HUE UNIVERSITY HUE UNIVERSITY OF SCIENCES NGUYEN THI QUYNH TRANG

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1 HUE UNIVERSITY HUE UNIVERSITY OF SCIENCES NGUYEN THI QUYNH TRANG RESEARCH ON THE DEVELOPMENT OF A CHEMOMETRIC METHOD FOR THE SIMULTANEOUS DETERMINATION OF MOLECULAR ABSORPTION SPECTRUM OVERLAPPING AND APPLICATION IN DRUG ANALYSIS THE ABSTRACT OF DOCTORAL DISSERTATION HUE

2 HUE UNIVERSITY HUE UNIVERSITY OF SCIENCES NGUYEN THI QUYNH TRANG RESEARCH ON THE DEVELOPMENT OF A CHEMOMETRIC METHOD FOR THE SIMULTANEOUS DETERMINATION OF MOLECULAR ABSORPTION SPECTRUM OVERLAPPING AND APPLICATION IN DRUG ANALYSIS MAJOR: ANALYTICAL CHEMISTRY CODE: THE ABSTRACT OF DOCTORAL DISSERTATION SCIENTIFIC SUPERVISORS: 1. Assoc.Prof.Dr. TRAN THUC BINH 2. Assoc.Prof.Dr. NGO VAN TU HUE

3 INTRODUCTION The term chemometric was first introduced in 1972 by Svante Wold (Swede) and Bruce R. Kowalski (American). The establishment of the Chemometric Association in 1974 provided the first definition of chemometrics, the application of mathematical, statistical, graphical methods.for experimental planning, optimize the chemical information extracted from the data set and provide the most useful information from the original data set. Chemometric is widely used in fields such as environmental chemistry, organic chemistry, biochemistry, theoretical chemistry, statistics in chemistry and has especially established an important position in analytical chemistry. Analytical chemistry is an effective tool in the fields of science and technology, such as chemistry, biology, agronomy, medicine, food... especially in the pharmaceutical industry. Chemometric methods have been used by researchers at domestic and foreign for many years to concurrently analyze a mixture of substances in a variety of subjects, including pharmaceuticals. Studies have shown that the most commonly used chemometric methods are the partial least squares (PLS) method, the Polimerase chain reaction method (PCR), classic least squares method (CLS), artificial neural network method (ANN), derivative method, kalman filter method... Each method has its own advantages and disadvantages. The CLS method can use the entire spectral data to set up the m equations in n unknowns (m> n). The transformation matrix based on the principle of least squares will produce the results of the error satisfying the requirements. However, if there is a lot of noise (or spectral error) in the spectrophotometer and/or when the constituents interact with each other, it produces an optical effect that changes the absorbance of each constituent, this method can not eliminate the noise leading to the analysis results have big errors. The ANN method has the disadvantage that the training time is long and it requires a lot of different algorithms, so that when building an analytical model, it requires testing different models to find the optimal network 1

4 structure. Derivative spectrophotometric method does not apply when the sample contains many constituents with absorbing optical spectrum overlapping or similar, since it is difficult to select an appropriate wavelength to determine a particular constituent, or their derivative spectrophotometric still have the same maximum absorption. Kalman filter method can eliminate most of the noise and therefore minimize errors, but the disadvantage of this method is that the initial values for the filter must be selected that means must choose the appropriate initial value of the content of analytes in their mixtures and the associated error (expressed by the variance). If the initial values (concentration and variance) do not match, the end result is a large error. In the world there have been some studies applying Kalman filter method to chemometric to simultaneously determine mixtures of 2 or 3 substances in the pharmaceutical. However, these studies neither offer a suitable initial value nor cover initial values and are therefore difficult to apply to analytical laboratories. In Viet Nam, Mai Xuan Truong has studied the application of Kalman filter method to simultaneously determine the vitamins in pharmaceuticals, rare earth elements... However, the author did not introduce how to choose the initial values and thus limited the possibility of applying the proposed method in practice. As a result of these issues, it is clear that the development studies of chemometric-photometric method combined with the use of Kalman filter methods is very necessary, especially to simultaneously determine mixtures of substances difficult to analyze that containing optical absorption spectrophotometer overlapping in various sample objects, including pharmaceutical samples. However, the challenge is to find a suitable solution to select the initial value for the Kalman filter to produce accurate analysis results (repeatability and accuracy) or acceptable error. At the same time, the analytical process needs to be developed that based on the chemometricphotometric method combined with the Kalman filter so that can be applied conveniently in the field of pharmaceutical testing in our country. For these reasons, the topic "Research on 2

