiso from the total Absorption of both at λiso. By this simple manipulation step, the absorbance value corresponding to X and Y could be obtained easily and separately at λiso. So, the concentration of each component could be obtained via the iso-absorptive point regression equation without any need for a complementary method or resolution step. This smart method enables quantitative estimation of both X and Y in their binary mixture (X + Y) through the same unified regression equation and by using simple mathe- matically calculated factor. The unified regression equation obtained simply by plotting the absorbance values of the zero order spectra of either X or Y at iso-absorptive point (λiso) against the corresponding concentrations of X or Y, respectively. The following equations explain: Absorbance of Y in the mixture at λiso = F × A2 (1) Absorbance of X in the mixture at λiso = Aiso (X+Y) – (F × A2) (2) where A2 is the absorbance at a selected wavelength (λ2) in the extended part and only represent Y [22]. 1.1.4. Derivative subtraction DS applies the same principal for Ratio Subtraction (RS) but on the first derivative spectra. It is used for binary mixture where the first derivative (D1) of one component of the mixture is more extended than the other. DS can solve either the extended or the less extended spectrum. By eliminate the spectra of one compound leaving the other alone on its D1 profile [23]. 1.1.5. Derivative subtraction spectrum subtraction This resolution technique is similar to Ratio Subtraction- Spectrum Subtraction (RS-SS) but on first derivative profile. It Measure the studied drugs in the first order profile. It has the advantage of being more sensitive as the extended part of the mixture becomes more obvious. Moreover, we can enhance the sensitivity further more by calculating the concentration of the component using the difference between maximum and minimum amplitude (Pmax-min) of first derivative. It is used for binary mixture where the first derivative (D1) of one component of the mixture is more extended than the other. It can determine either the extended or the less extended spectrum [24] as follows: (X+Y) / Y` = X/Y` + Y/Y`, were Y/Y`= constant (3) X/Y` + constant – constant = X/Y` (4) X/Y` *Y` = X (5) (X+Y) – X =Y (6) 2. Experimental 2.1. Materials and reagents Trandolapril and Verapamil hydrochloride reference standards were kindly supplied by Abbott laboratories for pharmaceuticals and chemical industries (USA). The purity of the standards was certified to be 99.85 and 99.87% for Trandolapril and Verapamil, respectively. Structures of the compounds are shown in Figure 1. Tarka® commercial tablets labeled to contain 2 mg Trandolapril and 180 mg Verapamil hydrochloride were purchased from local Egyptian market. HPLC grade Acetonitrile supplied from Sigma Aldrich (Germany). Double distilled water was used throughout the study and is indicated by the word water. 2.2. Instrumentation and conditions A double-beam UV/Visible spectrophotometer model J- 760, Jasco, Japan was used. The absorption spectra of the standard and the tested solutions were recorded in 1.0 cm quartz cells over the range 200-400 nm at room temperature using Spectramanager software. 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 196 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 N O OH O H N O O (a) O O N N O O (b) Figure 1. Chemical structures of a) Trandolapril and b) Verapamil. 2.3. Spectral characteristics and wavelength selection Zero-order (D0) absorption spectra of both Trandolapril and Verapamil (10 μg/mL), were scanned against a blank (200-400 nm), overlaid using the Spectramanager software to detect the spectral characteristics, extent of overlap, and to predict the best methods for resolution of the mixture. 2.4. Procedures 2.4.1. Preparation of standard stock and working solutions Primary stock solutions of standard Trandolapril and Verapamil were separately prepared in 100 mL volumetric flasks by dissolving 20 mg of each standard powder in the least amount of acetonitrile and completed to the volume by water. Primary stocks solutions of Trandolapril and Verapamil were diluted with water to prepare standard working solutions (100 µg/mL). 