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 - 2018

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: 62 44 01 18

THE ABSTRACT OF DOCTORAL DISSERTATION

SCIENTIFIC SUPERVISORS:

1. Assoc.Prof.Dr. TRAN THUC BINH

2. Assoc.Prof.Dr. NGO VAN TU

HUE - 2018

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

+ 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):

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

2.2. METHODOLOGY

2.2.1. 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 ε (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 ) = Cest ( k −1)

(2.1)

- Extrapolation of the covariance of the error:

(2.2)

Ppri( k ) = Pest ( k −1)

- Calculation Kalman Loop:

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

(

K(k ) = Ppri(k )εT (k ) ε(k ) Ppri(k)εT (k ) + R(k )

−1

)

(2.3)

- Updated status estimate:

(

Cest (k ) = C pri( k ) + K(k ) A( k ) − ε(k )C pri( k )

)

(2.4)

- Update the covariance of the error:

Pest ( k ) = INV − ε( k ) K ( k ) Ppri ( 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.

2.2.2. 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 ε of the

constituents: ε= (εij )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 = ε. C to find the concentration of C.

2.2.3. 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.

2.2.4. Computer programming method

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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;

2.2.5. 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

3.1.1. Select a random initial value

In this way, selecting a random initial value can select any

P

C

value for the concentration est (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

Cest (0) = 0,3 µg/mL and variance Pest (0) = 1.

Table 3.1. Results of determination of TEL and HYD

concentration in Kalman method with with random selection of

initial value (*)

Mixture

Co

(µg/mL)

TEL

C

(µg/mL)

RE (%)

Co

HYD

(µg/mL)

H1

H2

H3

H4

H5

H6

H7

H8

H9

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

-70

-85

-90

-93

-94

-95

-96

-96

-97

9,00

8,00

7,00

6,00

5,00

4,00

3,00

2,00

1,00

7

The abstract of doctoral dissertation

C

(µg/mL)

RE(%)

(*)

Nguyen Thi Quynh Trang

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

-97

-96

-96

-95

-94

-93

-90

-85

-70

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% - 96.7%). 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

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

0,300

20

0,325

0,307

-6

4,00

0,301

-93

H2

0,50

0,300

-40

0,65

0,304

-53

8,00

0,300

-97

H3

1,00

0,300

-70

1,30

0,302

-77

16,00

0,300

-98

H4

5,00

0,304

-94

5,00

0,299

-94

5,00

0,299

-94

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% - 98.1%). The lowest RE

value (-5.5%) corresponds to the standard concentration of

0.325 (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..

3.1.2. 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)

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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 =

3.10-7, calculate the variance by 0.003 and select this value as

the initial value.

3.1.2.1. 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 - 340 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

TEL

HYD

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

1,00

0,99

-0,9

9,00

8,91

-1,1

H2

2,00

1,99

-0,6

8,00

7,84

-2,0

H3

3,00

2,95

-2

7,00

6,86

-2,0

H4

4,00

3,88

-3

6,00

6,02

0,4

H5

5,00

5,03

-0,6

5,00

5,06

1,3

H6

6,00

6,07

1

4,00

3,95

-1,2

H7

7,00

7,18

3

3,00

3,01

0,3

H8

8,00

7,99

-0,1

2,00

1,98

-0,8

H9

9,00

9,00

0

1,00

1,03

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

TEL

Co (µg/mL)

C (µg/mL)

H1

1,00

0,30

H2

2,00

0,30

H3

3,00

0,31

H4

4,00

0,31

9

H5

5,00

0,32

H6

6,00

0,35

H7

7,00

0,38

H8

8,00

0,42

H9

9,00

0,48

The abstract of doctoral dissertation

HYD

(*)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

-70,0 -84,9 -89,8

9,00 8,00 7,00

0,30 0,31 0,31

-96,6 -96,2 -95,6

Nguyen Thi Quynh Trang

-92,3

6,00

0,31

-94,8

-93,5

5,00

0,31

-93,7

-94,2 -94,6 -94,7 -94,6

4,00 3,00 2,00 1,00

0,31 0,31 0,31 0,30

-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.

