Research Article Volume 7 Issue 1
^{1}Da Nang University of Medical Technology and Pharmacy, Vietnam
^{2}University of Sciences, Hue University, Vietnam
Correspondence: Tran Thuc Binh, Department of Chemistry, University of Sciences, Hue University, Hue 530000, Vietnam, Tel 84905382006
Received: May 20, 2023  Published: May 29, 2023
Citation: Luu ND, Duy TD, Binh TT. Simultaneous determination of paracetamol and codeine phosphate in pharmaceuticals using molecular absorption spectroscopy and classical least squares method. MOJ App Bio Biomech. 2023;7(1):4146. DOI: 10.15406/mojabb.2023.07.00174
In this article, a combined method of molecular absorption spectroscopy and classical least squares is used to simultaneously determine paracetamol (PAR) and codeine phosphate (COP) in pharmaceutical samples without the need for prior separation or extraction steps. The absorption spectra of standard solutions and samples were measured in the wavelength range of 210 to 290 nm with a step size of 0.5 nm. The concentrations of PAR and COP in the sample solutions were calculated using a selfmade program written in Microsoft Excel 2016 and Visual Basic for Applications (VBA). The reliability of the method was verified through the accuracy and reproducibility of the measurements when analyzing PAR and COP in EfferParalmax® Codeine tablets, and comparing the average values of their concentrations in the samples with the standard HPLC method.
Combining chemometrics with spectroscopic methods using fullspectrum data and various algorithms, statistics, and computers has been studied to simultaneously determine constituents in overlapping spectra mixtures. The advantages of these methods include a simple analysis process that does not require the separation or extraction of compounds from each other, and rapid execution that saves time, chemicals, and utilizes all data for calculations, resulting in increased accuracy in determination. These methods include classical least squares (CLS), partial least squares (PLS), principal component analysis (PCA), artificial neural networks (ANN), Kalman filtering, etc. Some authors have studied the application of these methods for analyzing real objects.^{1–8}
In this paper, we investigate the development of an analysis procedure for simultaneous determination of Paracetamol (PAR) and Codeine phosphate (COP) in EfferParalmax® Codeine effervescent tablets that are currently circulating in the Vietnamese market. PAR, with a molecular formula of C_{8}H_{9}NO_{2}, M = 151.17 g/mol, is a metabolite with activity of phenacetin, a painrelieving and antipyretic medication that is most effective in reducing pain, reducing body temperature in feverish patients by acting on the lower hypothalamus, dissipating heat by dilating blood vessels and increasing peripheral blood flow. COP, with a molecular formula of C_{18}H_{24}PNO_{7}, M = 397.00 g/mol, is a phenanthrene derivative, also known as methylmorphine, that has pharmacological effects of pain relief, cough suppression, and excellent antidiarrheal and neuropathic pain management. EfferParalmax Codein tablets combine two main components, PAR and COP, which are used to treat mild to moderate pain, fever reduction, and gastric irritation.^{9} To analyze these components, different individual analytical methods such as spectroscopic methods,^{10–12} and HPLC methods^{13} can be used. The individual analytical procedures require much time and complexity, and HPLC method has a significant advantage but a high cost. According to,^{10–12 }the absorption spectra of PAR and COP overlap, so we chose the UVVIS molecular absorption spectroscopy method with fullspectrum data and CLS algorithm to simultaneously determine the amount of Paracetamol and Codeine phosphate in pharmaceuticals. The proposed method opens up the possibility of fast, costeffective analysis that can be applied in practical analysis and pharmaceutical testing.
Equipment and chemicals
Equipment
Chemicals
Analysis method
