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Introduction

Propranolol (PRO), amiloride (AMI) and dipyridamole (DIP)

are widely used to treat several diseases. PRO and AMI1 are

antihypertensive substances, whereas DIP1 is an antithrombotic

agent. These components are classified as doping substances

and have been included in a list of forbidden substances2 by the

International Olympic Committee.

The sensitivity of fluorescence spectrometry has enabled it to

be a useful analytical tool for monitoring trace compounds of

biochemical interest. However, when substances whose

individual spectral profiles contain broad bands, which often

overlap, must be determined simultaneously by

spectrofluorometry, it would be difficult to select a pair ofexcitation and emission wavelengths which could permit the

determination of one of them without any interference of the

other. For such a reason, it is worth investigating new methods

to solve this problem without resorting to expensive or time-

consuming techniques.

Several approaches, such as synchronous,3 derivative4

fluorescence spectrometry as well as variable-angle

fluorescence5 spectroscopy have been developed to overcome

such problems without having to utilize time-consuming and

expensive procedures. All of these methods are based on

improving the selectivity of the coexisting components.

Chemometric methods, such as factor analysis,610 have

become even more popular in solving problems that are difficult

to handle using conventional techniques, without having to

resort to expensive or time-consuming procedures. Especially,

three-way resolution and calibration methods1113 play important

roles in solving the problem of closely overlapping fluorescence

spectra. These methods utilize mathematical separation

procedure to substitute the traditional chemical separation

procedure, which is different from those.35 In addition, these

approaches can not only determine the concentrations, but can

also provide spectral profiles of the components in the mixtures.

In this work, with both purposes, the present authors resolved

mixtures of the aforementioned three doping substances with

broad and highly overlapping excitation and emission spectra,

using a newly proposed modified PARAFAC algorithm with a

penalty digonalization error (PDE).14 One purpose is to solve

the spectral overlapping problem and to further extend the

applications of chemometric methods; another is to further

demonstrate the characteristic features of the PDE algorithm.

Theory

Before using the PDE algorithm, a simple introduction to it

should be presented. For details, the readers are recommended

to Ref. 14.

Trilinear model

According to three-dimentional fluorometry, the trilinear

model can be written as

X..k= ckfafbft+ E..k k= 1, 2, 3, , K, (1)

where F is the component number and K is the number of

samples (mixtures); af, bf and cf are the emission, excitation and

concentration profiles of thefth component. In matrix notation,

the trilinear model can also be equivalent to the following three

F

f=1

333ANALYTICAL SCIENCES MARCH 2002, VOL. 18

2002 The Japan Society for Analytical Chemistry

Spectrofluorometric Resolution of Closely Overlapping Drug

Mixtures Using Chemometrics Methods

Yu-Zhen CAO,*,** Cui-Yun MO,***Ji-gong LONG,**Hong CHEN,*Hai-Long WU,***andRu-Qin YU***

*Key Laboratory of New Packaging Materials & Technology of China National Packaging Corporation,Zhuzhou Institute of Technology, Zhuzhou, 412008, China

**Environmental Monitoring Central Station of Guangzhou City, NO. 95, Jixiang Road of Guangzhou City,Guangzhou, 510030, China

***College of Chemistry and Chemical Engineering, Hunan University, Changsha, 410082, China

A modified parallel factors analysis (PARAFAC) algorithm with a penalty diagonalization error (PDE), newly proposed

by the present authors, was utilized to simultaneously resolve drug mixtures of propranolol (PRO), dipyridamole (DIP)

and amiloride (AMI) without any loss of sensitivity. The analyses were performed in aqueous solution. The

experimental results demonstrated that the profiles of the spectra and the concentrations could be accurately resolved

using the PDE algorithm with a high sensitivity and stable repeatability. That is to say, the closely overlapping problem

of the spectra could be easily solved. Furthermore, simultaneous determinations of three kinds of tablets, which contain

PRO, AMI and DIP, respectively, were successfully performed with satisfactory results.

(Received July 9, 2001; Accepted November 16, 2001)

To whom correspondence should be addressed.

E-mail: yuzhencao@yeah.net

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equations:

Xi.. = Bdiag(ai)Ct+ Ei.. i = 1, 2, ,I, (2)

X.j. = Cdiag(bj)At+ E.j. j = 1, 2, ,J, (3)

X..k= Adiag(ck)Bt+ E..k k= 1, 2, , K, (4)

where I and J are the emission wavelength number and the

excitation wavelength number, respectively.

