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Thermodynamic solubility of pioglitazone HCl in polyethylene glycols 200, 400 or 600 + water mixtures at 303.2 and 308.2 K—Data report and modeling
Fluid Phase Equilibria 379 (2014) 180–184
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Thermodynamic solubility of pioglitazone HCl in polyethylene glycols 200, 400 or 600 + water mixtures at 303.2 and 308.2 K—Data report and modeling Shahla Soltanpour ∗ , Fatemeh Zohrabi, Zahra Bastami Faculty of Pharmacy, Zanjan University of Medical Sciences, Gavazang Road, Mahdavi St., Zanjan 45139, Iran
a r t i c l e
i n f o
Article history: Received 24 April 2014 Received in revised form 18 July 2014 Accepted 20 July 2014 Available online 29 July 2014 Keywords: Pioglitazone HCl Thermodynamic solubility Polyethylene glycols 200, 400 and 600 Modeling
a b s t r a c t The solubility of pioglitazone HCl (99 data points) in binary mixtures of polyethylen glycols (PEGs) 200, 400 or 600 + water at three different temperatures which ranged from 298.2 K to 308.2 K were reported. Three different cosolvency models; yalkowsky, Jouyban–Acree and combined version of the Jouyban–Acree model with van’t Hoff approach, have been used for correlating the reported data, and the correlation OMRDs are 65.2%, 18.0% and 17.8% respectively. Also, a previously trained version of the Jouyban–Acree model has been used for predicting these 99 reported data points which the prediction OMRD is 23.4%. © 2014 Published by Elsevier B.V.
1. Introduction Solubility is one of the most important fields in the pharmaceutical area. Because for starting the medical effects of the drugs in any form of the formulations, their molecules must across the cell membranes to reach the receptor, and before the acrossing process the drug molecules must be solubilized in the body liquids. It is obvious that for the liquid dosage forms the solubilization step would be skipped, so, whenever a molecule is prepared in liquid dosage form the medical effects start faster in the body. In the preparation of the liquid dosage form, the scientist must choose the best solvent or solvent mixture with the minimum toxicity and high safety for producing the desired solubility of the drug molecules. Pioglitazone HCl is an anti-diabetic drug which is described as a poorly water soluble and highly permeable drug (class II of biopharmaceutics classification system (BCS)) [1,2].
cosolvency models is predicting the drugs solubility in the desired solvent mixture with the minimum experimental data points. The simplest cosolvency model among the several models which have been proposed for correlation/prediction of the drugs solubility in the solutions [3], is log-linear model of Yalkowsky. It is suitable for the solutions that have the linear relationship between the drug solubility and the fractions of the solvents, it can be written as [4]: Sat log Xm = w1 log X1Sat + w2 log X2Sat
Sat is the solubility of the solute in the solvent mixture; where, Xm X1Sat and X2Sat denote the solubility in neat solvents 1 and 2, respectively; and w1 and w2 represent the mass fractions of solvents 1 (cosolvent) and 2 (water) in the absence of the solute. Eq. (1) can be rearranged as Eq. (2) by considering w2 = 1-w1 : Sat log Xm = log X2Sat + K1 w1
2. Computational methods
or
Using the cosolvency models is a best solution for saving time and cost in the obtaining suitable solvent or solvent mixtures for dissolving the drug molecules. The main goal of developing the
Sat log Xm = K0 + K1 w1
∗ Corresponding author. Tel.: +98 241 424 8874; fax: +98 241 427 3639. E-mail addresses: [email protected] (S. Soltanpour), [email protected] (Z. Bastami). http://dx.doi.org/10.1016/j.fluid.2014.07.024 0378-3812/© 2014 Published by Elsevier B.V.
(1)
(2)
(3)
By further investigations, K1 = A + BlogP was obtained in which logP is the partition coefficient of the drug [4]: Sat log Xm = log X2Sat + (A + B log P)w1
(4)
where, A and B are model constants and w1 is the mass fraction of the cosolvent.
