Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714

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Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa

UV spectrophotometric simultaneous determination of cefoperazone and sulbactam in pharmaceutical formulations by derivative, Fourier and wavelet transforms Vu Dang Hoang a,⇑, Nguyen Thi Loan a, Vu Thi Tho a, Hue Minh Thi Nguyen b a b

Department of Analytical Chemistry and Toxicology, Hanoi University of Pharmacy, 13-15 Le Thanh Tong, Hanoi, Viet Nam Center for Computational Science and Faculty of Chemistry, Hanoi National University of Education, Hanoi, Viet Nam

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Derivative, Fourier and wavelet

transforms can be used for the spectral resolution of cefoperazone– sulbactam binary mixtures.  Spectrophotometric methods are comparable, but preferable to RPHPLC.  Wavelet transforms have distinct advantages over derivative and Fourier transforms.  The use of double signal transform in the sequences is better than any signal transform.

a r t i c l e

i n f o

Article history: Received 15 September 2013 Received in revised form 12 November 2013 Accepted 14 November 2013 Available online 25 November 2013 Keywords: UV spectrophotometry Derivative Fourier Wavelet Cefoperazone Sulbactam

a b s t r a c t Signal processing methods based on the use of derivative, Fourier and wavelet transforms were proposed for the spectrophotometric simultaneous determination of cefoperazone and sulbactam in powders for injection. These transforms were successfully applied to UV spectra and ratio spectra to find suitable working wavelengths. Wavelet signal processing was proved to have distinct advantages (i.e. higher peak intensity obtained, additional smooth function and scaling factor process eliminated) over derivative and Fourier transforms. Especially, a better resolution of spectral overlapping bands was obtained by the use of double signal transform in the sequences such as (i) spectra pre-processed by Fractional Wavelet Transform and subsequently subjected to Continuous Wavelet Transform or Discrete Wavelet Transform, and (ii) derivative – wavelet transforms combined. Calibration graphs for cefoperazone and sulbactam were recorded for the range 10–35 mg/L. Good accuracy and precision were reported for all proposed methods by analyzing synthetic mixtures of cefoperazone and sulbactam. Furthermore, these methods were statistically comparable to RP-HPLC. Ó 2013 Elsevier B.V. All rights reserved.

Introduction Cefoperazone (Diagram 1A), a third generation cephalosporin antibiotic, exerts its bactericidal effect by binding to specific

⇑ Corresponding author. Tel.: +84 438 254539; fax: +84 438 264464. E-mail address: [email protected] (V.D. Hoang). 1386-1425/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.saa.2013.11.095

penicillin-binding proteins (PBPs) located inside the bacterial cell wall, causing the inhibition of the third and last stage of bacterial cell wall synthesis [1]. Sulbactam (Diagram 1B), a potent and specific b-lactamase inhibitor with high-level intrinsic activity against Acinetobacter baumannii [2,3], is commonly given in combination with cefoperazone to increase the antibacterial activity of cefoperazone against beta-lactamase producing organisms [4].

V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714

(A)

705

(B)

(6R,7R)-7-[(2R)-2-{[(4-ethyl-2,3-dioxopiperazin-1-

(2S,5R)-3,3-Dimethyl-7-oxo-

yl)carbonyl]amino}-2-(4-hydroxyphenyl)acetamido]-3-{[(1-

4-thia-1-

methyl-1H-1,2,3,4-tetrazol-5-yl)sulfanyl]methyl}-8-oxo-5-thia-1-

azabicyclo[3.2.0]heptane-2-

azabicyclo[4.2.0]oct-2-ene-2-carboxylic acid

carboxylic acid 4,4-dioxide

Diagram 1. Chemical structure of cefoperazone (A) and sulbactam (B).

Provided that cefoperazone is one of few cephalosporin antibiotics effective in treating Pseudomonas bacterial infections, the synergy of gatifloxacin with cefoperazone–sulbactam against clinical isolates of Pseudomonas aeruginosa was also reported [5]. This combination could be used in the treatment of nosocomial infections caused by multidrug-resistant pathogens in neonates [6]. It was found to be as useful as imipenem/cilastatin for treating patients with Acinetobacter bacteremia [7]; and comparable to carbapenems in bactericidal efficacy against A. baumannii strains in animal abscess model [8]. The role of cefoperazone–sulbactam combination when co-administered with other antibiotics for the treatment of severe infections was also noticed [9,10]. Clinically speaking, cefoperazone–sulbactam combination is effective and safe for the treatment of moderate-to-severe bacterial infections mainly caused by b-lactamase-producing organisms [11–13]. Regarding to the analysis of pharmaceutical multicomponent mixtures, the utility of UV absorption spectroscopy was originally, however, often limited due to the extensive overlap of spectral peaks. To overcome this drawback, the application of mathematical algorithms such as derivative and wavelet transforms to original absorption spectra was exploited. While the derivative transform still continues to be a promising tool to solve UV spectral overlapping of mixtures [14,15], the wavelet transform has been increasingly applied in the determination of analytes in samples in the field of analytical chemistry [16,17]. According to a set of functions called wavelet, this methodology can decompose the signal and translate it into a time–frequency domain through the translation and dilation operations. By doing so, it has some advantages over derivative spectrophotometry in some cases such as (i) the higher order differentiation process diminish peak amplitude as well as signal-to-noise ratio; (ii) the finding of zero-crossing points is very difficult and ratio spectra derivative working wavelength is undetermined. In the last decade, its application in analyzing antibiotic binary mixtures has been successfully studied [18–22]. In literature, the simultaneous determination of cefoperazone and sulbactam in pharmaceutical formulations was reported in numerous High Performance Liquid Chromatogram studies [23–28]. In contrast, their spectrophotometric simultaneous determination was only studied once by applying second order derivative approach [29]. It is noteworthy that differentiation and smoothing algorithms for UV derivative spectrophotometry in this

