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Modelling the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
Modelling the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban1*, M.A.A. Fakhree2, M. Hamzeh-Mivehroud3, W.E. Acree Jr.4 Faculty of Pharmacy and Drug Applied Research Center, Tabriz University of Medical Sciences, Tabriz 51664, Iran 2 Kimia Research Institute, PO Box 51665-171, Tabriz, Iran 3 Biotechnology Research Center, Tabriz University of Medical Sciences, Tabriz 51664, Iran 4 Department of Chemistry, University of North Texas, Denton, TX 76203-5070, United States *Correspondence: [email protected]
1
A quantitative-structure property relationship (QSPR) was proposed for modeling deviations of solubilities of drugs in water-dioxane mixtures at various temperatures from the predicted solubilities by the Jouyban-Acree model. The QSPR employed the normalized values of the hydration energy, energy of the highest occupied molecular orbital, total energy, logarithm of partition coefficient and molar volume of drugs computed using HyperChem software. The applicability of the proposed QSPR to real solubility data was evaluated employing 34 solubility data sets in water-dioxane mixtures at various temperatures by computing the mean percentage deviation (MPD) as an accuracy criterion. The overall MPD (± SD) of the QSPR was 17.9 ± 11.4% which is an acceptable error range in the pharmaceuticals field. The corresponding MPD (± SD) for 26 solubility data sets in ethanol-ethyl acetate mixtures at various temperatures was 9.6 ± 5.8%. Key words: Solubility prediction – Cosolvency – Jouyban-Acree model – Water-dioxane mixtures – Ethanol-ethyl acetate mixtures – QSPR.
Solubility of drugs/drug candidates is a challenging area in the pharmaceuticals industry and solvent mixing or cosolvency is one of the most reliable solubility alteration methods. In addition to experimental efforts to determine the solubility of drugs in solvent mixtures, a number of attempts have been made to provide prediction tools for ab initio estimation of solubilities or prediction based on a limited number of experimental data. In 1964, Paruta et al. tried to correlate the solubility of salicylic acid as a function of dielectric constant of the solvent mixture [1]. In 1972, Yalkowsky et al. proposed the loglinear model describing the solubility of drugs in water-cosolvent mixtures as algebraic summation of the solubilities in water-cosolvent mixtures considering solvent composition [2]. The log-linear model was extended to estimate the solubilities of various drugs employing the solubilization power approach of the cosolvent [3]. The Hildebrand solubility equation was extended to calculate the solubility of drugs in water-dioxane mixtures by Martin et al. in 1980 [4]. A model was developed by our group and showed accurate results for modeling the solubility of drugs in water-cosolvent mixtures at fixed [5] and various temperatures [6]. In the latest report [7], a trained version of the Jouyban-Acree model was reported for predicting the solubility of drugs in water-dioxane mixtures at various temperatures. The model was (Equation 1): 2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 ln X m ,T = f c ln X c ,T + f w ln X w,T + f c f w
T
+
T
+
T
more accurate solubility predictions in water-dioxane mixtures. The available solubility data of drugs were used to check the capability and accuracy of the proposed QSPR model. Dioxane is not a pharmaceutical cosolvent because of its toxicity. However it has been widely used in cosolvency modeling studies, is completely miscible with water and provides the widest polarity range. Therefore this cosolvent was chosen to check the applicability of the proposed QSPR.
I. Experimental data and computational methods
Available solubility data of drugs in water-dioxane mixtures were collected from the literature [4, 8-18] and listed in Table I. The 2D structure of each compound was drawn, converted to 3D using HyperChem 7.0 [19], and pre-minimized by Polak-Ribiere geometry optimization using MM+ method [20]. The structures were found by MM+, used as the starting point for re-minimization by Polak-Ribiere optimization using AM1 semi-empirical and also quantum mechanical methods. The energy optimized molecules were used to compute molecular descriptors. Grid (SAG) and approximate (SAA) surface areas, molar volume (Vol), hydration energy (HE), molar refractivity (MR), polarizability (Pol), logarithm of partition coefficient (logP), molecular weight (MW), total energy (TE), dipole moment (DM), energy of the highest occupied molecular orbital (HOMO) and energy of the lowest unoccupied molecular orbital (LUMO) were calculated using HyperChem software. The numerical values of the descriptors and their mean values were listed in Table II. The diversity of the drugs studied is reflected in the magnitude of the descriptors range, e.g. logP ranging from -1.98 to 1.39 and molar volume ranging from 429 to 780. The normalized descriptors are equal to zero for pure mono-solvent systems (when fc or fw is zero). To provide a normalized range for the numerical values of the descriptors, they were multiplied in fcfw and then divided by the mean values of the descriptors. As an example, the normalized molar volume (Vol’) of a drug is calculated by:
where fc and fw are the volume fractions of cosolvent and water in the absence of the solute, Xm,T, Xc,T and Xw,T are the mole fraction solubility of the solute in solvent mixture, cosolvent and water at temperature (T, K). Using the trained version of the model, only two solubility data points in neat dioxane and water are required for the prediction of solubility of a drug in the mixtures and the percentage deviation of the predicted data sets was 27% [7]. The model was developed based on assuming similar interactions between solvent mixture and the solutes. However, it is obvious that various drug molecules interact in different strengths with the solvent mixture because of the presence of various functional groups. These interactions could be represented using various chemical descriptors. The aim of this work is to present a quantitative structure property relationship (QSPR) model for providing