For determination of PAR and COP simultaneously in a mixed solution, we used the UVVIS molecular absorption spectroscopy method with a fullspectrum combined with the classic least squares method (CLS) and a calculation program written in Microsoft Excel 2016 and Visual Basic for Applications (VBA). The essence of the method is clearly presented in.^{8} The process of measuring and calculating the concentration of PAR and COP is as follows:
Step 1: Prepare standard solutions of each component to be determined and their mixed solutions.
Step 2: Scan the solutions in the appropriate wavelength range on the UVVis spectrophotometer, save and retrieve the measured data (Export data) in "*.CSV" file format.
Step 3: Run the CLSExcel program^{8} to calculate the concentration of components in the mixed solution.
Statistical quantities
Relative error
The relative error between the determined concentration and the prepared concentration (RE %) is calculated as:
$\text{RE\%=}\left(\text{C}{\text{C}}_{\text{0}}\right)\text{.}\text{100}\text{/}{\text{C}}_{\text{0}}$ (1)
Where C is the determined concentration (µg/mL) and C_{0} is the known standard solution concentration (µg/mL).
Repeatability
Repeatability is evaluated by the relative standard deviation value RSD%:
$\text{RSD}\text{\%=SD}\text{.}\text{100}\text{/}{\text{C}}_{\text{mean}}$ (2)
Here, SD is the standard deviation and C_{mean} is the average concentration after n measurements (µg/mL).
For internal laboratory quality control, the repeatability of the method is achieved when the RSD% values obtained are less than ${\text{1/2RSD}}_{\text{Horwitz}}$
${\text{RSD}}_{\text{H}}{\text{=RSD}}_{\text{Horwitz}}\text{=2}{}^{\text{(}\text{10}\text{.5\xb7lgC}\text{)}}$ (3)
where C is the concentration expressed as a fraction. (for example, C= 5 µg/mL = 5.10^{6})
Method accuracy
The recovery of the method is calculated based on the standard addition method using the following formula:
$\text{Rev\%=}\left({\text{C}}_{\text{2}}{\text{\u2013C}}_{\text{1}}\right)\text{.}\text{100/}{\text{C}}_{\text{add}}$ (4)
where C_{2} (µg/mL) is the determined concentration after adding the standard, C_{1} (µg/mL) is the determined concentration before adding the standard, and C_{add} (µg/mL) is the concentration of the added standard.
According to,^{14} to determine the accuracy of the method, the same sample can be analyzed repeatedly using both the research method and the standard method, and the two average sample values can be compared using the student's ttest.
${t}_{exp}=\frac{\left{\overline{X}}_{A}{\overline{X}}_{B}\right}{\sqrt{\left({S}_{A}^{2}/{n}_{A}\right)+\left(S{}_{B}^{2}/{n}_{B}\right)}}$ (5)
Where: t_{exp}: experimental student's tvalue, ${\overline{X}}_{A},{\overline{X}}_{B}$ : the average values of method A and B; ${n}_{A},{n}_{B}$ : numbers of experiment of method A and B. Compare the value of t_{exp} with the value of t(α, ν), in which α is the chosen significance level, ν is degrees of freedom of two methods. If t_{exp} < t(α,ν), then the difference in the average values of the two methods is not significant.
Accuracy and precision of the analytical method
Standard working solutions of PAR 25 μg/mL and COP 25 μg/mL were added to 12 volumetric flasks (VF) numbered from 1 to 12, each containing 25 mL, and the volume was adjusted to the mark with H_{2}OACN solvent mixture (9:1, V/V). In VF 13 containing 25 mL, 13.5 mL of PAR standard solution of 50 μg/mL and 3.0 mL of COP standard solution of 25 μg/mL were added and diluted to the mark with the solvent mixture. The solutions were scanned in the wavelength range of 210 – 290 nm with a step size of 0.5 nm. The preparation and measurement were repeated 3 times. The absorption spectra of the solutions are shown in Figure 1. The concentration of PAR and COP in the mixed solutions were calculated using the CLSExcel program, and the relative error RE% and relative standard deviation RSD% of the analytical results were determined. The analytical results of PAR and COP in the prepared mixed solutions in the laboratory along with the corresponding statistical parameters are presented in Table 1.
Sample N^{0} 
Conc. ratio (mg/mL) of PAR/COP 
Meas. time 
PAR 
COP 

