Solubility Parameter Estimation of Celecoxib by Current Methods

J Thimmasetty*^1and4, CVS Subrahmanyam², BA Vishwanath³, and PR Sathesh Babu²

¹Bapuji Pharmacy College, Davangere, Karnataka, India

²G.R. College of Pharmacy, Bachupally, Hyderabad, Andhra Pradesh, India

³The Bangalore Institute for Pharmacy Education and Research, Bangalore, Karnataka, India

⁴Vinayaka Missions University, Salem, Tamilnadu, India

*Corresponding Author E-mail: thimmasetty@yahoo.com

ABSTRACT

Models for predicting solubility of drugs in solvent mixtures have an important practical application in drug formulation.  Solvent mixtures are widely used in pharmacy, and theoretical and semiempirical approaches save experiments that are often expensive and time-consuming.  The study of solubility behaviour of celecoxib in solvent blends and individual solvents ranging from non-polar to highly polar is essential.  The total solubility parameter and partial solubility parameters explain the interactions of the drug. The solutions containing excess drug were shaken in a water bath for 72 h at 25^oC.  The solutions attained equilibrium were then filtered and analysed for drug content.  The extended Hildebrand solubility approach was used to process the solubility data of celecoxib.  For understanding the solute-solvent interactions, partial solubility parameters concept was utilized.  A multiple regression method using the extended Hansen’s partial solubility parameters was applied to verify the solubilities of celecoxib in pure polar and nonpolar solvents and to predict its solubility in untested solvents.  Group contribution methods were used to calculate the solubility parameter of celecoxib and to support the results obtained from various theories. The three parameter approach and the Flory-Huggins size correction term ‘B’ give the prediction of solubility with correlations up to 92%.  The four-parameter approach involving proton-donor and proton-acceptor parameters is also used in fitting the solubility data.  The correlations are appreciable (96%). There is a considerable evidence to suggest that celecoxib is soluble in solvents, through acid - base parts of molecule.  A criterion of the ideal mole fraction solubility intersecting the mole fraction solubility curve is proved to be successful in deciding the solubility parameter of celecoxib.  The celecoxib solutions behave as irregular solutions.  The total solubility parameter of celecoxib determined from the different methods of data analysis is finally assigned at 11 H. The partial solubility parameters obtained from four-parameter approach are d_2d = 7.88, d_2p = 2.49, d_2a = 2.12, and d_2b = 3.54, which give insights into the interaction capability of celecoxib and are consistent with its chemical structure.

Models for predicting solubility of drugs in solvent mixtures have an important application in drug formulation.  The study of solubility behaviour of celecoxib in solvent blends and individual solvents ranging from non-polar to highly polar is essential.  The total solubility parameter and partial solubility parameters explain the interactions of the drug. The solutions containing excess drug were shaken in a water bath for 72 h at 25^oC.  The solutions attained equilibrium were then filtered and analysed.  The extended Hildebrand solubility approach was used to process the solubility data of celecoxib.  For understanding the solute-solvent interactions, partial solubility parameters concept was utilized.  A multiple regression method using the extended Hansen’s partial solubility parameters was applied to verify the solubilities of celecoxib in polar and nonpolar solvents and to predict its solubility in untested solvents. The three parameter approach and the Flory-Huggins size correction term ‘B’ give the prediction of solubility with correlations up to 92%.  The four-parameter approach give appreciable correlations (96%). There is a considerable evidence to suggest that celecoxib is soluble in solvents, through acid - base parts of molecule.  A criterion of the ideal mole fraction solubility intersecting the mole fraction solubility curve is proved to be successful in deciding the solubility parameter of celecoxib.  The total solubility parameter of celecoxib determined from the different methods of data analysis is finally assigned at 11 H. The partial solubility parameters obtained from four-parameter approach give insights into the interaction capability of celecoxib and are consistent with its chemical structure.

KEY WORDS: Celecoxib; Solubility parameter; Extended Hildebrand approach; Extended Hansen’s approach.