2.4.2. Preparation of pharmaceutical dosage form To determine Trandolapril and Verapamil in commercial tablets (Tarka®), 10 tablets were finally powdered, then, a portion of the powder equivalent to one tablet was weighted accurately and transferred to a 100 mL beaker. 50 mL of acetonitrile was added, stirred using a magnetic stirrer for 15 min and filtered through 0.5 µm Whatman filter paper into a 100-mL volumetric flask. The residue was washed three times each time with 10 mL of acetonitrile and the solution was completed to the mark with water. 2.4.3. Validation The proposed methods were Validated according to International Conference on Harmonization (ICH) guidelines [25]. 2.4.3.1. Linearity and construction of calibration curves Accurately measured aliquots of Trandolapril and Verapamil were transferred from their working solutions into two separate series of 10 mL volumetric flasks and the volumes were completed to the mark with water to prepare standard solutions for the calibration samples consist of six concentrations covering a concentration range 1-30 µg/mL for Trandolapril and 2-50 µg/mL for Verapamil. Samples scanned from 200-400 nm and the obtained zero-order D0 spectra saved on the computer. 2.4.3.1.1. For absorbance subtraction method of both TR and VER Unified regression equation obtained from the calibration curve relating the absorbance at the iso-absorptive point of the scanned zero-order (D0) spectra of TR or VER at 217 nm to the corresponding concentrations. 2.4.3.1.2. For derivative subtraction of Trandolapril The first derivative (D1) of the stored zero-order (D0) absorption spectra are computed and stored. Regression equation for the calibration curve relating the peak amplitude of the first derivative spectra of Trandolapril at 217 nm to the corresponding concentrations was computed. 2.4.3.1.3. For derivative subtraction coupled with spectrum subtraction method of Verapamil The first order (D1) of the stored zero-order D0 absorption spectra were computed and stored. Regression equation for the calibration curve relating the difference between the maximum and minimum amplitudes (Pmax-min) of the first derivative (D1) spectra (amplitudes in the first order 238.5- 223.5) of Verapamil versus the corresponding concentrations was computed. 2.4.3.1.4. For constant value of both TR and VER By dividing the first-order spectrum of the more extended component VER by First order normalized spectrum divisor of VER (1 µg concentration), the constant was obtained from the extended plateau region which is related to the concentration. So, the calibration curve was constructed relating the concentration to the constant. For TR resolution technique DS- SS to eliminate VER spectrum was done first, then dividing the First-order spectrum of TR by First order normalized spectrum divisor of TR (1 µg concentration), the constant was 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 197 Figure 2. Zero-order absorption UV spectra of 5 µg /mL of Trandolapril (Green) (-----) and Verapamil (Blue) (____), separately in acetonitrile, and binary of a mixture of Trandolapril and Verapamil (Red) 2.5 µg /mL of each (- - -) in Acetonitrile showing iso-absorbtive point at 217 nm. obtained which is related only to TR concentration; So, the calibration curve was constructed relating the concentration to the constant. 2.4.3.2. Determination in laboratory prepared mixtures (selectivity) From the previously prepared stock solutions of Trandolapril and Verapamil, different mixtures were prepared by mixing accurate portions of both analytes and transferred to a series of 10 mL volumetric flasks. The final volume is completed by water. 2.4.3.3. Accuracy Three replicates of different concentrations of Trandolapril and Verapamil were used for checking accuracy of the developed methods. The concentrations were obtained from the corresponding regression equation for each method, from which the percentage recoveries suggested good accuracy of the proposed methods. 2.4.3.4. Repeatability and Intermediate precision Three concentrations of Trandolapril and Verapamil were analyzed intra-daily for three times using the proposed methods. The relative standard deviations were calculated. The previous procedures were repeated inter-daily on three different days for the analysis of the three chosen concentrations. The relative standard deviations were calculated. 