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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

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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

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

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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.

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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

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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

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+ 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).

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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  (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:

( ) ( 1)

Cpri k = Cest k

-(2.1)
- Extrapolation of the covariance of the error:

( ) ( 1)

Ppri k = Pest k- (2.2)

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(

)

( ) ( ) ( ) ( ) (k) ( ) ( )

T T

k pri k k k pri k k

K P e e P e R

-= + (2.3)

- Updated status estimate:

(

)

( ) ( ) ( ) ( ) ( ) ( )

est k pri k k k k pri k

C = C + K A - e C

(2.4)
- Update the covariance of the error:

( ) ( ) ( ) ( )

est k k k pri k

P = éêëINV- e K ùúûP

(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  of the
constituents: = (ij )mxn

Step 3: Record the optical absorption spectra of the mixed
solution, enter the optical absorption matrix measured A =
(Ai1)mx1

Step 4: Solve the system of m equations by the least
squares method: A = . C to find the concentration of C.

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.

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- 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

(F-test); 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
value for the concentration Cest(0) and variance Pest(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

(0)
est

C

= 0,3 µg/mL and variance

P

est(0)= 1.

Table 3.1. Results of determination of TEL and HYD 
concentration in Kalman method with with random selection of

initial value (*)

Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9

TEL
Co

(µg/mL) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00
C

(µg/mL) 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30
RE (%) -70 -85 -90 -93 -94 -95 -96 -96 -97
HYD Co

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(µg/mL) 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30 0,30
RE(%) -97 -96 -96 -95 -94 -93 -90 -85 -70

(*)C

o: 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

Mixture H1 H2 H3 H4
Co (µg/mL) 0,250 0,50 1,00 5,00
C (µg/mL) 0,300 0,300 0,300 0,304
RE (%) 20 -40 -70 -94

HYD

Co (µg/mL) 0,325 0,65 1,30 5,00
C (µg/mL) 0,307 0,304 0,302 0,299
RE (%) -6 -53 -77 -94

VAL

Co (µg/mL) 4,00 8,00 16,00 5,00
C (µg/mL) 0,301 0,300 0,300 0,299
RE (%) -93 -97 -98 -94

(*)C

o: 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

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- 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 H1 H2 H3 H4 H5 H6 H7 H8 H9
TEL

Co (µg/mL) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00
C (µg/mL) 0,99 1,99 2,95 3,88 5,03 6,07 7,18 7,99 9,00
RE (%) -0,9 -0,6 -2 -3 -0,6 1 3 -0,1 0
HYD

Co (µg/mL) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00
C (µg/mL) 8,91 7,84 6,86 6,02 5,06 3,95 3,01 1,98 1,03
RE (%) -1,1 -2,0 -2,0 0,4 1,3 -1,2 0,3 -0,8 3

(*)C

o: Concentration in standard mixed solution; C: Determined concentration

Table 3.4. The results of determination of TEL and HYD 
concentrations in the mixture by the Kalman method with the

choice of the assumed initial value – Option 2(*)
Mixture H1 H2 H3 H4 H5 H6 H7 H8 H9
TEL Co (µg/mL) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00

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RE (%) -70,0 -84,9 -89,8 -92,3 -93,5 -94,2 -94,6 -94,7 -94,6

HYD

Co (µg/mL) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00
C (µg/mL) 0,30 0,31 0,31 0,31 0,31 0,31 0,31 0,31 0,30
RE (%) -96,6 -96,2 -95,6 -94,8 -93,7 -92,2 -89,7 -84,7 -69,7

(*)C

o: 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 H1 H2 H3 H4

AML

Co (µg/mL) 0,250 0,50 1,00 5,00
C (µg/mL) 1,731 0,478 0,530 5,032
RE (%) -30,8 -4,5 -47 0,6
HYD

Co (µg/mL) 0,325 0,65 1,30 5,00
C (µg/mL) 2,794 0,495 1,610 5,910
RE (%) -14,0 -23,8 23,85 18,2
VAL