INTRODUCTION

An irregular solution is one in which self-association of solute or solvent, solvation of the solute by the solvent molecules, or complexation of two or more solute species are involved.  Polar systems exhibit irregular solution behaviour and are commonly encountered in pharmacy.¹  The extended Hildebrand solubility approach (EHS)^2,3 a modification of the Hildebrand-Scatchard equation, permits calculation of the solubility of polar and nonpolar solutes in solvents ranging from nonpolar hydrocarbons to highly polar solvents such as water, ethanol, and glycols.  The solubility parameters of solute and solvent were introduced to explain the behaviour of regular and irregular solutions.

Table 1. Solubility of celecoxib in the solvent series at 25^oC with related parameters

V1 (cm^3 /mol)	d1 (H)	A^a	X2 x 10^3  (exp)	(log g2)/ A (exp)
131.60	7.30^a	0.2028	0.0000228	15.6996
123.35	7.70^a	0.1962	0.0073384	3.4459
115.10	8.10^a	0.1805	0.0243556	0.8605
98.60	8.90^b	8.10E-2	0.1718000	-8.5511
88.58	9.925^b	3.65E-2	0.3025000	-25.6594
78.55	10.95^b	0.1564	0.0378619	-0.2317
58.50	13.00^c	0.1749	0.0159661	1.9361
54.45	14.04^c	0.1873	0.0079189	3.4338
50.40	15.08^c	0.1949	0.0035982	5.0549
46.35	16.12^c	0.1999	0.0011739	7.3607
42.30	17.16^c	0.2017	0.0004253	9.4847
38.25	18.20^c	0.2025	0.0001174	12.2099
34.20	19.24^c	0.2027	0.0000254	15.4702
30.15	20.28^c	0.2028	0.0000056	18.6862
26.10	21.32^c	0.2028	0.0000012	21.9263
22.05	22.36^c	0.2028	0.0000010	22.4937
18.00	23.40^c	0.2028	0.0000005	24.0170

H_f  = 7614.6595 cal/mol, T₀ = 164°C (437 K), Xⁱ₂ = 0.03495, V₂ = 271.3497 cm³/mol

^a Hexane-ethylacetate mixture; ^b Ethylacetate-ethanol mixture; ^c Ethanol-water mixture

Solubility parameter, d_T, is an intrinsic physicochemical property of a substance, and is expressed as square root of the cohesive energy density of the substance.  The cohesive energy density itself is defined as the ratio of the energy of vaporization to the molar volume at the same temperature.⁴  This has been used to explain drug action, structure activity relationship, drug transport kinetics, in situ release of drug, gas solid chromatography.^5-9  Therefore, the precise value of the solubility parameter of a drug is of interest. 

Fig. 1. Differential scanning calorimetry of celecoxib.

Fig. 2. Mole fraction solubility of celecoxib at 25^oC at different solubility parameters of the solvent series (diamonds).  Triangles represent ideal solubility.

10.95 H

Different methods are available to determine the solubility parameter of drugs.  Firstly, group contribution methods (theoretical methods) such as Fedors, Hoy, and partial solubility parameters methods are used to determine the solubility parameter of the drugs.^4,10,11 Secondly, Hildebrand regular solution theory according to which, peak solubility technique is used to obtain the solubility parameter of a solute.  In non-regular solutions, the peak solubility does not approximate the ideal solubility.  Therefore, a criterion X₂ (experimental solubility) = X₂ⁱ (ideal mole fraction solubility) is selected to decide the d_T value.  The total solubility parameters of paracetamol and trimethoprim were determined through this approach.^1,12  At present, for predicting the solubility, the extended Hildebrand solubility approach (EHS)^1,13 and the extended Hansen approach^14,15 have evoked considerable interest.  Both the approaches are largely empirical, employing statistical analysis of the experimental results to understand the solubility behaviour.  These approaches permit the estimation of solubility parameter also.

Celecoxib:

Celecoxib is a NSAID that is active at a low dose and has less gastric toxicity.  The drugs with low aqueous solubility i.e., less than 1 mg/ml usually suffer oral bioavailability problems because of limited gastrointestinal transit time of the undissolved drug particles and limited solubility at absorption site.¹⁶  Various methods such as preparation of complexes with b-cyclodextrins are studied for increasing the solubility.^16,17 Celecoxib is a moderately weak base.  For this drug, the in vitro dissolution testing is more stringent.  The solution behaviour of celecoxib in different solvents is not clearly understood and total solubility parameter of celecoxib is not reported.  Celecoxib is chemically nonploar with a functional group – SO₂NH₂, which may undergo ionization only at very high alkaline pH as its pK_a is 11.1. 