C_{PAR} (mg/mL) 
RE (%) 
Statistical quantities 
C_{COP} (mg/mL) 
RE (%) 
Statistical quantities 

M1 
19:1 
1 
18.961 
0.21 
C_{tb} = 19.019 RSD(%) = 0.267 1/2RSD_{H} = 5.136 RE_{tb}(%) = 0.10 
0.988 
1.20 
C_{tb} = 0.999 RSD(%)= 1.630 1/2RSD_{H} = 8.000 RE_{tb}(%)= 0.07 
2 
19.056 
0.29 
0.992 
0.80 

3 
19.040 
0.21 
1.018 
1.80 

M2 
18:2 
1 
18.077 
0.43 
C_{tb} = 17.991 RSD(%)= 0.414 1/2RSD_{H} = 5.178 RE_{tb}(%)= 0.05 
1.975 
1.25 
C_{tb} = 1.997 RSD(%)= 0.996 1/2RSD_{H} = 7.207 RE_{tb}(%)= 0.13 
2 
17.941 
0.33 
2.004 
0.20 

3 
17.956 
0.24 
2.013 
0.65 

M3 
17:3 
1 
17.070 
0.41 
C_{tb} = 17.075 RSD(%)= 0.029 1/2RSD_{H }= 5.223 RE_{tb}(%)= 0.44 
2.970 
1.00 
C_{tb} = 2.990 RSD(%)= 0.595 1/2RSD_{H }= 6.781 RE_{tb}(%)= 0.33 
2 
17.080 
0.47 
2.996 
0.13 

3 
17.076 
0.45 
3.004 
0.13 

M4 
16:4 
1 
15.998 
0.01 
C_{tb} = 16.008 RSD(%)= 0.097 1/2RSD_{H }= 5.271 RE_{tb} (%)= 0.05 
3.951 
1.23 
C_{tb} = 3.985 RSD(%)= 0.743 1/2RSD_{H }= 6.493 RE_{tb}(%)= 0.38 
2 
16.000 
0.00 
4.005 
0.12 

3 
16.026 
0.16 
3.999 
0.02 

M5 
15:5 
1 
15.027 
0.18 
C_{tb} = 15.027 RSD(%)= 0.010 1/2RSD_{H }= 5.322 RE_{tb}(%)= 0.18 
4.978 
0.44 
C_{tb} = 5.013 RSD(%)= 0.612 1/2RSD_{H }= 6.279 RE_{tb}(%)= 0.27 
2 
15.026 
0.17 
5.028 
0.56 

3 
15.029 
0.19 
5.034 
0.68 

M6 
14:6 
1 
14.123 
0.88 
C_{tb} = 14.128 RSD(%)= 0.046 1/2RSD_{H }= 5.378 RE_{tb} (%) = 0.92 
6.034 
0.57 
C_{tb} = 6.072 RSD(%)= 0.545 1/2RSD_{H }= 6.109 RE_{tb}(%) = 1.20 
2 
14.135 
0.98 
6.085 
1.42 

3 
14.125 
0.89 
6.096 
1.60 

M7 
13:7 
1 
13.068 
0.52 
C_{tb} = 12.973 RSD(%)= 0.654 1/2RSD_{H }= 5.438 RE_{tb}(%)= 0.21 
7.082 
1.17 
C_{tb} = 7.078 RSD(%)= 0.196 1/2RSD_{H }= 5.969 RE_{tb}(%)= 1.12 
2 
12.948 
0.40 
7.090 
1.29 

3 
12.904 
0.74 
7.063 
0.90 

M8 
12:8 
1 
12.029 
0.24 
C_{tb} = 11.953 RSD(%)= 0.551 1/2RSD_{H }= 5.504 RE_{tb} (%) = 0.39 
8.092 
1.15 
C_{tb} = 8.096 RSD(%)= 0.131 1/2RSDH = 5.850 RE_{tb}(%)= 1.20 
2 
11.911 
0.74 
8.088 
1.10 

3 
11.919 
0.67 
8.108 
1.35 

M9 
11:9 
1 
10.984 
0.15 
C_{tb} = 10.915 RSD(%)= 0.550 1/2RSD_{H }= 5.576 RE_{tb} (%) = 0.77 
9.088 
0.98 
C_{tb} = 9.095 RSD(%)= 0.077 1/2RSDH = 5.747 RE_{tb}(%)= 1.06 
2 
10.889 
1.01 
9.102 
1.13 