5 the development of chemometric method for the simultaneous determination of molecular absorption spectrum overlapping and application in drug was carried out for the following these purposes: i) Developed a chemometric-photometric analysis process in combination with Kalman filter method to simultaneously analyze mixtures of 2 and 3 substances with molecular absorption spectra overlapping in pharmaceutical samples; ii) Apply the process has been built to simultanneously analyze mixtures 2 and 3 substances in some pharmaceuticals are on the market Vietnam. Master thesis structure The thesis consists of 184 pages, with 50 tables and 14 figures, of which: - Table of contents, list of abbreviations, tables and figures: 09 pages - Introduction: 04 pages - Chapter 1: Overview 43 pages - Chapter 2: Content and Research Methods 16 pages - Chapter 3: Results and discussion 67 pages - Conclusion 02 pages - The list of published research results: 01 page - References: 15 pages, with 127 references CONTENT THESIS CHAPTER 1. LITERATURE REVIEW - The Bughe-Lambe-Bia law and Optical properties of optical absorption + The Bughe Lambe - Bia + Optical properties of optical absorption - Some UV-VIS spectrophotometric methods combined with chemometric simultaneously determine the components with absorption spectrum overlapping each other. + Vierordt method + Derivative spectrophotometric method + Full-partial method (least squares method) + The least squares method 3

6 + Principal Components Regression method + Artificial neural network method + Kalman Filter Method - Overview of multi-component pharmaceuticals and research active ingredients + Profile of the development of multi-component pharmaceuticals + Overview of telmisartan (TEL), hydrochlorothiazide (HYD) + Overview of paracetamol (PAR) and caffeine (CAF) + Overview of paracetamol (PAR) and ibuprofen (IB) + Overview of amlodipine besylate (AML), hydrochlorothiazide (HYD), valsartan (VAL) CHAPTER 2. RESEARCH SUBJECTS AND METHODOLOGY 2.1. CONTENT To achieve the objective of the thesis is to contribute to the development of chemometric-photometric method using the Kalman filtering algorithm to apply in pharmaceutical analysis, the research contents include: 1. Study to find the suitable solution to select the initial value (concentration value and initial variance) for the Kalman filter for using the chemometric - photometric method simultaneous determine of molecular absorption spectrum overlapping (mixture contains 2 substances and mixture contains 3 substances). 2. Construct a computer program based on the Kalman filter algorithm on Microsoft-Excel 2016 software with the Visual Basic for Applications programming language, it is possible to quickly calculates of the concentration of photocatalytic absorption spectra overlapped in the study system (containing 2 or 3 substances simultaneously). 3. Verification of the reliability of the analytical method - Chemometric-photometric method using the Kalman filter algorithm (calculated by software program has been built): 4

7 Comparison of analytical methods with the chemometric- Other photometry (least squares using full spectrum and diffusion method) when analyzing laboratory standard samples (containing 2 or 3 analyzes). 4. Develop a chemometric-photometric analysis using the Kalman filter algorithm (calculated by software program has been built). 5. Apply the analysis process has been built - analysis of multi-component pharmaceutical samples (containing 2 or 3 ingredients) are currently in circulation in Vietnam METHODOLOGY Kalman filter method and calculation program Based on the theoretical basis, the Kalman filter method and the calculation program are performed according to the following steps (Figure 2.1): i) Record the spectrum of the analytical solution (laboratory standard solution) and the mixture of analytes, obtaining the spectral data set (optical absorption at selected wavelength k) in the form of a file txt tail (number of wavelengths selected depending on the characteristics of the components in the study); ii) Enter the mono-particle and compound material data files into a computer software program (programmed in Microsoft-Excel 2016 software) to calculate the (molecular absorption) values of the monomers; iii) Run the Kalman filter: - Give the initial initial value, including the first estimate of the Cest(0) and the covariance of the error Pest(0) (study content (1) will give the initial value); - Extrapolation of concentration status: C pri ( k) = C est ( k- 1) - Extrapolation of the covariance of the error: (2.1) P pri ( k) = P est ( k- 1) (2.2) - Calculation Kalman Loop: 5

8 - T ( ) 1 T ( k) = pri ( k) e ( k) e( k) pri (k) e ( k) + (2.3) ( k) K P P R - Updated status estimate: ( e ) Cest ( k) = Cpri ( k) + K( k) A( k) - ( k) Cpri ( k) (2.4) - Update the covariance of the error: Pest ( k) = éinv e( k) K ù ê - ( k) P ë úû pri ( k) (2.5) The above calculation steps are performed from the first wavelength to the last wavelength. Finally, the calculation program will produce the result: the concentration of each constituent in the system and the covariance of the error. This variance is usually the smallest at the last wavelength Minimum squared method using simulan software [2] Step 1. Prepare standard solutions for each constituent and their mixtures. Step 2: Record the absorption spectra of the standard solution to calculate the absorption coefficient of the constituents: = ( ij )mxn Step 3: Record the optical absorption spectra of the mixed solution, enter the optical absorption matrix measured A = (Ai1)mx1 Step 4: Solve the system of m equations by the least squares method: A =. C to find the concentration of C Derivative spectrophotometric method Step 1. Prepare standard solutions for each constituent and their mixtures. Step 2: Record the optical absorption spectra and the spectrum, find the appropriate wavelength at which the derivative value of a substance to be analyzed is different from zero or maximum, and the other derivative value is equal to 0. Step 3: After determining the measured wavelength at a certain derivative, proceed to quantify the substances by the benchmark method or add standard Computer programming method 6