Table 2. Solubility parameter values for celecoxib by different methods

Sl No	Method / system	Solubility parameter
		H, Hildebrand (CGS units)	MPa^1/2, Mega Pascal (SI units)
1	Fedors^a	11.61	23.68
2	Hoy’s^b	11.10	22.64
		d2T (d2d, d2p, d2h)	d2T (d2d, d2p, d2h)
3	Group contribution method^c	10.05 (8.41, 3.04, 4.59)	20.50 (17.15, 6.20, 9.36)
4	Experimental peak solubility from the solvent series	09.93	20.25
6	From quadratic equation in the solvent series	09.83	20.05
7	From alcohol series peak solubility	12.00	24.48
8	From quadratic regression equation in normal alcohol series	12.82	26.15
9	Three-parameter approach with (log g 2)/A^d	14.11 (8.05, 3.60, 11.01)	28.78 (16.42, 7.34, 22.46)
10	Flory-Huggins size correction term B^e	12.60 (7.98, 3.56, 9.06)	25.70 (16.28, 7.26, 18.48)
11	Four-parameter approach with (log g 2)/A^f	09.13 (7.88, 2.49, 3.54)	18.63 (16.07, 5.08, 7.22)
12	When X2= X2^i ; second solvent series	10.95	22.33

^aEstimated from the Fedors molar attraction constants. (Fedors, 1974); ^bEstimated from the Hoy’s substituent method. (Hoy, 1970)

^cEstimated from the fragmental constants for partial solubility parameters. (Barton, 1975);  ^d Three parameter approach using (log g₂)/A, Equation (11).; ^e Three parameter approach using B replacing (log g₂)/A,  Equation (13).; ^f Four parameter approach using (log g₂)/A, Equation (18).

Table 3. Solubility of celecoxib in individual solvents at 25^oC with calculated parameters

S.No.	Solvent	Solvent Class	Molar volume	d1 (H ^a)	(A) ^b	(log g2)/A (exp) ^c	X2 x 10^3 (exp)
1	Hexane	NP	131.6	7.30	0.2028	15.6996	2.28E-05
2	Cyclohexane	N	108.7	8.20	0.2028	17.6330	9.24E-06
3	Butylacetate	B	132.5	8.50	0.1961	3.2518	8.02E-03
4	Carbon tetrachloride	N	97.1	8.70	0.2027	13.8014	5.54E-05
5	Ethyl acetate	B	98.6	8.90	0.0810	-8.5511	1.72E-01
6	Dioxane	-	85.7	10.00	0.0641	-11.6434	0.19433
7	n-Octanol	AB	157.7	10.23	0.2019	4.1702	5.14E-03
8	n-Heptanol	AB	141.9	10.28	0.2011	3.3555	0.00761
9	n-Hexanol	AB	125.2	10.41	0.2008	3.5943	0.00683
10	n-Pentanol	AB	108.6	10.59	0.1976	2.1828	1.34E-02
11	n-Butanol	AB	91.5	11.29	0.1957	2.2248	1.33E-02
12	Isopropyl alcohol	-	76.9	11.50	0.1905	3.1492	8.75E-03
13	n-Propanol	-	75.2	11.99	0.1897	1.7720	1.67E-02
14	Ethanol	B	58.5	13.00	0.1829	1.9356	1.60E-02
15	Methanol	B	40.7	14.49	0.1910	4.6718	4.46E-03
16	Propylene glycol	-	73.6	14.77	0.1994	5.9468	2.27E-03
17	Glycerin	-	73.3	17.70	0.2027	13.5293	6.30E-05
18	Water	P	18	23.40	0.2028	24.0170	4.68E-07

A – Acidic, B – Basic, N – Neutral, NP – Non-polar, P – polar, AB – Acidic, Basic; ^a Taken from Beerbower et al., 1984

^b Calculated using Eq.2. ;^c From Eq. (ln X₂ⁱ/ X₂)A

The present communication reports the behaviour of celecoxib solubility in the context of existing theories of solutions such as ideal, regular, and irregular solutions.  Furthermore, the solubility parameter and partial solubility parameters of celecoxib are determined using the three-parameter model, four-parameter model, and Flory-Huggins model.  Solubility of celecoxib in a number of solvents representative of several chemical classes ranging from nonpolar to highly polar was investigated to highlight the irregular solution behaviour.  Celecoxib is chosen for this study because the drug appears to be a better proton acceptor.  This allows to further test the reliability and validity of the models.

