The Expanded Hansen Approach to Solubility Parameters. Paracetamol and Citric Acid in Individual Solvents

In this study two solubility-parameter models have been compared using as dependent variables the logarithm of the mole fraction solubility, lnX₂^e, and ln(α)/U (originally used in the extended Hansen method), where α is the activity coefficient and U is a function of the molar volume of the solute and the volume fraction of the solvent. The results show for the first time the proton-donor and -acceptor hydrogen-bonding capacities of paracetamol, as measured by the acidic and basic partial-solubility parameters. The influence of solvents on the differential scanning calorimetry (DSC) pattern of the solid phases was also studied in relation to the solubility models tested. Citric acid was chosen as a test substance because of its high acidity and its proton donor capacity to form hydrogen bonds with basic solvents. The partial acidic and basic solubility parameters obtained from multiple regression were consistent with this property, validating the model chosen. The results show that the more direct lnX₂^e variable was more suitable for fitting both models, and the four-parameter model seemed better for describing the interactions between solvent and solute.     

The modified extended Hansen method to determine partial solubility parameters of drugs containing a single hydrogen bonding group and their sodium derivatives: benzoic acid/Na and ibuprofen/Na

Sodium salts are often used in drug formulation but their partial solubility parameters are not available. Sodium alters the physical properties of the drug and the knowledge of these parameters would help to predict adhesion properties that cannot be estimated using the solubility parameters of the parent acid. This work tests the applicability of the modified extended Hansen method to determine partial solubility parameters of sodium salts of acidic drugs containing a single hydrogen bonding group (ibuprofen, sodium ibuprofen, benzoic acid and sodium benzoate). The method uses a regression analysis of the logarithm of the experimental mole fraction solubility of the drug against the partial solubility parameters of the solvents, using models with three and four parameters. The solubility of the drugs was determined in a set of solvents representative of several chemical classes, ranging from low to high solubility parameter values. The best results were obtained with the four parameter model for the acidic drugs and with the three parameter model for the sodium derivatives. The four parameter model includes both a Lewis-acid and a Lewis-base term. Since the Lewis acid properties of the sodium derivatives are blocked by sodium, the three parameter model is recommended for these kind of compounds. Comparison of the parameters obtained shows that sodium greatly changes the polar parameters whereas the dispersion parameter is not much affected. Consequently the total solubility parameters of the salts are larger than for the parent acids in good agreement with the larger hydrophilicity expected from the introduction of sodium. The results indicate that the modified extended Hansen method can be applied to determine the partial solubility parameters of acidic drugs and their sodium salts.     

A Modification of the Extended Hildebrand Approach to Predict the Solubility of Structurally Related Drugs in Solvent Mixtures

Abstract— A modification of the extended Hildebrand equation is proposed to estimate the solubility of an organic drug in solvent mixtures. The equation accurately reproduces the solubility of four sulphonamides in dioxane-water mixtures without requiring the heat of fusion of the solute. A single equation is obtained for predicting the solubility of related drugs using the solubilities of the drugs in the pure solvents, dioxane and water, and solute-solvent interaction terms consisting of the solubility parameter, δ₂, of the solute and the solubility parameter, δ₁, and basic partial solubility parameter, δ_1b, of the solvent mixture. By this procedure a single equation was obtained to estimate the solubilities of three xanthines in dioxane-water and another equation to obtain the solubilities of four sulphonamides. The equation obtained for sulphonamides is able to predict the experimental solubilities of two parent compounds, sulphasomidine and sulphathiazole, and the solubilities of a drug of different structure, p-hydroxybenzoic acid. This suggests that the intermolecular solute-solvent interaction of sulphonamides and p-hydroxybenzoic acid are similar. The results indicate that the solubility behaviour of drugs having different structures may be modelled using a common equation provided that they show similar solute-solvent interactions.     

Proposition of group molar constants for sodium to calculate the partial solubility parameters of sodium salts using the van Krevelen group contribution method.