3.1.2.2. 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

AML

HYD

VAL

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

1,731

-30,8

0,325

2,794

-14,0

4,00

4,796

19,9

H2

0,50

0,478

-4,5

0,65

0,495

-23,8

8,00

11,053

38,2

10

H3

1,00

0,530

-47

1,30

1,610

23,85

16,00

29,067

81,7

H4

5,00

5,032

0,6

5,00

5,910

18,2

5,00

3,949

-21,03

The abstract of doctoral dissertation

(*)

Nguyen Thi Quynh Trang

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

AML

HYD

VAL

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

0,300

20,0

0,325

0,301

-7,4

4,00

0,319

-92,0

H2

0,50

0,300

-40,0

0,65

0,304

-53,2

8,00

0,454

-94,3

H3

1,00

0,282

-71,8

1,30

0,368

-71,7

16,00

0,542

-96,6

H4

5,00

0,477

-90,5

5,00

0,443

-91,1

5,00

0,289

-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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.1.3. 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

Cest(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);

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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 Pest(0); Value of variance

Pest(0) ) to the concentration Cest(0) for each of the components in

the system computed from the Horwitz equation as follows:

- From the formula (3.1),

R S D H o r w itz (% ) =

S

× 100

C est(0 )

(3.1)

Calculates the standard deviation S = [RSDHorwitz*Cest(0)]/100;

Therein, RSDHorwitz is calculated by the formula (3.2),

where Cest(0) is expressed by a fraction.

R S D H o r w i t z (% ) = 2

1− 0 . 5 l g C est ( 0 )

(3.2)

- From S, calculated the variance S2 = Pest(0).

3.1.3.1. 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

TEL

HYD

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

1,00

0,99

-0,9

9,00

8,93

-0,8

H2

2,00

1,99

-0,6

8,00

8,03

0,4

H3

3,00

2,95

-2

7,00

7,05

0,6

H4

4,00

3,88

-3

6,00

6,05

0,8

H5

5,00

5,03

-0,6

5,00

5,06

1,3

H6

6,00

6,07

1

4,00

3,95

-1,2

H7

7,00

7,18

3

3,00

3,00

0

H8

8,00

7,99

-0,1

2,00

1,99

0,7

H9

9,00

9,00

0

1,00

1,03

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%.

3.1.3.2. 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

AML

Co (µg/mL)

C (µg/mL)

H1

0,250

0,253

H2

0,50

0,511

13

H3

1,00

1,016

H4

5,00

4,981

The abstract of doctoral dissertation

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

HYD

VAL

(*)

1,2

0,325

0,320

-1,5

4,00

3,99

-0,2

Nguyen Thi Quynh Trang

2,2

0,65

0,646

-0,6

8,00

8,06

0,8

1,6

1,30

1,290

-0,8

16,00

16,05

0,3

0,4

5,00

5,064

1,3

5,00

4,821

-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).

3.2. COMPUTER PROGRAM FOR CALCULATING

ACCORDING

TO

THE

KALMAN

FILTER

ALGORITHM

The calculation process is described in Figure 3.1:

14

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.3.1. 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

3.3.2. Test method for laboratory standard solution

3.3.2.1. Compare three chemometric-photometric methods

15

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.3.2.2. 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 RSDH (5.3 - 8%). -> The

methods of achieving good repeatability.

3.4. 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).

3.4.1. Survey the absorption spectrum of the mixture

16

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.4.2. Evaluate the reliability of the method when analyzing

laboratory standard mixtures.

3.4.2.1. 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.

3.4.2.2. 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

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

Table 3.9. Determination of repeatability of the method for AML, HYD and VAL mixtures