MATERIALS AND METHODS:

Materials:

The celecoxib was a gift sample (Cipla Ltd, Mumbai, India) and used as received.  The binary mixtures were prepared by volume using hexane, ethylacetate, and ethanol (spectrophotometric grade) and double distilled water (prepared in the laboratory using all glass distillation apparatus). 

Solubility Determination:

The solubility of celecoxib was determined in mixed solvents as well as individual solvents.  About 10 ml of the solvent blend was introduced into the 25 ml volumetric flask containing excess celecoxib.  The flasks were agitated in a cryostat constant temperature reciprocating shaker bath (Research and test equipments, Bangalore, India) at room temperature (25 ± 1°C) for at least 72 h in order to obtain equilibrium.   Preliminary studies showed that this period was sufficient to ensure saturation at 25^oC. 

After 72 h of equilibrium, aliquots were withdrawn, filtered (0.22 mm pore size), diluted, and analyzed at 251 nm on Shimadzu UV/Vis spectrophotometer (UV-1601 PC, Shimadzu, Japan).  All solubility experiments were conducted in triplicate. 

Fig. 3. Mole fraction solubility of celecoxib in individual solvents – Partial solubility parameter: Four parameter approach using 12 solvents.  Key: ¨ Experimental and ■ Calculated.

Heat of fusion:

The heat of fusion of celecoxib was determined (DSC, Shimadzu, USA).  The thermogram is shown in Fig. 1.  The heat of fusion is 83.54 J/g (7614.6595 cal/mol).

Solubility Parameter of Mixed Solvents:

The solubility parameter, d₁, for a solvent blend (x and y) was calculated (5) from the relationship; d₁ = d_x f_x + d_y f_y ; where d_x and d_y are the solubility parameters of individual solvents (x and y) in the blend, respectively, and f_x and f_y are the volume fractions.

Volume Fraction and Mean Molar Volume in Mixed Solvents:

The volume fraction for a solvent blend (f₁) was calculated either by an iteration procedure (Martin and Mauger, 1988) or by using the experimental mole fraction solubility (X₂).¹⁸

                V₁ (1 – X₂)

f₁ =                                        ………………... (1)

                V₁ (1 – X₂) + V₂ X₂

Where, V₁ and V₂ are the molar volumes of the solvent blends and the solutes, respectively.  An iteration procedure was used for the analysis in binary solvents and Eq. 1 was used for the data in individual solvents.  The differences in the values obtained from these two methods are marginal (compare the A values in Table 1 with Table 3).  For each mixed solvent composed of solvents x and y in various proportions:

V₁ = X_x M_x + (1 - X_x) M_y / (r₁) …………….……….... (2)

Where, X  and M are the mole fraction and molecular weight of the particular solvent in the mixture, respectively, and r₁ is the density of the solvent mixture at 25^oC.

The mean molar volume of the solvent blend (V₁) is calculated by the equation, V₁ = V _x f_x + V _y f_y ; where V_x and V_y are the molar volumes of the respective solvents.  The partial solubility parameters of solvents were taken from the literature.¹⁹

Molar Volume of Celecoxib:

The molar volume of celecoxib taken as a supercooled liquid at 25^oC is calculated using the group contribution approach of Fedors.⁴  For the rest of the work, the molar volume of celecoxib was determined experimentally by the floatation technique by immersion of the solid in n-hexane (d = 7.3 H).²⁰ The properties of celecoxib are shown in the footnotes of Table 1. 

