Solubility of bosentan in polyethylene glycol 400 + water mixtures: Experimental and mathematical computations

Please cite this article as: Jafari P, Rahimpour E, Jouyban A. Solubility of bosentan in polyethylene glycol 400 + water mixtures: Experimental and mathematical computations. Abstract Background . To discover the optimal solvent amounts for using in a particular application, it is vital to achieve some useful information in regard with suitable pure or mixed solvent and drugs equilibrium solubility in them. It is known that the low water solubility of drugs such as bosentan (BST) negatively effects its in vitro and in vivo kinetics of dissolution, affecting in turn and its bioavailability along with making several difficulties around designing of its liquid formulations. Methods . Solubility of BST in some mixtures of polyethylene glycol 400 (PEG 400) and water was experimentally determined at T = (293.15 to 313.15) K by using a common shake-flask technique followed by Uv-visible spectroscopic method. The experimental solubility data at 298.15 K and w 1 =0.0, 0.5 and 1.0 at other temperatures were then correlated by cosolvency models including the Jouyban-Acree, the Jouyban-Acree-van't Hoff, and the double log-log models and some un-measured solubility data are predicted based on the obtained trained models. Results . The results presented that the aqueous solubility of BST is increased by increasing mass fraction of PEG 400 as well as increasing temperature and reached the maximum value in neat PEG 400 at 313.15 K. Conclusion . The BST solubility in water improved by addition of PEG 400 into it. According to the average relative deviations obtained from the back-computed data with trained models which were < 8.0%, it concluded that the selected modes were able to predict the un-measured data with high reliability.


Introduction
Bosentan (BST, Figure 1) is a twin endothelin receptor antagonist utilized inside the treatment of pulmonary arterial hypertension with an elimination half-life of 5 h. 1 It has a low water solubility (1 g. L -1 , pKa = 5.8 and log P = 4.94) and categorized as a class II based on the BSC classification. 2 Low values of bioavailability of BST (≈ 50%) and its solubility in water lead to variable blood concentration of it. 3 Considering to its application in therapeutic and its low solubility in water as well as low bioavailability, it is vital to measures BST solubility in various pharmaceutical solvent mixtures to formulate the liquid dosage forms.
" Figure 1" Several ways have been used to increases solubility of BST in water involving cosolvency, complexation, micellization and pH adjustments. [4][5][6][7][8] Among these methods, cosolvency is received more attention from scientific community due to its convenience, cost effectiveness and simplicity. [9][10][11][12][13] Most of drugs are nonpolar molecules and for enhancing their aqueous 4 Pharmaceutical Sciences (Indexed in ISI and Scopus) https://ps.tbzmed.ac.ir/ solubility, it is essential to diminishes the polarity of solvent systems and increment the drug's solubility by addition of one more less polar solvent to water. 14 Up to now, the increment of BST solubility in water by cosolvency approach has been investigated by addition of C2H5OH, 13 polyethylene glycol 200 (PEG 200) 11 and propylene glycol. 12 However, there is no report for BST solubility in water in the presence of PEG 400.
In continuation of previous works [11][12][13] in regard with the extension of BST solubility in water as an essential data in pharmaceutical industry, here, the solubility profile of BST was assessed in binary (PEG 400 + water) solvent mixtures. PEG is well-known as a low-toxic passive material (with a systemic absorption < 0.5%) and different medicinal application. 15   The reported solubility data were the mean of three repetitive experiments.

Computational section
The experimental Cm, T values of BST in the binary solutions of PEG 400 and water (i.e. w1 = 0.0 to w1 = 1.0 at 298.15 K and w1 = 0.0, 0.5, and 1.0 at the other working temperatures) were correlated with three accurate cosolvency models of Jouyban-Acree, the Jouyban-Acree-van't Hoff and the double log-log. Agreeing to acceptable ability of these models in solubility prediction and some previously reported ones, the solubility in w1 = 0.
here , mT C , 1,T C and 2,T C are BST molar solubility in the solvent systems, pure PEG 400 and pure water, respectively, at temperature T/K and Ji terms as the model constants are achieved from a simple regression analysis, 19 1 w and 2 w denote to mass fraction of pure PEG 400 and pure water in each binary mixture, respectively.