study were not clearly indicated, whereas they always play an important role in determining the sensitivity and accuracy of derivative techniques. The aim of this study was to develop derivative, Fourier- and wavelet-based UV spectrophotometric methods for the simultaneous determination of cefoperazone and sulbactam in powders for injection using Reversed Phase High Performance Liquid Chromatogram (RP-HPLC) as a reference method. This study, in particular, emphasized on exploiting the advantages of wavelet transform (i.e. Continuous, Discrete and Fractional Wavelet Transforms as abbreviated CWT, DWT and FWT, respectively) over both Fourier and derivative transforms as well as correcting shortcomings in the above-mentioned UV derivative spectrophotometry study.

Experimental Apparatus and software Absorption spectra were registered and treated by using a UNICAM UV 300 double beam spectrophotometer (Thermo Spectronic, USA) with a fixed slit width (1.5 nm) connected to an IBM computer loaded with Thermo Spectronic VISION32 software and 1-cm quartz cells. The zero-order spectra were recorded in the wavelength range of 190–325 nm against a blank (water) at Intelliscan mode to enhance the signal-to-noise ratio of absorbance peaks without extended scan duration with a Dk ¼ 0:1 nm (i.e. 30–120 nm/min). For derivative approach, the spectra were differentiated and smoothed by using Savitzky–Golay filter. For Fourier approach, the spectra were processed using Microsoft EXCEL 2007. For wavelet approach, the data treatment was done using MATLAB R2013a software (The MathWorks, Natick, MA, USA). FWT calculations were performed in MATLAB with its code of FWT performed by M. Unser and T. Blu. RP-HPLC analysis was performed on an Agilent 1100 Series Diode-Array-Detector chromatograph (Agilent Technologies, USA) at ambient temperature. An Apollo C18 (150  4.6 mm; 5 lm) column was used. All solutions were filtered through a 0.45 lm membrane filter before injection into the chromatograph. All solvents were filtered through a 0.45 lm Millipore filter and degassed in an ultrasonic bath.

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V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714

Cefoperazone (CP) and sulbactam (SB) were kindly provided by the National Institute of Drug Quality Control (Vietnam). De-ionized doubly distilled water was used throughout. All reagents were of analytical grade. Stock solutions of CP and SB (5000 mg/L) were freshly made in water. A concentration set of standard solutions were prepared in 50-mL calibrated flasks by using the same stock solutions.

where A denotes the absorbance at a set of (n + 1) equally spaced wavelengths; aj and bj are correspondingly the coefficients of cos jx và sin jx (j = 1, 2, 3,. . ., n); a0 is a constant component. Any coefficient of the combined trigonometric Fourier function, aj and bj (tj), can be calculated from a set of (n + 1) absorbances measured at equally spaced wavelengths, by the following summation, in which x takes values from 0 to 2p  [2p/(n + 1)], at intervals of 2p/(n + 1)

Sample solution

tj ¼

Reagents and standard solutions

n X Ai T ji i¼0

Four commercial formulations containing CP 500 mg + SB 500 mg per vial i.e. Sulperazon (Pfizer, USA); Jincetam (Hankook Korus Pharm. Co., Ltd., Republic of Korea) and Bacamp (Han Lim Pharmaceutical Co., Ltd., Republic of Korea) or CP 1000 mg + SB 1000 mg i.e. Cefactam (Laboratorio Libra S.A, Uruguay) were studied. For each formulation, the content of five vials was mixed well. A quantity equivalent to CP 250 mg + SB 250 mg was accurately weighed and dissolved in about 30 mL of water in a 50-mL volumetric flask by sonication for 20 min, subsequently diluted to the mark with the same solvent. Appropriate dilution was then made in a 50-mL volumetric flask to obtain the test solution ca. CP 20 mg/L + SB 20 mg/L. Theoretical background The theoretical background of derivative transform and smoothing of signals using Savitzky–Golay method [30], discrete Fourier transform [31] as well as the fundamentals of CWT, DWT [32] and FWT [33] are briefly described as follows. Derivative transform Savitzky–Golay method This method determines a derivative spectrum by moving a spectral window comprising 2n + 1 measurement points over an absorbance spectrum. Then a polynomial of order m is fitted to the measurement points inside the spectral window.

PðkÞ ¼ a0 þ a1 k þ a2 k2 þ    þ am km This fit polynomial introduces smoothing, which is dependent on the user selectable parameters n and m. From the resulting fit parameters a0. . .am, the derivatives at the window center k0 can be derived easily:

 dP ¼ a1 þ 2a2 k þ    þ mam km1 ¼ a1 dk k0 ¼0  2 d P  dk2 

¼ 2a2 þ    þ mðm  1Þam km2 ¼ 2a2

 3 d P  dk3 

¼ 6a3 þ    þ mðm  1Þðm  2Þam km3 ¼ 6a3

k0 ¼0

k0 ¼0

Once the derivatives are determined at k0, the window is moved one measurement point to the right followed by a polynomial fit inside this new window until it reaches the end of the spectrum. Discrete Fourier transform Absorption curves could be expanded as a finite Fourier series as follows.