3 
10.873 
1.15 
9.096 
1.07 

M10 
10:10 
1 
10.039 
0.39 
C_{tb} = 10.042 RSD(%)= 0.023 1/2RSD_{H }= 5.657 RE_{tb} (%) = 0.42 
10.083 
0.83 
C_{tb} = 10.152 RSD(%)= 0.586 1/2RSDH = 5.657 RE_{tb}(%)= 1.52 
2 
10.043 
0.43 
10.185 
1.85 

3 
10.043 
0.43 
10.187 
1.87 

M11 
27:3 
1 
26.990 
0.04 
C_{tb} = 26.990 RSD(%) = 0.007 1/2RSD_{H} = 4.871 RE (%) = 0.04 
2.970 
1.00 
C_{tb} = 2.998 RSD(%) = 1.01 1/2RSD_{H} = 6.781 RE (%) = 0.08 
2 
26.988 
0.06 
2.993 
0.23 

3 
26.992 
0.03 
3.030 
1.00 
Table 1 Analytical result of PAR and COP in laboratory mixtures by CLSExcel method with statistical quantities
Figure 1 Molecular absorption spectra of PAR10 and COP10 standard solutions and sample solutions at different concentration ratios in laboratoryprepared mixtures:
(1) PAR10 standard solution at 10 µg/mL
(2) COP10 standard solution at 10 µg/mL
(3) M1: Solution containing PAR 19 µg/mL and COP 1 µg/mL
(4) M2: Solution containing PAR 18 µg/mL and COP 2 µg/mL
(5) M3: Solution containing PAR 17 µg/mL and COP 3 µg/mL
(6) M4: Solution containing PAR 16 µg/mL and COP 4 µg/mL
(7) M5: Solution containing PAR 15 µg/mL and COP 5 µg/mL
(8) M6: Solution containing PAR 14 µg/mL and COP 6 µg/mL
(9) M7: Solution containing PAR 13 µg/mL and COP 7 µg/mL
(10) M8: Solution containing PAR 12 µg/mL and COP 8 µg/mL
(11) M9: Solution containing PAR 11 µg/mL and COP 9 µg/mL
(12) M10: Solution containing PAR 10 µg/mL and COP 10 µg/mL
(13) M11: Solution containing PAR 27 µg/mL and COP 3 µg/mL
Table 1 shows that at different concentration ratios of PAR and COP, all RE% values are very small (≤1.6%), therefore, within the concentration range of PAR (1027 μg/mL) and COP (110 μg/mL), with different concentration ratios, the method error for both compounds is small and acceptable. On the other hand, all calculated RSD% values are much smaller than 1/2RSD_{H}, so it can be concluded that the repeatability of the method is very good for laboratory mixed solutions with the investigated concentration ranges and concentration ratios of the compounds given above.
Development of actual sample analysis procedure
Sample preparation
Weigh 20 tablets, determine the average weight of each tablet (M_{mean}), grind into fine powder and mix well. Weigh an amount of the drug powder equal to the average weight of one tablet on an analytical balance, put it into a 250 mL flask, add about 150 mL of solvent H_{2}OACN 9:1 (V/V), then put it in an ultrasonic machine for about 30 minutes, volumetrically adjust with the solvent to the mark (solution 1). Then filter solution 1 through a blue ribbon filter paper and take 10 mL of the filtered solution into a 100 mL volumetric flask and add the solvent to the mark (solution 2), take 10 mL of solution 2 into a 100 mL volumetric flask and add the solvent to the mark (solution 3), shake well to get the sample solution. To compare the results, take 20 tablets (same batch number, manufacturer, and expiration date) to the Testing Center for Drugs, Food and Cosmetics of Thua Thien Hue to analyze by standard HPLC method.
$\text{H(mg/}\text{tablet)=}\left(\text{M/}\text{m}\right)\text{.}\left(\text{C}\text{.100}\text{.10}\text{.25}\right)\text{/1000=}\left({\text{M}}_{\text{mean}}\text{/}\text{m}\right)\text{.25}\text{.C}$ (6)
Where: C (µg/mL): concentration of each substance determined in the sample solution. m: mass of the sample weighed for analysis (mg), M_{mean}: average weight of one tablet.
Simultaneous quantification of PAR and COP in drug samples