The double log-log model
The double log-log model divides the measured Cm,T values to two parts, as presented in Eqs.
(4) and (5). 21 ) in which 1 C and 2 C are the molar solubility in the pure PEG 400 and pure water, is the molar solubility in PEG 400 + water at w1 = 0.5 and B and b are the model parameters.

Model accuracy
The ARD% of the back-calculated values of Cm,T were determined to reports the accuracy of each model.
here, the experimental molar solubility of BST, the back-calculated solubilities from each model and the number of data points are denoted as exp C , cal C and N, respectively.

BST solubility measurement and correlation
The experimental molar values of BST (Cm,T) in neat water and PEG 400 at 293. 15 Table 1.
" Table 1" Also, the measured solubility of BST in water at different temperature was compared with those reported in the literature [11] and the results are collected in Table 2. According to this Table, there is a good consistency between two series of solubility data.
" Table 2" The influenc of PEG molar mass on the solubility of BST were survayed by comparing the current data with the ones reported in the literature for the (PEG 200 + water) systems (11) in 9 Pharmaceutical Sciences (Indexed in ISI and Scopus) https://ps.tbzmed.ac.ir/ to previous works about BST solubility in the (cosolvent + water) mixtures, the least number of experimental data were measured using the aforementioned way and fitted with some mathematical models including the Jouyban-Acree and the Jouyban-Acree-van't Hoff which introduced as simple and accurate models in the literature. 22 To this reason, the experimental values of Cm,T given in Table 1 were utilized to train Eqs. (2) and (3). The trained models are as follow: The overall ARDs% (OARDs%) ± SDs for back-calculated data are 4.8% ± 5.2 and 6.2% ± 4.6 for the Jouyban-Acree and Jouyban-Acree-van't Hoff models, respectively. The low ARDs% obtained for the back-calculated data show that these models have enough reliability to predict solubility data. So, the Cm,T values of BST in untested mixtures are predicted with Eqs. (7) and (8) along with reporting the results in Table 3. " for 0 < w2 ≤ 0.5 The overall ARDs% (OARDs%) ± SDs for back-calculated data are 8.0% ± 4.6 and 6.5% ± 5.2 for Eqs. (9) and (10), respectively. In the following the previous calculation, this trained model is also used for solubility prediction in other temperatures. In this study, we have the Cm,T values in w1 = 0.0, 0.5 and 1 for other temperatures. On the other hand, this model divides the data set in two parts and use the data in w1 = 0.5 and each pure solvent for the prediction. The predicted solubility data are also reported in Table 3. Recent studies uncovered that by 11 Pharmaceutical Sciences (Indexed in ISI and Scopus) https://ps.tbzmed.ac.ir/ determination sufficient solubility data points and their training with an accurate model, it is possible to predict the solubility data at other solvent compositions and temperatures. 23 This ability can be cosidered as a stronght point for these models that can be helpful in the pharmacetical industries. Figure 3 For training Eq. (11), the reported Cm,T values in Table 1   terms, the obtained model is: which predicted the reported solubility data in the investigated PEG 400 + water mixtures at working temperatures with the ARD% of 41.1% ± 41.5 (N=21). It is obvious that we used only two new experimental data points for this prediction. To provide more accurate predictions, one may use a trained version of the Jouyban-Acree-van't Hoff model by combining Eq. (13) with the J terms calculated for the aqueous solubility data of BST in the presence of PEG 200 at working temperatures employing only three data points at 298.15 K (see Eq. (13) of ref. [11]). The combined model is: The ARD% for the back-computed values of Cm,T in PEG 400 + water at working temperatures with Eq. (14) is 20.1% ± 20.6 (N=21).

Conclusions
The BST molar solubilities in neat water, PEG 400 and their mixtures at polymer mass fraction of 0.5 at 293.15, 303.15, 308.15 and 318.15 K and also in binary mixtures of PEG 400 and water with polymer mass fraction of 0.1 to 0.9 at 298.15 K were experimentally determined.
Then, the current data were represented with the Jouyban-Acree, Jouyban-Acree-van't Hoff, and the double log-log models to obtain their trained models for prediction the solubility of revealing that these models can be used in industrial applications.

Conflict of interests
The authors declare no conflict of interest.