Formulation Optimization of Indomethacin Gels Containing a Combination of Three Kinds of Cyclic Monoterpenes as Percutaneous Penetration Enhancers

Formulation Optimization of lndomethacin Gels Containing a Combination of Three Kinds of Cyclic Monoterpenes as Percutaneous Penetration Enhancers KARINKRAGHLEVISON', KO20 TAKAYAMA'~, KOICHI ISOWA*, KEIICHIROOKABEa, AND TSUNEJINAGAI* Received April 14, 1994, from the 'Departmenf of Pbarmaceufics, Hoshi University, 2-4-41, Ebara, Sbinagawa-ku, Tokyo 142, Japan, #The Center of Japan Biological Chemistry Co. Lfd., 52, Fukue, Kaizu-cho, Gifu 506-06, Japan, and §Advance Company, Lfd., DDS R&D Center, 2-8-18, Ohashi, Meguro-ku, Tokyo 153, Japan. Accepted for publication June 21, 1994? Abstract 0 A computer optimization technique based on response surface methodology was applied for the optimization of a hydrogel formulation containing indomethacin as a model drug. As the penetration enhancer, a combination of three cyclic monoterpenes, limonene, menthol, and cineole, was employed. Pharmacokinetic parameters, from an in vivo percutaneous absorption study on rats of model formulations prepared according to the composite experimental design for five factors, were determined as prime response variables. The skin damage evoked by each formulation was microscopicallyjudged and graded as the response variable concerning skin safety. The response variables were predicted by multiple regression equations comprising combinations of the five formulation factors. The regression equations for the response variables assembled as a simultaneous optimization problem based on the generalized distance function. The simultaneous optimum was predicted as a function of individual optima within a 95% confidence region. The predicted response values for the optimum formulation have been successfully validated in a repeated in vivo percutaneous absorption study.

h i ~ l e . Another ~,~ synergistic effect has been found for propylene glycol combined with certain terpenes? For example, the activities of both limonene and cineole increased 4-fold when applied as a saturated solution of propylene glycol as compared to the neat terpene. For an eficacious transdermal gel formulation, we want to use the minimum amount of solvent to dissolve the drug and yet maintain a favorable permeability coefficient. At the same time, the vehicle components affecting the permeability should also be kept as low as possible to avoid skin irritation and irreversible damage. From the above reviewed data reporting different optimum enhancers and synergistic effects with solvents, it is not obvious how to choose the perfect formulation. In this study, the optimization of indomethacin hydrogels containing d-limonene, Z-menthol, and 1,8-cineole as absorption enhancers and ethanol and propylene glycol as solvents was performed on the basis of an improved response surface methodology.

Theoretical Section The success of a transdermal drug delivery system will depend on the ability of the drug to penetrate the stratum corneum at a rate sufficient to achieve concentrations in the systemic circulation necessary for the desired therapeutic effect. Achieving this usually demands an absorption promoter to be included in the transdermal formulation. A variety of terpenes has been investigated as enhancers for drugs such as indomethacin, ketoprofen, diclofenac sodium, and 5-fluorouracil.1-4 In earlier studies with indomethacin as a lipophilic penetrant model, drug absorption was markedly enhanced by the addition of limonene, menthane, etc., while hydrophilic terpene enhancers showed minor effects.l In contrast, a study performed under similar conditions, but with diclofenac sodium as a water soluble penetrant model, suggested menthol to be the most effective penetration e n h a n ~ e r . ~ Also, an experiment using 5-fluorouracil as a polar penetrant model clearly showed 1,8-cineoleas the optimum penetration e n h a n ~ e r .However, ~ this later study was performed under different conditions with pretreatment by the actual terpene and sequential penetration analysis, while the previously cited studies used an ointment containing both the model penetrant and enhancer in an ethanol-water-based formulation. Obata et al. have shown that terpene-enhancing activity is dependent on ethanol concentration so that, a t lower ethanol concentrations, hydrophilic terpenes have a greater promoting activity on diclofenac sodium than lipophilic terpenes. On the other hand, in the presence of high ethanol concentrations, the lipophilic terpenes showed the strongest a~tivities.~ It should be underscored that a synergy between ethanol and the terpenes menthol and cineole has been confirmed, whereas no significant synergy of limonene and ethanol was observed. Propylene glycol is a widely used solvent in pharmaceutical preparations and has been used in several studies of the percutaneous penetration of indomethacin as the basic ve-

A computer optimization technique based on response surface methodology has been applied to obtain the optimal formulation of pharmaceuticals by several w o r k e r ~ . ~ -In l~ overall design of a pharmaceutical dosage form, the simultaneous optimization of several responses is indispensable. Khuri and ConlonI4have approached this problem on the basis of the generalized distance between the individual optimal value for each response and the simultaneous one:

(1) where S(X) is the distance function generalized by the weighting coefficient, wi,F D i O is the optimum value of each objective function, Fi(X), optimized individually over the experimental region, and FOi(X) is the simultaneous optimum of Fi(X). The simultaneous optimum can be estimated by minimizing S(X) under the restriction of the experimental region. As a proper and significant way to determine the wi values, the following equation can be used:

m2

is the coefficient of determination which was where doubly adjusted with degrees of freedom15 and SDi is the standard deviation of the observed values for each response variable. Takayama and NagailG improved the distance function given in eq 1 in order to incorporate the user's preferability:

(3) Abstract published in Advance ACS Abstracts, August 1, 1994.

0 1994,American Chemical Society and American PharmaceuficalAssociation

0022-3549l94I1200-1367$04.50/0

i=l

Journal of Pharmaceutical Sciences / 1367 Vol. 83,No. 9,September 1994

Table 1-Composite Experimental Design for Five Factors

d-Lirnonene

l.~enrhol

1.8-Cinmle

Figure 1-Structure of cyclic monoterpenes used as penetration enhancers.

where P is a parameter relating to the impartiality among the response variables (1 5 P 5 w ) . When the P value is 1, the weighted distances of the predicted values of given responses from the individual optima can be treated impartially in eq 3. Increasing the P values leads to an enlargement in the importance of the response of which deviation from the individual optimum value was greater than that of the other responses. However, flexibility of the modified distance function given in eq 3 is not sufficient when some of the responses greatly deviate from their individual optima, as it is often observed in the practical pharmaceutical formulation. The individual optimum value, FDi(X), is given as the mean estimate from each regression equation and its variability can influence the determination of the simultaneous optimum of the generalized distance function, S(X). To account for this, we took confidence regions for all the individual responses, FDi(X), into consideration:

YL,rFD,(X) 5 YH,

i = 1, 2, ..., n

(4)

where YLj and YHi are the lower and upper limits of FDi(X), respectively. Statistically, the estimated values of the lower and upper limits for each FD(X) are given as

YH = FD(X)

+t,,~~X',,(X'~-'X,

(6)

where ij2 is the estimated value of error variance, X, is the specific value of the factor vector which gives FD(X), X',, is the transposed X, and (X'X)-' is the inverse matrix of the variance-covariance matrix of factor vector X. Considering a 95%confidence region of FD(X), we can use to.025 as the value of t d 2 in eqs 5 and 6. Although any set of ideal values can be incorporated in the distance function, SCX),within the restriction defined in eq 4,it may be reasonable to investigate overall combinations of YLi, YHj, and FDi(X).

Experimental Section Materials-Structures of the cyclic monoterpenes d-limonene, I-menthol, and 1,8-cineole used in this study are shown in Figure 1. All were of extrapure reagent grade and purchased from Tokyo Chemical Industries Co., Ltd., Tokyo, Japan. Indomethacin was purchased from Sigma Co., St. Louis, MO. Carboxyvinyl polymer, marketed as Hiviswako 105 was supplied by Wako Pure Chemical Industries Ltd., Tokyo, Japan. Other chemicals used were of reagent grade. Preparation of Hydrogel-The amount of limonene (XI),menthol (XZ),cineole (X3),ethanol (X4),and propylene glycol (X5)were selected as causal factors. The composite orthogonal experimental design for five factors was applied to prepare the model formulations. Central experimental points were repeated 10 times (formulation 27-36)in order to evaluate the experimental error. The experiments listed in Table 1 coded form were transformed to the physical units as summarized in Table 2. Based on the preliminary study, the concentrations of indomethacin, carboxyvinyl polymer, and triethanolamine in the hydrogels were fixed at 1%, 1.5%, and 2%, respectively. An appropriate amount of water was added to adjust the total weight of the hydrogels, which were prepared as follows: carboxyvinyl polymer and triethanolamine were dissolved in distilled water before indomethacin dissolved in ethanol with the terpenes was added and

1368 / Journal of Pharmaceutical Sciences Vol. 83, No. 9, September 1994

Formulation No.

