determination of stability constant of β-cyclodextrin complexes using the membrane permeation...

European Journal of Pharmaceutical Sciences, 8 (1999) 133–139

Determination of stability constant of b-cyclodextrin complexes using themembrane permeation technique and the permeation behavior of drug–

competing agent–b-cyclodextrin ternary systems*Naomi Ono, Fumitoshi Hirayama, Hidetoshi Arima, Kaneto Uekama

Faculty of Pharmaceutical Sciences, Kumamoto University, 5-1 Oe-honmachi, Kumamoto 862-0973, Japan

Received 8 October 1998; received in revised form 8 December 1998; accepted 23 December 1998

Abstract

The stability constants (Kc) of b-cyclodextrin (b-CyD) complexes with phenacetin and various benzoic acids were determined usingthe membrane permeation technique using a cellophane membrane permeable for guest molecules which was impermeable for b-CyDmolecules. The permeation rate equations of guests in the presence of b-CyD in the donor phase were derived and the permeation profileswere analyzed as a function of time to determine the Kc values. The Kc values determined using the membrane permeation techniquewere in close agreement with those determined by the conventional kinetic method and the solubility method. The membrane permeationtechnique is of greater advantage than the conventional methods, because in the former method the stability constant can be obtained fromonly one experimental run by analyzing the permeation data as a function of time. In the latter method, on the other hand, some propertychanges have to be measured at various CyD concentrations and in turn analyzed as a function of CyD concentration. The permeationprofiles of phenacetin of the drug–competing agent–b-CyD ternary system were estimated by using the stability constants and theexperimental curves closely matched the theoretically derived ones. 1999 Elsevier Science B.V. All rights reserved.

Keywords: b-Cyclodextrin; Inclusion complex; Stability constant; Membrane permeation

1. Introduction molecule with CyDs or vice versa and in turn the analysisof the CyD concentration dependence by means of the

Cyclodextrins (CyDs) are known to form inclusion Benesi-Hildebrand equation (Benesi and Hildebrand,complexes with various drug molecules and are utilized 1949), the Lineweaver-Burk equation (Lineweaver andsuccessfully for improvement of drug properties such as Burk, 1934) or their modified forms (Guttman, 1962). (2)solubility, stability and bioavailability, etc. (Uekama et al., The direct determination of free or complexed guest or1998). Since the changes of physicochemical and bio- host molecule. If the free component is separated fromlogical properties of a drug are dependent on the mag- CyD solutions, we can estimate directly the free con-nitude of the stability constant of CyD complexes, it is centration and then determine the stability constant. Forimportant for prediction or simulation of the property instance, Saito et al. (1998) employed static head-spacechange to determine accurately this parameter (Hirayama gas chromatography for determining the stability constantsand Uekama, 1987). There are many methods for de- of 2-hydroxypropyl–b-CyD complexes with volatile fragr-termination of stability constants of CyD complexes, using ances, assuming that only the free guest is in an equilib-techniques such as solubility (Higuchi and Connors, 1965), rium between gas and liquid phases whereas the com-potentiometry (Miyaji et al., 1976), high-pressure liquid plexed component is non-volatile. Therefore, the fragrancechromatography (Uekama et al., 1978), and kinetic (Ben- concentration in the head-space corresponds to that of theder and Komiyama, 1978) and spectroscopic (Cramer et free component. In the case of protein binding experimentsal., 1967; Thakkar et al., 1972) methods. These methods (Martin et al., 1983), the free fraction of a drug isare generally based on the following: (1) The titration of a separated from the protein-bound drug through a cel-certain averaged chemical or physical property of a guest lophane membrane and then the binding constant is

calculated. Sideris et al. (1994) developed the automated* flow-injection serial dynamic dialysis technique for de-Corresponding author. Tel.: / fax: 181-96-371-4160.E-mail address: [email protected] (K. Uekama) termination of stability constants of CyD complexes. In

0928-0987/99/$ – see front matter 1999 Elsevier Science B.V. All rights reserved.PI I : S0928-0987( 99 )00002-0