9 - Calculations to determine the concentration of substances by Kalman filter method is quite complex, so need to program on the computer to calculate fast and convenient for users; - Select open source software is Microsoft-Excel to not infringe copyright; - Select the language and the tool Visual basic for application; Data processing method Application of Microsoft-Excel 2016 software with Data Analysis tool to process experimental data: Calculation of statistical data (arithmetic mean, standard deviation, RSD); Comparison of two repetitions (or two variances), using F (Ftest); Comparing two mean values, using t-test; Compare two methods, using paired-t-test... CHAPTER 3. RESULTS AND DISCUSSION 3.1. CHOOSE THE INITIAL VALUE Select a random initial value In this way, selecting a random initial value can select any C value for the concentration est P (0) and variance est (0) [27], [112]. For a mixture containing 2 or 3 substances (a mixture of laboratory standard reagents), the initial values for each substance were randomly selected at a concentration of C est(0) = 0,3 µg/ml and variance P est (0) = 1. Table 3.1. Results of determination of TEL and HYD concentration in Kalman method with with random selection of initial value (*) TEL HYD Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9 C o (µg/ml) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 C (µg/ml) 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 RE (%) C o (µg/ml) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 7

10 C (µg/ml) 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 RE(%) (*) Co: Concentration in standard mixed solution; C: Determined concentration Table 3.1 shows that with different concentration ratios, between the concentration of the standard solution and the concentration determined to be relatively high RE% error (in the range of 69.7% %). The concentration values determined in all mixtures are equal to the initial concentration (0.3 μg / ml). Table 3.2. Results of determination of AML, HYD and VAL concentrations in Kalman method with random selection of initial value (*). AML HYD VAL Mixture H1 H2 H3 H4 C o (µg/ml) 0,250 0,50 1,00 5,00 C (µg/ml) 0,300 0,300 0,300 0,304 RE (%) C o (µg/ml) 0,325 0,65 1,30 5,00 C (µg/ml) 0,307 0,304 0,302 0,299 RE (%) C o (µg/ml) 4,00 8,00 16,00 5,00 C (µg/ml) 0,301 0,300 0,300 0,299 RE (%) (*) Co: Concentration in standard mixed solution; C: Determined concentration Table 3.2 shows that with different concentration ratios, the concentration of the standard solution and the concentration determined were very high (-5.5% %). The lowest RE value (-5.5%) corresponds to the standard concentration of (close to the initial concentration x = 0.3). The higher the initial concentration, the greater the RE % value. Thus, with the results of the tests in Table 3.1 and Table 3.2, it can be seen that the initial method of selecting the concentration value and the random variance are incomplete, the calculated results still have a relatively large error Select the assumed initial value In this study, we investigated a different set of assumed initial value in comparison with previous studies (for aquation of 2 or 3 substances) 8

11 - Option 1: Solution 2 (or 3) equation with 2 (or 3) (unknowns is the substance concentration) at 2 (or 3) wavelengths near each other (the equation depends on the optical absorption and the concentration of the substance in the mixture with the predicted molecular absorption coefficient, Calculates the magnetic spectrum of a monoclonal/monostable solution), determine the concentrations of the substances in the mixture, and take them as the initial concentration values. The initial value of the variance is randomly chosen, for example by 1. - Option 2: Select the initial randomized concentration - (But having purpose) is 0,3 µg/ml (for each substance in a mixture of 2 or 3 substances). But for variance, the initial value for it is not randomly selected, which is calculated by the Horwitz equation: At a concentration of C = 0.3 μg / ml = , calculate the variance by and select this value as the initial value For the system two constituents TEL and HYD Apply Kalman method for mono-spectral data and a mixture of two substances (in the range of 220 nm nm) with a choice of assumed initial values (according to option 1 and option 2), the results show in Table 3.3 and 3.4. Table 3.3. The results of determination of TEL and HYD concentrations in the mixture by the Kalman method with the choice of the assumed initial value Option 1 (*) Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9 C o (µg/ml) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 TEL C (µg/ml) 0,99 1,99 2,95 3,88 5,03 6,07 7,18 7,99 9,00 RE (%) -0,9-0, , ,1 0 C o (µg/ml) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 HYD C (µg/ml) 8,91 7,84 6,86 6,02 5,06 3,95 3,01 1,98 1,03 RE (%) -1,1-2,0-2,0 0,4 1,3-1,2 0,3-0,8 3 (*) Co: Concentration in standard mixed solution; C: Determined concentration Table 3.4. The results of determination of TEL and HYD concentrations in the mixture by the Kalman method with the choice of the assumed initial value Option 2 (*) Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9 C TEL o (µg/ml) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 C (µg/ml) 0,30 0,30 0,31 0,31 0,32 0,35 0,38 0,42 0,48 9