The algorithm

From Eqs. (2) (4), one can obtain the following three

equations for the diagonalization error:

B+Xi..(C+)t diag(ai) = B+Ei..(C+)t, (5)

C+X.j.(A+)t diag(bj) = C+E.j.(A+)t, (6)

A+

X..k(B+

)t

diag(ck) = A+

E..k(B+

)t

. (7)

By combining the diagonalization error with the PARAFAC

error, one can obtain three objective functions, as follows:

F(A) = ||Xi.. Bdiag(ai)Ct||F2 +||B+Xi..(C+)t diag(ai)||F2 , (8)

F(B) = ||X.j. Cdiag(bj)At||F2 +||C+X.j.(A+)t diag(bj)||F2 , (9)

F(C)= ||X..kAdiag(ck)Bt||F2 +||A+X..k(B+)tdiag(ck)||F2 . (10)

From Eqs. (8) (10), one can acquire the following equations to

express the factor matrices A, B and C:

pi = diag[B+Xi..(C+)t], i = 1, 2, 3, ,I;

P = [p1; p2; ;pI]; (11)

A = ( X..kBdiag(ck) + P)(I + diag(ck)BtBdiag(ck))1; (12)

qj = diag[C+X.j.(A+)t], j = 1, 2, 3, ,J;

Q = [q1; q2; ;qJ]; (13)

B = ( Xi..Cdiag(ai) + Q)(I + diag(ai)CtCdiag(ai))1; (14)

rk= diag[A+

X..k(B+

)t

], k= 1, 2, 3, , K;

R = [r1; r2; ;rK]; (15)

C = ( X.j.Adiag(bj) + R)(I + diag(bj)AtAdiag(bj))1. (16)

The PDE algorithm computes the loading matrix A using Eqs.

(11) and (12) with B and C fixed; then, it fixes C and renews A

to update B utilizing Eqs. (13) and (14); it finally calculates

matrix C with the renewed A and the updated B according to

Eqs. (15) and (16).

Experimental

Apparatus

All of the fluorometric measurements were performed on an

F-4500 fluorescence spectrophotometer (HITACHI).

j

j

i

i

k

k

K

k=1

J

j=1

I

i=1

Reagents

All of the experiments were performed with analytical

reagent-grade chemicals, pure solvent and doubly distilled

water. Stock solutions of PRO (The Fourth Pharmaceutical

Factory of Changzhou; 25 mg dissolved in 100 ml of water),

AMI (The Fourth Pharmaceutical Factory of Changzhou; 25 mg

dissolved in 100 ml of water) and DIP (The Fourth

Pharmaceutical Factory of Changzhou; 25 mg dissolved in 100

ml of ethanol) were diluted to prepare working solutions by

suitable dilutions using water. The stock solutions were stored

and protected from light. Three kinds of tablets (Amiloride,

Propranolol hydrochloride tablets and Persantin) containing

AMI, PRO and DIP, respectively, with nominal contents, were

randomly purchased from local pharmacies.

Procedure

The steady state fluorescence of 9 samples of the

aforementioned three species was measured in aqueous solution.

The concentrations of these species are listed in Table 1. The

excitation wavelength was set from 220 nm to 320 nm at an

interval of 4 nm, and the emission wavelength varied from 330

nm to 522 nm with an interval of 4 nm. The scan rate was 1200

nm/min. The effect of Rayleigh scattering was compensated by

subtracting the measurement matrix of a blank from the sample

measurements. Thus, a 49 26 9 data array was collected.This data array was treated using the PDE algorithm.

In order to analyze three tablets containing PRO, AMI andDIP respectively, the authors combined the mixture of the three

tablets with nine samples. The same treatment was made to

these samples and the mixture. Thus a 49 26 10 data arraywas collected. The data array was resolved using the PDE

algorithm.

Results and Discussion

Linear range

The linear ranges of PRO, AMI and DIP were investigated

before undertaking an experimental design. When PRO, AMI

and DIP were, respectively, in the range of 9 100 ng/ml, 10

150 ng/ml and 20

110 ng/ml, the correlation coefficients were

all above 0.9990.

Resolution of profiles in three modes

Figure 1 shows the resolved profiles using the PDE approach

334 ANALYTICAL SCIENCES MARCH 2002, VOL. 18

Table 1 Resolved concentrations with N = 3 and real

concentrations of 9 samples (g/ml)

a. MAE is defined as the mean absolute error.