134 N. Ono et al. / European Journal of Pharmaceutical Sciences 8 (1999) 133 –139

special cases of slow inclusion equilibrium, nuclear mag- YM1 and because of its impermeability for b-CyD underthe present experimental conditions (permeation of b-CyDnetic resonance peaks of the free and complexed guest or

for 6 h: ,0.04% through Spectra /Por MWCO 500,host molecules are separately observed and in turn theirwhereas about 3% through Spectra /Por MWCO 1000concentrations can be determined from each signal intensi-

24and 2000). The sample solution (generally 1.0310 Mty or area (Saito et al., 1990).22drugs and 1.0310 M b-CyD in 10 mM phosphate bufferWhile simulating on intestinal absorption of CyD com-

(pH 7.4, 55 ml) was put into the donor cell compartmentplexes using an artificial membrane permeable for drugswhile the same volume of the phosphate buffer solutionbut impermeable for CyDs, we observed that the permea-without samples was placed in the acceptor cell compart-tion rate of drugs is dependent not only on the CyDment. Both solutions in the permeation cells were stirredconcentration but also on the time of the permeation. Thisusing a stainless-steel bar at 100 rpm at 378C. At appro-may be due to the continuous change of the inclusionpriate intervals an aliquot (0.2 ml) was pipetted from theequilibrium in a donor phase, because the concentration ofdonor and acceptor cell compartments and the drugdrug decreases due to the permeation into an acceptor,concentrations were measured using high-performancewhereas that of CyDs is constant. Therefore, the permea-liquid chromatography (HPLC) under the following con-tion profile of the drug in the presence of CyDs in theditions. An equal volume of the phosphate buffer wasdonor phase has to implicate information of not only theadded to maintain a constant volume of the medium HPLCpermeation rate but also the stability constant of thecondition: a Hitachi 655A-11 HPLC chromatograph and acomplex. Incorporating this idea, we developed a newHitachi 655A UV monitor (Tokyo, Japan), a YMC ODSmethod for determination of the stability constant of b-AM-303-S-5 column (4.6 I.D.3250 mm, Kyoto, Japan), aCyD complexes, by analyzing the permeation profile as amobile phase of 150 mM phosphoric acid–acetonitrile (1:1function of time. Furthermore, the membrane permeation 21v /v), a flow-rate of 1.0 ml min , a detection of 240 nm.behavior of a drug from the ternary system, i.e., in theThe concentration of b-CyD in both cells was determinedpresence of both CyDs and competing agents, was simu-according to the method of Koizumi et al. (1985). Thelated to justify the validity of the method and to gain anexperiments were replicated generally three times and theinsight into the permeation mechanism of drugs.stability constants were expressed as a mean6standardPhenacetin and benzoic acid derivatives were employed asdeviation (S.D.).the model drug and competing agents, respectively, be-

cause they are known to form 1:1 inclusion complexes2.3. Solubility studieswith b-CyD (Lach and Chin, 1964; Connors and Lipari,

1976).The solubility method was carried out according to the

method of Higuchi and Connors (Higuchi and Connors,1965). The screw capped vials containing samples (10.0–2. Experimental procedures70.0 mg) in excess amounts in aqueous b-CyD solutions

22(3.0 ml of 0.0–2.0310 M in 10 mM phosphate buffer,2.1. MaterialspH 7.4) were shaken at 378C. After equilibrium wasattained (5 days), the solution was centrifuged at 2000 gCyDs were supplied from Japan Maize Co. (Tokyo,for 5 min and the supernatant was filtered through aJapan) and recrystallized from water. The following chemi-membrane filter (Advantec Dismic 13CP, Toyo-Roshi,cals were used after recrystallization from methanol–Tokyo, Japan) and analyzed using HPLC under the samewater: phenacetin (Sigma-Aldrich, USA), toluic acidscondition described above. The apparent 1:1 stability(Wako Pure Chemicals Co., Tokyo, Japan), chloro-,constant (Kc) of the complexes was calculated using Eq.bromo- and iodo-benzoic acids (Nakalai Tesqe or Tokyo(1) using the slope and an intercept of the initial straight-Kasei, Tokyo, Japan). All other chemicals and solventsline portion of the phase solubility diagrams (Higuchi andwere of analytical reagent grade, and deionized double-Connors, 1965). The 1:1 stoichiometry of b-CyD complex-distilled water was used throughout the study.es with benzoic acid derivatives employed in this studywas assumed because they showed a straight line in the2.2. Permeation studiesinitial portion of the phase solubility diagrams, as de-scribed later.Permeation behavior of phenacetin and benzoic acids

through a cellophane membrane (Spectra /Por MWCO Kc 5 slope / hintercept (1 2 slope)j (1)500, SPECTRUM, Houston, USA) was examined using theside-by-side type permeation cell apparatus, as reportedpreviously (Uekama et al., 1980; Ohki et al., 1980). The 3. Theorycellophane membrane was selected because it is lessadsorptive of benzoic acids compared with that of ultrafil- Fig. 1 shows a schematic representation for permeation

tration membranes such as Amicon Diaflow YC06 and of a drug through a cellophane membrane in the absence

N. Ono et al. / European Journal of Pharmaceutical Sciences 8 (1999) 133 –139 135

respectively. In the presence of CyDs in the donor phase,the rate equation for permeation is expressed by Eq. (3):

d[D] /dt 5 k[D] 2 k[D] (3)A F A

where [D] and [D] are the concentration of free drug inF A

the donor phase and that of a drug in the acceptor phase,respectively. The stability constant (Kc) of the 1:1 complexis defined by Eq. (4):

Kc 5 [complex] /([D] [CyD] )F F

5 ([D] 2 [D] 2 [D] ) /([D] [CyD] ) (4)0 F A F F

where [complex] and [CyD] are concentrations of theF

complex and the free CyDs in the donor phase, respective-ly. Eq. (5) is derived from Eq. (4) and substituting Eq. (5)for [D] in Eq. (3) yields Eq. (6) for the permeation rate.F

[D] 5 ([D] 2 [D] ) /(1 1 Kc[CyD] ) (5)F 0 A F

d[D] /dt 5 kh[D] 2 (2 1 Kc[CyD] )[D] j /A 0 F A

(1 1 Kc[CyD] ) (6)F

Integrating Eq. (6) yields Eq. (7) (logarithmic form) or Eq.(8) (exponential form), by assuming [CyD] 5[CyD] 5F T

constant in the case of the total CyD concentration[CyD] ..[D] (100:1 molar ratio in this study).T 0

lnh[D] 2 (2 1 Kc[CyD] )[D] j 5 2 kh(2 1 Kc[CyD] ) /0 T A T

(1 1 Kc[CyD] )jt 1 ln[D] (7)T 0

[D] 5 [D] h1 2 exp(2At)j /(2 1 Kc[CyD] ),A 0 T

where A 5 k(2 1 Kc[CyD] ) /(1 1 Kc[CyD] ) (8)T T

Therefore, the Kc and k values can be determined byanalyzing the data of concentrations, [D] , of a drug in theA

acceptor phase as a function of time, t, according to Eq.Fig. 1. Permeation of drug in the absence (A) and presence (B) of CyDs

(7) or Eq. (8), using a nonlinear least-squares method ofin donor phase through a cellophane membrane. k, permeation ratethe MULTI program (Yamaoka and Nakagawa, 1983).constant of drug; Kc, stability constant of drug/CyD complex.

When the Kc and k values are already known, the plot ofthe left-hand side of Eq. (7) vs. t gives a straight line.

and presence of CyDs in a donor phase. CyDs and itscomplexes are assumed to impermeate, because the mem-

4. Results and discussionbrane (Spectra /Por MWCO 500) employed is permeableonly for molecules with molecular weight less than about

4.1. Determination of stability constant using the500. The permeation rate of a drug in the absence of CyDsmembrane permeation techniqueis expressed by the well-known Eq. (2) (Lueck et al.,

1957).Fig. 2 shows the permeation profiles of phenacetin

24[D] 2 [D] 5 ([D] 2 [D] ) exp(22kt),t eq 0 eq (1.0310 M) in the absence and presence of b-CyD22(1.0310 M) in the donor phase. Without CyDs, thefor the donor phase;

concentration of phenacetin in the donor phase decreased[D] 2 [D] 5 [D] exp(22kt),eq t eq with time, while that of the acceptor phase simultaneously

increased, and both phases were equilibrated at a half offor the acceptor phase (2)the initial drug concentration after about 60 h. Thispermeation profile was analyzed according to Eq. (2) andwhere k is the permeation rate constant of the drug and

22 21[D] , [D] and [D] are concentrations in the donor or the permeation rate constant (k) of 4.42310 h was0 t eq

acceptor phase at times 0 and t and at the equilibrium, obtained. There was no dependence of the rate constant on


dialysis method for the determination of Kc values (Martinet al., 1983). However, this method was time-consumingand it took more than 60 h to attain the equilibriumbetween the donor and acceptor phases. Therefore, thepermeation profile of [D] vs. t was analyzed using Eq.A

(8) and data of an early stage of the permeation (within 6h) and the unknown parameters, k and Kc values, weredetermined by a nonlinear least-squares method (Yamaokaand Nakagawa, 1983). The Kc value of the phenacetin–b-

21CyD complex was 172 M (S.D.560, n53) and was inclose agreement with that determined using the solubility

21method (182 M , S.D.563, n53) as described later.The permeation rate constant (k) of phenacetin was 4.633

22 2110 h which was also in close agreement with that22 21(4.42310 h ) determined using Eq. (2) and the

permeation data in the absence of b-CyD. The plot24 according to Eq. (7) using the above k and Kc values gaveFig. 2. Permeation profiles of phenacetin (1.0310 M) in the absence

22(open symbols) and presence (closed symbols) of b-CyD (1.0310 M) a straight line (slope520.063, intercept529.208, corre-in donor phase through a cellophane membrane (MWCO 500) in isotonic lation coefficient50.999), warranting the above treatment.phosphate buffer (pH 7.4) at 378C. s, d, phenacetin in donor; n, m, The Kc value of the phenacetin–b-CyD complex wasphenacetin in acceptor. The solid lines were theoretical curves drawn

determined using a conventional kinetic method (Benderusing Eqs. (2) and (8).and Komiyama, 1978), i.e. the apparent permeation rate

22constants (k ) at 0.0–1.0310 M b-CyD concentrationsobs24 22initial concentrations in the range 1.0310 –1.0310 were calculated using Eq. (2) and the b-CyD concentration

M. The k values for other benzoic acids are listed in Table dependence of k values was analyzed using the Guttmanobs

1. In the presence of b-CyD, on the other hand, the equation (Eq. 9 of Guttman, 1962) assuming the formationequilibrium concentration of the drug in the donor phase of a non-productive complex:was higher than that in the acceptor phase. This is due to

k /k 5 Kc[CyD] 1 1 (9)the complexation of phenacetin with b-CyD in the donor 0 obs T

phase, i.e. the total concentration of the drug in the donorwhere k and k are the permeation rate constants ofphase is a sum of the free and complexed fractions, and 0 obs

24phenacetin (1.0310 M) in the absence and presence ofonly the free fraction of the drug is in equilibrium with thatb-CyD, respectively. The results were as follows: k 5in the acceptor phase (see Fig. 1). Thus, the stability 0

22 21 22 21 22 214.42310 h , k 53.02310 h , 2.48310 h ,constant (Kc) of the b-CyD complex with phenacetin was obs22 21 22 211.95310 h and 1.61310 h in the absence andcalculated using the drug concentrations in the donor phase

23 2323 presence of b-CyD (2.5310 M, 5.0310 M, 7.53(6.26310 M, 63% of the initial concentration) and the23 23 22acceptor phase (3.73310 M, 37% of the initial con- 10 M and 1.0310 M), respectively. The k valueobs

21centration) at 60 h and was 171 M (S.D.562, n53) decreased with the increase in b-CyD concentrations andThis method is essentially the same as the equilibrium the plot of k /k vs. [CyD] according to Eq. (9) gave a0 obs T

Table 1Stability constants (Kc) of b-CyD complexes with phenacetin and benzoic acids determined by the solubility method and by the membrane permeationtechnique and permeation rate constant (k) of guest molecules in isotonic phosphate buffer (pH 7.4) at 378C

a 21 b 21 c 21 d 21Guest Kc (M ) Kc (M ) k (h ) k (h )