Vol’ = fc · fw · Vol/[Mean of Vol (= 608.8)]
359
Eq. 2
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
Table I - Details of solubility data sets in water-dioxane mixtures, temperature (T, K), logarithm of solubility of the drugs in dioxane (ln Xc,T) and water (ln Xw,T) at T, number of data points in each set (N), the mean percentage deviation (MPD) for back-calculated and predicted solubilities using Equation 1 and the proposed model. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Solute Acetanilide Acetanilide Acetanilide Acetanilide Acetanilide Caffeine Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid p-Hydroxybenzoic acid Paracetamol Paracetamol Paracetamol Paracetamol Paracetamol Paracetamol Phenacetin Phenacetin Phenacetin Phenacetin Phenacetin Sulfadiazine Sulfadimidine Sulfamethizole Sulfamethoxazol Sulfanilamide Sulfapyridine Sulfisomidine Sulphamethoxypyridazine Theobromine Theophylline
Ref. 8 8 8 8 8 9 8 8 8 8 8 8 10 8 8 8 8 8 11 12 12 12 12 12 13 13 14 13 15 16 17 13 18 4
T 293 298 303 308 313 298 283 293 298 303 308 313 298 293 298 303 308 313 298 293 298 303 308 313 298 298 298 298 298 298 298 298 298 298
ln Xc,T -2.37 -2.12 -2.01 -1.81 -1.55 -4.77 -6.91 -6.76 -6.62 -6.50 -6.50 -6.40 -2.47 -3.70 -3.62 -3.53 -3.45 -3.34 -3.03 -4.26 -4.07 -3.84 -3.63 -3.48 -7.61 -6.51 -6.94 -3.51 -2.52 -10.29 -5.99 -3.74 -7.72 -5.95
ln Xw,T -7.26 -7.13 -7.01 -7.01 -6.81 -6.08 -13.23 -13.07 -12.94 -12.75 -12.53 -12.21 -7.42 -6.38 -6.27 -6.07 -5.95 -5.81 -6.27 -9.61 -9.41 -9.18 -9.04 -8.84 -12.33 -12.71 -10.25 -10.67 -7.35 -13.24 -9.21 -10.20 -10.32 -7.21
N 11 11 11 11 11 16 12 12 12 12 12 12 13 12 12 12 12 12 17 13 13 13 13 13 17 19 19 15 16 17 21 18 11 21
Overall MPD ± SD
MPD for back-calculated data
MPD for predicted data1
Eq. 1
Eq. 8
Eq. 1
Eq. 1 + QSPR
33.3 36.9 33.0 32.5 36.9 34.8 62.2 53.5 44.3 34.7 24.8 19.9 33.4 12.2 15.7 16.9 21.3 22.7 9.4 13.0 11.4 11.4 8.1 10.4 24.7 16.2 41.6 15.1 14.1 38.8 24.7 27.7 51.1 7.8
22.7 25.7 23.2 24.8 28.8 13.1 18.9 12.9 8.8 6.1 9.7 16.9 28.6 10.4 9.9 10.0 13.6 14.7 12.3 13.0 11.4 11.4 8.1 10.4 14.9 25.9 32.1 12.6 17.1 67.3 12.1 11.3 33.7 16.0
35.4 39.0 34.7 34.3 38.7 34.6 71.2 61.7 51.8 41.5 30.9 25.6 33.8 15.2 18.5 19.5 23.6 25.0 10.0 14.8 13.1 13.3 9.9 11.9 25.8 16.3 43.4 15.8 14.3 38.6 26.4 29.3 50.8 8.1
21.5 24.5 22.1 24.4 28.0 13.1 23.3 16.9 11.4 5.5 7.4 14.9 34.0 9.3 10.1 10.9 14.5 16.0 12.7 12.8 11.2 11.5 8.8 11.0 15.8 28.6 33.2 12.6 83.6 75.4 13.1 12.5 35.7 21.9
26.3 ± 14.22
17.9 ± 11.42
28.7 ± 15.43
20.8 ± 16.93
The model constants of the Jouyban-Acree model and the QSPR were computed using data sets after excluding data of the drug of interest, and then the solubility of the drug was predicted. 2 The overall MPD difference was statistically significant (p<0.001). 3 The overall MPD difference was statistically significant (p<0.02). 1
Table II - The numerical values of hydration energy (HE), the energy of the highest occupied molecular orbital (HOMO), total energy (TE), logarithm of partition coefficient (logP), molar volumes (Vol) of the drugs dissolved in water-dioxane mixtures computed using HyperChem software and their mean values. Solute
HE
HOMO
TE
Vol
log P
Acetanilide Caffeine Nalidixic acid p-Hydroxy benzoic acid Paracetamol Paracetamol Phenacetin Sulfadiazine Sulfadimidine Sulfamethizole Sulfamethoxazol Sulfanilamide Sulfapyridine Sulfisomidine Sulphamethoxypyridazine Theobromine Theophylline
-4.24 -2.30 -6.01 -13.72 -10.71 -10.71 -4.95 -14.39 -11.64 -18.65 -15.22 -13.26 -14.07 -11.79 -18.73 -5.09 -5.41
-8.910 -6.671 -9.151 -9.608 -8.460 -8.460 -8.513 -9.171 -9.131 -9.459 -9.126 -9.151 -9.192 -9.155 -9.080 -6.790 -6.798
-38633.82 -60552.97 -70944.80 -44749.11 -46028.73 -46028.73 -53199.47 -71018.59 -78205.20 -72540.01 -73912.91 -49060.67 -69522.53 -78208.32 -81978.76 -56974.05 -56971.42
471.5 568.1 682.6 429.1 499.8 499.8 604.5 676.7 779.1 691.9 696.9 489.8 686.9 780.2 751.9 521.1 520.0
-0.29 -1.06 1.39 -0.04 -1.32 -1.32 -0.95 -1.49 -0.50 -0.30 -1.54 -1.98 -1.31 -1.64 0.17 -1.31 -1.31
Mean values
-10.64
-8.64
-61678.82
608.8
-0.87
360
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
The numerical values of the deviations from the Jouyban-Acree model were computed using Equation 3: Eq. 3 2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 Y = ln X m,T − f c ln X c ,T + f w ln X w,T + f c f w + + T T T
14 R = 0.9958
12
Since the solvent system (i.e. water-dioxane) was the same, these deviations should be a function of the normalized descriptors of drugs and could be represented as:
-lnXm (Computed)
10
Eq. 4
Y = f(Vol’, HE’, log P’, …)
To calculate the numerical values of the QSPR model, the least square method was used, the validity of the QSPR was evaluated using the F test, the significance of the descriptor’s contribution in the model was checked using the t-test and the descriptors were included in the QSPR with the significance level of < 0.05. The mean percentage deviation (MPD) was used to check the accuracy of the prediction method and was calculated using: Calculated − X mObserved | 100 | X m MPD = ∑ Observed N Xm
|
2
0
Eq. 5
0
6
8
10
12
14
70
Eq. 1
60
Eq. 8
50 Relative frequency
Numerical values of the normalized descriptors were regressed against Y values of the collected data sets. All descriptors were considered in the linear regression model and the descriptors with significance level of > 0.05 were excluded from the model. The most accurate model for describing the solubility deviations from the Jouyban-Acree model was:
40 30 20 10
Y = 3.113(± 0.227 )HE ' − 5.124(± 0.611)HOMO' − 9.697(± 1.337 )TE ' Eq. 7 + 11 .782(± 1.696 )Vol ' + 0.238(± 0.069 )log P '
0
≤ 4%
4-30%
> 30%
IPD
The F value of Equation 7 was 63 which revealed that the correlation was statistically significant (p < 0.0005). The solubility of the studied drugs was back-calculated using a combination of Equations 1 and 7 (i.e. Equation 8), the MPD values were computed and listed in Table I:
+ 3.113(± 0.227 )HE ' − 5.124(± 0.611)HOMO' − 9.697(± 1.337 )TE '
4
Figure 1 - Plot of the computed -lnXm (by Equation 8) versus observed -lnXm of drugs in water-dioxane mixtures and the correlation coefficient.