AML

Parameter

H1

H2

H3

H4

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

Rep 1

Rep 2

0,253

0,252

HYD

Rep 3

Mean

Rep 1

Rep 2

0,254

0,253

0,320

0,320

0,4

0,253

0,253

0,254

0,510

0,253

0,319

0,319

0,514

0,510

0,512

0,646

0,512

0,645

1,016

1,290

1,017

1,284

4,831

3,993

3,981

4,987

5,064

4,846

5,109

4,009

3,994

0,647

8,060

8,044

8,109

8,071

0,646

8,059

8,043

8,107

8,070

1,291

16,050

15,994

16,114

16,053

16,101

16,040

4,844

4,825

4,898

4,878

0,4

1,284

16,037

15,980

0,4

5,5

5,069

4,821

4,811

0,4

5,135

0,4

6,3

3,993

0,4

5,9

5,089

5,099

4,010

0,4

1,290

5,054

Mean

0,4

6,5

0,4

4,865

0,4

6,3

0,319

0,5

7,9

5,008

Rep 3

0,4

1,296

1,279

0,4

4,841

3,980

0,4

1,021

4,971

3,990

0,649

1,286

0,4

8,0

4,981

0,320

0,5

8,6

1,020

1,013

0,321

0,650

0,644

0,4

1,017

Rep 2

0,5

0,514

1,013

Rep 1

0,321

0,645

0,4

8,9

1,016

Mean

0,4

9,5

0,4

0,511

Rep 3

0,3

0,4

9,9

0,511

VAL

5,114

4,873

4,864

0,4

6,3

CK, RSDK: Concentration, repeatability calculated by Kalman method;; CS, RSDS: Concentration, repeatability calculated by Simulan method;

18

3.6. PRACTICAL APPLICATION

3.6.1. Quality control analysis methods

3.6.1.1. 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 RSDH). Thus, the analytical procedure was used to

simultaneously determine the TEL and HYD in the sample for good

repeatability.

3.6.1.2. 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 80-110%, 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 3.40.

For a mixture of two substances: The repeatability of the three

methods Kalman, BPTT, and PĐH (evaluated by S or S2) are

different, but they both achieve good (for both PAR and IB) when

compared Compared to the HPLC method with p> 0.05.

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 tstat values were less

than the tcritical 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 = 0.55 - 0.96) than With

the BPTT method (p = 0.38 - 0.66) or in other words, the Kalman

method achieves better accuracy than the BPTT method (when

compared to the HPLC method)

19

Table 3.40. The results confirm the accuracy of the method when analyzing the actual sample of Exforge (*)

AML

Sample

Method

Ct

Cx

(µg/mL) (µg/mL)

HYD

Rev

(%)

Ct

(µg/mL)

Cx

(µg/mL)

0,965

0

1,168

1,200

94,0

0,30

1,451

Sample

1,415

90,0

0,60

1,710

B1

0,967

0

1,171

BPTT

1,202

94,0

0,30

1,457

1,418

90,2

0,60

1,719

0,980

0

1,186

Kalman

1,214

93,6

0,30

1,470

Sample

1,450

94,0

0,60

1,759

B2

0,981

0

1,189

BPTT

1,217

94,4

0,30

1,474

1,454

94,6

0,60

1,762

0,937

0

1,134

Kalman

1,171

93,6

0,30

1,416

Sample

1,397

92,0

0,60

1,698

B3

0,939

0

1,137

BPTT

1,173

93,6

0,30

1,422

1,400

92,2

0,60

1,697

RevTB (%)-Kalman

92,9

94,0

RevTB (%)-BPTT

93,2

94,2

(*)

Co: Concentration in the sample (µg / mL) (AML: HYD: VAL is 1.0: 1.25: 16)

Kalman

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

20

VAL

Rev

(%)

94,3

90,3

95,3

91,3

94,7

95,5

95,0

95,5

95,0

94,5

95,0

93,3

Ct

(µg/mL)

Cx

(µg/mL)

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

16,997

21,112

24,876

17,086

21,251

25,067

17,249

21,363

25,497

17,340

21,505

25,697

16,506

20,603

24,567

16,589

20,736

24,754

101,8

103,0

Rev

(%)

102,9

98,5

104,1

99,8

102,9

103,1

104,2

104,5

102,4

100,8

103,7

102,1

Tóm tắt Luận án Tiến sĩ

Nguyễn Thị Quỳnh Trang

Compared to the HPLC method:

Table 3.41. Comparison of chemometric methods with HPLC method

for determining the content of AML, HYD and VAL in Exforge

HCT(*)

analytical

substance

AML

HYD

Statistics

xi (mg/tablet)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

Texp/ t(0,05; f)

P

xi (mg/tablet)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

texp/ t(0,05; f)

P

xi (mg/tablet)

VAL

(*)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

texp/ t(0,05; f)

