Introduction

Until recently it has been believed that when a molecule forms a complex with cyclodextrin then some given lipophilic moiety of the molecule enters into the hydrophobic cyclodextrin cavity, i.e. that an inclusion complex is always formed. It has also been assumed that the aqueous complexation medium is an ideal solution where the individual complexes are independent of each other. The most common stoichiometry of drug/cyclodextrin complexes is 1:1, i.e. one drug molecule forms a complex with one cyclodextrin molecule, and the most common method for stoichiometric determination during formulation studies is the phase-solubility method [1–3]. However, studies by several different research groups have shown that cyclodextrins form both inclusion and non-inclusion complexes and that several different types of complexes can coexist in aqueous solutions. Furthermore, both cyclodextrins and cyclodextrin complexes are known to form aggregates and it is thought that these aggregates are able to solubilize drugs and other hydrophobic molecules through micellar-type mechanism [1, 4, 5]. In addition, common pharmaceutical excipients, such as polymers and buffer salts, can participate in the complex formation [6]. Thus, stability constants obtained from phase-solubility diagrams are apparent stability constants describing the combined effect of the various complex structures on the drug solubility.

To complicate matters further the apparent stability constant (K 1:1) of the apparent 1:1 drug/cyclodextrin complex is determined from the slope and the intrinsic solubility (S 0) of the drug in the aqueous complexation medium. Theoretically the intercept (S int) of the phase-solubility diagram should be identical to S 0 [2]. For poorly soluble drugs with aqueous solubility <0.1 mM, S 0 is in general much larger than S int resulting in non-linearity of otherwise linear (A L-type) phase-solubility diagram [7, 8]. This can lead to erroneous K 1:1-values. Thus, due to inaccuracy of the determined S 0 and S int values the apparent stability constants are frequently very inaccurate and very sensitive to the composition of the aqueous complexation medium. A more accurate method for determination of the solubilizing efficiency of cyclodextrins is to determine their complexation efficiency (CE), i.e. the concentration ratio between cyclodextrin in a complex and free cyclodextrin. CE is calculated from the slope of the phase-solubility diagrams and is independent of both S 0 and S int. The purpose of this study is to determine the CE of various drugs and cyclodextrins and show how the CE is used to determine the formulation bulk of solid dosage forms. Also, the relationship between the S0 or the lipophilicity of the water-insoluble drug and its CE was investigated.

Experimental

Data collection

The drug solubility data was generated in our lab over the past 15 years during various drug preformulation studies. Many of the formulation studies resulted in publication but some have remained unpublished [8].

Solubility determinations

The solubility of the drugs in water or aqueous cyclodextrin solutions was determined by a heating method [8, 9]. First, the stability of the drug in the aqueous complexation media was evaluated. Small amount of the drug to be tested was dissolved in aqueous cyclodextrin solution. The solution was then divided into four sealed vials that were heated in an autoclave for 0–3 heating cycles; each cycle consisted of heating to 121 °C for 20 min. The drug concentrations in the vials were then determined by a high-performance liquid chromatographic method (HPLC). If the drug degradation was less than 1% during one cycle then the heating method in an autoclave was applied. If the degradation was greater then heating in autoclave was replaced by heating in an ultrasonic bath for 1 h at 60–70 °C. The maximum allowable drug degradation during the solubility studies was under all circumstances 1%. The drug solubility was then determined as follows:

  1. 1.

    Specific amount of cyclodextrin was dissolved in water, aqueous buffer solution or the aqueous formulation vehicle.

  2. 2.

    An excess amount of the drug to be tested was added to the aqueous cyclodextrin solution.

  3. 3.

    The suspension formed was placed in a sealed container and heated in an autoclave (121 °C for 20 min) or sonicated in an ultrasonic bath (at e.g. 70 °C for 1 h). After cooling to ambient temperature the container was opened and a small amount of the solid drug added to the container to promote drug precipitation.

  4. 4.

    After equilibration at ambient temperature (22–23 °C) in a sealed container under constant agitation for 3–7 days, the suspension was filtered through a 0.45 μm membrane filter (discarding approx. the first third of the filtrate) and the solution analyzed by HPLC (after dilution with 70% aqueous methanol solution, if necessary). The time needed to reach equilibrium solubility was determined by analyzing samples of the equilibrating solution at different time points to establish constant drug solubility.

The CE was calculated from slope of the phase-solubility profiles where the molar cyclodextrin concentration is on the X-axis and the molar drug solubility on the Y-axis.