Sample

1 0.0000 0.0387 0.0602 0.0005 0.0389 0.0638

2 0.1044 0.0581 0.0602 0.1054 0.0553 0.0683

3 0.0835 0.0387 0.0803 0.0863 0.0397 0.0708

4 0.0626 0.0387 0.1004 0.0656 0.0416 0.0980

5 0.0835 0.0581 0.0602 0.0826 0.0549 0.0707

6 0.0626 0.0581 0.0803 0.0617 0.0524 0.0961

7 0.0835 0.0387 0.0000 0.0796 0.0355 0.0018

8 0.0626 0.0581 0.0000 0.0624 0.0530 0.0016

9 0.0835 0.0000 0.0803 0.0819 0.0015 0.0652

MAEa 0.0014 0.0025 0.0061

Real Resolved

AMI PRO DIP AMI PRO DIP

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withN= 3 and the actual ones of the PRO, AMI and DIP. The

concentration profiles of 9 samples are listed in Table 1. These

results are nearly the same as those of the true ones, which

illustrates that the PDE algorithm will provide an accurate

resolution of the substances that have seriously overlapping

spectral profiles when the correct component number is used in

the computation. The required iteration number for analyzing

this data array was merely 18, and the required time was only 3

s. These phenomena showed that the PDE algorithm was ableto recover the profiles of the data array accurately and rapidly,

which are characteristic features of the PDE algorithm.14

Figure 2 shows the resolved spectra of the data array using the

PDE algorithm withN= 4, in which an excess component was

used for the unknown background and the true profiles were

plotted for a comparison. The concentration profiles of the

three components of interest are listed in Table 2. These

recovered results further illustrated that the PDE algorithm is

insensitive for estimating the component number. That is to

say, the PDE algorithm can provide accurate solutions provided

that the number of factors used in a calculation is not less than

that of the actual underlying factors, which is one of the

characteristic features of the PDE approach.14

Simultaneous determination of contents of three kinds of tablets

Since the PDE algorithm was insensitive to estimating the

component number, the present authors resolved a 49 26 10data array using the PDE algorithm with N = 4, in which an

unknown background component was taken into consideration.

With the concentrations of the nine samples (mixtures) known,

the contents of three components were obtained using a second-

order calibration. The experiment was performed in parallel

four times; the calculated concentrations are given in Table 3.

These results demonstrate that the PDE algorithm can be used to

simultaneously determine practical samples of PRO, AMI andDIP with an unknown background.

Conclusion

In this paper, the newly proposed modified PARAFAC

algorithm using a penalty diagonalization error (PDE) was used

to resolve the system of propranolol (PRO), amiloride (AMI)

and dipyridamole (DIP). The resolved results showed that the

PDE approach could rapidly solve the problem of serious

fluorescence spectral overlapping of the three components with

an unknown background, and were insensitive to an estimation

of the component number.

Acknowledgements

This work was financially supported by Natural Science

335ANALYTICAL SCIENCES MARCH 2002, VOL. 18

Fig. 1 Resolved spectra (solid lines) and true spectra (dotted lines)using the PDE algorithm with N= 3. (a) Excitation spectra and (b)

emission spectra. Fig. 2 Recovered profiles (solid lines) and actual ones (dotted

lines) in three modes utilizing the PDE algorithm with N = 4. (a)

Excitation spectra and (b) emission spectra.

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Foundation of Hunan (Grant No. SSY2066) and the Key

Laboratory of New Packaging Materials and Technology of

China National Packaging Corporation.

References

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Drugs, 2nd ed., 1986, The Pharmaceutical Press, London,

362, 363, 562, 563, 1037 and 1038.

2. C. Rodrguez Burno, Dopaje, 1st ed., 1992, Mc-Graw

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Paczkowski, and I. C. Arruda,Anal. Sci., 2000, 16, 1337.

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10. L. F. Capitan-Vallvey, N. Navas, R. Avidad, I. Deorbe, and

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336 ANALYTICAL SCIENCES MARCH 2002, VOL. 18

Table 2 Recovered concentrations using the PDE algorithm

with N= 4 (g/ml)

a. MAE is defined as the mean absolute error.

Sample

1 0.0000 0.0387 0.0602 0.0010 0.0389 0.0637

2 0.1044 0.0581 0.0602 0.1055 0.0554 0.0682

3 0.0835 0.0387 0.0803 0.0859 0.0397 0.0707

4 0.0626 0.0387 0.1004 0.0656 0.0416 0.0978

5 0.0835 0.0581 0.0602 0.0828 0.0550 0.0708

6 0.0626 0.0581 0.0803 0.0623 0.0524 0.0961

7 0.0835 0.0387 0.0000 0.0798 0.0355 0.0017

8 0.0626 0.0581 0.0000 0.0623 0.0532 0.0016

9 0.0835 0.0000 0.0803 0.0821 0.0015 0.0653

MAEa 0.0014 0.0025 0.0061

Real Resolved

AMI PRO DIP AMI PRO DIP

Table 3 Calculated contents of three drugs for four parallel

experiments (mg)

Nominal contents 5 10 25

First time 5.15 9.90 25.20Second time 5.12 9.89 25.34

Third time 5.09 10.18 25.27

Four time 4.97 10.20 25.29

Mean values 5.08 10.04 25.28

Amiloride (AMI) Propranolol (PRO) Persantin (DIP)