Eq. 6
2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 ln X m ,T = f c ln X c ,T + f w ln X w,T + f c f w + + T T T
2
-lnXm (Observed)
II. Results and Discussion
+ 11 .782(± 1.696)Vol '+ 0.238(± 0.069)log P '
6
4
in which N is the number of solubility data points in each set. The individual percentage deviation (IPD) was also computed by:
| X Calculated − X mObserved IPD = 100 m X mObserved
8
Figure 2 - The relative frequency of the individual relative deviation (IPD) of back-calculated solubilities using Equations 1 and 8.
To assess the prediction capability of the proposed QSPR model, data set of each drug from Table I was taken out and the numerical values of the model constants of the QSPR were computed. Then the solubility of the data set was predicted using a combination of Equation 1 + QSPR and compared with the corresponding experimental solubility using MPD and IPD accuracy criteria. In this analysis, the only experimental data used in the prediction process was Xc,T and Xw,T of the drugs at the temperature of interest. The minimum and maximum MPDs for predictive analysis using Equation 1 + QSPR were 5.5 (for nalidixic acid at 303 K) and 83.6% (for sulfanilamide at 298 K) and the overall MPD (± SD) was 20.8 ± 16.9%, which is significantly (p < 0.02) less than corresponding overall MPD (28.7 ± 15.4) of the previous method (i.e. Equation 1 alone). This finding means that we are able to predict the solubility of a drug in waterdioxane mixtures at various temperatures using only its solubility data in water and dioxane (i.e. two experimental data) and the expected prediction error is ~ 21% which is an acceptable error range in the pharmaceuticals field [14, 21] and is also 8% less than the previously reported method [7]. From the IPD point of view, the QSPR produced reasonable distribution of error where the relative frequency of IPD < 4%, 4-30 and > 30 were 24, 54 and 22%, respectively, and this means that the predicted solubilities are within the acceptable error range in 78% of cases.
Eq. 8
The minimum MPD (6.1%) was observed for nalidixic acid at 303 K and the maximum MPD (67.3%) was observed for sulfapyridine data set. The overall MPD (±SD) was 17.9 ± 11.4% for this analysis. The corresponding figures for the previous model (i.e. Equation 1) were 7.8% (theophylline data set), 62.2% (nalidixic acid at 283 K) and 26.3 ± 14.2%, respectively. The overall MPD difference between Equations 1 and 8 was statistically significant (paired t-test, p < 0.001) revealing that the QSPR significantly improves the accuracy of the JouybanAcree model for representing the solubility of drugs in water-dioxane mixtures at various temperatures. Figure 1 showed the calculated -lnXm by Equation 8 versus experimental -lnXm with the correlation coefficient of 0.9958. The relative frequency of IPD values sorted in three subgroups was shown in Figure 2. In only 22% of cases the IPD was > 30% whereas the corresponding frequency for Equation 1 was 36% and a significant reduction (~ 14%) was achieved. 361
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
A similar numerical method could be used for modeling the deviations of predicted solubilities using the Jouyban-Acree model in other binary solvent mixtures. As an example, the method was applied to the solubility of drugs dissolved in ethanol (solvent 2)-ethyl acetate (solvent 1) mixtures (non-aqueous binary mixtures) at various temperatures and the resulting equation was: 881.9 289.4( f 1 − f 2 ) 494.1( f 1 − f 2 )2 ln X m ,T = f 1 ln X 1,T + f 2 ln X 2,T + f 1 f 2 + + T T T + 1.020(± 0.133)HE ' − 2.818(± 0.403)HOMO' − 1.143(± 0.380 )TE '
where X1,T and X2,T are the solubility of the drug in solvents 1 and 2 at temperature K, respectively, and f1 and f2 are the volume fraction of solvents 1 and 2 in the absence of the solute. Details of the experimental data and the computational descriptors are listed in Tables III and IV. The MPD of the basic Jouyban-Acree model [28] was 13.1 ± 8.1% and addition of the structural descriptors to the model, i.e. Equation 9, improved the MPD to 9.6 ± 5.8% where the reduction in MPDs was statistically significant (paired t-test, p < 0.003). In conclusion, the proposed method improved the accuracy of the solubility prediction of drugs in water-dioxane and ethanol-ethyl acetate mixtures at various temperatures and could be employed in
Eq. 9
+ 3.068(± 0.614 )Vol '−0.072(± 0.035)log P '
Table III - Details of solubility data sets in ethanol-ethyl acetate mixtures, temperature (T, K), logarithm of solubility of the drugs in ethyl acetate (lnX1,T) and ethanol (lnX2,T) at T, number of data points in each set (N), the mean percentage deviation (MPD) for back-calculated solubilities using the trained Jouyban-Acree model [28] and Equation 9. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Solute Acetanilide Benzocaine Caffeine Caffeine Caffeine Caffeine Caffeine Mefenamic acid (polymorph I) Mefenamic acid (polymorph II) Niflumic acid Niflumic acid Niflumic acid Niflumic acid Niflumic acid Niflumic acid Oxolinic acid Oxolinic acid Oxolinic acid Oxolinic acid Oxolinic acid Paracetamol Phenacetin Salicylic acid Sulfamethazine Sulfamethoxypyridazine Sulfanilamide
Ref.