AðkÞ ¼ a0 þ a1 cos x þ a2 cos 2x þ a3 cos 3x þ    b1 sin x þ b2 sin 2x þ b3 sin 3x þ   

D

where Ti represents the combined Fourier functions whose order j = 1, 2, 3, . . ., n. Ti = [cos jx + cos j(x + 2p/(n + 1))] or Ti = [sin jx  sin j(x + 2p/(n + 1))]; The denominator in the above equation denoted by D has a numerical value of e.g. 3 or 4 for six or eight points for the combined Fourier functions (Table 1). Wavelet transform Continuous Wavelet Transform (CWT) Given a time-varying signal f(t), wavelet transforms consist of computing coefficients, which are inner products of the signal and a family of wavelets. In a Continuous Wavelet Transform, the wavelet corresponding to scale a and time location b can be written in terms of the mother wavelet:

  1 tb with a; b 2 R; a–0 wa;b ðtÞ ¼ pffiffiffiffiffiffi w a jaj The Continuous Wavelet Transform (CWT) of f(t) is given by:

Z

W f ða; bÞ ¼

1

f ðtÞwa;b ðtÞdt

1

The inversion back to time domain is given by

f ðtÞ ¼

1 Cw

Z

1

1

1 a2

Z

1

 W f ða; bÞwa;b ðtÞdb da

1

When a Continuous Wavelet Transform is evaluated, the mother wavelet is scaled and translated to every possible values of a and b. Accordingly, at each location (translation) of the wavelet, information is obtained about the local contribution of each frequency (scaling) to the entire signal. Discrete Wavelet Transform (DWT) When the Discrete Wavelet Transform is used to analyze digitized signals, the scaling and the translation of the mother wavelet will be

wm;n ðtÞ ¼

  t  nb0 w m=2 am a0 0 1

The Discrete Wavelet Transform is then written as

W f ðm; nÞ ¼

Z

1

f ðtÞwm;n ðtÞdt

1

Usually, a0 = 2 and b0 = 1 values are chosen. The wavelet transform calculated is called diadic when a0 = 2. Fractional Wavelet Transform (FWT) B-spline. A B-spline is defined as a generalization of the Bezier curve. Let a vector known as the knot is defined T = {t0, t1,. . ., tm} where T is a non-decreasing sequence with ti e [0,1], and control points are defined as P0, Pn. Degree is defined as p = m  n  1. The knots tp+1,. . ., tmp1 are called internal knots. If the basis functional is defined as

707

V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714 Table 1 Combined trigonometric Fourier functions for (n + 1) equally spaced points. ni

x0i

cos xi + cos (xi + 60°)

cos 2xi + cos 2(xi + 60°)

sin xi  sin (xi + 60°)

sin 2xi  sin (xi + 60°)

0 1 2 3 4 5 D

0 60 120 180 240 300

1.5 0 1.5 1.5 0 1.5 3

0.5 1 0.5 0.5 1 0.5 3

0.866 0 0.866 0.866 0 0.866 3

0.866 1.732 0.866 0.866 1.732 0.866 3

ni

x0i

cos xi + cos (xi + 45°)

cos 2xi + cos 2(xi + 45°)

sin xi  sin (xi + 45°)

sin 2xi  sin 2(xi + 45°)

0 1 2 3 4 5 6 7 D

0 45 90 135 180 225 270 315

1.707 0.707 0.707 1.707 1.707 0.707 0.707 1.707 4

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 4

0.707 0.293 0.293 0.707 0.707 0.293 0.293 0.707 4

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 4

1.6

then the curve defined by CP 20 mg/L

CðtÞ ¼

SB 20 mg/L Addition spectrum

1.2

Pi N i;p ðtÞ

i¼0

CP 20 mg/L + SB 20 mg/L

Absorbance

n X

is a B spline. Fractional B-spline The fractional B-spline is defined as

0.8

baþ ðxÞ ¼

0.4

Pþ1

k¼0 ð1Þ

Daþ1 xa

þ

þ

Cða þ 1Þ

¼

k



aþ1 k

 a ðx  kÞþ

Cða þ 1Þ

where Euler’s gamma function is defined as follows

Cða þ 1Þ ¼

0

200

220

240

260

280

Fig. 1. Spectra of CP 20 mg/L, SB 32.5 mg/L, and their corresponding mixture and absorbance addition.

 Ni;0 ðtÞ ¼

1; if t i 6 t < tiþ1 and t i < t iþ1 and 0 otherwise

Ni;p ðtÞ ¼

t  ti t iþpþ1  t N i;p1 ðtÞ þ Niþ1;p1 ðtÞ tiþpþ1  t iþ1 t iþp  ti

þ1

xa ex dx and

0

300

Wavelength (nm)

Z

a

a

ðx  kÞþ ¼ max ðx  k; 0Þ

The forward fractional finite difference operator of order a is defined as

Daþ f ðxÞ ¼

  þ1 X a f ðx  kÞ ð1Þk k 0

where

Tree Diagram 1. Derivative and wavelet transforms for the simultaneous determination of CP and SB in binary mixtures.