2.4.3.5. Limit of quantitation (LOQ) and limit of detection (LOD) According to ICH recommendations, several approaches for determining the quantitation and detection limits are possible. The standard deviation of the intercept and the slope approach was used to calculate LOD and LOQ, where: LOD = 3.3 x SD of intercept / slope coefficient (7) LOQ = 10 x SD of intercept / slope coefficient (8) 2.4.4. Application to pharmaceutical dosage form From the previously prepared stock solutions of pharma- ceutical formulation further dilutions were prepared in the obtained linearity range using water. The stock was diluted to the concentration of 45 µg/mL Verapamil and 0.5 µg/mL Trandolapril in 100 mL volumetric flask, then, a portion from Trandolapril standard stock solution equivalent to 1.5 µg was added and then the solution completed to the mark with water. The Standard addition of Trandolapril is to increase its concentration to be within the linearity range, so the final concentration of dosage form will be 45 µg/mL Verapamil and 2.0 µg/mL Trandolapril. The validity was further assessed by the standard addition technique, by preparing another two dilutions of the dosage form; one for TR with concentration within its linearity range and another one for Verapamil with concentration within its linearity. 3. Results and discussion Several reported chromatographic methods were found for determination of the mixture. Also, two different colori- metric methods were found for the mixture [16,17]. But during the literature survey, there were no direct spectro- photometric methods for determination of Trandolapril and Verapamil combination. Trandolapril, in zero order profile, lacks a sharp peak which could be used for its direct determination. So, the challenge was to develop a spectro- photometric method for Trandolapril determination in a mixture with good accuracy and precision. In our present study, different univariate spectrophotometric methods were developed and validated for determination of Trandolapril and Verapamil combination. As shown in Figure 2, it is obvious that the spectra of the two drugs are severely overlapped. It was found that only Verapamil can be determined directly by zero order spectrophotometry at 277 nm. But unfortunately, the method will be insensitive as Verapamil here will be determined at its lowest peak. So, there was a need for a sensitive method for Verapamil determination at its λmax. 3.1. Methods development 3.1.1. Absorption subtraction Absorbance subtraction on the zero order absorption spectrum, where a unified regression equation is constructed at iso-absorptive point 217 nm as shown in Figure 2, and a factor is calculated by dividing VER zero order absorbance at 217 nm by its absorbance at 275 nm (A 217 nm / A 275 nm = 2.01491). By multiplication of the factor by the free peak absorbance at λ 275 nm, the absorbance due to VER at 217 nm is determined, Subtracting VER absorbance at 217 nm from the total absorbance of the lab mixture at 217 nm, the absorbance of TR is determined; and by substituted of both VER absorbance and TR absorbance in the unified regression equation; both VER and TR concentration is determined. 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 198 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 Figure 3. First order absorption UV spectra of 20 µg/mL Verapamil (-----) and 5 µg/mL Trandolapril (ـــــــــ) in acetonitrile. Figure 4. The division of first order spectra of laboratory prepared mixture of Verapamil and Trandolapril by 10 µg /mL of Verapamil as a divisor showing the constants. 