XI

x 2

1

2 3 4

-1 1 -1 1

-1 -1 1 1

5

-1

-1

6 7

-1

-1 -1 1

-1

1

-1

1

1

-1

1

1

1

-1

-1

1

1

-1

1 1 1 1 1 1

11

-1 1 -1

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

1 -1 -1 1 -1

-1

-1 -1

-1

18

x5

1

9 10 12 13 14 15 16 17

)6

-1 -1 -1 -1

-1 1

1

8

& -1

1

1

1 -1 -1 1

-1 -1 1

1

1

1

1 1

-2 2

0

0

0 -2 2 0 0 0

0 0 0

-1

0

0 0 0 0 0 0 0 0

0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0

-2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 0

0 0 0 0

-2 2 0 0 0 0 0

0 0 0 0 0 0 0

-1 -1 1 1 -1 1 -1 -1 1 0 0 0 0 0

0 0 0 -2 2 0 0 0 0 0 0 0 0

0 0

Table 2-Levels of Causal Factors in Physical Form Factor Level in Coded Form Factor (%)

-2

-1

0

1

2

&Limonene (XI) CMenthol (X,) 1,8Cineole (X3) Ethanol (&) Propylene glycol (Xs)

0

0.5 0.5 0.5

1.o 1.o 1.o

1.5 1.5 1.5

2.0

10.0

20.0 20.0

30.0 30.0

40.0 40.0

0 0 0 0

10.0

2.0 2.0

then thoroughly mixed. The hydrogels were stored a t room temperature under air-tight conditions until use the following day. In Viuo Percutaneous Absorption f r o m Rat Abdominal Skin-Male Wistar rats weighing 180-200 g were anesthetized with carbamic acid ethyl ester solution (25%; 4 m L k g ip) and secured on their backs. The abdominal hair was gently removed with a n electrical clipper. A glass cell (16mm inner diameter, 10 mm height) was attached on the shaved abdominal skin with cyanoacrylate type adhesives and filled with test ointment (2 mL) under occlusive conditions. Blood samples (0.3mL) were taken uia the jugular vein 0.5,1, 2, 3,4,6,8, and 10 h after application. Analysis of Indomethacin in Blood Samples-Each blood sample was centrifuged for 1 min and the plasma sample (100 pL) was thoroughly mixed with methanol (300 pL) containing a n appropriate amount of the internal standard (p-hydroxybenzoic acid n-hexyl ester, 5 pglmL). The mixture was again centrifuged for 5 min to precipitate to denatured protein and the supernatant solution was filtered using a disposable filter unit (Gelman Science Japan, Ltd. Ekikuro-Disk 3CR). The concentration of indomethacin in the filtrate was analyzed using a n HPLC system (Shimadzu Model LC3A,Shimadzu Corp., Kyoto, Japan) equipped with a variable wave-

Table 3-Pharmacokinetic Parameters of lndomethacin after Intravenous Administration (2.5 mgkg) in Rats ParameteP

a (hk’)

P (h-’) fiiz (h-’) kiz (h-’) ~~

Value

Parametera

Value

8.54 & 2.57 0.295 ? 0.140 2.05 & 1.43 5.02 f 1.77

kzi ( W kio (h-’) V, (mL) vdss (mL)

3.00 0.99 0.816 f0.283 13.4 f0.7 36.7 f 6.2

*

~

a and /3, hybrid first-order rate constants; t,f2,elimination halflife for the P phase; ki2, rate constant from the central to the tissue compartment; k2,, rate constant from the tissue to the central compartment; kio, elimination rate constant from the central compartment; V, and Vdss,distribution volume of central and tissue compartments. Each value represents the mean f SD of five animals. a Abbreviations:

length UV monitor (Shimadzu Model SPD-6A). The flow rate was 1 m u m i n and elution was carried out at ambient temperature. Other analytical conditions were as follows: column, YMC-Pack A-302 S-5 120 A ODS, 150 x 4.6 mm i.d. (Yamamura Chemical Laboratories Co., Ltd., Tokyo, Japan); UV detection, 254 nm; mobile phase, 0.1% phosphoric acid-methanol (25:75);retention time, 6.0 min. Intravenous Administration of Indomethacin in RatsIndomethacin solution (1mg/mL) was made by dissolving indomethacin in a tiny amount of ethanol with heat and diluting with 1/15 M, pH 7.8 phosphate buffer solution within 1h of injection. The solution (2.5 mLJkg) was administered by bolus injection via the right jugular vein of male Wistar rats (180-200 g). Blood samples (0.3 mL) were taken via the left jugular vein a t 5, 10, 15, 20. 30,60, 90, and 120 min. The blood samples were then handled the same way as already described. Evaluation of Skin Damage-The influence of each formulation of skin irritation after 10 h of exposure was microscopically investi-

a

gated. The application site for the in vivo percutaneous absorption experiment for each formulation was excised from the rat immediately after the 10-h administration had ended. The separated skins were fixed in 10% neutral carbonate-buffered formalin until routine processing and then cut vertically against the skin surface at the central region in a 4 mm width. Each section was dehydrated using a graded series of ethanol solutions and embedded in parafin wax. Tissues were divided into small pieces (about 3 pm in thickness) and stained with hematoxylin and eosin. All sections were examined by light microscopy. (Optiphoto microscope, Nikon, Tokyo, Japan). Computer Programs-The computation was carried out on a desk top digital computer (PC-9801 Rx,NEC Corp., Tokyo, Japan). The curve-fitting program M U L T P was applied to estimate the pharmacokinetic parameters. The simultaneous optimization was performed by the NOPCON program.ls