Solubility Parameter Determination:

Group contribution methods were used to calculate the total solubility parameter (d₂) and partial solubility parameters of celecoxib.  The total solubility parameter of celecoxib was calculated by the methods of Fedors and Hoy.^4,10   Partial solubility parameter values of celecoxib were calculated using group contribution method.¹¹  The solubility parameters of the solvents are collected from the literature²¹ and are shown in the Tables 1 and 3.  The solubility parameter, d_2, for celecoxib is also calculated by different statistical methods based on the experimental observations as explained in the later parts of this article.

Calculations of Ideal Solubility:

The ideal mole fraction solubility (X₂ⁱ) of crystalline solids in polar and non-polar solvents² is calculated from:

DS_f T₀

-log X₂ⁱ = log                 (3) 

     R T

The entropy of fusion, DS_f , is determined using the relationship DH_f = T_0. DS_f.  where DH_f is heat of fusion, T₀ is the melting point of solute in absolute scale, T is working temperature of solutions, and R is the gas constant,   The DSC of celecoxib is given in Fig. 1. 

Statistical Analysis:

The dependent variables were fitted to the three-parameter equation, Flory-Huggins size correction equation, and four-parameter equation.  Regression methods as well as analysis of residuals were used to detect inconsistencies of individual cases with the overall regression model.  For solubility calculations, the necessary in-house developed software GW BASIC was used.  Multiple regression analysis was performed on Lotus 1-2-3.  F-ratio was calculated using standard statistical parameters. The parameter ‘s’ represents the standard error of the ‘y’ estimate at the confidence level of 99%.  A P4 Wipro computer was used.

RESULTS AND DISCUSSION:

The absorption spectrum of celecoxib in 0.2 N sodium hydroxide solution was obtained (l_max - 251 nm).  The calibration curve was constructed and Beer’s law obeys in the concentration range of 2 – 20 mg/ml (n = 3, R² = 0.9999).  The DH_f value of 7614.6595 cal/mol and T₀ value of 437 K were obtained. Then DS_f  was calculated to yield a value of 17.4249 cal/mol/degree.  The ideal mole fraction solubility of celecoxib is 0.03495 (– log X₂ⁱ = 1.4565).²²  The experimental molar volume of celecoxib obtained is 271.3497 cm³/mol.  The molar volume from Fedors group contribution method is 316.7 cm³/mol.

The experimentally determined solubilities of celecoxib at 25^oC in the solvent series are found in the Table 1 together with the molar volumes and solubility parameters of solvent mixtures.  The (log g₂)/A (exp) values are also found in the Table 1. 

The experimental mole fraction solubility of celecoxib in the solvent series is recorded in Fig. 2.  The d value of benzoic acid was determined by measuring the solubility in different solvent blends.²³  The experimental mole fraction solubility of benzoic acid shows peak solubility and the d value of solvent blend at peak solubility is taken as the solubility parameter of benzoic acid.  According to regular solution theory, when d₁ = d₂, the experimental mole fraction solubility is equal to the ideal mole fraction solubility.  In regular solutions, maximum solubility occurs when d of the solvent is approximately equal to d of the solute.  The peak solubility for celecoxib in the solvent series is observed (Fig. 2) at the d value of solvent blend 9.93 H. 

In irregular solutions, these relations do not apply exactly as in regular solutions.  It appears that the condition X₂ = X₂ⁱ is still valid, although the peak solubility technique was disregarded.  In the case of the solubility of p-hydroxy benzoic acid in a dioxane-water system, the solute and solvent (Lewis acid-base) interaction might have unduly lowered the d₂ value.²⁴  Therefore, the peak solubility does not provide the d value of solute in irregular solutions. But the ideal mole fraction solubility intersects experimental solubility curve (X₂ = X₂ⁱ) at two points and the d values are 10.95 and 8.1 H.  The d value of 10.95 H (= 11.0 H) may be a reasonable estimate of the solubility parameter for celecoxib and is nearer to the values obtained by other methods.  The d value 8.1 H cannot be considered as it represents highly nonpolar solute.  Further, the solubility is observed in normal alcohol series and found that the highest mole fraction solubility was observed at d value of 12.0 H, which is nearer to the observed value.  The solubility parameter of celecoxib was computed by the methods of Hoy¹⁰ and Fedors⁴ and the values obtained are nearer to the observed value and are shown in the Table 2.   