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(*)C

o: Concentration in standard mixed solution; C: Determined concentration

Table 3.6. The result of determination of AML, HYD and VAL 
concentrations in the mixture by the Kalman method with a

choice of assumed initial value– Option 2(*)
Mixture H1 H2 H3 H4
AML

Co (µg/mL) 0,250 0,50 1,00 5,00
C (µg/mL) 0,300 0,300 0,282 0,477
RE (%) 20,0 -40,0 -71,8 -90,5
HYD

Co (µg/mL) 0,325 0,65 1,30 5,00
C (µg/mL) 0,301 0,304 0,368 0,443
RE (%) -7,4 -53,2 -71,7 -91,1
VAL

Co (µg/mL) 4,00 8,00 16,00 5,00
C (µg/mL) 0,319 0,454 0,542 0,289
RE (%) -92,0 -94,3 -96,6 -94,2

(*)C

o: 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%).

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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

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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),

RSD or (%) = ×100

(0)

H witz

est

S
C

(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.

( )

% 21 0.5lgCest( 0)

Hor witz

RSD =

(3.2)

- From S, calculated the variance S2  P
est(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 H1 H2 H3 H4 H5 H6 H7 H8 H9
TEL

Co (µg/mL) 1,00 2,00 3,00 4,00 5,00 6,00 7,00 8,00 9,00
C (µg/mL) 0,99 1,99 2,95 3,88 5,03 6,07 7,18 7,99 9,00
RE (%) -0,9 -0,6 -2 -3 -0,6 1 3 -0,1 0
HYD

Co (µg/mL) 9,00 8,00 7,00 6,00 5,00 4,00 3,00 2,00 1,00
C (µg/mL) 8,93 8,03 7,05 6,05 5,06 3,95 3,00 1,99 1,03
RE (%) -0,8 0,4 0,6 0,8 1,3 -1,2 0 0,7 2,7

(*)C

o: 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 H1 H2 H3 H4

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RE (%) 1,2 2,2 1,6 0,4
HYD

Co (µg/mL) 0,325 0,65 1,30 5,00
C (µg/mL) 0,320 0,646 1,290 5,064
RE (%) -1,5 -0,6 -0,8 1,3
VAL

Co (µg/mL) 4,00 8,00 16,00 5,00
C (µg/mL) 3,99 8,06 16,05 4,821
RE (%) -0,2 0,8 0,3 -3,6

(*)C

o: 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

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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

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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).

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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).

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

Parameter AML HYD VAL

Rep 1 Rep 2 Rep 3 Mean Rep 1 Rep 2 Rep 3 Mean Rep 1 Rep 2 Rep 3 Mean

CK (µg/mL) 0,253 0,252 0,254 0,253 0,320 0,320 0,321 0,320 3,990 3,980 4,010 3,993

RSDK (%) 0,4 0,3 0,4

CS (µg/mL) 0,253 0,253 0,254 0,253 0,319 0,319 0,321 0,319 3,993 3,981 4,009 3,994

RSDS (%) 0,4 0,4 0,4

½ RSDH 9,9 9,5 6,5

CK (µg/mL) 0,511 0,510 0,514 0,512 0,646 0,645 0,650 0,647 8,060 8,044 8,109 8,071

RSDK (%) 0,4 0,5 0,4

CS (µg/mL) 0,511 0,510 0,514 0,512 0,645 0,644 0,649 0,646 8,059 8,043 8,107 8,070

RSDS (%) 0,4 0,5 0,4

½ RSDH 8,9 8,6 5,9

CK (µg/mL) 1,016 1,013 1,020 1,016 1,290 1,286 1,296 1,291 16,050 15,994 16,114 16,053

RSDK (%) 0,4 0,4 0,4

CS (µg/mL) 1,017 1,013 1,021 1,017 1,284 1,279 1,290 1,284 16,037 15,980 16,101 16,040

RSDS (%) 0,4 0,5 0,4

½ RSDH 8,0 7,9 5,5

CK (µg/mL) 4,981 4,971 5,008 4,987 5,064 5,054 5,089 5,069 4,821 4,811 4,844 4,825