Phenacetin 18263 17260 0.0442 0.0463o-Toluic acid (o-TA) 10963 8460 0.00139 0.00150m-Toluic acid (m-TA) 15960 13960 0.00249 0.00261p-Toluic acid ( p-TA) 214615 20062 0.00377 0.00387o-Chlorobenzoic acid (o-CBA) 164612 18163 0.00189 0.00187p-Chlorobenzoic acid ( p-CBA) 3660 2261 0.00266 0.00293m-Bromobenzoic acid (m-BBA) 31265 26767 0.00469 0.00483p-Bromobenzoic acid ( p-BBA) 2660 1860 0.00279 0.00295o-Iodobenzoic acid (o-IBA) 283615 26769 0.00201 0.00218m-Iodobenzoic acid (m-IBA) 15468 15064 0.00336 0.00354

Each value represents the mean6S.D. of three experiments.a bStability constants determined by using Eq. (1); and Eq. (8).c dPermeability rate constants (S.D.,60.00002) of guest molecules determined by using Eq. (2); and Eq. (8).


21straight line with a slope of 172 M (Kc, S.D.562,n53) and an intercept of 0.993. This Kc value coincidedwith that determined using the membrane permeationtechnique.

In order to validate the membrane permeation technique,the Kc values of b-CyD complexes with various benzoicacids were determined and compared with those deter-mined using the solubility method. Fig. 3 shows permea-tion profiles of benzoic acids in the absence and presenceof b-CyD in the donor phase. These profiles are analyzedaccording to Eq. (2) (for the systems without b-CyD) andEq. (8) (for the systems with b-CyD) using a nonlinearleast-squares method. The results of Kc and k values aresummarized in Table 1, together with Kc values de-termined from the phase solubility diagrams of Fig. 4 (seeSection 2). The Kc values determined using the permeationtechnique were in close agreement with those determinedusing the solubility method, and the experimental dataconformed closely to the theoretical permeation curvescalculated by Eq. (8). As shown in Fig. 5, the plot of the

Fig. 4. Phase solubility diagrams of benzoic acid /b-CyD systems informer Kc values vs. the latter Kc values gave a straightisotonic phosphate buffer (pH 7.4) at 378C. s, phenacetin; d, o-TA; n,line with a slope of 1.0, an intercept of 211.8 and am-TA; m, p-TA; h, o-CBA; j, p-CBA; ,, m-BBA; ., p-BBA; x,

correlation coefficient of 0.993. When the data of o-TA, o-IBA; ♦, m-IBA.p-CBA and p-BBA were eliminated from the correlation,the plot gave a straight line with a slope of 0.959, anintercept of 1.230 and a correlation coefficient of 0.981, 4.2. Permeation behavior from drug–competing agent–suggesting that the K values determined using the solu- b-CyD ternary systembility method are slightly higher than those determined bythe membrane permeation method, particularly for the The permeation rate of CyD complexes is significantlycomplexes having smaller Kc values (,100). This subtle affected by the presence of second guest molecules, due todiscrepancy may be due to the difference in the experimen- competitive inclusion. For example, some part of thetal conditions, such as concentration range of the host and complexed fraction dissociates into free drug and CyD dueguest molecules. These results indicate that the membrane to the competition, thus increasing the fraction of perme-permeation technique described here is useful for the able free drug. The degree of the dissociation depends ondetermination of the stability constant of CyD complexes. the relative magnitude of stability constants of the com-

24 22Fig. 3. Permeation profiles of benzoic acids (1.0310 M) in the absence (s) and presence (d) of b-CyD (1.0310 M) through a cellophane membrane(MWCO 500) in isotonic phosphate buffer (pH 7.4) at 378C. The solid lines were theoretical ones drawn using Eqs. (2) and (8).