ln X1,T
ln X2,T
T
N
The basic model1
Eq. 9
22 22 23 23 23 23 23 24 24 23 23 23 23 23 23 25 25 25 25 25 11 22 22 26 27 26
-2.19 -1.80 -5.87 -5.67 -5.50 -5.32 -5.20 -5.57 -5.32 -3.80 -3.78 -3.71 -3.68 -3.64 -3.59 -10.82 -10.62 -10.43 -10.25 -10.06 -2.92 -4.17 -1.96 -6.38 -6.20 -4.70
-2.51 -1.89 -6.86 -6.63 -6.38 -6.15 -5.96 -6.31 -5.99 -4.58 -4.42 -4.31 -4.12 -3.98 -3.80 -11.91 -11.70 -11.47 -11.26 -11.03 -4.93 -4.24 -2.16 -7.12 -6.54 -4.88
298 298 278 288 298 308 313 298 298 283 288 293 298 303 308 293 298 303 308 313 298 298 298 298 298 298
6 6 11 11 11 11 11 10 8 9 9 9 9 9 9 9 9 9 9 9 13 11 11 14 14 10
30.9 13.3 28.5 19.0 10.6 3.0 18.0 16.7 8.9 8.5 8.3 8.3 7.0 6.8 5.6 10.2 8.2 7.7 6.4 6.0 24.6 14.7 32.9 11.6 13.8 12.3
17.2 8.4 10.9 4.8 4.7 10.5 12.3 9.0 4.9 6.9 5.7 4.9 4.4 3.8 2.7 10.5 9.5 9.9 7.6 6.8 24.4 13.8 26.6 7.7 7.6 13.4
13.12 (8.1)
9.62 (5.8)
Overall MPD (SD)
The trained Jouyban-Acree model reported in a previous paper [28] should be read as: ln Xm,T = [ƒ1 ln X1,T + ƒ2 ln X2,T + ƒ1 ƒ2 ({881.9/T} + {289.4(ƒ1 - ƒ2)/T} + {494.1 (ƒ1 - ƒ2)2/T}] The reported model constants in the paper have been calculated in log scale by mistake rather than ln scale. Therefore, the reported constants in the paper [28] should be multiplied in 2.303. 2 The overall MPD difference was statistically significant (p < 0.003). 1
Table IV - The numerical values of hydration energy (HE), the energy of the highest occupied molecular orbital (HOMO), total energy (TE), logarithm of partition coefficient (logP), molar volumes (Vol) of the drugs dissolved in ethanol-ethyl acetate mixtures computed using HyperChem software and their mean values. HE
HOMO
TE
Vol
log P
Acetanilide Benzocaine Caffeine Mefenamic acid Niflumic acid Oxolinic acid Paracetamol Phenacetin Salicylic acid Sulfamethazine Sulfamethoxypyridazine Sulfanilamide
Drug
-4.24 -4.24 -2.33 -7.23 -9.88 -10.58 -10.71 -4.51 -12.19 -11.62 -18.73 -13.26
-8.911 -8.911 -8.945 -8.561 -8.791 -8.864 -8.462 -8.357 -9.474 -9.133 -9.080 -9.157
-38633.8 -38633.8 -60617.4 -68599.9 -99136.5 -83568.1 -46028.5 -53201.5 -44749.0 -78205.2 -81978.8 -49060.7
471.7 471.7 569.5 744.1 718.5 701.8 498.9 612.0 424.0 778.2 751.9 490.6
-0.29 -0.29 -1.06 0.61 0.96 -1.59 -1.32 -0.95 -0.04 -0.50 0.17 -1.98
Mean values
-9.13
-8.887
-61867.8
602.7
-0.52
362
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
the pharmaceuticals industry where solubilization/desolubilization of drugs in mixed solvents at various temperatures is required.
17.
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27.
28.
solubility of sulfapyridine in solvent mixtures. - Drug Dev. Ind. Pharm., 21, 2073-2084, 1995. Martin A., Wu P.L., Velasquez T. - Extended Hildebrand solubility approach. Sulfonamides in binary and ternary solvents. - J. Pharm. Sci., 74, 277-282, 1985. Martin A., Paruta A.N., Adjei A. - Extended Hildebrand solubility approach: Methylxanthines in mixed solvents. - J. Pharm. Sci., 70, 1115-1120, 1981. HyperChem 7.0 - Molecular Mechanics and Quantum Chemical Calculations Package. - HyperCube Inc., Ontario, Canada, 2002. HyperCube - Extended MM2 Molecular Mechanics Method. HyperCube Inc., Ontario, Canada, 2002. Beerbower A., Wu P.L., Martin A. - Expanded solubility parameter approach 1. Naphthalene and benzoic acid in individual solvents. - J. Pharm. Sci., 73, 179-188, 1984. Pena M.A., Reillo A., Escalera B., Bustamante P.- Solubility parameter of drugs for predicting the solubility profile type of a wide polarity range in solvent mixtures. - Int. J. Pharm., 321, 155-161, 2006. Bustamante P., Navarro J., Romero S., Escalera B.- Thermodynamic origin of the solubility profile of drugs showing one or two maxima against the polarity of aqueous and nonaqueous mixtures: Niflumic acid and caffeine. - J. Pharm. Sci., 91, 874883, 2002. Romero S., Escalera B., Bustamante P.- Solubility behavior of polymorphs I and II of mefenamic acid in solvent mixtures. - Int. J. Pharm., 178, 193-202, 1999. Jouyban A., Romero S., Chan H.K., Clark B.J., Bustamante P.- A cosolvency model to predict solubility of drugs at several temperatures from a limited number of solubility measurements. - Chem. Pharm. Bull., 50, 594-599, 2002. Bustamante P., Ochoa R., Reillo A., Escalera J.B.- Chameleonic effect of sulfanilamide and sulfamethazine in solvent mixtures - solubility curves with 2 maxima. - Chem. Pharm. Bull., 42, 1129-1133, 1994. Escalera J.B., Bustamante P., Martin A.- Predicting the solubility of drugs in solvent mixtures - multiple solubility maxima and the chameleonic effect. - J. Pharm. Pharmacol., 46, 172-176, 1994. Jouyban A., Acree JR. W.E.- Prediction of drug solubility in ethanol- ethyl acetate mixtures at various temperatures using the Jouyban-Acree model. - J. Drug Del. Sci. Tech., 17, 159-160, 2007.
