Dissolution

The availability of a drug in the body depends on its ability to dissolve in the gastrointestinal (GI) fluids. If the rate of dissolution is the rate-limiting step in drug absorption, any factor affecting the dissolution rate will have an impact on bioavailability.

The dissolution rate of suspended, poorly soluble drugs according to the well known diffusion-layer model, modified Noyes-Whitney equation (Horter and Dressman, 1997; Nystrom, 1998) is as follows:

dt hv where D is the diffusion coefficient, h is the thickness of the diffusion layer at the solid liquid interface, A is the surface area of drug exposed to the dissolution media, v is the volume of the dissolution media, Cs is the concentration of a saturated solution of the solute in the dissolution medium at the experimental temperature, and C is the concentration of drug in solution at time t. The dissolution rate is given by dc/dt.

According to this model, dissolution rate is a function of:

• Drug solubility

• The diffusional transport of dissolved molecules away from the solid surface through a thin region of more or less stagnant solvent which surrounds the drug particles

• The solid surface area that is effectively in contact with the solvent

The physicochemical properties that influence the kinetics of drug dissolution can all be attributed to their effects on one or more of these factors. The detailed discussion on the theory of dissolution is covered in Chap. 3, thus will not be discussed here.

2.2.4 Solubility

Solubility is one of the most important properties impacting bioavailability because of its role in dissolution. It is one of two factors defining the biopharma-ceutics classification system (BCS) (Amidon et al., 1995).

Before the advent of combinatorial chemistry and high throughput screening in the late 1980s and early 1990s, most compounds that were considered poorly soluble had solubility in the range of 10-100 |g/mL (Lipinski et al., 1997). Practically, no marketed drug had solubility below 10 |g/mL. Today, compounds with solubility in the range of 1-10 |g/mL and even <1 |g/mL are very common. Having a good understanding of factors affecting solubility is crucial to our ability to address deficiencies in formulation caused by poor solubility.

2.2.4.1 Definition of Solubility

Based on the official IUPAC definition, Lorimer and Cohen-Adad (2003) more recently defined solubility in more broad terms:

Solubility was defined as the analytical composition of a mixture or solution that is saturated with one of the components of the mixture or solution, expressed in terms of the proportion of the designated component in the designated mixture or solution.

The term "saturated" implies equilibrium with respect to the processes of dissolution and crystallization for solubility of a solid in a liquid, and of phase transfer for solubility of a liquid in another liquid. The equilibrium may be stable or metastable, that is, the composition of a system may maintain a particular value for a long time, yet may shift suddenly or gradually to a more stable state if subjected to a specific disturbance. For example, the solid may be amorphous and may convert to a more stable crystalline form, bringing the system from a metastable equilibrium to a stable one.

In recent pharmaceutical literature, the terms "equilibrium solubility" and "kinetic solubility" are often used for the systems with stable and metastable equilibria, respectively (Lipinski et al., 1997; Huang and Tong, 2004; Borchardt etal., 2006).

2.2.4.2 Factors Contributing to Poor Aqueous Solubility

Two main factors governing aqueous solubility are heat of solvation and heat of fusion (Grant and Highuchi, 1990; Jain and Yalkowsky, 2000). The octanol/water partition coefficient (log P) is a good measure of the solvation energy, which is the energy associated with dissolving solute in water. Lipophilic compounds do not like to interact with water, thus the heat of solvation is small and not enough to overcome the strong hydrogen bonds between water molecules, leading to poor solubility. If the compound is crystalline, additional energy, characterized as heat of fusion, is also required to liberate the molecule from its crystal lattice before it can dissolve. Melting point is the property that is most useful in term of characterizing crystal packing interactions. Compounds with high melting point and large heat of fusion will have poor aqueous solubility unless this large heat of fusion is surpassed by the heat of solvation.

Many high throughput solubility screening methods do not use crystalline drug substance as the starting material. Some start the solubility study by adding dimethyl sulfoxide or DMSO solution in various solubility media. If the material remains as amorphous during the time solubility sample is equilibrated, the impact of heat of fusion on solubility can not be assessed. This is why many of these screening methods can not obtain results that correlate well with the results measured by the traditional shake flask method using crystalline material.

2.2.4.3 pH-Solubility Profile

Majority of drugs are ionizable; therefore, their solubilities are affected by the solution pH and the counter ions that can form salts with them. The solubility theory has been well reviewed in several recent publications (Pudipeddi et al., 2002; Tong, 2000), thus only a brief discussion of pH-solubility principles related to their importance to oral absorption will be presented here.