P

Analytical methods

Kalman

BPTT

HPLC

9,65/9,80/9,37

9,67/9,81/9,39

9,54/9,41/9,59

9,61

9,62

9,51

0,22

0,21

0,09

5,30/19

5,30/19

0,16

0,16

0,53/4,3

0,63/4,3

0,65

0,59

11,68/11,86/11,34 11,71/11,89/11,37 11,72/11,76/11,41

11,66

11,66

11,63

0,26

0,26

0,19

1,9/19

1,9/19

0,34

0,34

-0,06/4,3

0,51/4,3

0,96

0,66

169,97/172,49/

170,86/173,40/

166,35/168,81/

165,06

165,89

167,82

169,17

167,66

3,78

3,82

1,24

9,32/19

9,5/9

0,10

0,10

0,71/4,30

1,11/4,30

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

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

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, Trần Thúc Bình, Châu Viết Thạch

(2017). Xác định đồng thời Paracetamol và Cafein trong hỗn hợp

bằng phương pháp trắc quang kết hợp thuật toán lọc Kalman, Tạp

chí phân tích hóa, lý và sinh học, T-22, tr.14-21.

[2] Nguyen Thi Quynh Trang, 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.22-29.

[3] Tran Thuc Binh, Nguyen Thi Quynh Trang, 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 5th Analytica Vietnam

Conference 2017, pp.14-21.

[4] Nguyễn Thị Quỳnh Trang, Trần Thúc Bình, Ngô Văn Tứ

(2017). Xác định đồng thời amlodipine, hydrochlorothiazide và

valsartan trong dược phẩm bằng phương pháp trắc quangchemometric dùng phổ toàn phần. Tạp chí Khoa học - Khoa học

Tự nhiên, Đại học Huế, 126(1D), tr.125-137.

[5] Trần Thúc Bình, Nguyễn Thị Quỳnh Trang, Nguyễn Thị Hồng Vân

(2017). Xác định đồng thời Paracetamol và Ibuprofen trong dược

phẩm bằng phương pháp quang phổ đạo hàm, Tạp chí phân tích hóa,

lý và sinh học, T-22, tr.8-16.

23

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 - 2018

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: 62 44 01 18

THE ABSTRACT OF DOCTORAL DISSERTATION

SCIENTIFIC SUPERVISORS:

1. Assoc.Prof.Dr. TRAN THUC BINH

2. Assoc.Prof.Dr. NGO VAN TU

HUE - 2018

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

+ 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):

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

2.2. METHODOLOGY

2.2.1. 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 ε (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 ) = Cest ( k −1)

(2.1)

- Extrapolation of the covariance of the error:

(2.2)

Ppri( k ) = Pest ( k −1)

- Calculation Kalman Loop:

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

(

K(k ) = Ppri(k )εT (k ) ε(k ) Ppri(k)εT (k ) + R(k )

−1

)

(2.3)

- Updated status estimate:

(

Cest (k ) = C pri( k ) + K(k ) A( k ) − ε(k )C pri( k )

)

(2.4)

- Update the covariance of the error:

Pest ( k ) = INV − ε( k ) K ( k ) Ppri ( 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.

2.2.2. 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 ε of the

constituents: ε= (εij )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 = ε. C to find the concentration of C.

2.2.3. 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.

2.2.4. Computer programming method

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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;

2.2.5. 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

3.1.1. Select a random initial value

In this way, selecting a random initial value can select any

P

C

value for the concentration est (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

Cest (0) = 0,3 µg/mL and variance Pest (0) = 1.

Table 3.1. Results of determination of TEL and HYD

concentration in Kalman method with with random selection of

initial value (*)

Mixture

Co

(µg/mL)

TEL

C

(µg/mL)

RE (%)

Co

HYD

(µg/mL)

H1

H2

H3

H4

H5

H6

H7

H8

H9

1,00

2,00

3,00

4,00

5,00

6,00

7,00

8,00

9,00

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

-70

-85

-90

-93

-94

-95

-96

-96

-97

9,00

8,00

7,00

6,00

5,00

4,00

3,00

2,00

1,00

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The abstract of doctoral dissertation

C

(µg/mL)

RE(%)

(*)

Nguyen Thi Quynh Trang

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

0,30

-97

-96

-96

-95

-94

-93

-90

-85

-70

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% - 96.7%). 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

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

0,300

20

0,325

0,307

-6

4,00

0,301

-93

H2

0,50

0,300

-40

0,65

0,304

-53

8,00

0,300

-97

H3

1,00

0,300

-70

1,30

0,302

-77

16,00

0,300

-98

H4

5,00

0,304

-94

5,00

0,299

-94

5,00

0,299

-94

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% - 98.1%). The lowest RE

value (-5.5%) corresponds to the standard concentration of

0.325 (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..