Acknowledgment The authors would like to thank the Drug Applied Research Center, Tabriz University of Medical Sciences for its financial support of this work under grant No. 84-93.
Manuscript Received 20 February 2007, accepted for publication 6 June 2007.
363
Modelling the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban1*, M.A.A. Fakhree2, M. Hamzeh-Mivehroud3, W.E. Acree Jr.4 Faculty of Pharmacy and Drug Applied Research Center, Tabriz University of Medical Sciences, Tabriz 51664, Iran 2 Kimia Research Institute, PO Box 51665-171, Tabriz, Iran 3 Biotechnology Research Center, Tabriz University of Medical Sciences, Tabriz 51664, Iran 4 Department of Chemistry, University of North Texas, Denton, TX 76203-5070, United States *Correspondence: [email protected]
1
A quantitative-structure property relationship (QSPR) was proposed for modeling deviations of solubilities of drugs in water-dioxane mixtures at various temperatures from the predicted solubilities by the Jouyban-Acree model. The QSPR employed the normalized values of the hydration energy, energy of the highest occupied molecular orbital, total energy, logarithm of partition coefficient and molar volume of drugs computed using HyperChem software. The applicability of the proposed QSPR to real solubility data was evaluated employing 34 solubility data sets in water-dioxane mixtures at various temperatures by computing the mean percentage deviation (MPD) as an accuracy criterion. The overall MPD (± SD) of the QSPR was 17.9 ± 11.4% which is an acceptable error range in the pharmaceuticals field. The corresponding MPD (± SD) for 26 solubility data sets in ethanol-ethyl acetate mixtures at various temperatures was 9.6 ± 5.8%. Key words: Solubility prediction – Cosolvency – Jouyban-Acree model – Water-dioxane mixtures – Ethanol-ethyl acetate mixtures – QSPR.
Solubility of drugs/drug candidates is a challenging area in the pharmaceuticals industry and solvent mixing or cosolvency is one of the most reliable solubility alteration methods. In addition to experimental efforts to determine the solubility of drugs in solvent mixtures, a number of attempts have been made to provide prediction tools for ab initio estimation of solubilities or prediction based on a limited number of experimental data. In 1964, Paruta et al. tried to correlate the solubility of salicylic acid as a function of dielectric constant of the solvent mixture [1]. In 1972, Yalkowsky et al. proposed the loglinear model describing the solubility of drugs in water-cosolvent mixtures as algebraic summation of the solubilities in water-cosolvent mixtures considering solvent composition [2]. The log-linear model was extended to estimate the solubilities of various drugs employing the solubilization power approach of the cosolvent [3]. The Hildebrand solubility equation was extended to calculate the solubility of drugs in water-dioxane mixtures by Martin et al. in 1980 [4]. A model was developed by our group and showed accurate results for modeling the solubility of drugs in water-cosolvent mixtures at fixed [5] and various temperatures [6]. In the latest report [7], a trained version of the Jouyban-Acree model was reported for predicting the solubility of drugs in water-dioxane mixtures at various temperatures. The model was (Equation 1): 2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 ln X m ,T = f c ln X c ,T + f w ln X w,T + f c f w
T
+
T
+
T
more accurate solubility predictions in water-dioxane mixtures. The available solubility data of drugs were used to check the capability and accuracy of the proposed QSPR model. Dioxane is not a pharmaceutical cosolvent because of its toxicity. However it has been widely used in cosolvency modeling studies, is completely miscible with water and provides the widest polarity range. Therefore this cosolvent was chosen to check the applicability of the proposed QSPR.
