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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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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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- 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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