3.1.2. Derivative subtraction for determination of TR and derivative subtraction followed by spectrum subtraction for VER By obtaining the first order spectrum of both VER and TR, where TR sharp peak appeared at 217 nm as shown in Figure 3; so, the spectrum of the mixture of Trandolapril and Verapamil was divided by 10 µg/mL Verapamil as a divisor. After subtraction of the constant which is shown in Figure 4, multiplication by the divisor gives the 1st order spectrum of Trandolapril. After that; VER only could be obtained by Spectrum Subtraction (SS) method. This could be summarized by the following equations: TR + VR / VR’ = TR/VR’ + VR/VR’ = TR/VR’ + Constant – Constant = TR/VR’ (9) TR/VR’ X VR’ = TR first order curve (10) TR+VER –TR = VER first order curve (11) Then, Trandolapril could be measured at 217 nm in its 1st order curve, while the concentration of the extended compo- nent VER is calculated using the difference between maximum and minimum amplitude (Pmax-min) of first derivative spectra, thus decrease the error and increase the sensitivity of the method. The difference between maximum and minimum amplitude (Pmax and Pmin) used were 238.5 nm and 223.5 nm, respectively, as shown in Figure 3. 3.1.3. Constant value and concentration value for VER VER is extended more than TR in its first derivative spectra as shown in Figure 3. So, when the spectra of the mixtures of VER and TR are divided by the spectrum of normalized divisor of VER, a constant at the plateau region on the extended part 240 to 400 nm is obtained as shown in Figure 5. This constant is equivalent to the concentration of VER as it is resulting from dividing the spectra of the mixture by the normalized spectra of VER and in the extended part it’s related only to VER concentration according to the following equations: TR + VER / VER` = TR/VER` + VER/VER` (12) VER + TR / VER` = TR/VER` + constant (13) While VER` is a normalized divisor (1 µg/mL concent- ration) so that Constant is equal to the concentration of VER at this extended part where there is no contribution of TR. So for constant value we construct a calibration between that constant and corresponding concentration to correct any error as explained before and the concentration of VER is obtained from that calibration curve regression equation, for concentration value we directly get the concentration from the spectra plateau region using that constant. The results of both methods were compared and both have good recoveries. 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 199 Table 1. Validation parameters of the proposed spectrophotometric methods, determination of the studied drugs in the laboratory prepared mixtures, dosage form and application of standard addition technique. Method First derivative (D1) Zero order (D0) Derivative Subtraction (DS) Constant value Concent. value Abs. subtraction Drug Trandolapril Range (µg/mL) 1-30 2-30 Regression Equation y = 0.003x + 0.0002 y = 1.0004x - 0.0146 y = 0.0256x +0.0023 Correlation coefficient (r) r² = 0.9999 r² = 1 r² = 0.9999 Accuracy a 99.59±0.471 99.367±0.696 99.89±0.421 99.189±0.764 Repeatability b 99.771 99.995 100.305 99.384 RSD% 0.775 0.5 1.051 1.961 Intermediate precision c 99.159 99.368 100.305 101.054 RSD% 0.148 0.663 0.529 0.265 LOQ (µg/mL) 1 2 LOD (µg/mL) 0.33 0.67 Laboratory prepared mixtures n = 5 100.146±0448 99.846±0.359 99.973±0.459 99.8515±0.309 Recovery of pharmaceutical dosage form 100.871±1.342 100.022±1.920 99.958±1.549 100.313±1.489 Recovery of standard additions 100.410±0.990 101.109±1.906 100.097±1.091 99.508±1.110 Method First derivative (D1) Zero order (D0) Derivative subtraction spectrum subtraction DS-SS Constant value Concent. value Absorbance subtraction Drug Verapamil Range (µg/mL) 2-50 2-30 Regression Equation Pmax-min = 0.0024x + 0.0012 y = 0.997x + 0.009 y = 0.0256x +0.0023 Correlation coefficient (r) r² = 0.9999 r² = 1 r² = 0.9999 Accuracy a 100.304±0.529 99.985±1.028 100.013±0.619 100.42±0.547 Repeatability b 100.712 100.63 100.73 100.02 RSD% 0.806 0.789 0.797 0.984 Intermediate precision c 100.680 100.867 100.773 100.820 RSD% 0.132 0.066 0.033 0.017 LOQ (µg/mL) 2 LOD (µg/mL) 0.67 Laboratory prepared mixtures n = 5 99.735±0.620 100.0381±0.171 100.228±0.110 99.907±0.333 Recovery of pharmaceutical dosage form 100.44±1.651 100.06±0.0798 100.144±1.557 99.589±1.035 Recovery of standard additions 99.159±0.896 99.842±1.690 99.552±1.647 100.021±0.902 a Mean±SD. b Intra-day (n = 3), Average of three concentration of the analytes (5, 10 and 20 µg/mL) repeated three times within the same day. c Inter-day (n = 3), Average of three concentration of the analytes (5, 10 and 20 µg/mL) repeated three times in three different days. Figure 5. The constant value obtained after division of zero order spectra of Verapamil concentrations (2-50 µg/mL ) by the spectrum of Normalized 1 µg/mL devisor of Verapamil. 