I. Experimental data and computational methods
Available solubility data of drugs in water-dioxane mixtures were collected from the literature [4, 8-18] and listed in Table I. The 2D structure of each compound was drawn, converted to 3D using HyperChem 7.0 [19], and pre-minimized by Polak-Ribiere geometry optimization using MM+ method [20]. The structures were found by MM+, used as the starting point for re-minimization by Polak-Ribiere optimization using AM1 semi-empirical and also quantum mechanical methods. The energy optimized molecules were used to compute molecular descriptors. Grid (SAG) and approximate (SAA) surface areas, molar volume (Vol), hydration energy (HE), molar refractivity (MR), polarizability (Pol), logarithm of partition coefficient (logP), molecular weight (MW), total energy (TE), dipole moment (DM), energy of the highest occupied molecular orbital (HOMO) and energy of the lowest unoccupied molecular orbital (LUMO) were calculated using HyperChem software. The numerical values of the descriptors and their mean values were listed in Table II. The diversity of the drugs studied is reflected in the magnitude of the descriptors range, e.g. logP ranging from -1.98 to 1.39 and molar volume ranging from 429 to 780. The normalized descriptors are equal to zero for pure mono-solvent systems (when fc or fw is zero). To provide a normalized range for the numerical values of the descriptors, they were multiplied in fcfw and then divided by the mean values of the descriptors. As an example, the normalized molar volume (Vol’) of a drug is calculated by:
where fc and fw are the volume fractions of cosolvent and water in the absence of the solute, Xm,T, Xc,T and Xw,T are the mole fraction solubility of the solute in solvent mixture, cosolvent and water at temperature (T, K). Using the trained version of the model, only two solubility data points in neat dioxane and water are required for the prediction of solubility of a drug in the mixtures and the percentage deviation of the predicted data sets was 27% [7]. The model was developed based on assuming similar interactions between solvent mixture and the solutes. However, it is obvious that various drug molecules interact in different strengths with the solvent mixture because of the presence of various functional groups. These interactions could be represented using various chemical descriptors. The aim of this work is to present a quantitative structure property relationship (QSPR) model for providing
Vol’ = fc · fw · Vol/[Mean of Vol (= 608.8)]
359
Eq. 2
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
Table I - Details of solubility data sets in water-dioxane mixtures, temperature (T, K), logarithm of solubility of the drugs in dioxane (ln Xc,T) and water (ln Xw,T) at T, number of data points in each set (N), the mean percentage deviation (MPD) for back-calculated and predicted solubilities using Equation 1 and the proposed model. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
Solute Acetanilide Acetanilide Acetanilide Acetanilide Acetanilide Caffeine Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid Nalidixic acid p-Hydroxybenzoic acid Paracetamol Paracetamol Paracetamol Paracetamol Paracetamol Paracetamol Phenacetin Phenacetin Phenacetin Phenacetin Phenacetin Sulfadiazine Sulfadimidine Sulfamethizole Sulfamethoxazol Sulfanilamide Sulfapyridine Sulfisomidine Sulphamethoxypyridazine Theobromine Theophylline
Ref. 8 8 8 8 8 9 8 8 8 8 8 8 10 8 8 8 8 8 11 12 12 12 12 12 13 13 14 13 15 16 17 13 18 4
T 293 298 303 308 313 298 283 293 298 303 308 313 298 293 298 303 308 313 298 293 298 303 308 313 298 298 298 298 298 298 298 298 298 298
ln Xc,T -2.37 -2.12 -2.01 -1.81 -1.55 -4.77 -6.91 -6.76 -6.62 -6.50 -6.50 -6.40 -2.47 -3.70 -3.62 -3.53 -3.45 -3.34 -3.03 -4.26 -4.07 -3.84 -3.63 -3.48 -7.61 -6.51 -6.94 -3.51 -2.52 -10.29 -5.99 -3.74 -7.72 -5.95
ln Xw,T -7.26 -7.13 -7.01 -7.01 -6.81 -6.08 -13.23 -13.07 -12.94 -12.75 -12.53 -12.21 -7.42 -6.38 -6.27 -6.07 -5.95 -5.81 -6.27 -9.61 -9.41 -9.18 -9.04 -8.84 -12.33 -12.71 -10.25 -10.67 -7.35 -13.24 -9.21 -10.20 -10.32 -7.21
N 11 11 11 11 11 16 12 12 12 12 12 12 13 12 12 12 12 12 17 13 13 13 13 13 17 19 19 15 16 17 21 18 11 21
Overall MPD ± SD
MPD for back-calculated data
MPD for predicted data1
Eq. 1
Eq. 8
Eq. 1
Eq. 1 + QSPR
33.3 36.9 33.0 32.5 36.9 34.8 62.2 53.5 44.3 34.7 24.8 19.9 33.4 12.2 15.7 16.9 21.3 22.7 9.4 13.0 11.4 11.4 8.1 10.4 24.7 16.2 41.6 15.1 14.1 38.8 24.7 27.7 51.1 7.8
22.7 25.7 23.2 24.8 28.8 13.1 18.9 12.9 8.8 6.1 9.7 16.9 28.6 10.4 9.9 10.0 13.6 14.7 12.3 13.0 11.4 11.4 8.1 10.4 14.9 25.9 32.1 12.6 17.1 67.3 12.1 11.3 33.7 16.0
35.4 39.0 34.7 34.3 38.7 34.6 71.2 61.7 51.8 41.5 30.9 25.6 33.8 15.2 18.5 19.5 23.6 25.0 10.0 14.8 13.1 13.3 9.9 11.9 25.8 16.3 43.4 15.8 14.3 38.6 26.4 29.3 50.8 8.1
21.5 24.5 22.1 24.4 28.0 13.1 23.3 16.9 11.4 5.5 7.4 14.9 34.0 9.3 10.1 10.9 14.5 16.0 12.7 12.8 11.2 11.5 8.8 11.0 15.8 28.6 33.2 12.6 83.6 75.4 13.1 12.5 35.7 21.9
26.3 ± 14.22
17.9 ± 11.42
28.7 ± 15.43
20.8 ± 16.93
The model constants of the Jouyban-Acree model and the QSPR were computed using data sets after excluding data of the drug of interest, and then the solubility of the drug was predicted. 2 The overall MPD difference was statistically significant (p<0.001). 3 The overall MPD difference was statistically significant (p<0.02). 1