12 HYD RE (%) -70,0-84,9-89,8-92,3-93,5-94,2-94,6-94,7-94,6 C o (µg/ml) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 C (µg/ml) 0,30 0,31 0,31 0,31 0,31 0,31 0,31 0,31 0,30 RE (%) -96,6-96,2-95,6-94,8-93,7-92,2-89,7-84,7-69,7 (*) Co: Concentration in standard mixed solution; C: Determined concentration The results in Table 3.3 and 3.4 show that: - According to option 1, the Kalman method gives reliable results on the concentration of substances in the mixture with the error of RE <3% (for both TEL and HYD). However, under this option, the implementation is quite complex and depends on two wavelengths selected to solve the equation that determines the initial concentration values. On the other hand, when applied in practice, due to the influence of the matrix, spectral measurements may have greater errors, this option can be much bigger. - According to option 2, the Kalman method yields large error results, although the initial covariance value is assumed to be more appropriate than the choice of the random variance (1) as in the case before (Section 3.1.1). - The above results allow us to comment that between concentration and variance, the initial value of the concentration plays a more important (or more decisive) role than the error of the final result (when determined in the Kalman). Obviously, there should be a more appropriate way to choose concentration values For the 3-constituent system AML, HYD ANG VAL Table 3.5. The result of determination of AML, HYD and VAL concentrations in the mixture by the Kalman method with a choice of assumed initial value Option 1 (*) Sign H1 H2 H3 H4 C o (µg/ml) 0,250 0,50 1,00 5,00 AML C (µg/ml) 1,731 0,478 0,530 5,032 RE (%) -30,8-4,5-47 0,6 C o (µg/ml) 0,325 0,65 1,30 5,00 HYD C (µg/ml) 2,794 0,495 1,610 5,910 RE (%) -14,0-23,8 23,85 18,2 C o (µg/ml) 4,00 8,00 16,00 5,00 VAL C (µg/ml) 4,796 11,053 29,067 3,949 RE (%) 19,9 38,2 81,7-21,03 10

13 (*) Co: Concentration in standard mixed solution; C: Determined concentration Table 3.6. The result of determination of AML, HYD and VAL concentrations in the mixture by the Kalman method with a choice of assumed initial value Option 2 (*) Mixture H1 H2 H3 H4 C o (µg/ml) 0,250 0,50 1,00 5,00 AML C (µg/ml) 0,300 0,300 0,282 0,477 RE (%) 20,0-40,0-71,8-90,5 C o (µg/ml) 0,325 0,65 1,30 5,00 HYD C (µg/ml) 0,301 0,304 0,368 0,443 RE (%) -7,4-53,2-71,7-91,1 C o (µg/ml) 4,00 8,00 16,00 5,00 VAL C (µg/ml) 0,319 0,454 0,542 0,289 RE (%) -92,0-94,3-96,6-94,2 (*) Co: Concentration in standard mixed solution; C: Determined concentration The results in Tables 3.5 and 3.6 show that: - According to option 1, except for AML in H2 and H4 mixtures (RE error of 4.5%), the remaining cases had a large error with RE of about 14% - 82%. Thus, different from the system two constituents (Their concentration just have error with RE<3%), for the system 3 constituents error is much larger. Obviously, as the number of constituents in the system increases, their interaction will be greater, this leads to solve system of 3 equations with 3 unknowns (concentration of substance in the system) will make bigger error. Obviously, option 1 only applies to the system 2 constituents. On the other hand, this option is also quite complex, since the error of the method depends on the wavelength chosen to establish and solve the equation. - According to option 2, it is similar to the case of the system two constituents, although the introduction of the initial value for the variance is more realistic (as estimated from the Horwitz equation). The error is very large with RE about 7% - 97%). At this point, we can see that both ways of selecting the initial value for concentration and variance - select a random initial value and set a assumed initial value - have not produced good results (or a large error), unless the initial value of the 11

14 concentration is randomly selected, or is calculated as option 1 (in the alternative way of assuming the initial value), close to the actual value of the concentration in the system. Obviously, there is a need for a different initial value, so that the initial concentration of the substance in the system is as close to its actual value as possible. Starting from the above reasons, it is necessary to propose a solution to choose a new initialization value to meet three requirements: - The initial concentration value is as close as possible to the actual value of the substance in the system; - The variance (or error) of the concentration should not be chosen randomly, but should be selected in accordance with international guidelines when determining a concentration of C, for example, based on Horwitz equation to estimate the initial variance value; - The proposed solution should be so easy to apply in practice when analyzing any mixture of substances, without prior knowledge of their concentration Select the approximate initial value - Apply the least squares method (abbreviated as BPTT) to solve m equations with unknown numbers (m is the number of wavelengths selected for scanning the optical absorption spectra of the mixture of constituents, n is the number of constituents in the system), using the Gaussian elimination method to introduce the system of equations into the form of n equations with n unknown; The equations of the system have the linear form of multiplicity and satisfy the positive properties of optical absorption [2]. The concentration of the components obtained from the solution of the equation is chosen as the initial value of C est(0); In this way, the estimated initial values are relatively close to the actual value of the concentration of the constituent in the system under investigation, regardless of whether the system has known the actual concentration (eg, the standard solution of a mixture of constituents) or unknown concentrations of the constituents in the system (eg, actual sample); 12