3.1.4. Derivative subtraction constant value and derivative subtraction concentration value of TR In first order curve (D1) profile; First TR resolved from VER by Derivative Subtraction (DS) according to the following equations: (TR+VER)/VER` = TR/VER`+ VER/VER`, were VER/VER`= constant (14) TR/VER`+ constant – constant = TR/VER` (15) TR/VER`* VER` = TR (16) After that we divide the obtained spectra by a normalized spectrum divisor of TR. So, the constant obtained in the plateau region which shown in Figure 6 is related to TR concentration. So, for constant value, a calibration curve between that constant and corresponding concentration is constructed to correct any error as explained before and the concentration of TR is obtained from that calibration curve regression equation. While for concentration value, the concentration is directly obtained from the spectra plateau region using that constant. The results of both methods were compared and both have good recoveries. 3.2. Validation Validation of the proposed methods was assessed according to International Conference on Harmonization (ICH) guidelines [25]. Validation was done relative to linearity and range, accuracy, precision, selectivity, LOQ, and LOD. All the validation parameters are shown in Table 1. The proposed progressive and successive spectrophoto- metric methods were statistically compared with the reported HPLC method [12] and the results are tabulated in Table 2. It was found that there is no significant difference between developed methods and the reference method. 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 200 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 Table 2. Statistical comparison for the results obtained by the proposed methods and the reported method for the analysis of Trandolapril and Verapamil in bulk powder. Parameter Drug Method Mean S.D RSD% N Variance Student’s t-test (2.23) a F-test (5.05) a Developed method Verapamil First Derivative D1 DS-SS 100.304 0.529 0.527 6.000 0.280 0.625 1.286 Constant value 99.985 1.028 1.017 6.000 1.057 0.237 2.936 Conc. value 100.013 0.619 0.613 6.000 0.383 0.247 1.064 Zero order D0 Absorbance subtraction 100.042 0.547 0.545 6.000 0.299 0.175 1.204 Trandolapril First Derivative D1 DS 99.590 0.471 0.475 6.000 0.222 1.467 1.094 Constant value 99.367 0.696 0.700 6.000 0.484 1.812 2.384 Conc. value 99.890 0.421 0.425 6.000 0.177 0.358 1.146 Zero order D0 Absorbance subtraction 99.189 0.764 0.771 6.000 0.584 2.185 2.877 Reported method b Verapamil 100.10 0.600 6.000 0.360 Trandolapril 99.98 0.450 6.000 0.203 a The values in parenthesis are the corresponding theoretical values of t and F at p = 0.05. b Method [12]. Table 3. Results of ANOVA (single factor) for comparison of the proposed methods for the determination of Trandolapril and Verapamil in pure powder form. Source of variation SS a df b Variance F c P-value Fcritical d Trandolapril Between groups 1.6457 3 0.5486 1.4956 0.2462 3.098 Within groups 7.3360 20 0.3668 Total 8.9817 23 Verapamil Between groups 0.3899 3 0.1300 0.2575 0.8551 Within Groups 10.0950 20 0.5047 Total 10.4850 23 a Sum of squares. b degree of freedom between and within groups. c Calculated F. d Critical (tabulated) value for F at p = 0.05. Figure 6. The constant value obtained after division of Zero order spectra of Trandolapril concentrations (1-30 µg/mL) by the spectrum of Normalized 1 µg/mL devisor of Trandolapril. The results of proposed spectrophotometric methods were also compared statistically using One-way where there was no significant difference as shown in Table 3. 