The aim of this study is to propose, for the first time, a set of group molar constants for sodium to calculate the partial solubility parameters of sodium salts. The values were estimated using the few experimental partial solubility parameters of acid/sodium salt series available either from the literature (benzoic acid/Na, ibuprofen acid/Na, diclofenac Na) or determined in this work (salicylic acid/Na, p-aminobenzoic acid/Na, diclofenac), the group contribution method of van Krevelen to calculate the partial parameters of the acids, and three reasonable hypothesis. The experimental method used is a modification of the extended Hansen approach based on a regression analysis of the solubility mole fraction of the drug lnX(2) against models including three- or four-partial solubility parameters of a series of pure solvents ranging from non-polar (heptane) to highly polar (water). The modified method combined with the four-parameter model provided the best results for both acids and sodium derivatives. The replacement of the acidic proton by sodium increased the dipolar and basic partial solubility parameters, whereas the dispersion parameter remained unaltered, thus increasing the overall total solubility parameter of the salt. The proposed group molar constants of sodium are consistent with the experimental results as sodium has a relatively low London dispersion molar constant (identical to that of -OH), a very high Keesom dipolar molar constant (identical to that of -NO(2), two times larger than that of -OH), and a very high hydrogen bonding molar constant (identical to that of -OH). The proposed values are: F((Na)d)=270 (J cm(3))(1/2) mol(-1); F((Na)p)=1030 (J cm(3))(1/2) mol(-1); U((Na)h)=17000 J mol(-1). Like the constants for the other groups, the group molar constants proposed for sodium are certainly not the exact values. However, they are believed to be a fair approximation of the impact of sodium on the partial solubility parameters and, therefore, can be used as such in the group contribution method of van Krevelen.     

Determination of partial solubility parameters of five benzodiazepines in individual solvents

Three and four component partial solubility parameters for diazepam, lorazepam, oxazepam, prazepam and temazepam were determined using the extended and expanded Hansen regression models. A comparison was made also with solubility parameters calculated by the group contribution method proposed by Van Krevelen. Although a limited number of solvents was used, the results from the present study indicate that the partial solubility parameters obtained from the experimental regression models clearly reflect the structural differences in these five structurally related molecules. High R(2)-values were observed in the regression models (0.932 < or =R(2)< or =0.984), except for lorazepam (0.606 < or =R(2)< or =0.825). This was attributed to difficulties in obtaining reliable values of the temperature and heat of fusion due to thermal decomposition of this compound. Introduction of the Flory-Huggins size correction parameter did not improve the R(2)- and F-values in any of the regression models used.     

Improved group contribution parameter set for the application of solubility parameters to melt extrusion

Hot-melt extrusion is gaining importance for the production of amorphous solid solutions; in parallel, predictive tools for estimating drug solubility in polymers are increasingly demanded. The Hansen solubility parameter (SP) approach is well acknowledged for its predictive power of the miscibility of liquids as well as the solubility of some amorphous solids in liquid solvents. By solely using the molecular structure, group contribution (GC) methods allow the calculation of Hansen SPs. The GC parameter sets available were derived from liquids and polymers which conflicts with the object of prediction, the solubility of solid drugs. The present study takes a step from the liquid based SPs toward their application to solid solutes. On the basis of published experimental Hansen SPs of solid drugs and excipients only, a new GC parameter set was developed. In comparison with established parameter sets by van Krevelen/Hoftyzer, Beerbower/Hansen, Breitkreutz and Stefanis/Panayiotou, the new GC parameter set provides the highest overall predictive power for solubility experiments (correlation coefficient r = −0.87 to −0.91) as well as for literature data on melt extrudates and casted films (r = −0.78 to −0.96).     

Relationship between swelling of hydroxypropylmethylcellulose and the Hansen and Karger partial solubility parameters