The equilibrium for the dissociation of the monoprotonated conjugate acid of a basic compound may be expressed by:

where BH+ is the protonated species, B is the free base, and K'a is the apparent dissociation constant of BH+, which is defined as follows:

Generally, the relationships drawn in (2.2) and (2.3) must be satisfied for all weak electrolytes in equilibrium irrespective of pH and the degree of saturation. At any pH, the total concentration of a compound, ST, is the sum of the individual concentrations of its respective species:

In a saturated solution of arbitrary pH, this total concentration, St, is the sum of the solubility of one of the species and the concentration of the other necessary to satisfy the mass balance.

At low pH where the solubility of BH+ is limiting, the following relationship holds:

where pHmax refers to the pH of maximum solubility and the subscript pH < pHmax indicates that this equation is valid only for pH values less than pHmax. The subscript s indicates a saturated species. A similar equation can be written for solutions at pH values greater than pHmax where the free base solubility is limiting:

Each of these equations describes an independent curve that is limited by the solubility of one of the two species.

The pH-solubility profile is nonuniformly continuous at the juncture of the respective solubility curves. This occurs at the precise pH where the species are simultaneously saturated, previously designated as the pHmax.

Figure 2.3 is a typical pH-solubility profile for a poorly soluble basic drug (Tong, 2000). It is constructed by assuming that the solubilities of the hydrochloride salt and the free base (B) are 1 and 0.001 mg/mL, respectively, and the pKa' of the compound is equal to 6.5. The solubility under curve I is limited by the solubility of the salt, whereas the solubility under curve II is limited by the solubility of the free base.

Figure 2.3. pH-solubility profile of an ideal compound BH+Cl

Figure 2.3. pH-solubility profile of an ideal compound BH+Cl

The dissociation constant (pKa'), the intrinsic solubility of the unionized form, and the solubility of the salt are three determining factors defining the pH-solubility profile. All other factors being equal, each upward or downward shift in the pK a' is matched exactly by an upward or downward shift in pHmax. If the solubility of the free base is very small relative to that of the salt, the free base limiting curve (curve II) of the overall pH-solubility profile cuts deeply into the acidic pH range, resulting pHmax of several pH units smaller than pKa'. Every one-order-of-magnitude increase in the intrinsic solubility of the free base increases the pHmax by one unit, whereas every one-order-of-magnitude increase in the solubility of the salt results in a decrease in the pHmax by one unit. These effects are illustrated in Fig. 2.4 (Li et al., 2005).

FIGURE 2.4. Effect of relevant parameters on pH-solubility curves: (A) effect of intrinsic solubility So, (B) effect of pKa

For acidic compounds, the pH-solubility curve is the mirror image of the curve for basic compounds. Curve I, where solubility is limited by the salt, is on the right side and curve II, where solubility is limited by the free acid, is on the left side with lower pH values (Yalkowsky, 1999; Pudipeddi et al., 2002).

In the stomach, the acidic pH and high concentration of the chloride ion can be problematic for many basic compounds if their hydrochloride salts are poorly soluble. A more soluble salt may be advantageous from the absorption point of view since the conversion to the less soluble hydrochloride salt may not happen right away, maintaining a certain degree of supersaturation on the surface (Li et al., 2005). The conversion to the less soluble hydrochloride salt may be avoided by formulation means such as enteric coating (Tong, 2000). In the intestine, the presence of bile salts and other components such as fat and lipid typically can improve the intrinsic solubility of the free base, shifting pHmax to higher value.

The pH-solubility profile is also an important consideration in designing robust formulations. When the microenvironmental pH of a salt of a weakly acidic drug is less than the pHmax, conversion of the salt to the free acid may occur upon storage or formulation, leading to potential undesirable changes in product performance both in vitro and in vivo.

2.2.4.4 Effect of Temperature on Solubility

The van't Hoff equation defines the relationship between solubility and temperature:

ln s = A H/R(1/ T) + constant where s is the molar solubility at temperature T (K) and R is the ideal gas law constant. A H is the heat of solution, representing the heat released or absorbed when a mole of solute is dissolved in a large quantity of solvent. For most organic compounds, the heat of solution is about 10kcal/mol, suggesting that solubility differences between 25 and 37 °C are typically about two times. Practically, most of the solubility studies are done at room temperature for convenience. The two times solubility difference may not be significant when using solubility as criteria to rank order compounds for developability assessment. However, the temperature effect needs to be carefully studied to support formulation development, especially for liquid dosage form. After all, the solubility differences caused by most polymorphic changes are typically only less than two times (Pudipeddi and Serajuddin, 2005).