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
If there is no interaction between solvent–solvent or solvent–solute molecules, the model of Yalkowsky can predict the solubility well. However, most of the solvent mixtures are not ideal and interactions are existed; therefore, for considering the roles of these interactions on the drugs solubility it is necessary to add some terms to the basic log-linear model. For showing the variation of the solubility with both temperature and solvent composition we can use the Jouyban–Acree model which can compute the mathematical descriptors for the probable interactions in the mixture. The general form of the model for the solubility in binary solvent mixture at various temperatures can be written as [3]: sat sat sat log Xm,T = w1 × log X1,T + w2 × log X2,T +
× (w1 − w2 )
w1 × w2 × T
2
Ji
i=0
i
(5)
sat in which Xm,T
is the solute solubility in the solvent mixtures at temperature T (Kelvin), w1 and w2 are the mass fractions of the solvents Sat and X Sat are the solubility of the solute 1 and 2, respectively. X1,T 2,T in the neat solvents 1 and 2, respectively, and Ji are the constants of the model computed by regression analysis. A limitation for the Jouyban–Acree model is computing the model constants that require a number of experimental solubility data of the solute in the binary solvent mixtures. Solubility of the drugs in mono-solvents at different temperatures can be predicted using van’t Hoff approach (Eq. (6)) [5]. The required experimental data are solubilities in the mono-solvents at various temperatures (log XTSat ). log XTSat = A +
B T
(6)
where A and B are the model constants calculated by regression method. Combination of the Jouyban–Acree and van’t Hoff model enables the prediction of drug solubility in mixed solvents at different temperatures after training process using solubility data points; e.g. at the lowest and highest temperatures [6,7]. The combined version could be represented as:
sat log Xm,T = w1 A1 +
B1 T
+ w2 A2 +
B2 T
w1 × w2 Ji T 2
+
× (w1 − w2 )
i=0
(7)
where A1 , B1 , A2 , B2 and Ji terms are the model constants. These constants could be computed using a minimum number of experimental data points. With this combination we replace the experimental solubility data with the calculated ones, which in this case Eq. (7) is a valuable model for fitting the solubility data because it does not require any further experimental data as input. To evaluate the accuracy of the computational parts the mean relative deviation (MRD) between the calculated and observed solubilities was used. The MRD value is calculated using: 100 MRD = N
X Calculated − X Observed m,T
m,T
Observed Xm,T
(8)
181
was checked by measuring the melting point range (456.2–457.2 K) and by comparing the measured solubilities in monosolvents with the corresponding data from the literatures [8]. PEGs 200, 400 and 600 (99.5 w/w %) were purchased from Merck (Germany). Double distilled water was used for preparation of the solutions. 3.2. The drug solution preparation All binary mixtures were prepared with the accuracy of 0.001 mass fractions. 3.3. Solubility determination The solubility of pioglitazone HCl was determined by equilibrating an excess amount of the solid in the prepared binary solvent mixtures using a shaker (Behdad, Tehran, Iran) placed in an incubator equipped with a temperature-controlling system at different temperatures with the uncertainty of 0.2 K (Hoorteb, Tehran, Iran) for 3 days to reach the equilibrium at 298.2 K. After solubility determinations at 298.2 K, the remaining solutions containing excess solid were placed at 303.2 K for 2 days and the measurements were carried out and the same procedure was repeated at 308.2 K. The solutions were filtered using hydrophilic Durapore filters (0.45 m, Millipore, Ireland) and after diluting with methanol, the absorbance of these solutions were recorded at 267 nm using a UV–vis spectrophotometer (Beckman DU-650, Fullerton, USA). All the obtained concentrations are the average of at least three experimental measurements (diluting the main solutions and determining by UV), and the mean relative standard deviations (RSDs) of three repetitive experiments is 3.3%. 4. Results and discussions The minimum solubility of pioglitazone HCl is observed in aqueous solution at 298.2 K (0.000737 M) and the maximum solubility of pioglitazone HCl is observed in PEG 600 + water (0.9 + 0.1) at 308.2 K (0.065121 M), as a clear result for the experimental solubility data, addition of the cosolvent to the aqueous solutions and increasing the temperature make the solubility enhancement. Also, in our previously published papers we reported the solubility of pioglitazone HCl in aqueous mixtures of PEG 200, 400 or 600 at 298.2 K [9,10], so this paper could be the continuing of those works at different temperatures. Table 1 shows the mass fractions of the binary solvent mixtures, densities of the saturated solutions, experimental and back-calculated solubilities of pioglitazone HCl at different temperatures using three analyses which have been described as follow. Numerical analysis I includes fitting the binary solubility data to Eq. (4) (Yalkowsky). The highest MRD belongs to the aqueous PEG 600 binary set at 308.2 K with 92.1%. The lowest MRD is for aqueous PEG 200 binary set at 298.2 K with 49.6%. The MRD values of the reported data sets are listed in Table 2. The trained versions of the Yalkowsky’s linear model which has been produced by fitting the reported solubilities of pioglitazone HCl in binary aqueous mixtures of PEG 200, 400 and 600 at three different temperatures respectively are: Sat log Xm = log X2Sat + (0.353 × log P) × w1
(9)
Sat log Xm = log X2Sat + (0.360 × log P) × w1
(10)
3. Materials and methods
Sat log Xm
(11)
3.1. Materials
In numerical analysis II solubility data were fitted to Eq. (5) (Jouyban–Acree model), the highest MRD is 26.5% for solubilities in binary aqueous mixtures of PEG 200 at 298.2 K, and the lowest one is 12.4% for the solubilities in binary aqueous mixtures of PEG
where N was the number of data points in each set.