708

V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714 1.0

0.4

(A)

0.5

228.0

286.0

(A)

0.3

SB 10 - 35 mg/L CP 10 - 35 mg/L

0.0

Fourier Spectra

D Spectra

0.2

-0.5

1

-1.0

0.1

278.0

0 -1.5

246.0

-0.1

-2.0

CP 10 - 35 mg/L SB 10 - 35 mg/L -0.2

-2.5 210

240

270

215

300

235

255

275

295

Wavelength (nm)

Wavelength (nm) 4

200

(B)

286.0

D Ratio Spectra

2

Fourier Ratio Spectra

100

266.0

0

-2

-4

1

0

(B)

-100

-6

CP (10 - 35 mg/L) / SB 20 mg/L

CP (10 - 35 mg/L) / SB 20 mg/L

[CP (10 - 35 mg/L) + SB 20 mg/L] / SB 20 mg/L

[CP (10 - 35 mg/L) + SB 20 mg/L] / SB 20 mg/L -8 220

240

260

-200

280

300

Wavelength (nm) 210

240

270

300

Wavelength (nm) 0.1

(C)

0 0.08 0.06

-1

237.5 -1.5

0.04 0.02 0 -0.02

250.0

1

D Ratio Spectra

(C)

Fourier Ratio Spectra

-0.5

-0.04

SB (10 - 35 mg/L)/ CP 10 mg/L [CP 20 mg/L + SB (10 - 35 mg/L)] / CP 10 mg/L

-0.06

-2

SB (10 - 35 mg/L) / CP 10 mg/L [SB(10 - 35 mg/L) + CP 20 mg/L] / CP 10 mg/L

-0.08 220

-2.5 220

225

230

235

240

245

Fig. 2. First-order derivatives of spectra (A) and first-order derivatives of ratio spectra (B and C).

 

a k

Cða þ 1Þ ¼ Cðk þ 1ÞCða  k þ 1Þ

260

280

Wavelength (nm)

250

Wavelength (nm)

240

Fig. 3. Discrete Fourier transform of spectra (A) and first-order derivatives of ratio spectra (B and C).

The above defined B-splines fulfill the convolution property

baþ1  baþ2 ¼ baþ1 þa2 The centered fractional B-splines of degree a are given by

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V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714 1000

10

(A)

(A)

8

293.5

Haar-Ratio Spectra

6

Sym6-FWT Spectra

4 2 0 -2

500 CP (10 - 35 mg/L) / SB 20 mg/L [CP (10 - 35 mg/L) + SB 20 mg/L] / SB 20mg/L

0

249.2 265.4 -4 -6

SB 10 - 35 mg/L CP 10 - 35 mg/L

-8

-500 200

-10 200

220

240

260

280

220

300

240

260

280

300

Wavelength (nm)

Wavelength (nm) 2

(B)

25

(B)

241.5

Haar-Ratio Spectra

20

Mexh- FWT Spectra

15 10 231.3

5

SB (10 - 35 mg/L) / CP 10 mg/L [SB (10 - 35 mg/L) + CP 20 mg/L] / CP 10 mg/L 1

0 240.4

-5

SB 10 - 35 mg/L CP 10 - 35 mg/L

-10

0 240

245

-15 200

220

240

260

280

300

Wavelength (nm)

250

255

260

Wavelength (nm) Fig. 5. Haar transform of ratio spectra (A and B).

Fig. 4. Sym6 (A) and mexh (B) transforms of spectra.

ba ðxÞ ¼

  X a þ 1 1 jx  kja ð1Þk   Cða þ 1Þ k2Z k  a

where jxj has the following form

8 jxja > ; a not even < 2 sin ðp2aÞ a jxj ¼ 2n x > : x log ; a even ð1Þ1þn p

Fractional B-spline wavelets The fractional B-spline wavelets are defined as follows

waþ

Z

x

2

¼

X ð1Þk X a þ 1  2a

k2Z

12Z

1

 b2 aþ1 ð1 þ k  1Þbaþ ðx  kÞ

The fractional splines wavelets obey þ1

1

xn waþ ðxÞdx ¼ 0

and the Fourier transform fulfills the following relations

^ a ð-Þ ¼ Cðj-Þaþ1 as x ! 0 w  ^a

aþ1

w ð-Þ ¼ Cðj-Þ

as x ! 0

^ a ð-Þ is symmetric. The fractional spline wavelets behave like Here w  fractional derivative operator as indicated by the last formulas.

Results and discussion Fig. 1 shows the zero-order UV absorption spectra after being smoothed by Savitzky–Golay algorithm (Order: 3; No. of coefficients: 125). It is clear that (i) the additivity of absorbances was obeyed for the mixture of CP 20 mg/L + SB 20 mg/L over the range 210–300 nm and (ii) the determination of SB in this mixture was impossible because CP spectrum completely covered its spectrum over the wavelength range studied. In order to determine simultaneously CP and SB in binary mixtures, their overlapping spectra were resolved using derivative, Fourier and wavelet transforms as graphically depicted in Tree Diagram 1. In principle, these transforms could be applied to spectra or ratio spectra. While finding zero-crossing or crossing points is a must to the transformed spectra, the applicability of transformed ratio spectra depends on finding a point or a region over which the coincidence of signals is observed for the transformed ratio spectra of a compound and its corresponding mixture. Method development Derivative transform Fig. 2A displays the first derivative spectra of these pure drugs after their original spectra being differentiated (Order: 5; No. of coefficients: 9) and smoothed (Order: 3; No. of coefficients: 125) by Savitzky–Golay algorithm. It reveals zero-crossing points at