4. Conclusion Trandolapril lacks a sharp peak in its zero-order curve. So, its determination by direct spectrophotometric method with acceptable accuracy and precision was a challenge. So, a new method is developed for the determination of TR in the mixture without depending on its shoulder peak. Furthermore, a new sensitive method developed for the determination of VER. All the spectrophotometric methods were developed and validated for the determination of Trandolapril and Verapamil combination in both laboratory prepared mixtures and marketed dosage forms and was found to be accurate, reproducible, and selective. All the developed methods showed no significant difference with each other and with the reference HPLC method. The developed methods could be used in quality control laboratories for fast determination of the cited drugs. Disclosure statement Conflict of interests: The authors declare that they have no conflict of interest. Author contributions: All authors contributed equally to this work. Ethical approval: All ethical guidelines have been adhered. Sample availability: Samples of the compounds are available from the author. ORCID Ragaa Magdy http://orcid.org/0000-0003-2086-1142 Ahmed Hemdan http://orcid.org/0000-0002-3836-2811 References [1]. Guay, D. R. Clin. Ther. 2003, 25, 713-775. [2]. Wiseman, L. R.; McTavish, D. Drugs 1994, 48, 71-90. [3]. Zannad, F. Drugs 1993, 46, 172-181. 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 http://orcid.org/0000-0003-2086-1142 http://orcid.org/0000-0002-3836-2811 Magdy et al. / European Journal of Chemistry 9 (3) (2018) 194-201 201 [4]. Duc, L. N.; Brunner, H. R. Am. J. Cardiol. 1992, 70, 27D-34D. [5]. Sharma, S. K.; Ruggenenti, P. Remuzzi, G. Vasc. Health Risk Manag. 2007, 3, 453-465. [6]. Franz, D. N.; Cardiovascular Drugs, in Remington: The Science and Practice of Pharmacy, A. R. Gennaro, Editor, Mack Publishing Company, 1995, Pennsylvania. 951. [7]. 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This work is published and licensed by Atlanta Publishing House LLC, Atlanta, GA, USA. The full terms of this license are available at http://www.eurjchem.com/index.php/eurjchem/pages/view/terms and incorporate the Creative Commons Attribution-Non Commercial (CC BY NC) (International, v4.0) License (http://creativecommons.org/licenses/by-nc/4.0). By accessing the work, you hereby accept the Terms. This is an open access article distributed under the terms and conditions of the CC BY NC License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited without any further permission from Atlanta Publishing House LLC (European Journal of Chemistry). No use, distribution or reproduction is permitted which does not comply with these terms. Permissions for commercial use of this work beyond the scope of the License (http://www.eurjchem.com/index.php/eurjchem/pages/view/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). 2018 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.9.3.194-201.1727 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms http://creativecommons.org/licenses/by-nc/4.0 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms 1. Introduction 1.1. Theoretical background 1.1.1. Constant value (CV) 1.1.2. Concentration value 1.1.3. Absorbance subtraction method 1.1.4. Derivative subtraction 1.1.5. Derivative subtraction spectrum subtraction 2. Experimental 2.1. Materials and reagents 2.2. Instrumentation and conditions 2.3. Spectral characteristics and wavelength selection 2.4. Procedures 2.4.1. Preparation of standard stock and working solutions 2.4.2. Preparation of pharmaceutical dosage form 2.4.3. Validation 2.4.3.1. Linearity and construction of calibration curves 2.4.3.1.1. For absorbance subtraction method of both TR and VER 2.4.3.1.2. For derivative subtraction of Trandolapril 2.4.3.1.3. For derivative subtraction coupled with spectrum subtraction method of Verapamil 2.4.3.1.4. For constant value of both TR and VER 2.4.3.2. Determination in laboratory prepared mixtures (selectivity) 2.4.3.3. Accuracy 2.4.3.4. Repeatability and Intermediate precision 2.4.3.5. Limit of quantitation (LOQ) and limit of detection (LOD) 2.4.4. Application to pharmaceutical dosage form 3. Results and discussion 3.1. Methods development 3.1.1. Absorption subtraction 3.1.2. Derivative subtraction for determination of TR and derivative subtraction followed by spectrum subtraction for VER 3.1.3. Constant value and concentration value for VER 3.1.4. Derivative subtraction constant value and derivative subtraction concentration value of TR 3.2. Validation 4. Conclusion Disclosure statement ORCID References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField15: PrintField16: PrintField17: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: PrintField25: PrintField26: PrintField27: