Simultaneous Determination of Binary Mixture of Estradiol and Progesterone Using Different Spectrophotometric Methods

: Four rapid, accurate and very simple derivative spectrophotometric techniques were developed for the quantitative determination of binary mixtures of estradiol (E2) and progesterone (PRG) formulated as a capsule. Method I is the first derivative zero-crossing technique, derivative amplitudes were detected at the zero-crossing wavelength of 239.27 and 292.51 nm for the quantification of estradiol and 249.19 nm for Progesterone. Method II is ratio subtraction, progesterone was determined at λmax 240 nm after subtraction of interference exerted by estradiol. Method III is modified amplitude subtraction, which was established using derivative spectroscopy and mathematical manipulations. Method IIII is the absorbance ratio technique, absorbance of both medicines was measured at two wavelengths λ1= 260, iso -absorptive point and λ2=240, λmax of progesterone. The Q equations were used to calculate the final concentrations. The calibration curve is linear from 5.0–140 and 2.0–32.0 µg/ml for estradiol and progesterone respectively. The proposed techniques' selectivity was tested using synthetic combinations created in the lab and assessed using the standard addition method. Using one-way ANOVA, the outputs of the proposed ways were compared, and the result showed no significant differences between the proposed techniques


Introduction:
Steroid hormones are synthesized from cholesterol, and many are of great clinical importance.As illustrated in Fig. 1a, E2 has a chemical formula C18H24O2.E2 is mostly created in the ovary, although minor amounts are also produced in the adrenal cortex and testis 1 .Estradiol, the most common type of estrogen, was once thought to be both male and female sex hormone.Estradiol, which is generated from the ovaries, is the most powerful natural estrogen 2,3 .The ovaries are the primary source of E2 in premenopausal female 4,5 .Progesterone (PRG) is a steroid hormone that regulates women's generative processes.It has a chemical formula of (C21H30O2) 6 .Female reproductive functions are regulated by progesterone.During the luteal phase, or the second half of the menstrual cycle, PRG is formed largely by the corpus luteum in the ovaries.Progesterone is well formed in the adrenal glands to a lesser level during pregnancy 7,8 .Progesterone is involved in every stage of human pregnancy.It has a key role in tissues other than the reproductive system, such as the mammary gland in the preparation for lactation, the circulatory system, the central nervous system, and bones 9,10 .
In recent years, analytical methods ultraviolet spectrophotometric method 6,11 , derivative spectrophotometry DS [12][13][14] , HPLC 12,15 , IGC/MS stands for isotope dilution-gas chromatography/mass spectrometry 16 , LCTMS 17 , and GC-MS/MS 4,18 for estradiol and progesterone levels in human serum or plasma samples, as well as a pharmaceutical formulation, have been created.This study aims to develop new and very simple techniques for resolving overlap spectra in their mixtures and pharmaceutical formulations without the need for separation.To measure E2 and PRG simultaneously in medicinal formulation, four distinct spectrophotometric techniques were used.The techniques are illustrated with mathematical explanations.The techniques do not require any complicated equipment or programming, and they are straightforward, accurate, and exact.

Theoretical Background Derivative Spectrophotometry (DS)
By differentiating the sample's absorbance concerning to wavelength (λ), DS transforms a normal spectrum (basic, zero-order spectrum) into its 1 st , 2 nd , or higher derivative spectra.Derivative spectra offer a more distinctive shape in comparison to the parent shape; new maxima and minima appear as well as places where derivative spectra cross the X-axis.When the height of an analyte's derivative peak is measured at wavelengths where the spectra of other components are zeroed, the measured amplitude is related to the analyte's concentration.This method involves quantifying the amplitude of the derivative spectrum of a mixture at different wavelengths to identify the presence of numerous components in a combination.The "zerocrossing technique" is the name given to this method of quantitative determination 19-22.

Ratio Subtraction Method (RSM)
If you have a mixture of 2 drugs, X (PRG) and Y (E2) with overlapping spectra, and the spectrum of Y is extended more than X, the determination of X can be done by dividing the spectrum of the mixture by a certain concentration of Y as a divisor (Y') 19 represent in Eq. 1

…………………….. 1
The division in Eq. 1 will give a new curve that represents in Eq.2The constant can be determined directly from Eq. 1 by the straight line that is parallel to the wavelength axis in the region where Y is extended 23,24.

Modified Amplitude Subtraction Method (MAS)
When having a mixture of two drugs, X (PRG) and Y(E2), and the first derivative spectra of both drugs show overlapped peaks at λ1, while only the first derivative spectra of Y show a peak at λ2.Two calibration curves are constructed relating the peak amplitude of Y at λ1 and λ2 verses the corresponding concentration of Y, and one calibration curve constructed relating the peak amplitude of X at λ1 verses the corresponding concentration of X (by first derivative for example) Py = a+by at λ1 ……………………….5 Py = a+by at λ2 ….…………………….6 PX= a+bx at λ1 ………………………….7Where Py: absorbance of Y (E2), a: absorptivity and y: concentration of y (E2) at λ1and λ2.PX: absorbance of X (PRG), X: concentration of X (PRG) at λ1, b: slop.The mixture is scanned, and the first derivative spectrum of the mixture is determined.We obtain the peak amplitude of mixture at λ1 (Pmix1) and λ2 (Pmix2).By substitute Pmix2 in Eq.6, so the concentration of Y can be calculated.Pmix2 = a+by (at λ2) conc. of y …………... 8 Then the calculated concentration of Y in Eq. 8 is substituted in Eq.5 to determine the peak amplitude of Y in the mixture at λ1 Py in the mixture = a+b(conc.of y) .…………….9Where Pmix1 absorbance of mixture of [X (PRG) + Y (E2)] at λ 1 Pmix2: absorbance of mixture of [X (PRG) + Y (E2)] at λ 2 Where Py in the mixture: absorbance of y (E2) in the mixture, y: concentration of y (E2) Subtracting calculate concentration of Y in Eq.8 by Pmix1 Pmix1-(Py in the mix) = P in the mixture ……..10 Where Pmix1: absorbance of mixture of [X (PRG) + Y (E2)] at λ 1, Py in the mixture: absorbance of y (E2) in the mixture and P in the mixture: absorbance of X (PRG) in the mixture By subsuming Eq.10 in Eq.7 the concentration of drug X (PRG) can be determined P in the mixture = a+b ……………11 Where P: absorbance of X (PRG) in the mixture, a: absorptivity, b: slop, X: concentration of X (PRG) in the mixture 25 .

Q-Absorbance Ratio Spectra Method
For this strategy, regardless of concentration or path length, the ratio of absorbance at any two wavelengths for a chemical that obeys Beer's law is a constant number.The technique necessitates absorbance measurements at two λmax, one of which is the maximum absorptivity of one of the components λ2 and another is the iso-absorptive point, which is a wavelength with same absorptivity of the two components λ1.Mathematical equations can be used to compute the concentrations of each component.CX= (QM-Qy/QX-Qy) × A/a1 ………………….. 12 Cy = (QM-QX/Qy-Qx) × A/a2 ………………….13  Where Cx and Cy are the x and y concentrations, A is the sample's absorbance at iso-absorptive λmax, and a1 and a2 are the x and y absorptivity at iso-absorptive λmax, respectively.QM= A2 / A1 ………………………………..14 QX= a  2/ a  1 ………..……………………..15 Q y= ay2/ay1 …………………………………16 Where, A1 and A2 were absorbance of combination at λiso and λ max a 1 and ay1 are absorptivities of  and y at λ iso a 2 and ay2 are absorptivities of  and y at λ max 26- 28

A
Shimadzu UV-V twin beam spectrophotometer (demonstrate UV 1800, Japanese) with a fixed 1nm bandwidth and a 1 cm quartz cell was used for spectrophotometric measurements, with a laptop attached to the double beam spectrophotometer to record normal spectrum.All computations were performed by Matlab 6.5 and Microsoft Excel.ANOVA was performed using SPSS.All of the reagents used in this investigation are analytical grade.
Preparation Standard Stock Solutions of E2 (200 µg /ml) and PRG (100 µg /ml) (Sigma Aldrich): were made by dissolving 0.0200 g of E2 and 0.0100 g of PRG in absolute ethanol, diluting to 100 ml in a volumetric flask, and daily working solutions were made by diluting stock solutions with absolute ethanol 4,29 Synthetic sample simulating to capsule was prepared in laboratory, consisted of 1.0 mg of E2 and 100 mg of PRG with excipients 45 mg of lactose, 9.0 mg of microcrystalline cellulose and 5.0 mg polyethylene glycol) per one capsul 30,31 Absolute ethanol was used as a blank to capture the normal spectra of the two components throughout range of wavelength 200-400 nm.

Construction of Calibration Graphs
Serial dilutions of (5.0-140) µg E2 and (2.0-32.0)µg PRG are correctly transferred from the standard working solution into two different sets of 10.0 ml volumetric flasks, then brought up to volume with absolute ethanol.From 200 to 400 nm, the spectra of the created standard solutions are scanned and saved in the laptop.

The First Derivative Spectrophotometric Technique (1D)
Aliquots of 1.0 mL from E2 and PRG standard working solution, equal to 200 µg/ml and 100 µg/ml for both drugs, were separately transferred into two 10.0 mL volumetric flasks, and then the volume was completed with absolute ethanol.The spectra of these two solutions were scanned against a blank solution of absolute ethanol and their absorptions were computed.The concentration of each drug was quantified by drawing a calibration graph with the drug concentrations as abscissa and dA/dλ as ordinate at the determined zero crossing point of the other.The first derivative spectra were recorded under certain selected instrumental parameters such as, ∆λ, scaling factor and wavelength range.After that the working wavelengths of the two drugs, at the zero crossing points were recorded 32 .

Ratio Subtraction Method (RSM)
Standard working solutions were precisely measured and aliquots ranging from (2.0-32.0µg) PRG were put into 10.0 mL volumetric flasks.The prepared standard solutions' spectra were scanned after adding absolute ethanol to the final volume.A calibration graph was used to generate the regression formula, which linked the absorbance of PRG normal spectra at max 240 nm to the proper concentration.The regression equation is obtained by constructing a calibration chart comparing the absorbance of normal spectra of E2 at 281.40 nm, where PRG display no interference, to the appropriate concentrations.

Modified amplitude subtraction method (MAS)
Standard working solutions containing (5.0-140 µg) E2 and (2.0-32.0µg) PRG were meticulously measured and deposited individually into 10.0 ml volumetric flasks.Absolute ethanol was used to finish the volume.Each solution was scanned throughout a certain λmax range.The 1D of each solution was then calculated and recorded.Three calibration graphs were created: one matching PRG's peak values at 243.66 nm to its corresponding concentration, and the other two linking E2's peak amplitudes at 243.66 nm and 292.51 nm to their respective concentrations.Three regression equations were calculated.

Q-Absorbance Ratio Spectra Method
Different aliquots corresponding to (5.0-140) µg E2 and (2.0-32.0)µg PRG were correctly transfer based on their standard solutions into two distinct sets of 10.0ml volumetric flasks and volumetric flasks were filled to volume with absolute ethanol.Absolute ethanol was used as a blank to record the normal spectra from 200 -400nm of these solutions.The absorbance values for both medications at the indicated wavelengths were computed using the absorbance values observed at 262nm, iso-absorptive point (λiso) and λ2 =240nm (λmax of PRG).

Analysis of Synthetic Pharmaceutical Dosage Forms
Five capsules of E2 and PRG were powdered and mixed well.Correctly weighed amount of the powdered capsules equal to 160 mg of one capsule was dissolved in 100 ml absolute ethanol with the aid of sonication and filtered to make stock solution.A viable solution filtrate was diluted with absolute ethanol to a concentration of 15.0 µg in a 10.0 ml volumetric flask, and the methods for linearity or laboratory generated mixtures of each technique were followed.The procedures' validity was tested by injecting known amounts of standard drug powders into the pharmaceutical dose forms (standard addition technique).After implementing the offered procedures, the recovery of the extra standards was estimated.

Results and Discussion:
For analytical research, spectrophotometric approaches such as DS, ratio spectra spectrophotometry, and other chemometric methods are relevant.Quality control and drug analysis are common uses for them.They are also chosen over other analytical techniques such as GC, LC-MS, and LC-NMR, which are more sophisticated and time-consuming than spectrophotometric procedures.Furthermore, they necessitate preceding extraction and separation operations, resulting in a cost and time increase.Spectrophotometric techniques are commonly used because they are simple to use, quick, accurate and inexpensive.As a result, spectrophotometric resolution of multicomponent combinations with overlapping spectra is a fascinating topic in analytical 20,[33][34][35][36] First Derivative Zero-crossing Method (1D) Estradiol (E2) has a UV absorption spectrum that overlaps with progesterone's range (PRG).The zero-order absorption spectra of E2 and PRG, as well as their mixture, is shown in Fig. 2.0, with absolute ethanol serving as a reagent blank.There is a significant overlap of the spectrum.As a corollary, direct absorbance measurements will not be able to determine PRG during the occurrence of E2 or vice versa.Resolving mixtures using traditional spectrophotometry is difficult.As a result, derivative spectrophotometry can provide a satisfactory solution to this problem.As shown in Fig. 3, first derivative spectrum of E2 solution undergoes zero absorption at wavelength 249.19nm, while PRG solution has absorption at this point.From this point of view zero-cross technique is used for determination of PRG in the presence of E2 in the solution.On the other hand, PRG solution has zero absorption at wavelength 239.27nm and 292.51 nm, while E2 solution has absorption at this point.So, E2 has been determined in the presence of PRG in the solution.
Table1.demonstrates the results of statistical data of the calibration graphs using 1D spectrophotometry for simultaneous quantification of each E2 and PRG in binary mixture , Fig. 4 shows 1D ratio spectra of (2.0 -32) µg/ml of PRG and (5.0 -140 )µg/ml of E2.

Ratio Subtraction Method (RSM)
The RSM starts with a scan of the normal spectra of PRG standard solutions prepared in absolute ethanol, then confirms the linearity between absorbance at the chosen λmax of 240 nm and related to PRG concentration 19,30 .The determination of PRG (X) can be achieved by scanning the zero order absorption spectra of the laboratory prepared mixtures (PRG and E2), dividing them by a carefully chosen concentration (50 µg /ml ) of standard E2 (Y' = divisor) producing a new ratio spectra (X/Y') + constant as illustrated in Fig. 5.This was followed by subtraction of the absorbance values of these constants (Y / Y') in plateau region 268 -300 nm as shown in Fig. 6, followed by multiplication of the obtained spectra by (Y') the divisor as shown in Fig. 7. Finally, the original spectrum of PRG (X) was obtained and used for direct determination of PRG(X) at 240nm and the concentration calculated from the Eq.17 PPRG = 0.0382  -0.0156 …………………….17Where  is the concentration of PRG in µg/ml and P is the peak values of the normal spectrum of PRG at 240 nm.Though, to determine E2 alone, a calibration graph is created by connecting the absorbance of 0 D E2 spectra at 281.40 nm, wherever PRG illustrated no absorbance Fig. 2, concentration of E2(Y) can be calculated in Eq. 18 PE2 = 0.0079  + 0.0306 ………………………18 Where  is the E2 concentration in µg/ml, and P is the peak value of E2's normal spectrum at 281.40 nm.Table .1,displays the statistical results from the quantified calibration curves for simultaneous PRG and E2 evaluation using the ratio subtraction.

Wavelength (nm)
Figure7.Normal absorption spectra of PRG gained by RSM for the analysis of laboratory generated combinations after multiplication by 50 µg/ml of E2 divisor.
The concentration of E2 may be simply estimated using the obtained regression Eq. 19 after scanning the mixture and detecting the peak value at 292.51 nm.Using the acquired regression equation and the computed E2 concentration, the peak amplitude of E2 at 243.66 nm may be determined in Eq.20.Finally, by subtraction the hypothesized peak values of E2 at 243.66 nm from the measured peak values of the mixture at the same λmax, the peak values of PRG can be derived.The concentration of PRG may be estimated using the Eq.21 that represents a linear correlation between the peak values first derivative spectra of PRG at 243.66 nm from 2.0-32.0µg/ml.Table1 illustrates the results of statistical data of the calibration graphs using modified amplitude subtraction method for simultaneous quantification each of E2 and PRG in binary mixture

Wavelength (nm)
Figure8.First derivative spectra of (a) 20.0 µg /ml PRG and (b) 20.0 µg/ ml of E2 Q-Absorbance Ratio Spectra Method Fig. 9 shows the iso-absorptive point at which both drugs have the same absorbance value and λ max for PRG.Absorbance of each drug was measured twice; at the iso-absorptive point and at λ max for PRG, then calibration for each drug alone was performed and specific absorptivities of both drugs were determined.Relative concentration of the two drugs in the mixture was calculated by applying the Eq.22 and 23.A1 and A2 are the absorbance of the mixture at 262 nm and 240 nm, respectively.ax1 and ay1 are the absorptivities of PRG and E2 at 262 nm, ax2 and ay2 are the absorptivities of PRG and E2 at 240 nm.Table 1.illustrates the results of statistical data of the calibration graphs using Q-absorbance ratio spectra technique for simultaneous quantification each of E2 and PRG in binary combination.

Accuracy and Precision
Under the optimum conditions, the accuracy and precision of the (1st derivative spectrophotometric, RSM , AMS and Q-Absorbance ratio spectra technique) techniques for simultaneous determination of E2 with PRG in binary mixture under linearity were studied depending upon the values of the error percentage (Error %) and relative standard deviation percentage (RSD %) for five replicated measurements of three different standard concentrations.The results of error studies for both drugs, are not greater than ±5.0 % which designates that the proposed methods have acceptable accuracy.Moreover, the RSD values for the determination of drugs are less than 4.44 %.The results are illustrated in Table.

Statistical Analysis
The E2 and PRG employed a one-way ANOVA test to compare the ratio subtraction modified amplitude subtraction and Q-absorbance ratio spectra approach with traditional derivative spectrophotometry (zero-crossing methodology).Snedecor's F-values were computed and compared to the conventional tabular value (P = 0.05) for this purpose.For each insecticide, the same computing procedures were used.Table .5. demonstrates that in the analysis of variance, the calculated or experimental F values are less than the tabulated values, indicating that there were no significant differences between the four approaches.

Comparison with Other Methods
A comparison has been done between some of analytical variables obtained from the proposed methods for determination of estradiol and progesterone with other previous published methods [11][12][13] and the results summarized in Table.6.

Greenness Assessment
The analyst's first aim is to develop an environmentally friendly technique that can be easily employed in routine analysis and has high efficiency and low cost.The goal of green analytical chemistry (GAC) is to develop an ecological approach that doesn't harm the environment or deal with dangerous compounds.Utilizing two analytical tools, the proposed methods' "greenness" was evaluated 40,41 Green Analytical Procedure Index (GAPI) Approach GAPI is a new tool to estimate the greenness of the overall method in the analytical process based on 15 different factors.According to the strength of the environmental influence, five pentagrams were created and coloured, each divided into three or four section.While yellow and red indicated medium and high environmental effects, respectively, green represented moderate environmental impact 40,42-44.The proposed techniques showed eight green shaded sections, while the literature HPLC 15 technique demonstrated five green-shaded sections as shown in Fig. 10.Analytical eco-scales are one of the greenness assessment tools that are skilled at assessing the efficacy of the technique and extracting measurable information about the method's environmental compatibility, taking into account the employed chemicals, instruments, and created waste.This tool relies on computing the analytical eco-scale value, which is obtained by assigning penalty points to all factors that hurt the environment, adding up all of these points, and then subtracting from a base of 100.The approach has a good green profile the higher the eco-scale value (greater than 85) that is obtained.Scores greater than 50 indicate competent green analysis, while scores less than 50 indicate insufficient green analysis 39,43,[45][46][47] The result of eco-scale values for the proposed technique and literature HPLC method 15 are shown in Table .7.

Conclusions:
The main task of this study is to find fast, accurate, sensitive and cost-effective spectrophotometric methods for the simultaneous quantification of E2 and PRG in pharmaceutical formulation.This research, employed the zerocrossing technique, RSM, MSM and Q-absorbance technique to identify a binary mixture of E2 and PRG in synthetic mixture samples.When employed to resolve a binary combination, these four approaches produced good results and did not need the use of complicated or costly gear.The efficacy of the recovered values ranged from 98.38 to 100.76percent with an RSD < 4.44 %.The impact of the proposed methods on the environment was assessed by the eco scale and green analytical procedure index (GAPI) tools, where the results take that proposed methods were the greenest than literature methods.Statistical studies shows that there is no discernible difference between the four strategies presented.Therefore, these four proposed approaches are typically suitable for the measurement of E2 and PRG.

Figure 5 .Figure 6 .
Figure 5. Ratio spectra of laboratory generated combinations of PRG (X) and E2 (Y) using 50 µg/ml of E2 (Y') as a divisor and absolute ethanol as a blank.

Figure 10 .
Analytical comparison between pictograms of (a) the proposed techniques and (b) other literature HPLC 15 ones for assessment of greenness Analytical Eco-scale Approach

Table 2 . Accuracy and Precision of the proposed techniques for simultaneous quantification of E2 and PRG in a binary combination.
The results of the application and recovery study are summarized in Table.4.