710

V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714 200

15

(A)

(A)

150

10

255.8

50

Haar- 1 D Spectra

1 D-Sym6-FWT

Spectra

100

0 257.7

-50

5 241.6 0

273.6

-5

-100

-10

SB 10 -35 mg/L

-150

CP 10 -35 mg/L

CP 10 - 35 mg/L

-200 210

230

250

270

SB 10 - 35 mg/L

-15 210

290

240

Wavelength (nm)

270

300

Wavelength (nm) 60

(B)

25

(B)

20

40

D-Sym6 Spectra

20

10

231.3

5

0

220.7

1

Mexh-FWT Spectra

15

287.5

-20

0

240.4

-5

-40

SB 10 -35 mg/L CP 10 -35 mg/L

-10

CP 10 - 35mg/L -60 200

-15 200

220

240

260

280

SB 10 - 35 mg/L

220

240

300

260

280

300

Wavelength (nm)

Wavelength (nm) 200

(C)

Fig. 6. Sym6 (A) and mexh (B) transforms of FWT-processed spectra. 150 100 1 D-Mexh-FWT Spectra

228.0 and 286.0 nm for CP and SB, respectively. Both wavelengths were subsequently chosen for the simultaneous determination of SB and CP due to their derivative amplitudes proportional to the concentration ranges studied of SB and CP (10–35 mg/L). Fig. 2B and C present the first-order derivatives of ratio spectra after the ratio spectra being differentiated (Order: 5; No. of coefficients: 9) and smoothed (Order: 3; No. of coefficients: 125) by Savitzky–Golay algorithm. To optimize this technique, the influence of divisor standard concentration was investigated with the concentration ranges for Lambert–Beer’s law compliance. SB 20 mg/L and CP 10 mg/L were considered as suitable for the determination of CP and SB, respectively. The determination of each component was based on the proportionality of its concentrations to relevant first-order derivative amplitudes at a suitable wavelength. The two points, 286.0 and 237.5 nm, at which the highest amplitude and coincidence of derivative signals seen with an error less than 3%, were selected as the working wavelengths for analyzing CP and SB, respectively. The fact that our data are different from previously published work on derivative spectrophotometric determination of CP and SB in their mixture [29] could be attributed to the difference in differentiating and smoothing manner, and equipment used. Nevertheless, our experimental set up seems to be better when referring to (i) the simultaneous determination of both compounds possibly realized with first-order derivative transform

258.9

50 0 -50

269.2

-100 SB 10 - 35 mg/L CP 10 - 35 mg/L

-150 -200 210

230

250

270

290

Wavelength (nm) Fig. 7. Derivative – wavelet transforms combined: haar transform of first-order derivative spectra (A); derivative transform of sym6-transformed spectra (B); derivative transform of mexh-FWT processed spectra (C).

and (ii) much higher amplitudes of derivative signals obtained for the same concentration range. Discrete Fourier transform Fig. 3A–C exhibit the discrete Fourier transformed signals of Savitzky–Golay smoothed zero-order spectra and ratio spectra (Or-

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V.D. Hoang et al. / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 121 (2014) 704–714

Fig. 8. Typical liquid chromatogram of a binary mixture of CP 20 mg/L and SB 20 mg/L.

Table 2 Statistical analysis of calibration graphs of the proposed spectrophotometric methods (10–35 mg/L; n = 6). Method Derivative transform 1 D-spectra 1

D-ratio spectra

Fourier transform Fourier-spectra Fourier-ratio spectra Wavelet transform Sym6-spectra Haar-spectra Mexh-spectra Haar-ratio spectra Sym6-FWT spectra Haar-FWT spectra Mexh-FWT spectra

Compound

Wavelength (nm)

a

b

Sa

Sb

Sy.x

R2

CP SB CP SB

286.0 228.0 286.9 237.5

0.0541 0.0142 2.3004 0.0264

0.0115 0.0001 0.7769 0.0497

0.0004 0.0001 0.0243 0.0002

0.0113 0.0030 0.5867 0.0068

0.0098 0.0026 0.5099 0.0059

0.9996 0.9996 0.9995 0.9995

CP SB CP SB

278.0 246.0 266.0 250.0

0.0010 0.0010 0.1829 0.0023

0.0289 0.0003 0.0196 0.0003

0.0001 0.0001 0.0007 0.0001

0.0004 0.0006 0.0183 0.0007

0.0003 0.0005 0.0159 0.0006

0.9987 0.9972 0.9999 0.9993

CP SB CP SB CP SB CP SB CP SB CP SB CP SB

274.0 231.8 288.8 222.8 241.4 281.0 293.5 241.5 265.4 249.2 257.5 262.3 231.3 240.4

0.0342 0.0136 0.0779 0.0280 0.3005 0.0275 23.594 0.0404 0.0788 0.0406 0.1503 0.0682 0.2051 0.0469

0.0206 0.0072 0.0152 0.0066 0.1375 0.0634 13.685 0.0025 0.2110 0.0637 0.1397 0.1032 0.1948 0.0974

0.0004 0.0002 0.0005 0.0003 149.01 0.0006 0.3316 0.0003 0.0022 0.0005 0.0016 0.0008 0.0030 0.0011

0.0104 0.0060 0.0142 0.0088 2.8326 0.0151 7.9806 0.0078 0.0551 0.0140 0.0399 0.0208 0.0735 0.0288