3.1.2. 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)

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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 =

3.10-7, calculate the variance by 0.003 and select this value as

the initial value.

3.1.2.1. 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 - 340 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

TEL

HYD

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

1,00

0,99

-0,9

9,00

8,91

-1,1

H2

2,00

1,99

-0,6

8,00

7,84

-2,0

H3

3,00

2,95

-2

7,00

6,86

-2,0

H4

4,00

3,88

-3

6,00

6,02

0,4

H5

5,00

5,03

-0,6

5,00

5,06

1,3

H6

6,00

6,07

1

4,00

3,95

-1,2

H7

7,00

7,18

3

3,00

3,01

0,3

H8

8,00

7,99

-0,1

2,00

1,98

-0,8

H9

9,00

9,00

0

1,00

1,03

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

TEL

Co (µg/mL)

C (µg/mL)

H1

1,00

0,30

H2

2,00

0,30

H3

3,00

0,31

H4

4,00

0,31

9

H5

5,00

0,32

H6

6,00

0,35

H7

7,00

0,38

H8

8,00

0,42

H9

9,00

0,48

The abstract of doctoral dissertation

HYD

(*)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

-70,0 -84,9 -89,8

9,00 8,00 7,00

0,30 0,31 0,31

-96,6 -96,2 -95,6

Nguyen Thi Quynh Trang

-92,3

6,00

0,31

-94,8

-93,5

5,00

0,31

-93,7

-94,2 -94,6 -94,7 -94,6

4,00 3,00 2,00 1,00

0,31 0,31 0,31 0,30

-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.

3.1.2.2. 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

AML

HYD

VAL

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

1,731

-30,8

0,325

2,794

-14,0

4,00

4,796

19,9

H2

0,50

0,478

-4,5

0,65

0,495

-23,8

8,00

11,053

38,2

10

H3

1,00

0,530

-47

1,30

1,610

23,85

16,00

29,067

81,7

H4

5,00

5,032

0,6

5,00

5,910

18,2

5,00

3,949

-21,03

The abstract of doctoral dissertation

(*)

Nguyen Thi Quynh Trang

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

AML

HYD

VAL

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

0,250

0,300

20,0

0,325

0,301

-7,4

4,00

0,319

-92,0

H2

0,50

0,300

-40,0

0,65

0,304

-53,2

8,00

0,454

-94,3

H3

1,00

0,282

-71,8

1,30

0,368

-71,7

16,00

0,542

-96,6

H4

5,00

0,477

-90,5

5,00

0,443

-91,1

5,00

0,289

-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

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.1.3. 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

Cest(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);

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The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

- 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 Pest(0); Value of variance

Pest(0) ) to the concentration Cest(0) for each of the components in

the system computed from the Horwitz equation as follows:

- From the formula (3.1),

R S D H o r w itz (% ) =

S

× 100

C est(0 )

(3.1)

Calculates the standard deviation S = [RSDHorwitz*Cest(0)]/100;

Therein, RSDHorwitz is calculated by the formula (3.2),

where Cest(0) is expressed by a fraction.

R S D H o r w i t z (% ) = 2

1− 0 . 5 l g C est ( 0 )

(3.2)

- From S, calculated the variance S2 = Pest(0).

3.1.3.1. 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

TEL

HYD

(*)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

H1

1,00

0,99

-0,9

9,00

8,93

-0,8

H2

2,00

1,99

-0,6

8,00

8,03

0,4

H3

3,00

2,95

-2

7,00

7,05

0,6

H4

4,00

3,88

-3

6,00

6,05

0,8

H5

5,00

5,03

-0,6

5,00

5,06

1,3

H6

6,00

6,07

1

4,00

3,95

-1,2

H7

7,00

7,18

3

3,00

3,00

0

H8

8,00

7,99

-0,1

2,00

1,99

0,7

H9

9,00

9,00

0

1,00

1,03

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%.