Table II - The numerical values of hydration energy (HE), the energy of the highest occupied molecular orbital (HOMO), total energy (TE), logarithm of partition coefficient (logP), molar volumes (Vol) of the drugs dissolved in water-dioxane mixtures computed using HyperChem software and their mean values. Solute
HE
HOMO
TE
Vol
log P
Acetanilide Caffeine Nalidixic acid p-Hydroxy benzoic acid Paracetamol Paracetamol Phenacetin Sulfadiazine Sulfadimidine Sulfamethizole Sulfamethoxazol Sulfanilamide Sulfapyridine Sulfisomidine Sulphamethoxypyridazine Theobromine Theophylline
-4.24 -2.30 -6.01 -13.72 -10.71 -10.71 -4.95 -14.39 -11.64 -18.65 -15.22 -13.26 -14.07 -11.79 -18.73 -5.09 -5.41
-8.910 -6.671 -9.151 -9.608 -8.460 -8.460 -8.513 -9.171 -9.131 -9.459 -9.126 -9.151 -9.192 -9.155 -9.080 -6.790 -6.798
-38633.82 -60552.97 -70944.80 -44749.11 -46028.73 -46028.73 -53199.47 -71018.59 -78205.20 -72540.01 -73912.91 -49060.67 -69522.53 -78208.32 -81978.76 -56974.05 -56971.42
471.5 568.1 682.6 429.1 499.8 499.8 604.5 676.7 779.1 691.9 696.9 489.8 686.9 780.2 751.9 521.1 520.0
-0.29 -1.06 1.39 -0.04 -1.32 -1.32 -0.95 -1.49 -0.50 -0.30 -1.54 -1.98 -1.31 -1.64 0.17 -1.31 -1.31
Mean values
-10.64
-8.64
-61678.82
608.8
-0.87
360
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
The numerical values of the deviations from the Jouyban-Acree model were computed using Equation 3: Eq. 3 2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 Y = ln X m,T − f c ln X c ,T + f w ln X w,T + f c f w + + T T T
14 R = 0.9958
12
Since the solvent system (i.e. water-dioxane) was the same, these deviations should be a function of the normalized descriptors of drugs and could be represented as:
-lnXm (Computed)
10
Eq. 4
Y = f(Vol’, HE’, log P’, …)
To calculate the numerical values of the QSPR model, the least square method was used, the validity of the QSPR was evaluated using the F test, the significance of the descriptor’s contribution in the model was checked using the t-test and the descriptors were included in the QSPR with the significance level of < 0.05. The mean percentage deviation (MPD) was used to check the accuracy of the prediction method and was calculated using: Calculated − X mObserved | 100 | X m MPD = ∑ Observed N Xm
|
2
0
Eq. 5
0
6
8
10
12
14
70
Eq. 1
60
Eq. 8
50 Relative frequency
Numerical values of the normalized descriptors were regressed against Y values of the collected data sets. All descriptors were considered in the linear regression model and the descriptors with significance level of > 0.05 were excluded from the model. The most accurate model for describing the solubility deviations from the Jouyban-Acree model was:
40 30 20 10
Y = 3.113(± 0.227 )HE ' − 5.124(± 0.611)HOMO' − 9.697(± 1.337 )TE ' Eq. 7 + 11 .782(± 1.696 )Vol ' + 0.238(± 0.069 )log P '
0
≤ 4%
4-30%
> 30%
IPD
The F value of Equation 7 was 63 which revealed that the correlation was statistically significant (p < 0.0005). The solubility of the studied drugs was back-calculated using a combination of Equations 1 and 7 (i.e. Equation 8), the MPD values were computed and listed in Table I:
+ 3.113(± 0.227 )HE ' − 5.124(± 0.611)HOMO' − 9.697(± 1.337 )TE '
4
Figure 1 - Plot of the computed -lnXm (by Equation 8) versus observed -lnXm of drugs in water-dioxane mixtures and the correlation coefficient.
Eq. 6
2206.9 1173 .1( f c − f w ) 1997.4( f c − f w )2 ln X m ,T = f c ln X c ,T + f w ln X w,T + f c f w + + T T T
2
-lnXm (Observed)
II. Results and Discussion
+ 11 .782(± 1.696)Vol '+ 0.238(± 0.069)log P '
6
4
in which N is the number of solubility data points in each set. The individual percentage deviation (IPD) was also computed by:
| X Calculated − X mObserved IPD = 100 m X mObserved
8
Figure 2 - The relative frequency of the individual relative deviation (IPD) of back-calculated solubilities using Equations 1 and 8.
To assess the prediction capability of the proposed QSPR model, data set of each drug from Table I was taken out and the numerical values of the model constants of the QSPR were computed. Then the solubility of the data set was predicted using a combination of Equation 1 + QSPR and compared with the corresponding experimental solubility using MPD and IPD accuracy criteria. In this analysis, the only experimental data used in the prediction process was Xc,T and Xw,T of the drugs at the temperature of interest. The minimum and maximum MPDs for predictive analysis using Equation 1 + QSPR were 5.5 (for nalidixic acid at 303 K) and 83.6% (for sulfanilamide at 298 K) and the overall MPD (± SD) was 20.8 ± 16.9%, which is significantly (p < 0.02) less than corresponding overall MPD (28.7 ± 15.4) of the previous method (i.e. Equation 1 alone). This finding means that we are able to predict the solubility of a drug in waterdioxane mixtures at various temperatures using only its solubility data in water and dioxane (i.e. two experimental data) and the expected prediction error is ~ 21% which is an acceptable error range in the pharmaceuticals field [14, 21] and is also 8% less than the previously reported method [7]. From the IPD point of view, the QSPR produced reasonable distribution of error where the relative frequency of IPD < 4%, 4-30 and > 30 were 24, 54 and 22%, respectively, and this means that the predicted solubilities are within the acceptable error range in 78% of cases.