We conducted a determination of the amounts of PAR and COP in EfferParalmax® Codein tablets manufactured by BOSTON Vietnam Pharmaceutical JointStock Company, located at No. 43 Street 8, VietnamSingapore Industrial Park, Thuan An, Binh Duong, Vietnam, with the label indicating 500 mg PAR and 30 mg COP per tablet. Batch number: 9003, date of manufacture: 25/12/2021, expiration date: 25/12/2024. The average weight of one tablet was M = 3215.0 mg. The sample was processed as described in Section 3.2.1. Accurately weighed 3215.0 mg of the drug powder and processed it into a sample solution. The sample solution was scanned in the wavelength range of 210290 nm with a step of 0.5 nm. The CLSExcel program was used to determine the concentrations of PAR and COP in the sample solutions. The amounts of PAR and COP in EfferParalmax® Codein were calculated according to equation (6). The absorption spectra of the EfferParalmax® Codein drug sample solutions are shown in Figure 2. The results of the analysis of EfferParalmax® Codein tablets are presented in Table 2.
Figure 2 Molecular absorption spectra of standard solutions of PAR and COP, and the sample solution of EfferParalmax® Codein.
(1) Standard solution of PAR at 10 µg/mL
(2) Standard solution of COP at 10 µg/mL
(3) Sample solution of EfferParalmax® Codein
Sample N^{0} 
H_{(PAR)} (mg/tablet) 
H_{(COP)} (mg/tablet) 
M1 
514.03 
31.15 
M2 
523.90 
30.30 
M3 
504.93 
31.83 
Average 
514.28 
31.09 
Announced 
500.00 
30.00 
RE% 
2.86 
3.64 
RSD(%) 
1.845 
2.458 
*1/2RSD_{H} 
5.075 
7.739 
Table 2 Quantities of PAR and COP in EfferParalmax® Codein tablets
(*The values of 1/2RSDH were calculated based on the average concentration of the measured sample solutions).
The results presented in Table 2 from the simultaneous quantification of PAR and COP in EfferParalmax® Codeine effervescent tablets showed that the analytical method had a relative error (RE%) of less than 5%, which is in accordance with the Vietnamese Pharmacopoeia standard.^{15} The experimental relative standard deviation (RSD%) was also less than 1/2 of the Horwitz RSD (RSD_{H}), indicating good repeatability of the method.
Reliability of the analytical procedure
To demonstrate the reliability of the analytical procedure, its repeatability and accuracy were evaluated.
Repeatability
The results from Table 2 showed that the method had good repeatability, with RSD% values for both analytes below 2.5% and below 1/2 of RSD_{H}.
Accuracy
The accuracy was determined by calculating the recovery and comparing the results obtained from the study method with those obtained from the standard HPLC method.
Recovery
To determine the recovery, the sample powder mass was weighed using the average mass of one tablet. The first sample did not contain any standards, while the remaining samples contained increasing amounts of both PAR and COP standards. The samples were processed according to the procedure described in 3.2.1 to obtain the sample solution without standards and three sample solutions with added standards. The spectra of the PAR 10 µg/mL and COP 10 µg/mL standard solutions, as well as the spectra of the sample solution without standards (S0) and the sample solutions with added standards (S1, S2, and S3), were recorded. The concentrations of PAR and COP in the sample solutions and the sample solutions with added standards were calculated using the CLSExcel filter program. The spectra of the standard and sample solutions with added standards are presented in Figure 3, while the concentrations of the added standards and the calculated concentrations of the sample solutions without and with added standards are shown in Table 3. The recovery of the two analyte concentrations in the samples with added standards was calculated using Equation (4).
Figure 3 The molecular absorption spectra of standard solutions, sample solutions, and standardspiked sample solutions.
1. PAR10: standard solution PAR 10 µg/mL; 2. COP10: standard solution COP 10 µg/mL
S0: sample without added; S1: sample added standard the first time (PAR = 2,0 µg/mL, COP = 0,5 µg/mL)
S2: sample added standard the 2sd time (PAR = 4,0 µg/mL, COP = 1,0 µg/mL)
S3: sample added standard 3rd time (PAR = 6,0 µg/mL, COP = 1,5 µg/mL)
Sample 
Substance 
C_{1} (µg/mL) 
C_{2} (µg/mL) 
C_{add }(µg/mL) 
Rev (%) 
S1 
PAR 
20.461 
22.514 
2.0 
102.65 
COP 
1.246 
1.739 
0.5 
98.60 