3.1.3.2. 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

AML

Co (µg/mL)

C (µg/mL)

H1

0,250

0,253

H2

0,50

0,511

13

H3

1,00

1,016

H4

5,00

4,981

The abstract of doctoral dissertation

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

Co (µg/mL)

C (µg/mL)

RE (%)

HYD

VAL

(*)

1,2

0,325

0,320

-1,5

4,00

3,99

-0,2

Nguyen Thi Quynh Trang

2,2

0,65

0,646

-0,6

8,00

8,06

0,8

1,6

1,30

1,290

-0,8

16,00

16,05

0,3

0,4

5,00

5,064

1,3

5,00

4,821

-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).

3.2. COMPUTER PROGRAM FOR CALCULATING

ACCORDING

TO

THE

KALMAN

FILTER

ALGORITHM

The calculation process is described in Figure 3.1:

14

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.3.1. 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

3.3.2. Test method for laboratory standard solution

3.3.2.1. Compare three chemometric-photometric methods

15

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.3.2.2. 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 RSDH (5.3 - 8%). -> The

methods of achieving good repeatability.

3.4. 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).

3.4.1. Survey the absorption spectrum of the mixture

16

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

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.

3.4.2. Evaluate the reliability of the method when analyzing

laboratory standard mixtures.

3.4.2.1. 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.

3.4.2.2. 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

The abstract of doctoral dissertation

Nguyen Thi Quynh Trang

Table 3.9. Determination of repeatability of the method for AML, HYD and VAL mixtures

AML

Parameter

H1

H2

H3

H4

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

CK (µg/mL)

RSDK (%)

CS (µg/mL)

RSDS (%)

½ RSDH

Rep 1

Rep 2

0,253

0,252

HYD

Rep 3

Mean

Rep 1

Rep 2

0,254

0,253

0,320

0,320

0,4

0,253

0,253

0,254

0,510

0,253

0,319

0,319

0,514

0,510

0,512

0,646

0,512

0,645

1,016

1,290

1,017

1,284

4,831

3,993

3,981

4,987

5,064

4,846

5,109

4,009

3,994

0,647

8,060

8,044

8,109

8,071

0,646

8,059

8,043

8,107

8,070

1,291

16,050

15,994

16,114

16,053

16,101

16,040

4,844

4,825

4,898

4,878

0,4

1,284

16,037

15,980

0,4

5,5

5,069

4,821

4,811

0,4

5,135

0,4

6,3

3,993

0,4

5,9

5,089

5,099

4,010

0,4

1,290

5,054

Mean

0,4

6,5

0,4

4,865

0,4

6,3

0,319

0,5

7,9

5,008

Rep 3

0,4

1,296

1,279

0,4

4,841

3,980

0,4

1,021

4,971

3,990

0,649

1,286

0,4

8,0

4,981

0,320

0,5

8,6

1,020

1,013

0,321

0,650

0,644

0,4

1,017

Rep 2

0,5

0,514

1,013

Rep 1

0,321

0,645

0,4

8,9

1,016

Mean

0,4

9,5

0,4

0,511

Rep 3

0,3

0,4

9,9

0,511

VAL

5,114

4,873

4,864

0,4

6,3

CK, RSDK: Concentration, repeatability calculated by Kalman method;; CS, RSDS: Concentration, repeatability calculated by Simulan method;

18

3.6. PRACTICAL APPLICATION

3.6.1. Quality control analysis methods

3.6.1.1. 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 RSDH). Thus, the analytical procedure was used to

simultaneously determine the TEL and HYD in the sample for good

repeatability.

3.6.1.2. 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 80-110%, 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 3.40.

For a mixture of two substances: The repeatability of the three

methods Kalman, BPTT, and PĐH (evaluated by S or S2) are

different, but they both achieve good (for both PAR and IB) when

compared Compared to the HPLC method with p> 0.05.