A model that relates the equilibrium swelling of hydroxypropylmethylcellulose to the partial solubility parameters of both the polymer and the solvents is proposed to interpret and correlate the experimental data. The non-specific interactions are expressed as the dispersion delta(d) and polar delta(p) solubility parameters of Hansen, or as a combination of both. Hydrogen bonding is represented by the acidic delta(a) and the basic delta(b) Karger solubility parameters. The results are compared with models including the same parameters for non-specific interactions (delta(d) and delta(p)) and the Hansen hydrogen bonding parameter delta(h). Equilibrium swelling of this hydrophilic polymer that is widely used in drug formulation is measured in pure solvents covering a wide polarity range. In a qualitative way, swelling increases in solvents with higher Hildebrand solubility parameters and stronger hydrogen bonding capability, and it decreases in non-polar solvents. Single polarity indexes, such as the Hildebrand solubility parameter or the partition coefficient (PC), do not fit well the overall experimental data. The best correlations were obtained with the proposed model, providing at the same time an interpretation consistent with the physical meaning of the terms included in the equation. Swelling increases as the non-specific interactions of the polymer and the solvents become alike, and as the Lewis acid-base interactions of the polymer (1) and the solvent (2) represented by the products delta(1a)delta(2b) and delta(1b)delta(2a) become greater. Conversely, hydrogen bonding self association of the solvents (the product delta(1a)delta(1b)) lowers swelling. The results show that the Karger hydrogen bonding parameters provide a better approach than the Hansen hydrogen bonding parameter to correlate the swelling behavior of a hydrophilic polymer.     

High throughput screening: an in silico solubility parameter approach for lipids and solvents in SLN preparations

Objective: The present paper describes an in silico solubility behavior of drug and lipids, an essential screening study in preparation of solid lipid nanoparticles (SLN).

Materials and methods: Ciprofloxacin HCl was selected as a model drug along with 11 lipids and 5 organic solvents. In silico miscibility study of drug/lipid/solvent was performed using Hansen solubility parameter approach calculated by group contribution method of Van Krevelen and Hoftyzer. Predicted solubility was validated by determining solubility of lipids in various solvent at different temperature range, while miscibility of drug in lipids was determined by apparent solubility study and partition experiment.

Results and discussion: The presence of oxygen and OH functionality increases the polarity and hydrogen bonding possibilities of the compound which has reflected the highest solubility parameter values for Geleol and Capmul MCM C8. Ethyl acetate, Geleol and Capmul MCM C8 was identified as suitable organic solvent, solid lipid and liquid lipid respectively based on a solubility parameter approach which was in agreement with the result of an apparent solubility study and partition coefficient.

Conclusion: These works demonstrate the validity of solubility parameter approach and provide a feasible predictor to the rational selection of excipients in designing SLN formulation.     

A new method to determine the partial solubility parameters of polymers from intrinsic viscosity.

A modification of the extended Hansen method, formerly used to determine the partial solubility parameters of drugs and non-polymeric excipients is tested with a polymer for the first time. The proposed method relates the logarithm of the intrinsic viscosities of the polymer in a series of solvents and solvent mixtures with the Hansen (three parameter model) and Karger (four parameter model) partial solubility parameters. The viscosity of diluted solutions of hydroxypropyl methylcellulose (HPMC) was determined in pure solvents and binary mixtures of varying polarity. The intrinsic viscosity was obtained from the common intercept of the Huggins and Kraemer relationships. The intrinsic viscosity tends to increase with increasing the solubility parameter of the medium. The results show that hydrogen bonding and polarity of the polymer largely determine polymer-solvent interactions. The models proposed provided reasonable partial and total solubility parameters for the polymer and enable one to quantitatively characterize, for the first time, the Lewis acid-base ability of a polymer thus, providing a more realistic picture of hydrogen bonding for solvent selection/compatibility and to predict drug-polymer interactions. Combination of the dispersion and polar parameters into a single non-specific solubility parameter was also tested. The results extend earlier findings and suggest that the models are quite versatile and may be applied to drugs, non-polymeric and polymeric excipients.     

Predicting the solubility of sulfamethoxypyridazine in individual solvents. I: Calculating partial solubility parameters

Sulfamethoxypyridazine, a representative model of a drug molecule, is used to test the extended Hansen method for estimating partial solubility parameters of solid compounds. Solubilities are determined in polar and nonpolar solvents. The method provides reasonable partial parameters for the sulfonamide, and it may be useful in obtaining partial parameters for other drug molecules. A four-parameter extended Hansen approach involving proton donor and acceptor parameters is used in fitting the data to a theoretical model. A term, Wh, is introduced as an empirical measure of solute-solvent interactions due to hydrogen bonding. The use of the empirical term Wh allows the researcher to fit experimental solubilities and thus design regression models and equations which provide a reasonable prediction of solubilities of a polar drug in a number of very different solvents. A Flory-Huggins size correction term improves the prediction of sulfamethoxypyridazine solubilities in these irregular solutions.     