Pioglitazone HCl (99.9 w/w %) was purchased from Osveh Pharmaceutical Company (Tehran, Iran). The purity of pioglitazone HCl
=
log X2Sat
+ (0.404 × log P) × w1
182
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
Table 1 Sat ) and mole fractions (mf) of pioglitazone HCl in aqueous binary Mass fractions (w1 ) of PEGs 200, 400 or 600, and (w2 ) water and the experimental molar solubility (Xm mixtures of PEGs 200, 400 or 600 at 303.2 and 308.2 K. w1
w2
PEG 200
PEG 400
PEG 600
Water
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – – – 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 – – – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000
1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000
Data for 298.2 K were taken from the previous works [9,10].
T/K
Sat Xm
mf
303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2
0.002766 0.006308 0.009608 0.012280 0.015832 0.017499 0.020978 0.027540 0.041706 0.031186 0.024915 0.004004 0.009637 0.017009 0.021738 0.028144 0.031936 0.038039 0.045851 0.050184 0.056340 0.030967 0.002766 0.008833 0.012676 0.014353 0.016114 0.019238 0.022051 0.023936 0.044414 0.035185 0.027186 0.004004 0.012270 0.016707 0.020280 0.022051 0.023936 0.027332 0.032873 0.048080 0.040393 0.033477 0.002766 0.010166 0.016781 0.020155 0.022738 0.024051 0.031019 0.043893 0.048414 0.053559 0.032779 0.004004 0.016218 0.022249 0.024259 0.030186 0.033165 0.035206 0.051247 0.055913 0.065121 0.038831
0.000289 0.000660 0.001002 0.001275 0.001644 0.001816 0.002175 0.002858 0.004248 0.003099 0.002462 0.000415 0.001000 0.001767 0.002260 0.002930 0.003323 0.003959 0.004775 0.005116 0.005586 0.003037 0.000289 0.001802 0.002578 0.002888 0.003207 0.003783 0.004323 0.004627 0.008480 0.006638 0.005095 0.000415 0.002500 0.003388 0.004077 0.004386 0.004694 0.005351 0.006342 0.009169 0.007613 0.006270 0.000289 0.002995 0.004904 0.005836 0.006579 0.006951 0.008907 0.012502 0.013257 0.014601 0.009119 0.000415 0.004773 0.006497 0.007018 0.008685 0.009515 0.010070 0.014599 0.015304 0.017742 0.010679
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184 Table 2 MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the loglinear Yalkowsky model.
183
Table 5 Prediction MRDs and OMRD by the trained version (Eq. (12)) for the solubility of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K).
Solvent mixture
N
T/K
MRD
solvent mixture
N
T/K
MRD
PEG 200 − water PEG 200 − water PEG 200 − water
11 11 11
11 11 11
11 11 11
PEG 400 − water PEG 400 − water PEG 400 − water
11 11 11
PEG 600 − water PEG 600 − water PEG 600 − water
11 11 11
46.9 55.4 63.2 56.0 57.2 60.1 75.1 64.1 62.8 71.7 92.1 75.5 65.2
PEG 200 − water PEG 200 − water PEG 200 − water
PEG 400 − water PEG 400 − water PEG 400 − water
298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD final OMRD
PEG 600 − water PEG 600 − water PEG 600 − water
11 11 11
298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD final OMRD
23.5 11.0 21.7 18.7 36.9 11.4 9.5 19.3 47.3 25.1 23.8 32.1 23.4
200 at 308.2 K. Table 3 lists the model constants and the MRD values of the reported data sets. In numerical analysis III the reported solubility data were fitted to Eq. (7) (combined version of the Jouyban–Acree model with van’t Hoff approach), the highest MRD belongs to the aqueous binary mixtures of PEG 400 at 298.2 K with 38.8%, and the lowest MRD is for the aqueous binary mixtures of PEG 600 at 303.2 K with 7.1%. Table 4 lists the model constants and the MRD values of the reported data sets. According to Tables 2–4 the lowest and highest OMRD values belong to analysis III and I with 17.8% and 65.2%, respectively. In this part we would like to test a trained version of the Jouyban–Acree model which has been proposed previously for PEGs 200, 400 or 600 − water binary mixtures, but because of there is no trained version for all of the desired mixtures, we decided to test the only trained version for this group which is for PEG 400 − water mixtures. From the structure point of view PEG
200, 400 and 600 approximately are the same; just PEG 600 has much more branches which make it heavier with higher molecular weight. Therefore the trained version of the model for PEG 400 aqueous mixtures can predict the solubilities in aqueous mixtures of PEGs 200 or 600. The generally trained version of the Jouyban–Acree model has been reported for PEG 400–water binary mixtures is [11]: w1 w2 Sat Sat Sat = w1 log C1,T + w2 log C2,T + log Cm,T T
× 394.82 − 355.28 (w1 − w2 ) + 388.89(w1 − w2 )2
(12)
In the numerical analysis IV Eq. (12) was used for predicting the solubility of pioglitazone HCl in the reported mixtures at three different temperatures. The highest and lowest prediction MRDs are for the solubility sets of PEG 600 + water and PEG 400 + water at 298.2 K and 308.2 K with 47.3% and 9.5%, respectively and the
Table 3 Model constant, MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the Jouyban–Acree model.. N
Solvent mixture
MRD
J0
J1
J2
600.918
a
a
472.586
−306.118
1102.664
601.615
.327.431
1301.828
T/K
PEG 200 − water
33
PEG 400 − water
33
PEG 600 − water
33
a
298.2
303.2
308.2
26.5 OMRD 21.4 OMRD 22.5 OMRD final OMRD
18.7
12.4 19.2 15.1 17.2 16.3 17.7 18.0
15.2 14.3
Not significant.