S2 
PAR 
20.461 
24.568 
4.0 
102.68 
COP 
1.246 
2.240 
1.0 
99.40 

S3 
PAR 
20.461 
26.550 
6.0 
101.48 
COP 
1.246 
2.730 
1.5 
98.93 
Table 3 Recovery of the method for EfferParalmax® Codeine effervescent tablets
From the results of the Rev% recovery calculation presented in Table 3, it can be seen that the recovery of the method is approximately 100% for both substances. This confirms that the analytical method has good accuracy.
Comparison of the analysis results of the research method with HPLC method
To continue the objective evaluation of the accuracy of the current research method, we compared the results of the determination of the amount of substance in the EfferParalmax® Codeine drug sample using the analytical method with the results of the standard HPLC method performed by the Drug, Food, and Cosmetics Testing Center of Thua Thien Hue province. We evaluated the results of the two methods statistically.^{14} The results are presented in Table 4.
H_{PAR} (mg/tablet) 
H_{COP} (mg/tablet) 

CLS 
HPLC 
CLS 
HPLC 
514.03 
520.10 
31.15 
32.87 
523.90 
527.68 
30.30 
32.08 
504.93 
514.14 
31.83 
32.12 
H_{1(mean)}= 514.28 
H_{2(mean)}= 520.64 
H_{1(mean)}= 31.09 
H_{2(mean)}= 32.36 
t_{exp} = 0.944 
t_{exp} = 2.478 

t_{(0.05; 4)} = 2.78 
t_{(0.05; 4)} = 2.78 
Table 4 Comparison of the analysis results of PAR and COP content determination in the EfferParalmax® Codeine drug sample using the CLS method and the HPLC method
The results obtained in Table 4 show that all t_{exp} values are smaller than t(0.05; 4), therefore, the results of the analysis of the two active ingredients PAR and COP in EfferParalmax® Codein tablets by the CLS method and the HPLC standard method are statistically equivalent with a significance level of α = 0.05, and it can be said that the analysis results of the CLS method are not different from the results of the standard HPLC method.
With the goal of applying the UVVis molecular absorption spectroscopy method combined with the classic least squares (CLS) method to simultaneously determine the content of Paracetamol and Codeine phosphate in EfferParalmax® Codein effervescent tablets, we have achieved the following results:
Suitable conditions were studied and selected to simultaneously determine PAR and COP in laboratory mixed solutions containing the two substances with different concentration ratios using the molecular absorption spectroscopy method combined with the CLS method, specifically: Water: Acetonitrile (9:1 v/v) was chosen as the solvent for dissolution; The appropriate wavelength range for spectrum scanning is from 210 nm to 290 nm with a step of 0.5 nm. With different concentration ratios of PAR and COP in the mixed solution, the method errors were less than or equal to 2% for both PAR and COP, and the RSD% values were all small (<1.7). Therefore, the method ensures accuracy and repeatability.
The analytical procedure for the tablet samples containing PAR and COP was established using the UVVis molecular absorption spectroscopy method combined with the CLS method, and the reliability of the analysis procedure was demonstrated through the analysis of EfferParalmax® Codeine tablets. The results of the analysis drug content had a relative error compared to the label RE% < 5%, which is comply with the quality standards of the Vietnamese Ministry of Health.^{15} The experimental RSD% was less than 1/2RSD_{H}, so the method has good repeatability. Comparing the results of determining the content of PAR and COP in EfferParalmax® Codeine analyzed by the research method and the standard HPLC method showed that the results of the two methods are identical at a significance level of α = 0.05.
None.
The data used to support the finding of this study are available from the corresponding author upon request.
None.
The authors declare that they have no conflicts of interest.
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