0.0090 0.0052 0.0123 0.0077 0.0421 0.0131 6.9362 0.0068 0.0479 0.0122 0.0346 0.0181 0.0639 0.0250

0.9993 0.9986 0.9997 0.9993 0.9998 0.9979 0.9992 0.9997 0.9966 0.9991 0.9995 0.9993 0.9991 0.9974

240.4 216.1 273.6 241.6 252.1 223.7 287.5 220.7 276.2 223.8 261.8 223.7 255.8 257.7 265.4 269.5 258.9 269.2

0.3399 0.1267 0.2588 0.0773 0.0984 0.2521 0.4952 0.2053 0.5388 0.1650 0.8480 0.5775 1.8591 0.8496 1.9755 0.8533 2.5491 0.5514

0.0601 0.1564 0.2340 0.2865 0.2507 0.0334 0.1949 0.0161 0.5837 0.1305 0.6199 0.6921 5.1380 1.4507 4.0002 1.2967 2.1140 1.2897

0.0036 0.0009 0.0029 0.0022 0.0031 0.0032 0.0053 0.0090 0.0068 0.0057 0.0058 0.0078 0.0535 0.0156 0.0393 0.0253 0.0399 0.0203

0.0883 0.0223 0.0713 0.0548 0.0748 0.0771 0.1296 0.2172 0.1643 0.1395 0.1410 0.1877 1.2877 0.3756 0.9478 0.6093 0.9609 0.4901

0.0768 0.0193 0.0620 0.0476 0.0650 0.0670 0.1126 0.1888 0.1428 0.1212 0.1226 0.1632 1.1192 0.3264 0.8238 0.5296 0.8351 0.4259

0.9995 0.9997 0.9994 0.9965 0.9960 0.9993 0.9995 0.9923 0.9993 0.9950 0.9998 0.9992 0.9966 0.9986 0.9984 0.9964 0.9990 0.9945

Derivative – wavelet transforms combined Sym6-1D spectra CP SB 1 Haar- D spectra CP SB Mexh-1D spectra CP SB 1 D-Sym6 spectra CP SB 1 D-Haar spectra CP SB 1 D-Mexh spectra CP SB 1 D-Sym6-FWT spectra CP SB 1 D-Haar-FWT spectra CP SB 1 D-Mexh-FWT spectra CP SB

Y = aC + b; where C is concentration in mg/L and Y in signal’s amplitude unit. a: Slope; b: intercept; Sa: SD of the slope; Sb: SD of the intercept; Sy.x: SD of the residuals; R2: coefficient of determination.

der: 3; No. of coefficients: 125). These spectra were convoluted and the coefficients tj were calculated using 8-point Ti = (cos x + cos (x + 45°)) combined trigonometric functions for the range 210–300 nm. Using this transform, Dk = 4 nm (Fig. 3A and C) and 0.1 nm (Fig. 3B) were chosen for Fourier transformed signals of spectra and ratio spectra. Although the amplitudes of Fourier transformed signals was smaller than their corresponding derivative ones, no smoothing step was further required to all Fourier

spectra obtained. Thus, the discrete Fourier transform could be served to de-noise UV spectra as previously suggested [34]. Wavelet transform Basically, the wavelet analysis procedure is based on the adoption of a wavelet prototype function i.e. mother wavelet. Because original spectra can be represented in terms of a wavelet expansion by using coefficients in a linear combination of the wavelet func-

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Table 3 Assay results for the determination of CP and SB in powders for injection. % of label claim (mean ± SD, n = 6) Method

Cefactam CP

Sulperazon SB

Jincetam

CP

SB

CP

Bacamp SB

CP

SB

RP-HPLC

100.1 ± 1.1

99.3 ± 1.2

100.4 ± 0.9

100.3 ± 1.2

9.8 ± 0.7

99.1 ± 1.0

100.9 ± 1.1

100.8 ± 0.8

Derivative transform 1 D-spectra 1 D-ratio spectra

99.4 ± 0.7 100.4 ± 0.9

99.3 ± 1.7 99.2 ± 0.8

99.9 ± 1.3 100.5 ± 0.6

99.4 ± 1.8 99.7 ± 1.3

100.6 ± 1.0 100.0 ± 0.8

99.6 ± 1.2 100.8 ± 0.8

101.6 ± 0.7 100.2 ± 1.0

101.2 ± 1.3 100.6 ± 1.1

Fourier transform Fourier-spectra Fourier-ratio spectra

100.2 ± 0.7 99.5 ± 0.9

100.0 ± 0.9 100.3 ± 1.0

99.5 ± 0.8 99.8 ± 1.0

99.9 ± 1.5 100.6 ± 1.0

99.5 ± 1.2 100.3 ± 1.0

100.4 ± 1.0 100.6 ± 1.2

100.2 ± 1.3 99.9 ± 1.3

101.5 ± 1.0 100.8 ± 1.2

Wavelet transform Sym6-spectra Haar-spectra Mexh-spectra Haar-ratio spectra Sym6-FWT spectra Haar-FWT spectra Mexh-FWT spectra

100.7 ± 0.6 100.0 ± 0.7 99.9 ± 0.7 100.0 ± 1.0 100.3 ± 0.8 100.1 ± 1.1 99.8 ± 0.9