Table 4 Model constant, MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the combined version of Jouyban–Acree model and van’t Hoff approach. Solvent mixture
N
MRD
A1
B1
A2
B2
J0
J1
J2
4.680
−1879.604
17.897
−6206.366
455.939
a
a
A
−477.672
a
−814.055
469.914
−268.024
1095.988
A
−455.616
14.371
−5173.455
595.359
−300.752
1286.189
T/K
PEG 200 − water
33
PEG 400 − water
33
PEG 600 − water
33
a
Not significant.
298.2
303.2
308.2
31.5 OMRD 38.8 OMRD 13.2 OMRD final OMRD
15.0
13.0 19.8 20.5 23.2 11.0 10.4 17.8
10.4 7.1
184
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
OMRD is 23.4% for all 99 data points. The predicting MRD values for this analysis are listed in Table 5. 5. Conclusion Experimental solubilities of pioglitazone HCl are reported in aqueous binary mixtures of PEG 200, 400 or 600 at three different temperatures; 298.2 K, 303.2 K and 308.2 K, which extended the available solubility database of pharmaceuticals in mixed solvents [12]. The main goal of this research was to improve the aqueous solubility of pioglitazone HCl by adding cosolvent and increasing the temperature. Additions of PEGs 200, 400 or 600 and temperature enhancement make increasing in the solubility of pioglitazone HCl dramatically. PEGs 200, 400 and 600 are safe and pharmaceutical cosolvents and for formulating pioglitazone HCl in the liquid forms (oral or parenteral), could be used after doing the toxicity tests on them. In the modeling works, the simplest model is the best one unless its high error percentage. In this work as the results shown the combined version of the Jouyban–Acree model with the van’t Hoff approach has the lowest fitting MRD values comparing with two other models. The noticeable point is in this model there is no experimental data point as the input data; in fact the experimental data points have been replaced with the calculated values. Therefore the scientist for predicting the solubility of the drug in any fractions of the cosolvent has not to measure the solubility in neat solvents. With these explanations one can say that these MRD values for this model are very valuable, because of not using any experimental data point.
But in the Yalkowsky’s log-linear model and the Jouyban–Acree model the aqueous solubility and the solubilities in neat co-solvents at each temperature, are needed respectively. Generally the MRD values in the analysis part show the good ability of all three models for fitting and predicting the solubility of pioglitazone HCl in the reported solvent mixtures at different temperatures. Acknowledgments This paper is resulted from a Pharm.D thesis through grant No. A-11-387-4. The authors are grateful for financial support from Zanjan University of Medical Sciences, Iran. References [1] A. Umar faruksha, T. Vetrichelvan, T. Int. J. Pharm. Tech. Res. 5 (2013) 754–766. [2] P.K. Mantada, M. Jeyabaskaran, J. Kumar Raja, Ch. Kalyani, Int. J. Drug Formul. Res. 2 (2011) 296–311. [3] A. Jouyban, J. Pharm. Pharm. Sci. 11 (2008) 32–58. [4] J.W. Millard, F.A. Alvarez-Nunez, S.H. Yalkowsky, Int. J. Pharm. 245 (2002) 153–166. [5] D.J.W. Grant, M. Mehdizadeh, Int. J. Pharm. 18 (1984) 25–38. [6] A. Jouyban, M.A.A. Fakhree, Experimental and computational methods pertaining to drug solubility Toxicity and Drug Testing, 1, Intech Co., New York, 2012. [7] F. Sardari, A. Jouyban, Ind. Eng. Chem. Res. 52 (2013) 14353–14358. [8] A.C. Moffat, Clarke’s Analysis of Drug and Poisons, Pharmaceutical Press, London, 2004. [9] Sh. Soltanpour, W.E. Acree Jr., A. Jouyban, AAPS PharmSciTech 10 (2009) 1153–1157. [10] Sh. Soltanpour, A. Jouyban, AAPS PharmSciTech 11 (2010) 1713–1717. [11] A. Jouyban, Chem. Pharm. Bull. 54 (2006) 1561–1566. [12] A. Jouyban, Handbook of Solubility Data for Pharmaceuticals, CRC Press, Boca Raton, FL, 2009.