Results and Discussion Percutaneous Absorption-Indomethacin was administered intravenously in order to pharmacokinetically investigate the percutaneous absorption of indomethacin from the model formulations. The plasma concentration of indomethacin after iv injection declined in a biexponential manner, so the pharmacokinetic parameters of indomethacin were calculated according to the two-compartment open model. The parameters are listed in Table 3. The apparent penentration rate, R,, was estimated from a simple pharmacokinetic model (eq 7) based on the assumption that, after an initial lag time period, the penetration rate of

b

Figure 2-Microscopic photos of rat skin at 10 hours after application of model formulations. H & E stain, x100: (a) formulation number 1; (b) formulation number 16.

Journal of Pharmaceutical Sciences / 1369 Vol. 83, No. 9, September 1994

Table 4-Experimental Values of Response Variables ~

~~

~

TIS

Formulation No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

25.1 27.0 32.7 459 31 .O 115 170 128 257 811 214 651 158 657 492 41 6 70.9 341 37.7 741 274 537 9.22 429 157 420 426 309 41 3 304 285 359 383 227 512 345

1.56 1.21 1.69 1.53 1.55 2.65 1.71 1.65 0.346 1.94 1.98 1.95 2.04 1.32 0.448 1.24 1.41 0.270 1.60 1.52 1.53 0.879 4.06 1.86 0.770 0.680 1.57 1.05 1.29 0.380 1.40 1.63 1.54 1.28 1.39 1.88

0 0 0 11 0

3 4 1 13 24 21 21 12 22 16 28 0 8 0 9 9 9 0 25 2 26 12 11 9 9 12 3 9 9 12 9

indomethacin absorbed from the particular hydrogel is constant:

where C is the plasma concentration, R, is the apparent penetration rate, t is time, and t~ is the lag time. Other parameters are the same as those in Table 3. Skin-Damage-The skin irritation of model formulations after 10-h exposure was histopathologicallyinvestigated. The findings were graded in the five levels of irritation from no change (level 0 ) to a marked one (level 4)according to the epidermis liquefaction and desquamation and collagen fiber swelling in dermis and hypodermis, together with edema and inflammatory cell infiltrations, as well as degeneration of skin appendages. For example, formulation number 1 gave no irritation, as can be seen in Figure 2a from the microscopic photo of the rat skin a t 10 h after application of the formulation. On the other hand, formulation number 16 and number 26 were highly irritant. This can easily be seen from photo Figure 2b of the rat skin exposed t o formulation number 16 which shows moderate epidermis liquefaction and desquamation and marked collagen fiber swelling, edema, and degeneration of skin appendages. Regression Analysis-The penetration rate (R,)and lag ) employed as the response variables concerning time ( t ~were the percutaneous absorption of indomethacin from the model formulations. A total irritation score (TIS) was obtained by 1370 / Journal of Pharmaceutical Sciences Vol. 83, No. 9, September 1994

Table 5-Optimum Regression Equation for Each Response Variable Determined by Multiple Regression Analysis log RP

2.53 0.188 0.202 0.0555 0.385 0.0828 -0.0768 a -0.0731 a 0.0644 -0.0689

a -0.126

a a -0.0636 -0.0707 -0.175 -0.155 a

0.978 0.130 33.1e

tL

TIS

1.37

9.42 2.50 1.92

a a

a -0.253 0.154 -0.109

a a a a a -0.250 a -0.153 a -0.209 a 0.421

a -0.137 0.837 0.414 7.90e

a 7.83 3.25 -0.979

a a 1.38 a -0.854 a a 1.38 a a a 1.15

a 1.52 0.948 3.14 22.3e

a Not included in the optimum regression equation. Multiple correlation coefficient. Standard deviation of residual. dObserved F vaiue (mean square regressionhean square residual). p c 0.01.