100.9 ± 1.3 100.8 ± 1.1 99.1 ± 1.1 99.7 ± 1.5 100.1 ± 1.2 99.6 ± 1.3 99.7 ± 0.8

101.3 ± 0.9 100.0 ± 1.2 100.0 ± 1.1 99.7 ± 1.3 99.6 ± 0.9 99.8 ± 1.2 100.2 ± 1.3

100.9 ± 1.7 100.9 ± 1.7 100.4 ± 1.3 100.8 ± 1.9 100.3 ± 1.5 100.6 ± 1.6 100.1 ± 1.7

100.7 ± 0.9 100.0 ± 0.8 101.1 ± 0.9 100.3 ± 0.7 100.2 ± 0.8 99.9 ± 1.1 99.8 ± 1.0

99.5 ± 1.5 100.8 ± 0.8 100.7 ± 1.1 100.9 ± 1.0 99.6 ± 1.1 99.8 ± 1.3 99.5 ± 1.4

101.1 ± 0.9 100.2 ± 1.0 101.0 ± 1.1 100.5 ± 1.2 100.8 ± 1.3 10.6 ± 1.3 101.0 ± 0.9

100.7 ± 0.9 100.6 ± 1.1 99.6 ± 1.9 100.6 ± 1.4 100.9 ± 1.1 101.3 ± 1.2 100.7 ± 1.0

100.6 ± 1.1 100.7 ± 1.4 100.1 ± 1.0 99.3 ± 0.7 99.7 ± 0.8 99.9 ± 0.8 100.8 ± 1.0 100.8 ± 1.0 99.7 ± 1.2

100.4 ± 1.1 99.7 ± 1.4 99.9 ± 1.9 100.7 ± 1.5 100.5 ± 0.8 99.5 ± 1.4 100.1 ± 1.1 100.8 ± 1.0 99.7 ± 0.9

99.8 ± 1.3 99.7 ± 1.9 10.8 ± 1.5 100.5 ± 1.7 100.6 ± 1.7 9.7 ± 1.4 99.9 ± 1.6 100.2 ± 1.0 100.1 ± 1.2

100.5 ± 1.1 99.4 ± 0.9 99.7 ± 0.9 99.7 ± 1.3 99.6 ± 1.4 100.1 ± 1.1 100.5 ± 1.3 100.6 ± 1.4 99.8 ± 1.0

100.2 ± 0.9 100.6 ± 0.9 100.5 ± 1.3 100.6 ± 1.4 99.4 ± 1.5 99.7 ± 1.0 100.2 ± 0.8 100.7 ± 0.9 100.8 ± 0.9

100.7 ± 0.8 100.6 ± 0.9 100.9 ± 1.1 101.1 ± 1.0 100.7 ± 1.1 101.2 ± 0.9 100.3 ± 1.3 100.6 ± 1.4 100.6 ± 1.1

99.9 ± 1.5 100.5 ± 1.2 100.9 ± 1.5 100.7 ± 1.7 101.1 ± 1.8 101.3 ± 0.9 100.8 ± 1.1 100.7 ± 1.0 100.9 ± 0.9

Derivative – wavelet transforms combined Sym6-1D spectra 99.9 ± 1.1 Haar-1D spectra 100.6 ± 0.7 1 Mexh- D spectra 10.5 ± .7 1 D-Sym6 spectra 99.6 ± 0.8 1 D-Haar spectra 100.1 ± 1.0 1 D-Mexh spectra 99.4 ± 1.2 1 D-Sym6 FWT spectra 100.6 ± 0.6 1 D-Haar FWT spectra 99.5 ± 1.1 1 D-Mexh FWT spectra 100.3 ± 0.8

tions, the wavelet transform of spectra could be carried out by using just these corresponding wavelet coefficients. In this study, CWT and DWT were applied to unsmoothed spectra and ratio spectra for the resolution of CP and SB in their binary mixtures. For the optimization of the wavelet analysis, various wavelet transform methods at different dilation parameter (a) were tested to identify wavelet transform families to provide the best spectral recovery values. In the above test, sym6, haar and mexh were found to be appropriate for the transformation of spectral signals of the two compounds and their mixtures. In addition, several dilation parameters (a) with frequency (f) for these CWT and DWT approaches were tested to find optimal signal processing parameters. For this, a = 256 with f = 0.182 (sym6), f = 0.249 (haar), f = 0.063 (mexh) were determined. The application of these families to resolve spectra and ratio spectra is selectively displayed in Figs. 4 and 5. Spectra processing data indicate that the highest number of zero-crossing points was obtained with sym6 transform; whereas the highest amplitude of signal seen with mexh transform. In contrast, CP and SB could be only simultaneously determined by haar transform of ratio spectra. FWT is a new promising method in signal and image analysis, which offers the functions of data compression and de-noising to effectively extract the important form of complex original spectra. It is noticeable that the selected columns among the whole FWTcoefficients contain low frequency information in high scales i.e. the absorption spectrum is smooth and possesses high amplitude. In this study, the use of double signal transform in the sequences, FWT and CWT or DWT with zero crossing technique was exploited. In order to do so, FWT signal analysis approach was first applied to the zero-order absorption spectra in the wavelength range of 200.0–302.3 nm (i.e. 1024 points). Several parameters a and depths of the decomposition (J) were tested for optimizing the fractional signal processing. a = 0.3 and J = 1 were found to be the optimal one. The type of B-splines was considered to be causal