Contents lists available at ScienceDirect
Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid
Thermodynamic solubility of pioglitazone HCl in polyethylene glycols 200, 400 or 600 + water mixtures at 303.2 and 308.2 K—Data report and modeling Shahla Soltanpour ∗ , Fatemeh Zohrabi, Zahra Bastami Faculty of Pharmacy, Zanjan University of Medical Sciences, Gavazang Road, Mahdavi St., Zanjan 45139, Iran
a r t i c l e
i n f o
Article history: Received 24 April 2014 Received in revised form 18 July 2014 Accepted 20 July 2014 Available online 29 July 2014 Keywords: Pioglitazone HCl Thermodynamic solubility Polyethylene glycols 200, 400 and 600 Modeling
a b s t r a c t The solubility of pioglitazone HCl (99 data points) in binary mixtures of polyethylen glycols (PEGs) 200, 400 or 600 + water at three different temperatures which ranged from 298.2 K to 308.2 K were reported. Three different cosolvency models; yalkowsky, Jouyban–Acree and combined version of the Jouyban–Acree model with van’t Hoff approach, have been used for correlating the reported data, and the correlation OMRDs are 65.2%, 18.0% and 17.8% respectively. Also, a previously trained version of the Jouyban–Acree model has been used for predicting these 99 reported data points which the prediction OMRD is 23.4%. © 2014 Published by Elsevier B.V.
1. Introduction Solubility is one of the most important fields in the pharmaceutical area. Because for starting the medical effects of the drugs in any form of the formulations, their molecules must across the cell membranes to reach the receptor, and before the acrossing process the drug molecules must be solubilized in the body liquids. It is obvious that for the liquid dosage forms the solubilization step would be skipped, so, whenever a molecule is prepared in liquid dosage form the medical effects start faster in the body. In the preparation of the liquid dosage form, the scientist must choose the best solvent or solvent mixture with the minimum toxicity and high safety for producing the desired solubility of the drug molecules. Pioglitazone HCl is an anti-diabetic drug which is described as a poorly water soluble and highly permeable drug (class II of biopharmaceutics classification system (BCS)) [1,2].
cosolvency models is predicting the drugs solubility in the desired solvent mixture with the minimum experimental data points. The simplest cosolvency model among the several models which have been proposed for correlation/prediction of the drugs solubility in the solutions [3], is log-linear model of Yalkowsky. It is suitable for the solutions that have the linear relationship between the drug solubility and the fractions of the solvents, it can be written as [4]: Sat log Xm = w1 log X1Sat + w2 log X2Sat
Sat is the solubility of the solute in the solvent mixture; where, Xm X1Sat and X2Sat denote the solubility in neat solvents 1 and 2, respectively; and w1 and w2 represent the mass fractions of solvents 1 (cosolvent) and 2 (water) in the absence of the solute. Eq. (1) can be rearranged as Eq. (2) by considering w2 = 1-w1 : Sat log Xm = log X2Sat + K1 w1
2. Computational methods
or
Using the cosolvency models is a best solution for saving time and cost in the obtaining suitable solvent or solvent mixtures for dissolving the drug molecules. The main goal of developing the
Sat log Xm = K0 + K1 w1
∗ Corresponding author. Tel.: +98 241 424 8874; fax: +98 241 427 3639. E-mail addresses: [email protected] (S. Soltanpour), [email protected] (Z. Bastami). http://dx.doi.org/10.1016/j.fluid.2014.07.024 0378-3812/© 2014 Published by Elsevier B.V.
(1)
(2)
(3)
By further investigations, K1 = A + BlogP was obtained in which logP is the partition coefficient of the drug [4]: Sat log Xm = log X2Sat + (A + B log P)w1
(4)
where, A and B are model constants and w1 is the mass fraction of the cosolvent.
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
If there is no interaction between solvent–solvent or solvent–solute molecules, the model of Yalkowsky can predict the solubility well. However, most of the solvent mixtures are not ideal and interactions are existed; therefore, for considering the roles of these interactions on the drugs solubility it is necessary to add some terms to the basic log-linear model. For showing the variation of the solubility with both temperature and solvent composition we can use the Jouyban–Acree model which can compute the mathematical descriptors for the probable interactions in the mixture. The general form of the model for the solubility in binary solvent mixture at various temperatures can be written as [3]: sat sat sat log Xm,T = w1 × log X1,T + w2 × log X2,T +
× (w1 − w2 )
w1 × w2 × T
2
Ji
i=0
i
(5)
sat in which Xm,T
is the solute solubility in the solvent mixtures at temperature T (Kelvin), w1 and w2 are the mass fractions of the solvents Sat and X Sat are the solubility of the solute 1 and 2, respectively. X1,T 2,T in the neat solvents 1 and 2, respectively, and Ji are the constants of the model computed by regression analysis. A limitation for the Jouyban–Acree model is computing the model constants that require a number of experimental solubility data of the solute in the binary solvent mixtures. Solubility of the drugs in mono-solvents at different temperatures can be predicted using van’t Hoff approach (Eq. (6)) [5]. The required experimental data are solubilities in the mono-solvents at various temperatures (log XTSat ). log XTSat = A +
B T
(6)
where A and B are the model constants calculated by regression method. Combination of the Jouyban–Acree and van’t Hoff model enables the prediction of drug solubility in mixed solvents at different temperatures after training process using solubility data points; e.g. at the lowest and highest temperatures [6,7]. The combined version could be represented as:
sat log Xm,T = w1 A1 +
B1 T
+ w2 A2 +
B2 T
w1 × w2 Ji T 2
+
× (w1 − w2 )
i=0
(7)
where A1 , B1 , A2 , B2 and Ji terms are the model constants. These constants could be computed using a minimum number of experimental data points. With this combination we replace the experimental solubility data with the calculated ones, which in this case Eq. (7) is a valuable model for fitting the solubility data because it does not require any further experimental data as input. To evaluate the accuracy of the computational parts the mean relative deviation (MRD) between the calculated and observed solubilities was used. The MRD value is calculated using: 100 MRD = N
X Calculated − X Observed m,T
m,T
Observed Xm,T
(8)
181
was checked by measuring the melting point range (456.2–457.2 K) and by comparing the measured solubilities in monosolvents with the corresponding data from the literatures [8]. PEGs 200, 400 and 600 (99.5 w/w %) were purchased from Merck (Germany). Double distilled water was used for preparation of the solutions. 3.2. The drug solution preparation All binary mixtures were prepared with the accuracy of 0.001 mass fractions. 3.3. Solubility determination The solubility of pioglitazone HCl was determined by equilibrating an excess amount of the solid in the prepared binary solvent mixtures using a shaker (Behdad, Tehran, Iran) placed in an incubator equipped with a temperature-controlling system at different temperatures with the uncertainty of 0.2 K (Hoorteb, Tehran, Iran) for 3 days to reach the equilibrium at 298.2 K. After solubility determinations at 298.2 K, the remaining solutions containing excess solid were placed at 303.2 K for 2 days and the measurements were carried out and the same procedure was repeated at 308.2 K. The solutions were filtered using hydrophilic Durapore filters (0.45 m, Millipore, Ireland) and after diluting with methanol, the absorbance of these solutions were recorded at 267 nm using a UV–vis spectrophotometer (Beckman DU-650, Fullerton, USA). All the obtained concentrations are the average of at least three experimental measurements (diluting the main solutions and determining by UV), and the mean relative standard deviations (RSDs) of three repetitive experiments is 3.3%. 4. Results and discussions The minimum solubility of pioglitazone HCl is observed in aqueous solution at 298.2 K (0.000737 M) and the maximum solubility of pioglitazone HCl is observed in PEG 600 + water (0.9 + 0.1) at 308.2 K (0.065121 M), as a clear result for the experimental solubility data, addition of the cosolvent to the aqueous solutions and increasing the temperature make the solubility enhancement. Also, in our previously published papers we reported the solubility of pioglitazone HCl in aqueous mixtures of PEG 200, 400 or 600 at 298.2 K [9,10], so this paper could be the continuing of those works at different temperatures. Table 1 shows the mass fractions of the binary solvent mixtures, densities of the saturated solutions, experimental and back-calculated solubilities of pioglitazone HCl at different temperatures using three analyses which have been described as follow. Numerical analysis I includes fitting the binary solubility data to Eq. (4) (Yalkowsky). The highest MRD belongs to the aqueous PEG 600 binary set at 308.2 K with 92.1%. The lowest MRD is for aqueous PEG 200 binary set at 298.2 K with 49.6%. The MRD values of the reported data sets are listed in Table 2. The trained versions of the Yalkowsky’s linear model which has been produced by fitting the reported solubilities of pioglitazone HCl in binary aqueous mixtures of PEG 200, 400 and 600 at three different temperatures respectively are: Sat log Xm = log X2Sat + (0.353 × log P) × w1
(9)
Sat log Xm = log X2Sat + (0.360 × log P) × w1
(10)
3. Materials and methods
Sat log Xm
(11)
3.1. Materials
In numerical analysis II solubility data were fitted to Eq. (5) (Jouyban–Acree model), the highest MRD is 26.5% for solubilities in binary aqueous mixtures of PEG 200 at 298.2 K, and the lowest one is 12.4% for the solubilities in binary aqueous mixtures of PEG
where N was the number of data points in each set.
Pioglitazone HCl (99.9 w/w %) was purchased from Osveh Pharmaceutical Company (Tehran, Iran). The purity of pioglitazone HCl
=
log X2Sat
+ (0.404 × log P) × w1
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S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
Table 1 Sat ) and mole fractions (mf) of pioglitazone HCl in aqueous binary Mass fractions (w1 ) of PEGs 200, 400 or 600, and (w2 ) water and the experimental molar solubility (Xm mixtures of PEGs 200, 400 or 600 at 303.2 and 308.2 K. w1
w2
PEG 200
PEG 400
PEG 600
Water
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – – – 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 – – – – – – – – – – – – – – – – – – – – – –
– – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – – 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000
1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000 1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 0.200 0.100 0.000
Data for 298.2 K were taken from the previous works [9,10].