recovered by the addition of m-BBA. m-BBA exhibited aninsignificant effect on the permeation rate of phenacetin,indicating no interaction between the guest molecule andthe competing agent. The permeation of the ternary systemis schematically illustrated in Fig. 7, and the permeationrate equations of the drug and the competing agent aredescribed by Eqs. (6) and (10), respectively:

d[CA] /dt 5 kh[CA] 2 (2 1 K [CyD] )[CA] jA 0 CA F A

/(1 1 K [CyD] ) (10)CA F

where [CA] and [CA] are the concentrations of the0 A

competing agent at times 0 and t, respectively, and K isCA

the stability constant of the b-CyD complex with thecompeting agent. In contrast to the drug–b-CyD binarysystem, [CyD] in Eq. (10) can not be approximated asFig. 5. Plot of Kc values determined by the membrane permeation F

technique vs. those determined by the solubility method (see Table 1). [CyD] 5[CyD] 5constant, because the concentration ofF T

b-CyD was only slightly higher than that of m-BBA(molar ratio of m-BBA/b-CyD51/10–1/1). Therefore,

plexes with a drug and a competing agent. Such competi- the differential equations Eqs. (6) and (10) were numeri-tion may occur in gastrointestinal fluids after oral adminis- cally integrated using the Runge-Kutta-Gill methodtration of CyD complexes because of the presence of (Yamaoka and Nakagawa, 1983), in order to simulate thebiological components. Therefore, the membrane permea- permeation profiles. The [CyD] values were estimatedF

tion behavior of a drug in the presence of competing using the values of Kc, K , [CyD] , [D] and [CA] . AsCA T 0 0

agents was investigated to justify the validity of the shown in Fig. 6, the permeation data of phenacetin in themembrane permeation technique for determination of ternary system fitted closely to the theoretical curves,stability constants of CyD complexes and to gain an supporting the permeation mechanism depicted in Fig. 7.insight into the permeation of drug–competing agent–b- In conclusion, the stability constant of b-CyD complex-CyD ternary systems. Fig. 6 shows the permeation profiles es with phenacetin and benzoic acids were determined

24of phenacetin (1.0310 M) in the absence and presence using the membrane permeation technique using a cel-of m-bromobenzoic acid (m-BBA, employed as a compet- lophane membrane permeable for guests but impermeable

22 22ing agent, 0.0–1.0310 M) and b-CyD (1.0310 M) to b-CyD. This technique was validated as useful for thein the donor phase. The permeation rate of phenacetin was determination of the stability constant, particularly in thedecelerated by the addition of b-CyD whereas it was case of 1:1 stoichiometry, and it is more advantageous than

the conventional methods, because in the membranepermeation technique the stability constant can be obtained

24Fig. 6. Permeation profiles of phenacetin (1.0310 M) in the b-CyDbinary system and the b-CyD/m-BBA ternary systems through a cel-lophane membrane (MWCO 500) in isotonic phosphate buffer (pH 7.4) at378C. s, phenacetin alone; d, phenacetin /m-BBA/b-CyD (molar Fig. 7. Permeation of drug in the b-CyD/competing agent ternary system.ratio)51/0 /100; n, 1 /10/100; m, 1 /50 /100; h, 1 /100/100. The solid k, permeation rate constant of drug; k , permeation rate constant ofCA

lines were theoretical curves calculated by Runge-Kutta-Gill method competing agent; Kc, stability constant of the complex with drug; K ,CA

using Eqs. (6) and (10). stability constant of the complex with competing agent.


Lineweaver, H., Burk, D., 1934. The determination of enzyme dissocia-from only one experimental run by analyzing the permea-tion constants. J. Am. Chem. Soc. 56, 658–666.tion data as a function of time. The permeation profiles of

Lueck, L.M., Wurster, D.E., Higuchi, T., Lemberger, A.P., Busse, L.W.,phenacetin in the drug–competing agent–b-CyD ternary 1957. Investigation and development of protective ointments I;systems fitted closely to those of the theoretical curves development of a method for measuring permeation of mechanicalcalculated using the stability constants. Knowledge of this barriers. J. Am. Pharm. Assoc. 46, 694–698.

Martin, A., Swarbrick, J., Cammarata, A., 1983. Physical Pharmacy. Leasort may be useful for the simulation of absorptionand Febiger, Philadelphia, p. 336.behavior of drugs in gastrointestinal tracts after oral

Miyaji, T., Kurono, Y., Uekama, K., Ikeda, K., 1976. Simultaneousadministration of CyD complexes, although it can not determination of complexation equilibrium constants for conjugateddirectly be applied since the appearance and disappearance guest species by the extended potentiometric titration method on theof biological competing agents and their concentrations are barbiturate-b-cyclodextrin system. Chem. Pharm. Bull. 24, 1155–

1159.not fully known.Ohki, A., Takagi, M., Ueno, K., 1980. Ion transport through liquid

membrane driven by redox potential: Multi-component ion carrier as amediator. Chem. Lett. 1591–1594.