Extended Hildebrand Solubility Approach

The EHS approach was proposed to understand the non-regular behaviour of solutions.  This involves regression of the experimental data (log g₂)/A values against a power series, namely quadratic, cubic, or quartic, of the solvent solubility parameter.^1,13  The g₂ is the ratio of the ideal mole fraction solubility to the experimental mole fraction solubility.  The values are calculated and given in Table 1.  The quadratic regressed expression for celecoxib in the solvent series is chosen as it provides precise results.

   log g₂

    = 16.6007 –3.4870d₁ + 0.1717d₁²............. (4)

     A

n = 17,    S = 8.3769,      R² = 0.6099

Where,

f₁²V₂

A =                                  …………………... (5)

                2.303RT

Random scattering of points in the residual plot (scattergram not shown) for Eq. (4) was satisfactory.  The solubility parameters of parabens are determined from the solubilities in a series of normal alcohols, using the regression equation of second degree power series.²⁵  The equation used for such a method is obtained by rearranging the Hildebrand-Scatchard equation for the rational activity coefficient (g₂).

  log g₂ log(X₂ⁱ/X₂)

                                               =  (d₁² + d₂² – 2d_1.d₂) .. (6)

    A                      A

Rearranging the Eq. 4 by making the coefficient of d₁² to unity gives

  log g₂

 = 0.1717 (d₁²– 20.3042d₁ + 96.6646)…. (7)

A

Comparing the Eqs. 6 and 7, d₂ value of 9.83 H was obtained.  However, the standard error of estimate is high and regression coefficient is low.  Hence further methods are tested. 

Partial Solubility Parameters

The group contribution method is used to calculate partial solubility parameters.¹¹  The solubility of celecoxib in individual solvents was determined to allow analysis of the data using the extended Hansen method (Table 4). 

Hansen solubility equation involving partial parameters is extended and a regression model is developed to predict the solubility.^{15, 19} The Hansen equation is

[log (X₂ⁱ/X₂) / A]  = [log g₂ /A] = [C₀ + C₁ (d_1d - d_2d)² + C₂(d_1p- d_2p)² + C₃ (d_1h - d_2h)²] ............................. ... (8)

Where, d_1d, d_1p, d_1h, d_2d, d_2p, and d_2h are the partial solubility parameters of solvent and solute, respectively, represent London dispersion forces (d), Keesom dipolar interactions (p), and hydrogen bonding and other interaction (h), respectively, and C₀-C₃ are the constants and 1 is for solvent and 2 for solute.  The value of ‘A’ is taken on natural logarithms (Eq. 7).  Now Eq. 8 can be written as  a regression model, where parameters related to the solute are constants.  The regression equation is

[log g₂ / A] = [D₁ d_1d + D₂ d_1d ² + D₃ d_1p + D₄ d_1p ² + D₅ d_1h + D₆ d_{1 h} ² + D₀] ............ (9)    

Where, D₀ to D₆ are the constant coefficients obtained by regression analysis.  Since the solvent related parameters are independent variables, the data is regressed against partial parameters of solvents.

[log g₂ / A] = – 924.11 + 234.4621d_1d  – 14.572d_1d² – 13.4061d_1p + 1.8599d_1p² + 1.343d_1h – 0.061d_1h².........(10)

                                n = 18,    s = 2.9955,      R² = 0.9234

Eq. 10 can be written according to the model Eq. 8

[log g₂/ A] = – 16.0282 (d_1d – 8.0449)² + 1.8599 (d_1p – 3.6039)²  …………………………………..……... (11)

The R² value is high (R² = 0.9234) and the signs of coefficients change alternatively showing the validity of the equation.  The solubility parameters of celecoxib determined by various methods are given in Table 2. The equations for the calculation of solubility parameter are given beneath the Table 2. 