T/K
Sat Xm
mf
303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 303.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2 308.2
0.002766 0.006308 0.009608 0.012280 0.015832 0.017499 0.020978 0.027540 0.041706 0.031186 0.024915 0.004004 0.009637 0.017009 0.021738 0.028144 0.031936 0.038039 0.045851 0.050184 0.056340 0.030967 0.002766 0.008833 0.012676 0.014353 0.016114 0.019238 0.022051 0.023936 0.044414 0.035185 0.027186 0.004004 0.012270 0.016707 0.020280 0.022051 0.023936 0.027332 0.032873 0.048080 0.040393 0.033477 0.002766 0.010166 0.016781 0.020155 0.022738 0.024051 0.031019 0.043893 0.048414 0.053559 0.032779 0.004004 0.016218 0.022249 0.024259 0.030186 0.033165 0.035206 0.051247 0.055913 0.065121 0.038831
0.000289 0.000660 0.001002 0.001275 0.001644 0.001816 0.002175 0.002858 0.004248 0.003099 0.002462 0.000415 0.001000 0.001767 0.002260 0.002930 0.003323 0.003959 0.004775 0.005116 0.005586 0.003037 0.000289 0.001802 0.002578 0.002888 0.003207 0.003783 0.004323 0.004627 0.008480 0.006638 0.005095 0.000415 0.002500 0.003388 0.004077 0.004386 0.004694 0.005351 0.006342 0.009169 0.007613 0.006270 0.000289 0.002995 0.004904 0.005836 0.006579 0.006951 0.008907 0.012502 0.013257 0.014601 0.009119 0.000415 0.004773 0.006497 0.007018 0.008685 0.009515 0.010070 0.014599 0.015304 0.017742 0.010679
S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184 Table 2 MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the loglinear Yalkowsky model.
183
Table 5 Prediction MRDs and OMRD by the trained version (Eq. (12)) for the solubility of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K).
Solvent mixture
N
T/K
MRD
solvent mixture
N
T/K
MRD
PEG 200 − water PEG 200 − water PEG 200 − water
11 11 11
11 11 11
11 11 11
PEG 400 − water PEG 400 − water PEG 400 − water
11 11 11
PEG 600 − water PEG 600 − water PEG 600 − water
11 11 11
46.9 55.4 63.2 56.0 57.2 60.1 75.1 64.1 62.8 71.7 92.1 75.5 65.2
PEG 200 − water PEG 200 − water PEG 200 − water
PEG 400 − water PEG 400 − water PEG 400 − water
298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD final OMRD
PEG 600 − water PEG 600 − water PEG 600 − water
11 11 11
298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD 298.2 303.2 308.2 OMRD final OMRD
23.5 11.0 21.7 18.7 36.9 11.4 9.5 19.3 47.3 25.1 23.8 32.1 23.4
200 at 308.2 K. Table 3 lists the model constants and the MRD values of the reported data sets. In numerical analysis III the reported solubility data were fitted to Eq. (7) (combined version of the Jouyban–Acree model with van’t Hoff approach), the highest MRD belongs to the aqueous binary mixtures of PEG 400 at 298.2 K with 38.8%, and the lowest MRD is for the aqueous binary mixtures of PEG 600 at 303.2 K with 7.1%. Table 4 lists the model constants and the MRD values of the reported data sets. According to Tables 2–4 the lowest and highest OMRD values belong to analysis III and I with 17.8% and 65.2%, respectively. In this part we would like to test a trained version of the Jouyban–Acree model which has been proposed previously for PEGs 200, 400 or 600 − water binary mixtures, but because of there is no trained version for all of the desired mixtures, we decided to test the only trained version for this group which is for PEG 400 − water mixtures. From the structure point of view PEG
200, 400 and 600 approximately are the same; just PEG 600 has much more branches which make it heavier with higher molecular weight. Therefore the trained version of the model for PEG 400 aqueous mixtures can predict the solubilities in aqueous mixtures of PEGs 200 or 600. The generally trained version of the Jouyban–Acree model has been reported for PEG 400–water binary mixtures is [11]: w1 w2 Sat Sat Sat = w1 log C1,T + w2 log C2,T + log Cm,T T
× 394.82 − 355.28 (w1 − w2 ) + 388.89(w1 − w2 )2
(12)
In the numerical analysis IV Eq. (12) was used for predicting the solubility of pioglitazone HCl in the reported mixtures at three different temperatures. The highest and lowest prediction MRDs are for the solubility sets of PEG 600 + water and PEG 400 + water at 298.2 K and 308.2 K with 47.3% and 9.5%, respectively and the
Table 3 Model constant, MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the Jouyban–Acree model.. N
Solvent mixture
MRD
J0
J1
J2
600.918
a
a
472.586
−306.118
1102.664
601.615
.327.431
1301.828
T/K
PEG 200 − water
33
PEG 400 − water
33
PEG 600 − water
33
a
298.2
303.2
308.2
26.5 OMRD 21.4 OMRD 22.5 OMRD final OMRD
18.7
12.4 19.2 15.1 17.2 16.3 17.7 18.0
15.2 14.3
Not significant.