Predicting the solubility of sulfamethoxypyridazine in individual solvents. II: Relationship between solute-solvent interaction terms and partial solubility parameters

In the first paper in the series, an expanded system of parameters was devised to account for orientation and induction effects, and the term Wh was introduced to replace delta 1h delta 2h of the extended Hansen solubility approach. In the present report, a new term, Kh = Wh/delta 1h delta 2h is observed to take on values larger or smaller than unity depending on whether the hydrogen bonded solute-solvent interaction is larger or smaller than predicted by the term delta 1h delta 2h. The acidic delta a and basic delta b solubility parameters are used to represent two parameters, sigma and tau, suggested by Small in his study of proton donor-acceptor properties. The Small equation, including a heat of mixing term for hydrogen bonded species, is shown to be capable of semiquantitative evaluation. A partial molar heat delta H2h of hydrogen bonding is calculated using delta h and Wh terms; delta H2h is found to be correlated with the logarithm of the residual activity coefficient, In alpha R, a term representing strong solute-solvent interaction. The terms Wh, delta H2h, and In alpha 2R may be used to test the deviation from the geometric mean assumed in regular solution theory, and to replace the hydrogen bonding terms of the extended Hansen three-parameter model. The solubility of sulfamethoxypyridazine in 30 solvents is used to test the semiempirical solubility equations. The results are interpreted in terms of partial solubility parameters and the proton donor-acceptor properties of the solvents.     

Enthalpy and Entropy Contributions to the Solubility of Sulphamethoxypyridazine in Solvent Mixtures Showing Two Solubility Maxima

The solubility of sulphamethoxypyridazine was measured at several temperatures in mixtures of water: ethanol and ethanol: ethyl acetate. Sulphamethoxypyridazine was chosen as a model drug to compare the solvation effects of proton donor-proton acceptor (water and ethanol) and proton acceptor (ethyl acetate) solvents and mixtures of these solvents because this drug contains functional groups capable of Lewis acid-base interaction. A plot of the mole fraction solubility against the solubility parameter (δ₁) of these solvent mixtures showed two solubility maxima, one at δ₁ = 30·87 MPa^1/2 (20:80 v/v water: ethanol) and another at δ₁ = 20·88 MPa^1/2 (30:70 v/v ethanol: ethyl acetate) at all the temperatures under study. The enthalpies and entropies of mixing as well as the enthalpies and entropies of transfer of sulphamethoxypyridazine from ethanol to water:ethanol and ethanol:ethyl acetate mixtures were calculated to compare solvation characteristics of the solvent mixtures toward the drug. As ethanol is added to water, the entropy increases and the structure of the solvent mixture became less ordered, favouring the interaction of the drug with the solvent mixture. On the other hand, in the case of the ethanol: ethyl acetate mixture, solubility is favoured by the more negative enthalpy values. This way, the same result, i.e. a solubility maximum, is obtained by different routes. In the ethanol: water mixtures, the dissolution process is entropy-controlled while enthalpy is the driving force in the case of ethanol: ethyl acetate mixtures. The two solvent systems show enthalpy-entropy compensation. Water deviates from the linear relationship due possibly to its hydrophobic effect.     

Ex vivo study of transdermal permeation of four diclofenac salts from different vehicles

The ex vivo permeation of diclofenac was studied using four different salts (sodium, potassium, diethylamine, and epolamine) dissolved in four different solvents (water, propylene glycol (PG), Transcutol, and oleic acid (OA)) as donor phases through a human skin membrane. The four salts show different solubility values and different behavior in the four solvents, which are also permeation enhancers and this fact further is connected to the permeation results. The same order of magnitude of fluxes through the membrane as those previously reported for acidic diclofenac released from buffer solutions of pH >7 were found, taking into account differences originated by different membranes and other parameters tested in the experiments. Saturation concentration for the four salts in different solvents, necessary to calculate permeation coefficients, was critically evaluated; a short discussion made it possible to explain that corrections in the solubility values must be considered, related to the complex behavior in solution of these salts. Statistical processing of the experimental data suggests that differences between the four salts in promoting absorption of the drug is unproven; while differences are evident between the solvents, water is the most effective enhancing vehicle. Aqueous formulations containing diclofenac salt with an organic base appear to be the best combination to promote permeation in topical applications.     