Theoretical background

The most common type of cyclodextrin complexes is the apparent 1:1 drug/cyclodextrin complex (D/CD) where one drug molecule (D) forms a complex with one cyclodextrin molecule (CD):

$$ {\hbox{D}}\,{\hbox{ + }}\,{\hbox{CD}}\,\overset {K_{{\hbox{1:1}}} } \leftrightarrows \,{\hbox{D/CD}} $$
(1)

The value of the stability constant (K 1:1) is used to compare the affinity of drugs for different cyclodextrins or cyclodextrin derivatives. The total solubility of drug (S t) in aqueous cyclodextrin solution will then be:

$$ S_{\hbox{t}} \, = \,S_0 \, + \,\frac{{K_{1:1} \, \cdot \,S_0 }} {{1\, + \,K_{1:1} \, \cdot \,S_0 }}\, \cdot \,\left[ {{\hbox{CD}}} \right]_{\hbox{t}} $$
(2)

where S 0 is the intrinsic solubility of the drug, i.e. the solubility when no cyclodextrin is present, and [CD]t is the total concentration of cyclodextrin in the aqueous medium. A plot of S t versus [CD]t, according to Eq. (2) (i.e. a phase-solubility profile), will give a straight line with a slope (K 1:1·S 0/(1 + K 1:1·S 0)) less than unity and an intercept (S int) equal to S 0. Then K 1:1 is calculated from the slope and S 0 according to Higuchi and Connors [2]:

$$ K_{1:1} \, = \,\frac{{{\hbox{Slope}}}} {{S_0 \left( {1 - {\hbox{Slope}}} \right)}} $$
(3)

However, the K 1:1 value determined by Eq. (3) is strongly affected by the S 0 value which is usually very inaccurate for compounds with S 0 < 0.1 mg/ml [8].

It is well documented that both cyclodextrins and cyclodextrin complexes self-aggregate and that cyclodextrins are able to form non-inclusion complexes in addition to the well-known inclusion complexes (Table 1). In a recent publication Bonini et al. describe how β-cyclodextrin (βCD) aggregates in pure water to form differently shaped aggregates with a minimum hydrodynamic radius of about 90 nm at low βCD concentration that are in equilibrium with larger structures (i.e. disks and sheets) at higher βCD concentrations [10]. Previously Coleman et al. [11] had shown that the three natural cyclodextrins, αCD, βCD and γCD, exist as aggregates in solution bound together by a network of hydrogen bonds. The self-aggregation is partly concentration dependent, increasing with increasing cyclodextrin concentration. Furthermore, multi component ternary and quaternary cyclodextrin complexes have also been observed [6, 12, 13]. Thus, stability constants, such as K 1:1, obtained from phase-solubility diagrams are most frequently observed constants that are composed of a number of true stability constants for multiple types of coexisting water-soluble drug complexes in the aqueous complexation media. This coexistence of multiple types of complexes could also explain why the experimentally determined values of K 1:1 are highly sensitive to both the method applied and the composition of the medium [1]. A more reliable method for evaluation of cyclodextrins and their solubilizing potentials is to determine the CE, which is equal to the complex to free cyclodextrin concentration ratio and can be obtained from the slope of their phase-solubility profile [14]:

$$ {\hbox{CE}}\, = \,S_0 \cdot K_{1:1} \, = \,\frac{{\left[ {{\hbox{D/CD}}} \right]}} {{\left[ {{\hbox{CD}}} \right]}}\, = \,\frac{{{\hbox{Slope}}}} {{\left( {1 - {\hbox{Slope}}} \right)}} $$
(4)
Table 1 Some publication showing formation of cyclodextrin aggregates and/or non-inclusion complex formation
Full size table

Where [D/CD] is the concentration of dissolved complex, [CD] is the concentration of dissolved free cyclodextrin and Slope is the slope of the phase-solubility profile. The CE can be used to calculate the D:CD ratio, which can be correlated to the expected increase in formulation bulk:

$$ {\hbox{D:CD}}\, = \,1:\left( {1 + \frac{{\hbox{1}}} {{{\hbox{CE}}}}} \right) $$
(5)

Results and discussion

Table 2 displays the CE for a number of drugs and a number of cyclodextrins although mainly for 2-hydroxypropyl-βCD (HPβCD) and randomly methylated βCD (RMβCD). The mean (±standard deviation (SD)) CE of HPβCD (degree of substitution 0.6) for 13 different drugs in Table 2 in pure water was determined to be 0.39 ± 0.47 indicating that on the average only about 1 out of every 3–4 HPβCD molecules in solution are forming a water-soluble complex with the poorly soluble drug, assuming 1:1 drug/HPβCD complex formation (i.e. that the D:CD ratio is on the average about 1:3.6). For six of the drugs in Table 2, the CE for both RMβCD (randomly methylated βCD, degree of substitution 1.8) and HPβCD (degree of substitution 0.6) was determined under identical conditions. For those six drugs the mean (±SD) value for CE in pure water at room temperature (22–23 °C) was 1.04 ± 0.75 for RMβCD (D:CD ratio is on the average about 1:2) but 0.63 ± 0.50 for HPβCD (D:CD ratio is on the average about 1:2.6). This confirms what a number of other studies have shown, that in aqueous solutions RMβCD is most often a better solubilizer than HPβCD.