Additionally, the dependence of solubility on temperature will most likely change for different solubilizing systems (Tong, 2000). For example, temperature changes may affect the micellar size and the degree of drug uptake, leading to a dependence of solubilization on temperature. For solubilizing systems containing complexing agents, because the standard enthalpy change accompanying the complexing process is generally negative, increasing temperature will reduce the degree of complexation. For cosolvent systems, because the heat of solution in different solvent systems is generally different, the temperature effect on solubility in these systems is also different. Detailed solubility mapping in the solvents of interest, including the effect of pH (for ionizable compounds), temperature, and cosolvent compositions is typically required in order to develop a robust formulation, such as a soft gel formulation (Winnike, 2005).

2.2.4.5 Solubility in Gastric and Intestinal Fluids

In the stomach and intestine, drug solubility can be enhanced by the food and bile components such as bile salts, lecithin, and monooleins. Depending on the properties of the drugs, the degree of solubilization differs. Increases in solubility of up to 100-fold upon addition of physiological concentrations of bile salts to aqueous media have been reported for some hydrophobic compounds. Based on the solubility studies of 11 steroidal and nonsteroidal compounds, Michani et al. (1996) found that the solubility enhancement by bile salts is a function of the log P. Other factors that may affect the extent of solubilization include MW of the drug and specific interactions between drug and bile salts (Horter and Dressman, 1997).

Supersaturation in the intestinal fluid is an important property that can play a significant role in drug absorption. This is because for compounds with poor intrinsic solubility in the intestinal fluid, solubility is often a limiting factor for absorption. Creating or maintaining supersaturation in the intestinal fluid is necessary to enhance absorption of these compounds. For example, hydroxypropylmethyl-cellulose (HPMC-AC) has been shown to significantly enhance the absorption of several poorly soluble compounds (Shanker, 2005). Several dissolution systems that are shown to be able to better estimate or predict the supersaturation phenomenon have recently been reported (Kostewicz et al., 2004; Gu et al., 2005).

To realistically estimate the impact of solubility on absorption, solubilities and the degree of supersaturation in more physiologically relevant media should be determined. Two media that were developed based on literature and experimental data in dogs and humans have been used extensively in the industry and academic research (Greenwood, 1994; Dressman, 2000). The compositions of these media, FaSSIF, simulating fasted state of intestinal fluid and FeSSIF, simulating fed state of intestinal fluid, are given below (Table 2.1).

Table 2.1. Compositions of FaSSIF and FeSSIF

FaSSIF

FeSSIF

KH2PO4

Acetic acid Na taurocholate Lecithin KCl pH

na: not applicable

2.2.4.6 Solubility as a Limiting Factor to Absorption

Since oral drug absorption is a consecutive and continuous process of dissolution and permeation, poor absorption is traditionally considered to be caused by poor dissolution and/or poor permeation. However, with the more recent drug candidates becoming less soluble, there are cases where the dissolution of a compound is relatively fast and membrane permeability is also already relatively high, but the oral absorption is still poor. In these cases, solubility becomes the limiting factor to absorption since the gut is already saturated and further increase of dose does not increase the absolute amount of drug absorbed.

Lipinski (1997) noted that solubility is not likely to be the limiting factor for absorption for an orally administered drug with a dose of 1 mg/kg, if the solubility is greater than 65 |g/mL, but is likely to limit absorption if the solubility is less than 10 |g/mL (Lipinski et al., 1997). These estimates are supported by the concept of maximum absorbable dose (MAD) (Johnson and Swindell, 1996; Curatolo, 1998). MAD is a conceptual tool that relates the solubility requirement for oral absorption to the dose, permeability and GI volume and transit time. It is defined as:

MAD(mg) = S(mg/mL) x Ka(1/min) x SIWV(mL) x SITT(min) (2.7)

where S is solubility at pH 6.5 reflecting typical small intestine condition; Ka is trans-intestinal absorption rate constant determined by a rat intestinal perfusion experiment; SIWV is small intestinal water volume, generally considered to be 250 mL; and SITT is small intestinal transit time, typically around 270 min. A more simplified and conservative approach is adopted by the FDA to define a BCS (Amidon et al., 1995). This system defines low solubility compounds as those whose aqueous solubility in 250 mL of pH 1-7.5 aqueous solution is less than the total dose.