Comparison of bioavailability and pharmacokinetics of diclofenac sodium and diclofenac potassium in normal and dehydrated rabbits

Two different salts of diclofenac, diclofenac sodium and diclofenac potassium, in tablet dosage form were tested for their bioavailability and disposition kinetics in a group of eighteen rabbits in normal and experimentally induced dehydrated conditions with a wash out period of 7 days between both stages of study.  Biochemical and physiological parameters were also measured in both normal and dehydrated states.  Diclofenac levels in plasma were determined using a validated reversed phase HPLC method.  Primary kinetic parameters i.e.  AUC_0－¥, C_max, T_max and other disposition kinetics were obtained with non-compartmental procedure.  Biochemical parameters i.e. packed cell volume, plasma glucose and total lipid concentration in dehydrated rabbits increased significantly.  Plasma concentration of diclofenac sodium and diclofenac potassium decreased significantly in water deprived rabbits.  In comparison, diclofenac potassium in normal and dehydrated state of the same group of rabbits showed a significantly increased plasma concentration when compared with diclofenac sodium.     

Estimation of the solubility parameter of trimethoprim by current methods

Group contribution, the extended Hildebrand solubility (EHS) and the extended Hansen solubility approaches are utilised to estimate the solubility parameter value of trimethoprim. The solubility data in the binary solvent series showed peak solubility at the solubility parameter of solvent, 11.7 H. The regression expression on the lines of the EHS approach yielded 12.06 H. The data on the solubility of trimethoprim in individual solvents was processed as per the extended Hansen approach. The partial solubility parameters were obtained and are used to estimate the solubility parameter, 12.93 H. Extending the Flory-Huggins size correction to this approach gave a value of 10.95 H and improved the correlation coefficient by 3 percent. Partitioning of hydrogen bonding (four parameter approach) didn't improve the value.     

The use of quantitative analysis and Hansen solubility parameter predictions for the selection of excipients for lipid nanocarriers to be loaded with water soluble and insoluble compounds

The aim of these studies was to determine the miscibility of different API with lipid excipients to predict drug loading and encapsulation properties for the production of solid lipid nanoparticles and nanostructured lipid carriers. Five API exhibiting different physicochemical characteristics, viz., clarithromycin, efavirenz, minocycline hydrochloride, mometasone furoate, and didanosine were used and six solid lipids in addition to four liquid lipids were investigated. Determination of solid and liquid lipids with the best solubilization potential for each API were performed using a traditional shake-flask method and/or a modification thereof. Hansen solubility parameters of the API and different solid and liquid lipids were estimated from their chemical structure using Hiroshi Yamamoto’s molecular breaking method of Hansen Solubility Parameters in Practice software. Experimental results were in close agreement with solubility parameter predictions for systems with ΔδT < 4.0 MPa^1/2. A combination of Hansen solubility parameters with experimental drug-lipid miscibility tests can be successfully applied to predict lipids with the best solubilizing potential for different API prior to manufacture of solid lipid nanoparticles and nanostructured lipid carriers.     

Hildebrand solubility parameter to predict drug release from hydroxypropyl methylcellulose gels

An equation including the Hildebrand solubility parameter δ of the drugs is used for the first time to model drug release from hydroxypropyl methylcellulose (HPMC) gels: l nM = -21.578 + 2.102 δ-0.037 δ(2)+0.48 ln t + 1.028 ln C(i) (r(2) = 0.94 for a total of 286 cases). The experimentally determined release data of six drugs having different polarity (caffeine, theophylline, paracetamol, salicylic acid, naproxen and diclofenac) at several initial concentrations C(i) were included in the equation. In general, the amount of drug delivered is linear at the first 5-6h of the release profiles and the zero order constants K(o) increase as the solubility parameter of the drugs become larger. The Peppas exponential law M/M(∞) = Kt(n) is applicable to larger fractional release, until 67-87% (48-51 h) for the less polar drugs (diclofenac and naproxen, lower δ values) and more than 80% (26-28 h) for the more polar drugs (higher δ values, theophylline, salicylic acid, caffeine and paracetamol). The Peppas release rate (lnK) shows a parabolic relationship with the drug solubility parameter. The diffusional exponent n varies between 0.40 and 0.58 indicating that drug release is mainly controlled by diffusion. An extended form of the Peppas equation is also tested for each drug including all the initial concentrations: lnM = a + b ln t + c ln C(i) (r(2) = 0.88-0.94). The logarithm of the octanol-water partition coefficients can also be used in combination with the drug concentrations.     