Some solutions deviate from regular solutions, when substantial size differences between solute and solvent exist.  To account for the deviation, Flory-Huggins size correction (B) has been applied to the regression model.¹⁴  A high level of correction was observed in case of the solubility of tamazepam in individual solvents.²⁶  The equation for Flory-Huggins size correction is

          RT

B =              [ ln g₂ – ln (V₂/V₁) –1 + (V₂/V₁) ]

        V₂f₁²

The Flory-Huggins term, B, is regressed as a dependent variable against the solvent partial solubility parameters.  The equation is as follows:

B = – 122737 + 31006.6d_1d  – 1943.74d_1d² – 1145.64d_1p +  161.1061d_1p² + 252.5178d_1h – 13.932d_1h² ……….  (13)

                                n = 18,    s = 282.5773,       R² = 0.9174

Eq. 13 is rewritten in the form of Eq. 8 to calculate partial solubility parameters and the values are d_2d = 7.9760 H, d_2p = 3.5556 H, d_2h = 9.0625 H.  Thus the total solubility parameter is d_2T = 12.60 H.    There is no improvement in the correlation coefficient over Hansen’s extended solubility approach and hence there is a need of model with high correlation coefficient.

A four parameter model involving proton donor and proton acceptor parameter, d_a and d_b, in place of d_h of the solvents¹⁹ is attempted and the equation is

[log g₂/ A] = D₁ (d_1d – d_2d)² + D₂ (d_1p – d_2p)² + 2D₃ (d_1a – d_2a) (d_1b – d_2b) + D₀ ………………….. (14)

Where, D₀ to D₃ are the constant coefficients and other terms are explained earlier.  The regression equation for the present data is

[log g₂ / A]  = 116.6263 – 23.8433d_1d + 1.345d_1d² + 2.9937d_1p – 0.394d_1p² – 8.3239d_1a – 1.3092d_1b + 1.9129d_1ad_{1b........................................................................................................} (15)

n = 18,  s = 7.549,   R² = 0.5577

Rearranging the equation (15) into the standard format of the model equation (14), gives the equation.  

[log g₂ /A] = 1.345 (d_1d – 8.8637)² – 0.394 (d_1p – 3.7991)² + 1.9129 (d_1a – 0.6844) (d_1b –4.3515) – 10.9463 ………………………………………………………...(16)

The partial parameters obtained from analysis of equation (16) are as follows, d_2d = 8.8637 H; d_2p = 3.7991 H; d_2a = 0.6844 H, and d_2b = 4.3515 H.  The total solubility parameter of celecoxib by this method is d_2T = 9.95 H.  The hydrogen bonding parameter in calculation of d_2T was calculated from acidic and basic parameters d_2h² = 2 d_ad_b, therefore_, d_2h = 2.4406 H_.  Equation (16) has not improved correlation and standard error of estimate. 

Therefore, further analysis was done to increase the correlation coefficient by considering only 12 solvents and omitting 6 solvents (ethyl acetate, octanol, hexanol, pentanol, methanol, and propylene glycol), which showed high percent error.  The following regression equation using the four partial solubility parameters approach is obtained.

[(log g₂)/ A]  =  497.5949 – 122.502 d_1d  + 7.7743d_1d² + 9.8842d_1p –  19846d_1p²–  10.5414 d_1a – 6.3285d_1b + 2.9779 d_1ad_1b ............................................................ (17)

                                 n = 12,      s = 3.141,     R² = 0.9617

The‘s’ value is lowered and the R² value was improved by 41% in comparision with equation (15). Equation (17) has significant contribution for solubility predictions.  The regressed equation (17) is used for back calculating (log g₂)/A and employed for further calculation of X_2(cal) values.  The calculated and experimental X₂ values are given in Fig. 3.  The differences between the experimental and the calculated solubility values are found to be low (except in two solvents).

The signs of coefficients are agreeing with the standard format of equation i.e., signs are changed alternatively.  Equation (20) is written according to the model equation, as given below.

[log g₂ /A] = 7.7743 (d_1d – 7.8787)² – 1.9846 (d_1p – 2.4902)² + 2.9779 (d_1a – 2.1252) (d_1b – 3.5399) + 4.9195………………………………………………... (18)

The partial parameters of the solute, calculated from the equation (18) according to extended Hansen’s method are; d_2d = 7.8787 H, d_2p = 2.4902 H, d_2a = 2.1252 H, and d_2b = 3.5399.  The total solubility parameter of celecoxib by this method is d_2T = 9.13 H.  The hydrogen bonding parameter (used in calculation of d_2T) is calculated from acidic and basic parameters d_2h² = 2 d_ad_b, therefore_, d_2h = 3.8789 H.  There is a considerable evidence to suggest that celecoxib will be soluble in solvents, through acid - base parts of molecule. 