It is important to remember that the BCS was created more as a guideline to determine whether an in vitro and in vivo correlation (IVIVC) can be expected and whether a biowaiver could be made on the basis of dissolution tests. Many compounds that are classified as low solubility (classes II and IV) have been shown to be well absorbed. Based on historical data, even the MAD can be considered as a very conservative and simple approach. Certain compounds such as basic compounds with low pK a may have poor solubility in the intestinal fluid, but they may be soluble in the stomach and may be able to maintain supersaturation in the intestine. Other compounds may have much improved solubility in the intestinal fluids such as FaSSIF and FeSSIF compared to pure buffer solutions. In these cases, it may be more realistic to use the kinetic solubility in either FaSSIF or FeSSIF to estimate the MAD.

2.2.4.7 Solubility Determination

The most traditional method for measuring equilibrium solubility is the shake flask method. An excess amount of material is equilibrated in a vial or flask with the solubility medium. The vial or flask is shaken or stirred under a controlled temperature, and the amount of drug is determined at various time intervals by analysis of the supernatant fluid. The equilibrium is considered reached when solubility is not changing any more in two consecutive samples. The residual solid from the solubility studies should be examined for any form changes. Care should be taken when studying the residual solid to make sure a hydrate is not missed. For this reason, a powder X-ray diffraction (PXRD) run with both wet and dry samples is very useful.

For poorly soluble compounds, the time required to reach equilibrium may be rather long due to the poor dissolution rate. There are several practical ways to improve the saturation rate, mainly by manipulating the dissolution rate. Using excess amount of material can increase the effective surface area for dissolution. The surface area of the solid can also be increased by preprocessing the solubility samples. Both vortexing with a small teflon ball in the suspension and sonication are very effective techniques for this purpose. Adding amorphous samples to the solubility sample may create temporary supersaturation, making the dissolution rate a nonlimiting step in reaching equilibrium.

Extra care must be given to determine solubility of salts to avoid the impact of potential conversion of salts to the free form. This conversion is common for salts of compounds with very low intrinsic solubility and weak basicity or acidity. One way to avoid this problem is to determine solubility in a diluted acidic solution using the same acid that formed the salt with the base (Tong, 2000). The solubility can then be calculated by correcting for the common ion effect from the acid. It is only in a suspension with a pH value that is below pHmax for basic compounds (or above pHmax for acidic compounds) that the solubility is limited by the solubility of the salt. In case the solid salts are not available, solubility of salts may be estimated by the in situ salt screening method (Tong and Whitesell, 1998).

For discovery, sometimes a nonequilibrium solubility, often called "kinetic solubility," which is determined by adding a compound's DMSO solution to aqueous buffers, may be useful. This is because many experiments in drug discovery are conducted using compound's DMSO solution. Additionally, the kinetic solubility may help identify poorly soluble compounds early since it is rather unlikely that compounds with poor kinetic solubility will show much improved equilibrium solubility later on when the solid crystalline material is used to measure the solubility.

Several high throughput assays for the kinetic solubility have been described using different analytical methods (Lipinski et al., 1997; Bevan and Lloyd, 2000; Avdeef, 2001). Compared to equilibrium method, some differences in solubility results are expected since for compounds with poor solubility, because of high crystallinity, kinetic methods will obviously overestimate the solubility. Thus, understanding the usefulness and limitation of the kinetic solubility data is important when interpreting results and making important decision in drug candidate selection.

2.2.4.8 Solubility Prediction

Solubility prediction may be useful in early drug discovery phases when solubility measurement is not yet possible. The predicted solubility data may provide guidance in screening of computer designed combinatorial libraries and in lead optimization.

Unfortunately, despite all the effort in the last few decades, there is not a simple reliable method yet up to today for predicting solubility (Taskinen and Yliruusi, 2003). Yalkowsky and Valvani (1980) have introduced a model for solubility of nonelectrolytes which contains only two parameters, log P for liquid phase effects and the melting point (MP) for solid phase effects. Although the model has shown to give reasonable predictions for diverse organic compounds (Jain and Yalkowsky, 2000; Ran et al., 2001), it requires an experimental parameter, the melting point, which is as difficult a problem for prediction as solubility. According to this model, solubility of the solid nonelectrolyte (S) can be calculated from MP and log P by the following equation:

Several neural network methods have been developed to predict solubility and other physicochemical properties. While some methods provide as accurate data as experimental results, others do not (Glomme et al., 2004; Huuskonen et al., 1998). The lack of adequate diversity in the training set is believed to be the main reason for the inaccuracy. As more experimental data with more structure diversity and good quality become publicly available, it is reasonable to assume that a better solubility prediction model will emerge in the future.

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