RSDK (%) 0,4 0,4 0,4

CS (µg/mL) 4,841 4,831 4,865 4,846 5,109 5,099 5,135 5,114 4,873 4,864 4,898 4,878

RSDS (%) 0,4 0,4 0,4

½ RSDH 6,3 6,3 6,3

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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

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

Sample Method

AML HYD VAL

Ct
(µg/mL)

Cx
(µg/mL)
Rev
(%)
Ct
(µg/mL)
Cx
(µg/mL)
Rev
(%)
Ct
(µg/mL)
Cx
(µg/mL)
Rev
(%)
Sample
B1
Kalman

0 0,965 0 1,168 0 16,997

0,25 1,200 94,0 0,30 1,451 94,3 4,0 21,112 102,9
0,50 1,415 90,0 0,60 1,710 90,3 8,0 24,876 98,5

BPTT

0 0,967 0 1,171 0 17,086

0,25 1,202 94,0 0,30 1,457 95,3 4,0 21,251 104,1

0,50 1,418 90,2 0,60 1,719 91,3 8,0 25,067 99,8

Sample
B2

Kalman

0 0,980 0 1,186 0 17,249

0,25 1,214 93,6 0,30 1,470 94,7 4,0 21,363 102,9
0,50 1,450 94,0 0,60 1,759 95,5 8,0 25,497 103,1

BPTT

0 0,981 0 1,189 0 17,340

0,25 1,217 94,4 0,30 1,474 95,0 4,0 21,505 104,2
0,50 1,454 94,6 0,60 1,762 95,5 8,0 25,697 104,5

Sample
B3

Kalman

0 0,937 0 1,134 0 16,506

0,25 1,171 93,6 0,30 1,416 95,0 4,0 20,603 102,4
0,50 1,397 92,0 0,60 1,698 94,5 8,0 24,567 100,8

BPTT

0 0,939 0 1,137 0 16,589

0,25 1,173 93,6 0,30 1,422 95,0 4,0 20,736 103,7
0,50 1,400 92,2 0,60 1,697 93,3 8,0 24,754 102,1

RevTB (%)-Kalman 92,9 94,0 101,8

RevTB (%)-BPTT 93,2 94,2 103,0

(*) C

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Table 3.41. Comparison of chemometric methods with HPLC method 
for determining the content of AML, HYD and VAL in Exforge

HCT(*)

analytical

substance Statistics

Analytical methods

Kalman BPTT HPLC

AML

xi (mg/tablet) 9,65/9,80/9,37 9,67/9,81/9,39 9,54/9,41/9,59

TB (mg/tablet) 9,61 9,62 9,51

S (mg/tablet) 0,22 0,21 0,09

Fexp/ F(0,05;2;2) 5,30/19 5,30/19

Sp 0,16 0,16

Texp/ t(0,05; f) 0,53/4,3 0,63/4,3

P 0,65 0,59

HYD

xi (mg/tablet) 11,68/11,86/11,34 11,71/11,89/11,37 11,72/11,76/11,41

TB (mg/tablet) 11,66 11,66 11,63

S (mg/tablet) 0,26 0,26 0,19

Fexp/ F(0,05;2;2) 1,9/19 1,9/19

Sp 0,34 0,34

texp/ t(0,05; f) -0,06/4,3 0,51/4,3

P 0,96 0,66

VAL

xi (mg/tablet) 169,97/172,49/

165,06

170,86/173,40/
165,89

166,35/168,81/
167,82

TB (mg/tablet) 169,17 167,66

S (mg/tablet) 3,78 3,82 1,24

Fexp/ F(0,05;2;2) 9,32/19 9,5/9

Sp 0,10 0,10

texp/ t(0,05; f) 0,71/4,30 1,11/4,30

P 0,55 0,38

(*) The results of the analysis are repeated (i = 1-3); F

exp = 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

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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).

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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 quang-
chemometric dùng phổ toàn phần. Tạp chí Khoa học - Khoa học 
Tự nhiên, Đại học Huế, 126(1D), tr.125-137.

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