The regressed equation (18) is used for back calculating (log g₂)/A and employed for further calculation of X_2(cal) values.  The calculated and experimental X₂ values are given in Fig. 3.

The solvent series appears to be an ideal solvent system and the technique of ideal mole fraction solubility intersecting the solubility curve reasonably predicts the solubility parameter of celecoxib.  The usefulness of a theoretical approach is the ability to calculate solubilities of a drug in mixed or pure solvents, using only fundamental physicochemical properties of the solute and solvent.

The partial parameters values obtained were found to vary with the method used in analyzing the solubility data.  They may also vary with the nature and number of solvents used for the correlations. This may be a resultant effect of solute-solvent interactions.  The partial solubility parameters obtained for celecoxib are consistent with the behaviour that should be expected from the mainly Lewis-base nature of the drug.  The celecoxib’s basic partial parameter d_2b is more than its acidic partial parameter d_2a.  The value of d_2a/d_2b for celecoxib (0.60) suggests that the drug is a better proton acceptor than a proton donor.  This could be anticipated because of the presence of proton-accepting (Lewis base) group (–NH₂ group) in the molecule.  The behaviour of celecoxib can be compared with two weakly basic drugs; piroxicam and pimozide.^27,28  The ratio is lesser in piroxicam (0.43) than celecoxib as the former possesses two carbonyl groups and a -NH group.  On the other hand pimozide has higher value (0.77) than celecoxib.  It could be because of presence of a carbonyl group and NH group inside the ring of the former.

The experimental total solubility parameter of celecoxib (11 H) falls between piroxicam (13.69 H) and pimozide (10.43).  This agrees with the fact that celecoxib is less polar than piroxicam and more polar than pimozide (celecoxib has three hydrophobic rings, where as piroxicam has two rings and pimozide has five rings).

This result is very interesting as it demonstrates the validity of the four parameter model for a mainly proton acceptor compound.  This observation is in accordance with the behaviour found in case of piroxicam and pimozide. ^27,28

Celecoxib is expected to be of lower polarity due to the presence of three hydrophobic rings.  However, the higher solubility of celecoxib in normal alcohols could be credited to their strong hydrogen bonding capacity. 

The dispersion solubility parameter represents London forces, a kind if interaction that is common to all polar and nonpolar molecules.²⁹ The dipole (d_2p) and hydrogen bonding parameters (d_2h, d_2a, and d_2b) are not so close, being lower in all cases, as was also found for pimozide, citric acid, paracetamol, niflumic acid, and piroxicam and therefore, contribute most to the observed differences among the total solubility parameter. ^28-30  On the other hand, the polar and hydrogen bonding parameters seem to be more important to differentiate the behaviour of celecoxib in solutions rather than the dispersion parameter.

The structure of celecoxib reveals the necessity of separation of the hydrogen bonding parameter into acidic and basic parameters to provide a better description of the system.  This confirms previous findings for pimozide, citric acid, paracetamol, niflumic acid, and piroxicam.  Celecoxib is a moderately weak base, probably due to the low value of the ratio of the partial acidic parameter to the partial basic parameter.  The values of the partial solubility parameters give insights into the interaction capability of the drug and are consistent with its chemical structure.  Hence celecoxib is a proton acceptor and thus is a Lewis base.  

CONCLUSIONS:

In this work two additional techniques are employed.  Both are an extension of the Hildebrand solubility approach for evaluating the solubility predictions of drug in solvents.  The first technique involved the intersecting of the observed mole fraction solubility of celecoxib at ideal mole fraction solubility.  This technique is quite useful, when it is nearer to the peak solubility.  Secondly, the work is not a new theory but is a technique partly based on polynomial regression for back calculating solubilities of drugs and other solutes in solvent blends of different polarity.  Hydrogen bonding partial parameters provided reasonable explanation of celecoxib solubility.  The total solubility parameter of celecoxib is ~ 11 H.

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Received on 31.03.2009        Modified on 22.05.2009

Accepted on 10.06.2009        © AJRC All right reserved

Asian J. Research Chem.  2(2): April.-June, 2009 page 188-195