15 - Apply the Horwitz equation to estimate the value of the variance corresponding to the C concentration of each constituents in the system and accept the obtained value as the initial value for the variance for each P est(0); Value of variance P est(0) ) to the concentration C est(0) for each of the components in the system computed from the Horwitz equation as follows: - From the formula (3.1), S RSD Horwitz (%) = 100 Cest (0) 13 (3.1) Calculates the standard deviation S [RSD Horwitz*C est(0)]/100; Therein, RSD Horwitz is calculated by the formula (3.2), where C est(0) is expressed by a fraction lgC est ( 0) RSD Horwitz (%) = 2 (3.2) - From S, calculated the variance S 2 P est(0) For the 2-constituent system TEL and HYD Table 3.7. Results of determination of TEL and HYD concentrations in the mixture by Kalman method with selection of approximate initial value (*). Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9 C o (µg/ml) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00 TEL C (µg/ml) 0,99 1,99 2,95 3,88 5,03 6,07 7,18 7,99 9,00 RE (%) -0,9-0, , ,1 0 C o (µg/ml) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00 HYD C (µg/ml) 8,93 8,03 7,05 6,05 5,06 3,95 3,00 1,99 1,03 RE (%) -0,8 0,4 0,6 0,8 1,3-1,2 0 0,7 2,7 (*) Co: Concentration in standard mixed solution; C: Determined concentration The above results show that for all 9 mixes with a TEL / HYD concentration ratio (ppm/ppm) from 1/9 to 9/1, the Kalman method yields reliable results with error very small, RE 3% For the 3-constituent system AML, HYD and VAL Table 3.8. Results of determination of AML, HYD and VAL concentrations in the mixture by Kalman method with selection of approximate initial value (*) Mixture H1 H2 H3 H4 C AML o (µg/ml) 0,250 0,50 1,00 5,00 C (µg/ml) 0,253 0,511 1,016 4,981

16 HYD VAL RE (%) 1,2 2,2 1,6 0,4 C o (µg/ml) 0,325 0,65 1,30 5,00 C (µg/ml) 0,320 0,646 1,290 5,064 RE (%) -1,5-0,6-0,8 1,3 C o (µg/ml) 4,00 8,00 16,00 5,00 C (µg/ml) 3,99 8,06 16,05 4,821 RE (%) -0,2 0,8 0,3-3,6 (*) Co: Concentration in standard mixed solution; C: Determined concentration The results show that the method yields reliable results on the concentration of the three constituents in the system with a small error, RE 4 %. Thus, for both systems 2 and 3 constituents, the solution for selecting the approximate initial value gives more reliable results than the two options for selecting random and assumed initial values. However, to make a more certain assertion about the choice of approximate initial value as well as the advantage of the Kalman method (with that option), there should be comparative studies of the Kalman method with some Other traditional methods such as chemometric-photometry using the least squares algorithm (abbreviated as BPTT), derivative spectrophotometric method (abbreviated as PĐH) when determining the concentration of constituents in their mixture both in standard solution and actual sample (pharmaceutical form) COMPUTER PROGRAM FOR CALCULATING ACCORDING TO THE KALMAN FILTER ALGORITHM The calculation process is described in Figure 3.1: 14

17 Figure 3.1. The program computes diagram according to Kalman filter algorithms with an approximate initial value selection solution (applied to systems 2 and 3 constituents). The program allows to print results on the concentration of each component in the mixture and the relative error RE corresponding 3.3. VERIFY KALMAN METHOD FOR MIXTURE OF 2 CONSTITUENTS Verify method for the simultaneous determination of a mixture of two substances including Telmisartan (TEL) and Hydrochlorothiazide (HYD); Paracetamol (PAR) and Caffeine (CAF); Paracetamol (PAR) and Ibuprofen (IB). Use chemometric methods (Kalman method, BPTT and derivative) to calculate Spectral absorption spectrum and spectral derivative Survey results of the Spectral absorption spectrum and spectral derivative of the mixtures showed that the content of TEL and HYD, PAR and CAF, PAR and IB can be simultaneously determined by the spectral and spectral derivative methods Test method for laboratory standard solution Compare three chemometric-photometric methods 15

18 All three methods - the Kalman method, the BPTT method and the PĐH method are used to determine the concentration of substances (or constituents) in their mixture solution. The mixed solutions were prepared from laboratory standard solutions. The criteria for comparative assessment of the results of the three methods are relative error (RE). The results show that when determining the concentration of substances, for the Kalman filter the maximum error is -3.7% (when determining the IB in the PAR and IB mix), the smallest error is 0% (when determining the HYD in the TEL and HYD mixture); For the method of contraception, the maximum error is -3.7% (when determining IB in PAR and IB), the smallest error is 0% (when defining TEL in the TEL and HYD mixture); For the spectral derivative method, the maximum error is 4.0% (when determining IB in PAR and IB), the smallest error is 0.0% (when determining IB in the PAR mixture and IB). The methods for accepting results with small RE error (%) are good enough Repetition of the method when analyzing the laboratory standard solution The results show that RSD values of all substances in the range of 0.1 to 2% are less than ½ RSD H (5.3-8%). -> The methods of achieving good repeatability TEST METHOD WHEN DETERMINE THE CONCENTRATION SIMULTANEOUSLY THREE SUBSTANCES Because with the mixture of three substances to find the wavelength there the spectrum of a non-zero, and the spectrum of the two remaining 0 is very difficult. This is also a disadvantage of the spectral method. Therefore, in this section only the full spectrum and Kalman method results are calculated and the CLS method (Test with mixtures: Amlodipine (AML), hydrochlorothiazide (HYD), valsartan (VAL) Survey the absorption spectrum of the mixture 16