Table 4 Model constant, MRDs and OMRDs of fitting solubility data of pioglitazone HCl in the aqueous binary mixtures of PEGs 200, 400 or 600 at three different temperatures (T/K) to the combined version of Jouyban–Acree model and van’t Hoff approach. Solvent mixture
N
MRD
A1
B1
A2
B2
J0
J1
J2
4.680
−1879.604
17.897
−6206.366
455.939
a
a
A
−477.672
a
−814.055
469.914
−268.024
1095.988
A
−455.616
14.371
−5173.455
595.359
−300.752
1286.189
T/K
PEG 200 − water
33
PEG 400 − water
33
PEG 600 − water
33
a
Not significant.
298.2
303.2
308.2
31.5 OMRD 38.8 OMRD 13.2 OMRD final OMRD
15.0
13.0 19.8 20.5 23.2 11.0 10.4 17.8
10.4 7.1
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S. Soltanpour et al. / Fluid Phase Equilibria 379 (2014) 180–184
OMRD is 23.4% for all 99 data points. The predicting MRD values for this analysis are listed in Table 5. 5. Conclusion Experimental solubilities of pioglitazone HCl are reported in aqueous binary mixtures of PEG 200, 400 or 600 at three different temperatures; 298.2 K, 303.2 K and 308.2 K, which extended the available solubility database of pharmaceuticals in mixed solvents [12]. The main goal of this research was to improve the aqueous solubility of pioglitazone HCl by adding cosolvent and increasing the temperature. Additions of PEGs 200, 400 or 600 and temperature enhancement make increasing in the solubility of pioglitazone HCl dramatically. PEGs 200, 400 and 600 are safe and pharmaceutical cosolvents and for formulating pioglitazone HCl in the liquid forms (oral or parenteral), could be used after doing the toxicity tests on them. In the modeling works, the simplest model is the best one unless its high error percentage. In this work as the results shown the combined version of the Jouyban–Acree model with the van’t Hoff approach has the lowest fitting MRD values comparing with two other models. The noticeable point is in this model there is no experimental data point as the input data; in fact the experimental data points have been replaced with the calculated values. Therefore the scientist for predicting the solubility of the drug in any fractions of the cosolvent has not to measure the solubility in neat solvents. With these explanations one can say that these MRD values for this model are very valuable, because of not using any experimental data point.
But in the Yalkowsky’s log-linear model and the Jouyban–Acree model the aqueous solubility and the solubilities in neat co-solvents at each temperature, are needed respectively. Generally the MRD values in the analysis part show the good ability of all three models for fitting and predicting the solubility of pioglitazone HCl in the reported solvent mixtures at different temperatures. Acknowledgments This paper is resulted from a Pharm.D thesis through grant No. A-11-387-4. The authors are grateful for financial support from Zanjan University of Medical Sciences, Iran. References [1] A. Umar faruksha, T. Vetrichelvan, T. Int. J. Pharm. Tech. Res. 5 (2013) 754–766. [2] P.K. Mantada, M. Jeyabaskaran, J. Kumar Raja, Ch. Kalyani, Int. J. Drug Formul. Res. 2 (2011) 296–311. [3] A. Jouyban, J. Pharm. Pharm. Sci. 11 (2008) 32–58. [4] J.W. Millard, F.A. Alvarez-Nunez, S.H. Yalkowsky, Int. J. Pharm. 245 (2002) 153–166. [5] D.J.W. Grant, M. Mehdizadeh, Int. J. Pharm. 18 (1984) 25–38. [6] A. Jouyban, M.A.A. Fakhree, Experimental and computational methods pertaining to drug solubility Toxicity and Drug Testing, 1, Intech Co., New York, 2012. [7] F. Sardari, A. Jouyban, Ind. Eng. Chem. Res. 52 (2013) 14353–14358. [8] A.C. Moffat, Clarke’s Analysis of Drug and Poisons, Pharmaceutical Press, London, 2004. [9] Sh. Soltanpour, W.E. Acree Jr., A. Jouyban, AAPS PharmSciTech 10 (2009) 1153–1157. [10] Sh. Soltanpour, A. Jouyban, AAPS PharmSciTech 11 (2010) 1713–1717. [11] A. Jouyban, Chem. Pharm. Bull. 54 (2006) 1561–1566. [12] A. Jouyban, Handbook of Solubility Data for Pharmaceuticals, CRC Press, Boca Raton, FL, 2009.