orthonormal. After that, the WFT spectra were subjected to further wavelet transform (sym6, haar, mexh) to find zero-crossing points for the simultaneous determination of CP and SB in their mixtures. It is remarkable that the resolution of the overlapping bands of CPSB mixtures was much improved by this double signal transform i.e. an increase in wavelet amplitudes and/or number of zero-crossing points observed with all wavelet families studied when comparing CWT and DWT transformed signals of original spectra (Fig. 4A–B) to those of FWT processed spectra (Fig. 6A–B). These findings further support the idea of combining CWT and FWT for spectral analysis of binary system first proposed by Dinç et al. [35]. Derivative – wavelet transforms combined In another development, the combination of derivative and wavelet transforms was performed in an effort to increase the number of zero-crossing points as well as to obtain a higher sensitivity and selectivity as compared to original derivative or wavelet spectra. This approach was successfully done with wavelet transform (sym6, haar and mexh) of first-order derivative spectra (e.g. Fig. 7A), first-order derivative transform of wavelet transformed spectra (e.g. Fig. 7B). Especially, the amplitudes of derivative signals were markedly enhanced with the spectra first processed by FWT and subsequently by sym6, haar and mexh wavelet families (e.g. Fig. 7C). Reversed Phase High Performance Liquid Chromatography analysis In this study, the RP-HPLC for the analysis of binary mixtures containing CP and SB was used as a reference method. The condition of RP-HPLC analysis was selectively chosen as already studied in the literature [23–28]. CP and SB were chromatographically analyzed by isocratic elution with a flow rate of 0.8 mL/min. The mobile phase composition was acetonitrile – phosphoric acid pH 3.2 (75: 25, v/v). Injection volume was 20 lL and detection wavelength was 210.0 nm for both compounds. Under our chromatographic

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Table 4 Results of one-way ANOVA and Bartlett tests at the significance level 5% by applying spectrophotometric and chromatographic methods to four commercial pharmaceutical formulations. Source of variation

Compound

One-way ANOVA test Sum of squares

CP

SB

Degree of freedom Mean of squares

CP

SB

Calculated F value

CP

SB

I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV

Tabulated F value Bartlett test Degree of freedom Calculated v2 value

CP

SB

I II III IV I II III IV

Tabulated v2 value

Between-groups

Within-groups

Total

19.63 27.18 24.12 18.71 39.78 24.19 38.23 22.74 20 0.981 1.359 1.206 0.935 1.989 1.210 1.911 1.137 1.255 1.122 1.125 0.783 1.533 0.522 1.470 0.716 1.671

82.10 127.20 112.55 125.40 136.25 243.45 136.55 166.75 105 0.782 1.211 1.072 1.194 1.298 2.319 1.300 1.588

101.73 154.38 136.67 144.11 176.03 267.64 174.78 189.49 125

20 7.910 9.177 8.108 6.204 10.502 6.176 7.479 11.316 31.410

I: Cefactam; II: Sulperazon; III: Jincetam; IV: Bacamp.

conditions, the retention times were found to be 2.7 and 4.4 min for SB and CP, respectively (Fig. 8). The chromatographic parameters such as resolution (Rs = 12), peak asymmetry (AF = 1.2), and plate number (ca. 1000/15 cm) were satisfactory for both compounds obviously confirming the suitability of our RP-HPLC method.

95% confidence level, there was no significant difference between the accuracy (evaluated by one-way ANOVA test, calculated F value < tabulated F value) and precision (evaluated by Bartlett test, calculated v2 value < tabulated v2 value) among all proposed methods (Table 4). Conclusion

Method validation and application The validity of the proposed spectrophotometric methods was assessed by accuracy, precision, and linearity. For studying the accuracy and within-run precision (repeatability), six synthetic mixtures of CP 20 mg/L + SB 20 mg/L were analyzed in parallel (data not shown in detail). The average percent recoveries obtained were 99.5–101.6% and low RSD values (6 2.0%) for both compounds indicating the methods’ good accuracy and precision. The calibration graphs for UV spectrophotometric determination with the linear concentration ranges of CP and SB (10–35 mg/L) are summarized in Table 2. By analogy, the RP-HPLC method was also examined for accuracy (99.3–100.8% recovered), precision (RSD < 1.5%) and linearity range (10–50 mg/L, R2 > 0.990). The proposed techniques were successfully applied to the simultaneous determination of CP and SB in their powders for injection. The spectrophotometric results were statistically compared with those obtained by RP-HPLC (Table 3). It is seen that at

UV spectrophotometric methods based on first-order derivative, Fourier and wavelet transforms of spectra and ratio spectra were developed for the resolution of CP and SB in their binary mixtures without prior separation step. Among these transforms, wavelet transform showed some distinct advantages over derivative and Fourier ones such as higher peak intensity obtained, additional smooth function and scaling factor process eliminated. Especially, the use of double signal transform in the sequences such as (i) spectra pre-processed by FWT and subsequently transformed by CWT and DWT, and (ii) derivative – wavelet transforms combined, was successfully studied as evidenced by a significant increase in amplitudes and/or number of zero-crossing points in transformed spectra. All the proposed spectrophotometric methods were simple and statistically compared to liquid chromatographic data in terms of precision and accuracy. These spectrophotometric methods, however, are found to be preferable to RP-HPLC with reference to the use of eco-friendly solvent, cost and time saving.

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Acknowledgement This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 104.07-2012.58.

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