19 Results of absorption spectra of the mixtures showed that the content of AML, HYD and VAL can be simultaneously determined using the full spectrum spectrometric method Evaluate the reliability of the method when analyzing laboratory standard mixtures The error of the method The results showed that with different concentration ratios, the concentration of the standard solution and the determined concentration were limited to RE (%). For the Kalman filter, the smallest error was -3.6%, the maximum error was 2.2%; For the CLS method, the smallest error is -3.2%, the maximum error is 2.2%. The methods for accepting results with small error RE (%) have good accuracy Evaluate the repeatability of the method when analyzing the laboratory standard solution The results show that the RSD values of AML and VAL all three repeated measurements for samples from H1 to H4 were 0.4%, HYD from 0.4% to 0.5% <½ RSDH Methods achieving good repeatability (table 3.21). The mean concentrations of the three substances AML, HYD and VAL in H1 and H2 samples were calculated in the same way (p> 0.05). H3 and H4 concentrations were determined in two different ways (p <0.05). To assess whether these differences are statistically significant, use the t-test to compare the mean of the two methods, the results obtained in Tables 3.23 and 3.9. From Table 3.23 a paired-t-test was used to show that: When using two methods Kalman and BPTT to calculate the concentration of AML, HYD and VAL in the sample H4 has been collected ttính > tlt.thus, it can be concluded that the mean concentrations obtained from the two methods are significantly different (p <0.05).. 17

20 Table 3.9. Determination of repeatability of the method for AML, HYD and VAL mixtures H1 H2 H3 H4 Parameter AML HYD VAL Rep 1 Rep 2 Rep 3 Mean Rep 1 Rep 2 Rep 3 Mean Rep 1 Rep 2 Rep 3 Mean CK (µg/ml) 0,253 0,252 0,254 0,253 0,320 0,320 0,321 0,320 3,990 3,980 4,010 3,993 RSDK (%) 0,4 0,3 0,4 CS (µg/ml) 0,253 0,253 0,254 0,253 0,319 0,319 0,321 0,319 3,993 3,981 4,009 3,994 RSDS (%) 0,4 0,4 0,4 ½ RSDH 9,9 9,5 6,5 CK (µg/ml) 0,511 0,510 0,514 0,512 0,646 0,645 0,650 0,647 8,060 8,044 8,109 8,071 RSDK (%) 0,4 0,5 0,4 CS (µg/ml) 0,511 0,510 0,514 0,512 0,645 0,644 0,649 0,646 8,059 8,043 8,107 8,070 RSDS (%) 0,4 0,5 0,4 ½ RSDH 8,9 8,6 5,9 CK (µg/ml) 1,016 1,013 1,020 1,016 1,290 1,286 1,296 1,291 16,050 15,994 16,114 16,053 RSDK (%) 0,4 0,4 0,4 CS (µg/ml) 1,017 1,013 1,021 1,017 1,284 1,279 1,290 1,284 16,037 15,980 16,101 16,040 RSDS (%) 0,4 0,5 0,4 ½ RSDH 8,0 7,9 5,5 CK (µg/ml) 4,981 4,971 5,008 4,987 5,064 5,054 5,089 5,069 4,821 4,811 4,844 4,825 RSDK (%) 0,4 0,4 0,4 CS (µg/ml) 4,841 4,831 4,865 4,846 5,109 5,099 5,135 5,114 4,873 4,864 4,898 4,878 RSDS (%) 0,4 0,4 0,4 ½ RSDH 6,3 6,3 6,3 CK, RSDK: Concentration, repeatability calculated by Kalman method;; CS, RSDS: Concentration, repeatability calculated by Simulan method; 18