奥卡西平半片制剂的往复筒溶出方法研究及分剂量评价

目的 建立往复筒溶出方法考察奥卡西平刻痕片仿制药与原研药分割后半片制剂的体外溶出行为相似性,评价原研药和仿制药的分剂量药学特性差异。方法 以pH 1.2盐酸溶液、pH 4.5醋酸盐缓冲液、pH 6.8磷酸盐缓冲液和水(均含0.5%十二烷基硫酸钠250 mL)为溶出介质,往复频率为10 dip·min^-1,采用往复筒溶出装置测定仿制药和原研药的溶出曲线,结合相似因子(f₂)法评价仿制药和原研药的溶出行为相似性,并与桨法进行比较。采用脆碎度检测仪及电子天平,通过人工掰分法和切药器法测定各厂家半片制剂的脆碎度、分割后质量差异及质量损失。结果 仿制药A在4种溶出介质中的f₂均>50,与原研药的溶出行为相似;仿制药B在4种溶出介质中f₂均<50,和原研药的溶出行为不相似。仿制药A、B分割后质量差异、质量损失和脆碎度均高于原研药。结论 采用往复筒法测定奥卡西平半片制剂的溶出曲线相较于桨法具有良好的区分力,且仿制药的分剂量质量控制相较于原研药仍有一定差距。     

A Relative Permittivity Approach for Fast Drug Solubility Screening of Solvents and Excipients in Lipid-Based Delivery

Drug solubility screening in solvents and lipids is central for the development of lipid-based formulations (LBFs), and any guidance to reduce the experimental workload would be highly desirable. Solubility parameters are interesting as they can be predicted in silico for a drug but they are hardly predictable for complex lipids. This paper uses a new approach to convert an in silico drug solubility parameter to an estimated relative permittivity, ε_r. Diverse solvents and lipid-based excipients were then experimentally tested for ε_r and solubility using fenofibrate as model. The typical excipients and solvents used in LBFs showed an ε_r range of about 2-24, and good solubility of fenofibrate was indeed evidenced in vicinity of its estimated relative permittivity 13.2 ± 2.7. Mixtures of promising excipients were studied subsequently, and the obtained ε_r was predictable based on the known values of the individual components. The novel permittivity approach has demonstrated its usefulness, it has much potential in early development for ranking of suitable excipients, and it gives an initial orientation to design formulations. Future research may clarify further opportunities and limits of the novel approach for LBFs.     

Comparative study of anti-inflammatory activity of some branded generic and generic non-steroidal anti-inflammatory drugs

Generic drugs play a very important role in health care. A study was undertaken to ascertain the equality or inequality between generics and branded generics. NSAIDs are the most commonly used drugs. So these drugs were chosen for the study. Selected branded generic and generic products of ibuprofen, nimesulide, and diclofenac sodium were tested by oral administration of their suspensions to different groups of rats. Freshly prepared drug suspensions equivalent to doses of 40, 10, and 5?mg/kg of ibuprofen, nimesulide, and diclofenac sodium, respectively, were administered orally to the rats and anti-inflammatory activity was measured by the carrageenan-induced rat paw edema model employing Zeitlin’s apparatus to measure the paw thickness. Statistical analysis by t-test, of the activity at the point of maximum difference indicated that with respect to anti-inflammatory activity generic ibuprofen and generic diclofenac sodium are better than branded generic ibuprofen and branded generic diclofenac sodium, respectively, and generic nimesulide is similar to branded generic nimesulide. All the products studied meet the Pharmacopoeial requirements. Hence it may be concluded that branded generic and generic NSAIDs, tested in this study, are of the same efficacy and inter-changeability among branded generics, and switching between branded generics and generics would not result in any difference in efficacy.