Table 2 Physicochemical properties, CE and formulation bulk of selected drugs
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Equation (6) shows the correlation between the increase in formulation bulk and molecular weights of the cyclodextrin (MWCD) and the drug (MWDrug), and the value of CE:

$$ {\hbox{Increase in Formulation bulk = }}\frac{{{\hbox{MW}}_{{\hbox{CD}}} }} {{{\hbox{MW}}_{{\hbox{Drug}}} }}{\hbox{ $ \times $ }}\left( {{\hbox{1 + }}\frac{{\hbox{1}}} {{{\hbox{CE}}}}} \right) $$
(6)

The new formulation bulk can be found by multiplying the number obtained from Eq. (6) with the drug dose. The MW of the natural βCD is 1,135 Dalton and the MW of the three most common βCD derivatives are 1,310 Dalton for RMβCD, 1,400 Dalton for HPβCD and 2,163 Dalton for sulfobutylether β-cyclodextrin sodium salt (SBEβCD). Thus, based on Eq. (6) the βCD derivatives will result in 15–90% greater increase in the formulation bulk than the parent βCD, assuming that the CE will not be effected by the derivation of the βCD molecule.

Figure 1 shows the CE as function of the octanol/water partition coefficient (logK o/w), the intrinsic solubility (S 0) in pure water, the melting point (MP) and the molecular weight (MW) of the drug. No linear correlation is between CE and any of these physicochemical properties. However, the figure shows that drugs possessing logK o/w between 1 and 4 frequently show good CE with both HPβCD and RMβCD, and that drugs possessing logK o/w greater than 4 are likely to have low CE with these same βCD derivatives (Fig. 1A). Equations (1) and (4) indicate that drugs possessing very low S 0 (i.e. low [D]) should in general have low CE and Fig. 1B appears to confirm that, since the highest CE is obtained with drugs possessing S 0 greater than about 0.01 mg/ml. The four most lipophilic drugs in Fig. 1A have logK o/w greater than six and it could be assumed that these same four drugs would also have the lowest S 0 values. However, although their mean logK o/w value is 7.6 (range 6.3–10) their mean S 0 value is 0.07 (range 0.03–0.1) mg/ml, or well above 0.01 mg/ml (Table 2). There is no obvious correlation between the CE and the MW or MP of the drug (Fig. 1C and D).

Fig. 1
figure 1

The CE as a function of (A) the logarithm of the n-octanol/water partition coefficient (logK o/w), (B) logarithm of the intrinsic solubility (S 0) in pure water, (C) the melting point (MP) in °C, and (D) the molecular weight (MW) in Dalton. HPβCD (○) and RMβCD (●)

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The CE can be estimated by determining the solubility of a given drug at two to three cyclodextrin concentrations in pure water or a medium constituting the pharmaceutical formulation such as parenteral solution or aqueous eye drop formulation. Based on the CE value the drug:cyclodextrin ratio can be determined in the complexation medium as well as the increase in the formulation bulk in a solid dosage form. Determination of the CE is a simple method for a quick evaluation of the solubilizing effects of different cyclodextrins and/or the effects of excipients on the solubilization.

The CE can be used asses the feasibility of using cyclodextrins in the formulation of drugs. For example, a reasonable upper limit for the maximum bulk of a cyclodextrin formulation, to be used in a solid oral dosage form, would be one gram. Analysis of the data in Table 2 (Fig. 2) shows that this target cannot be reached when the single oral dose of a drug is greater than 250 mg. In general, the formulation bulk will be less than one gram when the single oral dose is less than 50 mg and CE is greater than 0.1. This applies to only half of the more potent drugs possessing CE less than 0.1. Consequently, when cyclodextrin formulation for oral dosage forms is to be considered the drug has to be relatively potent and preferably it’s CE has to be greater than 0.1. For other types of drug formulations, such as eye drops or infusion solutions, more stringent or relaxed conditions for potency and CE can be defined.

Fig.2
figure 2

The CE as a function of formulation bulk for drugs with a single oral dose of ≥250 mg (□), between ≥50 and <250 mg (◢) or <50 mg (■). Based on the data presented in Table 1

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