21 3.6. PRACTICAL APPLICATION Quality control analysis methods Repetition Survey results of samples containing mixtures TEL and HYD; PAR and CAF; PAR and IB; AML, HYD and VAL The RSD repeatability is: from 0,8 % to 5,7 %; from 0,3 % to 0,9 %; from 0,2 % to 1,2 %, from 2,2 % to 2,3 % ( < ½ RSD H). Thus, the analytical procedure was used to simultaneously determine the TEL and HYD in the sample for good repeatability Correctness Analysis standard template: Analysis results for the mixtures 2 constituents (TEL and HYD mixes, PAR and CAF mixes, PAR and IB mixes) and the mixtures 3 constituents (AML, HYD and VAL) showed that: Kalman method, least squares, universal derivative gain good enough with satisfactory recovery: According to AOAC (Association of Official Analytical Chemists), when analyzing concentration levels of 1 ppm - 10 ppm (ppm g / ml), if recovery is achieved in the range of %, is satisfactory. Specifically: Kalman and BPTT methods achieved a recovery of 90% (when determining AML in AML, HYD and VAL mixtures) to 107% (when determining IB in PAR and IB mix). The PĐH method achieves a recovery rate of 93% to 113% (when defining TEL in the TEL and HYD mix). Typically, AML recovery results in AML, HYD and VAL are shown in Table For a mixture of two substances: The repeatability of the three methods Kalman, BPTT, and PĐH (evaluated by S or S 2 ) are different, but they both achieve good (for both PAR and IB) when compared Compared to the HPLC method with p> For the mixture of three substances: the results of the Kalman and BPTT methods gave no statistically significant difference compared to the HPLC method (because the t stat values were less than the t critical p> 0.30). However, based on p (statistically significant) values, it can be observed that the Kalman method is closer to the results of the HPLC method (p = ) than With the BPTT method (p = ) or in other words, the Kalman method achieves better accuracy than the BPTT method (when compared to the HPLC method) 19

22 Table The results confirm the accuracy of the method when analyzing the actual sample of Exforge (*) Sample Sample B1 Sample B2 Sample B3 Method Kalman BPTT Kalman BPTT Kalman BPTT Ct (µg/ml) AML HYD VAL Cx (µg/ml) Rev (%) Ct (µg/ml) Cx (µg/ml) Rev (%) Ct (µg/ml) Cx (µg/ml) 0 0, , ,997 0,25 1,200 94,0 0,30 1,451 94,3 4,0 21, ,9 0,50 1,415 90,0 0,60 1,710 90,3 8,0 24,876 98,5 0 0, , ,086 0,25 1,202 94,0 0,30 1,457 95,3 4,0 21, ,1 0,50 1,418 90,2 0,60 1,719 91,3 8,0 25,067 99,8 0 0, , ,249 0,25 1,214 93,6 0,30 1,470 94,7 4,0 21, ,9 0,50 1,450 94,0 0,60 1,759 95,5 8,0 25, ,1 0 0, , ,340 0,25 1,217 94,4 0,30 1,474 95,0 4,0 21, ,2 0,50 1,454 94,6 0,60 1,762 95,5 8,0 25, ,5 0 0, , ,506 0,25 1,171 93,6 0,30 1,416 95,0 4,0 20, ,4 0,50 1,397 92,0 0,60 1,698 94,5 8,0 24, ,8 0 0, , ,589 0,25 1,173 93,6 0,30 1,422 95,0 4,0 20, ,7 0,50 1,400 92,2 0,60 1,697 93,3 8,0 24, ,1 RevTB (%)-Kalman 92,9 94,0 101,8 RevTB (%)-BPTT 93,2 94,2 103,0 (*) Co: Concentration in the sample (μg / ml) (AML: HYD: VAL is 1.0: 1.25: 16) Rev (%) 20

23 Tóm tắt Luận án Tiến sĩ Nguyễn Thị Quỳnh Trang Compared to the HPLC method: Table Comparison of chemometric methods with HPLC method for determining the content of AML, HYD and VAL in Exforge HCT(*) analytical substance AML HYD VAL Statistics Analytical methods Kalman BPTT HPLC xi (mg/tablet) 9,65/9,80/9,37 9,67/9,81/9,39 9,54/9,41/9,59 TB (mg/tablet) 9,61 9,62 9,51 S (mg/tablet) 0,22 0,21 0,09 Fexp/ F(0,05;2;2) 5,30/19 5,30/19 Sp 0,16 0,16 Texp/ t(0,05; f) 0,53/4,3 0,63/4,3 P 0,65 0,59 xi (mg/tablet) 11,68/11,86/11,34 11,71/11,89/11,37 11,72/11,76/11,41 TB (mg/tablet) 11,66 11,66 11,63 S (mg/tablet) 0,26 0,26 0,19 Fexp/ F(0,05;2;2) 1,9/19 1,9/19 Sp 0,34 0,34 texp/ t(0,05; f) -0,06/4,3 0,51/4,3 P 0,96 0,66 xi (mg/tablet) 169,97/172,49/ 170,86/173,40/ 166,35/168,81/ 165,06 165,89 167,82 TB (mg/tablet) 169,17 167,66 S (mg/tablet) 3,78 3,82 1,24 Fexp/ F(0,05;2;2) 9,32/19 9,5/9 Sp 0,10 0,10 texp/ t(0,05; f) 0,71/4,30 1,11/4,30 P 0,55 0,38 (*) The results of the analysis are repeated (i = 1-3); Fexp = Variance of the Kalman method (or BPTT)/ Variance of the HPLC method; F(0,05;2;2): The critical value of F is 0.05 and the 2 degrees of freedom of the two numerator and denominator variants; Sp: pooled variance, calculated from two covariates of two methods when two covariates of the two methods are the same (ie when Ftính< F(0,05;2;2)); t (0.05; f = 4): The critical value of t is statistically significant p = 0.05 and the degree of freedom f = 4. CONCLUSION From the results of theoretical and empirical research, the thesis has the following main conclusions: 21