References Saito, H., Yonemura, H., Nakamura, H., Matsuo, T., 1990. Stability andexchange properties of through-ring cyclodextrin complexes; effects ofchain length in polymethylene bis[1-pyridinium] as guest molecules.Bender, M.L., Komiyama, M., 1978. Cyclodextrin Chemistry. Springer-Chem. Lett. 535–538.Verlag, Berlin, p. 33.

Saito, Y., Tanemura, I., Ueda, H., Sato, T., 1998. Simultaneous de-Benesi, H.A., Hildebrand, J.H., 1949. A spectrophotometric investigationtermination of the stability constants for fragrance materials withof the interaction of iodine with aromatic hydrocarbons. J. Am. Chem.2-hydroxylpropyl-b-cyclodextrin by static head-space gas chromatog-Soc. 71, 2703–2707.raphy. Chem. Pharm. Bull. 46, 1177–1179.Connors, K.A., Lipari, J.M., 1976. Effect of cycloamyloses on apparent

Sideris, E.E., Georgiou, C.A., Koupparis, M.A., Macheras, P.E., 1994.dissociation constants of carboxylic acids and phenols: EquilibriumAutomated flow-injection serial dynamic dialysis technique in theanalytical selectivity induced by complex formation. J. Pharm. Sci. 65,study of drug binding with cyclodextrins. Anal. Chimica Acta 289,379–383.87–95.Cramer, F., Saenger, W., Spatz, H.-Ch., 1967. Inclusion compounds; XIX;

Thakkar, A.L., Kuehn, P.B., Perrin, J.H., Wilham, W.L., 1972. Cyclohep-the formation of inclusion compounds of a-cyclodextrin in aqueoustaamylose-barbiturate inclusion complexes; solubility and circularsolutions; thermodynamics and kinetics. J. Am. Chem. Soc. 89, 14–20.dichroism studies. J. Pharm. Sci. 61, 1841–1843.Guttman, D.E., 1962. Complex formation influence on reaction rate I;

Uekama, K., Hirayama, F., Irie, T., 1978. The new method for de-effect of caffeine on riboflavin base-catalyzed degradation rate. J.termination of the stability constants of cyclodextrin-prostaglandinPharm. Sci. 51, 1162–1166.inclusion complexes by liquid chromatography. Chem. Lett. 661–664.Higuchi, T., Connors, K.A., 1965. Phase-solubility techniques. Adv.

Uekama, K., Hirayama, F., Irie, T., 1998. Cyclodextrin drug carrierAnal. Chem. Instr. 4, 117–212.systems. Chem. Rev. 98, 2045–2076.Hirayama, F., Uekama, K., 1987. Methods of investigating and preparing

Uekama, K., Matsuo, N., Hirayama, F., Ichibagase, H., Arimori, K.,ˆinclusion compounds. In: Duchene, D. (Ed.), Cyclodextrins and theirTsubaki, K., Satake, K., 1980. Enhanced bioavailability of acetohex-´Industrial Uses. Editions de Sante, Paris, pp. 131–172.amide by b-cyclodextrin complexation. Yakugaku Zasshi 100, 903–Koizumi, K., Kubota, Y., Okada, Y., Utamura, T., 1985. Microanalyses of909.b-cyclodextrin in plasma by high-performance liquid chromatography.

Yamaoka, K., Nakagawa, T., 1983. A nonlinear least squares programJ. Chromatogr. 341, 31–41.based on differential equations MULTI (Runge), for microcomputers.Lach, J.L., Chin, T.F., 1964. Interaction of pharmaceuticals with schard-J. Pharmacobio-Dyn. 6, 595–603.inger dextrins III; interactions with mono-halogenated benzoic acids

and aminobenzoic acids. J. Pharm. Sci. 53, 69–73.

determination of stability constant of β-cyclodextrin complexes using the membrane permeation...

Documents