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 tstat values were less

than the tcritical 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 = 0.55 - 0.96) than With

the BPTT method (p = 0.38 - 0.66) or in other words, the Kalman

method achieves better accuracy than the BPTT method (when

compared to the HPLC method)

19

Table 3.40. The results confirm the accuracy of the method when analyzing the actual sample of Exforge (*)

AML

Sample

Method

Ct

Cx

(µg/mL) (µg/mL)

HYD

Rev

(%)

Ct

(µg/mL)

Cx

(µg/mL)

0,965

0

1,168

1,200

94,0

0,30

1,451

Sample

1,415

90,0

0,60

1,710

B1

0,967

0

1,171

BPTT

1,202

94,0

0,30

1,457

1,418

90,2

0,60

1,719

0,980

0

1,186

Kalman

1,214

93,6

0,30

1,470

Sample

1,450

94,0

0,60

1,759

B2

0,981

0

1,189

BPTT

1,217

94,4

0,30

1,474

1,454

94,6

0,60

1,762

0,937

0

1,134

Kalman

1,171

93,6

0,30

1,416

Sample

1,397

92,0

0,60

1,698

B3

0,939

0

1,137

BPTT

1,173

93,6

0,30

1,422

1,400

92,2

0,60

1,697

RevTB (%)-Kalman

92,9

94,0

RevTB (%)-BPTT

93,2

94,2

(*)

Co: Concentration in the sample (µg / mL) (AML: HYD: VAL is 1.0: 1.25: 16)

Kalman

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

0

0,25

0,50

20

VAL

Rev

(%)

94,3

90,3

95,3

91,3

94,7

95,5

95,0

95,5

95,0

94,5

95,0

93,3

Ct

(µg/mL)

Cx

(µg/mL)

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

0

4,0

8,0

16,997

21,112

24,876

17,086

21,251

25,067

17,249

21,363

25,497

17,340

21,505

25,697

16,506

20,603

24,567

16,589

20,736

24,754

101,8

103,0

Rev

(%)

102,9

98,5

104,1

99,8

102,9

103,1

104,2

104,5

102,4

100,8

103,7

102,1

Tóm tắt Luận án Tiến sĩ

Nguyễn Thị Quỳnh Trang

Compared to the HPLC method:

Table 3.41. Comparison of chemometric methods with HPLC method

for determining the content of AML, HYD and VAL in Exforge

HCT(*)

analytical

substance

AML

HYD

Statistics

xi (mg/tablet)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

Texp/ t(0,05; f)

P

xi (mg/tablet)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

texp/ t(0,05; f)

P

xi (mg/tablet)

VAL

(*)

TB (mg/tablet)

S (mg/tablet)

Fexp/ F(0,05;2;2)

Sp

texp/ t(0,05; f)

P

Analytical methods

Kalman

BPTT

HPLC

9,65/9,80/9,37

9,67/9,81/9,39

9,54/9,41/9,59

9,61

9,62

9,51

0,22

0,21

0,09

5,30/19

5,30/19

0,16

0,16

0,53/4,3

0,63/4,3

0,65

0,59

11,68/11,86/11,34 11,71/11,89/11,37 11,72/11,76/11,41

11,66

11,66

11,63

0,26

0,26

0,19

1,9/19

1,9/19

0,34

0,34

-0,06/4,3

0,51/4,3

0,96

0,66

169,97/172,49/

170,86/173,40/

166,35/168,81/

165,06

165,89

167,82

169,17

167,66

3,78

3,82

1,24

9,32/19

9,5/9

0,10

0,10

0,71/4,30

1,11/4,30

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

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

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, Trần Thúc Bình, Châu Viết Thạch

(2017). Xác định đồng thời Paracetamol và Cafein trong hỗn hợp

bằng phương pháp trắc quang kết hợp thuật toán lọc Kalman, Tạp

chí phân tích hóa, lý và sinh học, T-22, tr.14-21.

[2] Nguyen Thi Quynh Trang, 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.22-29.

[3] Tran Thuc Binh, Nguyen Thi Quynh Trang, 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 5th Analytica Vietnam

Conference 2017, pp.14-21.

[4] Nguyễn Thị Quỳnh Trang, Trần Thúc Bình, Ngô Văn Tứ

(2017). Xác định đồng thời amlodipine, hydrochlorothiazide và

valsartan trong dược phẩm bằng phương pháp trắc quangchemometric dùng phổ toàn phần. Tạp chí Khoa học - Khoa học

Tự nhiên, Đại học Huế, 126(1D), tr.125-137.

[5] Trần Thúc Bình, Nguyễn Thị Quỳnh Trang, Nguyễn Thị Hồng Vân

(2017). Xác định đồng thời Paracetamol và Ibuprofen trong dược

phẩm bằng phương pháp quang phổ đạo hàm, Tạp chí phân tích hóa,

lý và sinh học, T-22, tr.8-16.

23

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