24 Tóm tắt Luận án Tiến sĩ Nguyễn Thị Quỳnh Trang 1) Based on the survey of options for initial values for the Kalman filter algorithm, a new solution has been found for the first time - selecting the approximate initial value of the concentration (by means of the quadratic least squares) and variance (calculated by the Horwitz equation). This new solution allows for the convenient application of the chemometric-photometric method using the Kalman filter algorithm (Kalman method) to simultaneously determine two or three substances with an opaque absorption spectrophotometer in their mixture. 2) Kalman method test results for three standard solutions (two solutions containing each) and a mixture of three substances (molecular absorption overlapping) showed that when the measurement of optical absorption has a significant error (or large measurement noise), especially for a mixture containing three substances, the Kalman method is less error-prone and has a better repeatability than the least squares method using the full spectrum. 3) It was first established the process of analyzing concurrent photocatalytic absorption spectrometry in multi-component pharmaceutical formulations containing two or three active ingredients by the Kalman method. On the other hand, a computer program that uses the Visual Basic for Applications programming language is included in the Microsoft software - Excel 2016, which is included in the analysis and thus allows for quick and convenient calculations when applied. Practical testing of pharmaceuticals in our laboratories. The process is not only simpler to implement, but also reduces the cost of analysis compared to the standard method of High Performance Liquid Chromatography (HPLC). (4) Correctness and repeatability of the analytical process (or methodology) was examined when analyzing drug samples containing two or three active subtances (active substances with molecular absorption overlapping): For drugs containing two active subtances, the method was well tolerated with recovery of 93% - 102% and good repetition with RSD <2.5% (n = 3); For drugs containing 3 active substances, the method also achieved good accuracy with recovery of 90% - 107% and good repetition with RSD <3.5% (n = 3). Compared with standard HPLC methods, the Kalman method achieved good accuracy (p <0.05) when analyzing drugs containing two or three components. 22

25 Tóm tắt Luận án Tiến sĩ Nguyễn Thị Quỳnh Trang 5) A constructional analysis procedure has been applied to determine concurrently the mixture of 2 or 3 active substances with absorption spectra interlaced in some multi-component drugs currently circulating on the market, different types of drugs: blood pressure, antipyretic and analgesic, cardiovascular medication. In particular, the Kalman method first identified three active substances (AML, HYD and VAL) in Exforge HTC and achieved good repeatability and accuracy, not inferior to other methods of are using today. This will contribute positively to the field of pharmaceutical testing in our country. THE LIST OF PUBLISHED RESEARCH RESULTS [1] Nguyễn Thị Quỳnh Trang, Trâ n Thu c Bi nh, Châu Viết Tha ch (2017). Xác định đô ng thơ i Paracetamol va Cafein trong hô n hơ p bă ng phương pháp trắc quang kết hơ p thuật toán lo c Kalman, Ta p chi phân ti ch ho a, ly va sinh ho c, T-22, tr [2], Tran Thuc Binh, Vo Thi Kim Truc, Ngo Van Tu (2017). Simultaneous determination of telmiasartan and hydrochlorothiazide in pharamacy by full spectrum spectrophometric method using Kalman filter algorithm, Conference proceeding, The 5th Analytical Vietnam Conference 2017, pp [3] Tran Thuc Binh,, Vo Thi Kim Truc, Ngo Van Tu (2017). Simultaneous spectrophotometric determination of telmiasartan and hydrochlorothiazide in pharamaceutical product by least-square method using full spectra, Conference proceeding, The 5 th Analytica Vietnam Conference 2017, pp [4] Nguyễn Thị Quỳnh Trang, Trâ n Thu c Bi nh, Ngô Văn Tứ (2017). Xác định đô ng thơ i amlodipine, hydrochlorothiazide va valsartan trong dươ c phẩm bă ng phương pháp trắc quangchemometric dùng phổ toa n phâ n. Ta p chi Khoa ho c - Khoa ho c Tự nhiên, Đa i ho c Huế, 126(1D), tr [5] Trâ n Thu c Bi nh, Nguyễn Thị Quỳnh Trang, Nguyễn Thị Hô ng Vân (2017). Xác định đô ng thơ i Paracetamol va Ibuprofen trong dươ c phẩm bă ng phương pháp quang phổ đa o ha m, Ta p chi phân ti ch ho a, ly va sinh ho c, T-22, tr

26 Tóm tắt Luận án Tiến sĩ Nguyễn Thị Quỳnh Trang [6] Nguyễn Thị Quỳnh Trang, Trâ n Thu c Bi nh, Nguyễn Thị Hô ng Vân (2017). Xác định đô ng thơ i paracetamol va ibuprofen trong dươ c phẩm bă ng phương pháp trắc quang phổ toa n phâ n dùng thuật toán lo c Kalman. Ta p chi Khoa ho c va Công nghệ, Chuyên san Khoa ho c Tự nhiên, Kỹ thuật va Công nghệ, Trường Đa i ho c Khoa ho c, Đa i ho c Huế, 11(1), tr