Eq. 8
The minimum MPD (6.1%) was observed for nalidixic acid at 303 K and the maximum MPD (67.3%) was observed for sulfapyridine data set. The overall MPD (±SD) was 17.9 ± 11.4% for this analysis. The corresponding figures for the previous model (i.e. Equation 1) were 7.8% (theophylline data set), 62.2% (nalidixic acid at 283 K) and 26.3 ± 14.2%, respectively. The overall MPD difference between Equations 1 and 8 was statistically significant (paired t-test, p < 0.001) revealing that the QSPR significantly improves the accuracy of the JouybanAcree model for representing the solubility of drugs in water-dioxane mixtures at various temperatures. Figure 1 showed the calculated -lnXm by Equation 8 versus experimental -lnXm with the correlation coefficient of 0.9958. The relative frequency of IPD values sorted in three subgroups was shown in Figure 2. In only 22% of cases the IPD was > 30% whereas the corresponding frequency for Equation 1 was 36% and a significant reduction (~ 14%) was achieved. 361
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
A similar numerical method could be used for modeling the deviations of predicted solubilities using the Jouyban-Acree model in other binary solvent mixtures. As an example, the method was applied to the solubility of drugs dissolved in ethanol (solvent 2)-ethyl acetate (solvent 1) mixtures (non-aqueous binary mixtures) at various temperatures and the resulting equation was: 881.9 289.4( f 1 − f 2 ) 494.1( f 1 − f 2 )2 ln X m ,T = f 1 ln X 1,T + f 2 ln X 2,T + f 1 f 2 + + T T T + 1.020(± 0.133)HE ' − 2.818(± 0.403)HOMO' − 1.143(± 0.380 )TE '
where X1,T and X2,T are the solubility of the drug in solvents 1 and 2 at temperature K, respectively, and f1 and f2 are the volume fraction of solvents 1 and 2 in the absence of the solute. Details of the experimental data and the computational descriptors are listed in Tables III and IV. The MPD of the basic Jouyban-Acree model [28] was 13.1 ± 8.1% and addition of the structural descriptors to the model, i.e. Equation 9, improved the MPD to 9.6 ± 5.8% where the reduction in MPDs was statistically significant (paired t-test, p < 0.003). In conclusion, the proposed method improved the accuracy of the solubility prediction of drugs in water-dioxane and ethanol-ethyl acetate mixtures at various temperatures and could be employed in
Eq. 9
+ 3.068(± 0.614 )Vol '−0.072(± 0.035)log P '
Table III - Details of solubility data sets in ethanol-ethyl acetate mixtures, temperature (T, K), logarithm of solubility of the drugs in ethyl acetate (lnX1,T) and ethanol (lnX2,T) at T, number of data points in each set (N), the mean percentage deviation (MPD) for back-calculated solubilities using the trained Jouyban-Acree model [28] and Equation 9. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Solute Acetanilide Benzocaine Caffeine Caffeine Caffeine Caffeine Caffeine Mefenamic acid (polymorph I) Mefenamic acid (polymorph II) Niflumic acid Niflumic acid Niflumic acid Niflumic acid Niflumic acid Niflumic acid Oxolinic acid Oxolinic acid Oxolinic acid Oxolinic acid Oxolinic acid Paracetamol Phenacetin Salicylic acid Sulfamethazine Sulfamethoxypyridazine Sulfanilamide
Ref.
ln X1,T
ln X2,T
T
N
The basic model1
Eq. 9
22 22 23 23 23 23 23 24 24 23 23 23 23 23 23 25 25 25 25 25 11 22 22 26 27 26
-2.19 -1.80 -5.87 -5.67 -5.50 -5.32 -5.20 -5.57 -5.32 -3.80 -3.78 -3.71 -3.68 -3.64 -3.59 -10.82 -10.62 -10.43 -10.25 -10.06 -2.92 -4.17 -1.96 -6.38 -6.20 -4.70
-2.51 -1.89 -6.86 -6.63 -6.38 -6.15 -5.96 -6.31 -5.99 -4.58 -4.42 -4.31 -4.12 -3.98 -3.80 -11.91 -11.70 -11.47 -11.26 -11.03 -4.93 -4.24 -2.16 -7.12 -6.54 -4.88
298 298 278 288 298 308 313 298 298 283 288 293 298 303 308 293 298 303 308 313 298 298 298 298 298 298
6 6 11 11 11 11 11 10 8 9 9 9 9 9 9 9 9 9 9 9 13 11 11 14 14 10
30.9 13.3 28.5 19.0 10.6 3.0 18.0 16.7 8.9 8.5 8.3 8.3 7.0 6.8 5.6 10.2 8.2 7.7 6.4 6.0 24.6 14.7 32.9 11.6 13.8 12.3
17.2 8.4 10.9 4.8 4.7 10.5 12.3 9.0 4.9 6.9 5.7 4.9 4.4 3.8 2.7 10.5 9.5 9.9 7.6 6.8 24.4 13.8 26.6 7.7 7.6 13.4
13.12 (8.1)
9.62 (5.8)
Overall MPD (SD)
The trained Jouyban-Acree model reported in a previous paper [28] should be read as: ln Xm,T = [ƒ1 ln X1,T + ƒ2 ln X2,T + ƒ1 ƒ2 ({881.9/T} + {289.4(ƒ1 - ƒ2)/T} + {494.1 (ƒ1 - ƒ2)2/T}] The reported model constants in the paper have been calculated in log scale by mistake rather than ln scale. Therefore, the reported constants in the paper [28] should be multiplied in 2.303. 2 The overall MPD difference was statistically significant (p < 0.003). 1
Table IV - The numerical values of hydration energy (HE), the energy of the highest occupied molecular orbital (HOMO), total energy (TE), logarithm of partition coefficient (logP), molar volumes (Vol) of the drugs dissolved in ethanol-ethyl acetate mixtures computed using HyperChem software and their mean values. HE
HOMO
TE
Vol
log P
Acetanilide Benzocaine Caffeine Mefenamic acid Niflumic acid Oxolinic acid Paracetamol Phenacetin Salicylic acid Sulfamethazine Sulfamethoxypyridazine Sulfanilamide
Drug
-4.24 -4.24 -2.33 -7.23 -9.88 -10.58 -10.71 -4.51 -12.19 -11.62 -18.73 -13.26
-8.911 -8.911 -8.945 -8.561 -8.791 -8.864 -8.462 -8.357 -9.474 -9.133 -9.080 -9.157
-38633.8 -38633.8 -60617.4 -68599.9 -99136.5 -83568.1 -46028.5 -53201.5 -44749.0 -78205.2 -81978.8 -49060.7
471.7 471.7 569.5 744.1 718.5 701.8 498.9 612.0 424.0 778.2 751.9 490.6
-0.29 -0.29 -1.06 0.61 0.96 -1.59 -1.32 -0.95 -0.04 -0.50 0.17 -1.98
Mean values
-9.13
-8.887
-61867.8
602.7
-0.52
362
Modelling of the deviations of solubilities in water-dioxane mixtures from predicted solubilities by the Jouyban-Acree model A. Jouyban, M.A.A. Fakhree, M. Hamzeh-Mivehroud, W.E. Acree Jr.
J. DRUG DEL. SCI. TECH., 17 (5) 359-363 2007
the pharmaceuticals industry where solubilization/desolubilization of drugs in mixed solvents at various temperatures is required.
17.
References 1. 2. 3. 4. 5.
6. 7. 8.
9. 10. 11.
12. 13.
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Acknowledgment The authors would like to thank the Drug Applied Research Center, Tabriz University of Medical Sciences for its financial support of this work under grant No. 84-93.
Manuscript Received 20 February 2007, accepted for publication 6 June 2007.
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