the summation of the irritation scores already described and used as an index of skin damage caused by the model formulations. The values for all response variables are summarized in Table 4. A large deviation was observed among the R, values ranging from 9 to 800 ,ugh, clearly showing that the amount of ethanol was one of the most important factors in the formulation. There is no ethanol included in formulation 23, which has the lowest penetration rate of only 9 ,ugh. The values also reflect the combined effect of terpenes on the indomethacin penetration rate; for example, formulation 4 has a significantly higher penetration rate (Rp = 459 ,ugh) than both formulations 6 and 7, which only differ in the combination of terpenes. High concentrations of limonene and menthol are apparently the most potent enhancer combination. Also, concerning the total irritation scores, we found a wide range of TIS data showing that the formulation variables are factors that significantly affect the skin irritation. The following second-order polynomial equation was used for the prediction of each response variable:

where F(X, is the response variable, bo is a constant, and bi and b,j.are coefficients of each monomial, and Xi and Xj are the causal factors in coded form. The optimum regression equation which comprised the combination of statistically significant factors was obtained by the forward selective stepwise regression analysis. The coefficient of determination, which was doubly adjusted with degrees of freedom, was used as a judgment standard for selecting the optimum combination of factors.15 The optimum regression equations selected are summarized in Table 5. Logarithmic transformation was performed on the R , response variable, which is in agreement with the higher deviations of high penetration rates compared t o those of low

Figure 3-Contour diagrams of lop Rp as a function of Xi, XZ, and X, at constant values of X3 and Xs (X3 = Xs = 0) under the restriction of the experimental region (Xi2 + X2’ + X32 + &’ + Xsz 5 4.0).

Figure 4-Contour diagrams of TlS as a function of X., X, and )(d at constant values of X3 and X5 (X3 = Xs = 0) under the restriction of the experimental region (XI2

+ Xz2 + X$ + X? + X5’

5

4.0).

penetration rates and corresponding to low plasma levels of indomethacin. Only log R, and TIS were accurately predicted since the values of multiple correlation coefficient, r, were satisfactory and regression equations were significant with high FO values (mean square regressiodmean square residual). It is interesting to see that X3 is completely left out of the optimum regression equation concerning TIS, which indicates that cineole does not cause irritation within the experimental region. The lag times could not be satisfactorily predicted, eventually being due to only small differences in t~ from the chosen formulation combination or difficulty in correctly predicting the lag time by current kinetic model, and therefore the lag time was left out during further processing of the data. Contour Diagram-On the basis of the optimal regression equations, the contour diagrams for log R, and TIS are illustrated in Figures 3 and 4, respectively, as a function of X I (limonene) and X4 (ethanol) under the restriction of experimental region (X12 Xzz Xa2 X42 Xsz 5 4.0). Both graphs were drawn by using the combination of the cross section of the Xz (menthol) axis against the response surfaces. X3 (cineole) and X5 (propylene glycol) were kept constant for all diagrams since the effect of these two factors on the response variables was relatively minor compared to the selected three factors. The log R, value became larger with increasing amounts of limonene ( X I )and ethanol (X4)formulated in the gels (Figure 3). The increase in the amounts of menthol (Xz)was also effective for the enhancement of the R , value. On the other hand, the TIS value tended to be higher with increasing amounts of ethanol ( X J , although the influence of limonene (XI) or menthol (Xz) on the TIS value was rather weak (Figure 4). It is obvious from these diagrams that a formulation with a high penetration rate of indomethacin causes considerable damage t o the skin. Simultaneous Optimization-The individual optima with confidence limits were calculated by maximizing or minimiz-

+ + + +

Table 6-Mean Estimates, Lower Limits, and Upper Limits of Individual Optima for log Rp and TIS ~

Response

Mean Estimate

log RP TIS

-0.78a

2.93

~

~

~~~~

Lower Limit

Upper Limit

2.81

3.04

-3.398

1.80

a Because of the second-order polynomial fitting (eq 8),these values were estimated as negative quantities in this work, while they were out of the physical reality.

ing the regression equations for log R, or TIS under the restriction of the experimental region (X12 Xzz Xs2 X4z X52 5 4.0). Results are summarized in Table 6. The confidence intervals of log R, and TIS were divided into nine subintervals each, and the simultaneous optima for log R, and TIS were estimated using the individual optimal values corresponding to each grid point, according to the distance function defined in eq 1. Figure 5 graphically depicts the predicted log R , and TIS as functions of the individual optima of each response. It should be noted that the lower the TIS the better, while the log R , should be preferentially high. There is a clear tendency for both simultaneous optimal values of log R, and TIS to increase when the individual optima move from the lower part of the confidence interval to the upper limits thereof. This may suggest that the formulation surpassing the safety to the skin has a poor absorbability of drugs through the skin. Combinations of individual optima, such as the lower limit of log R, - the upper limit of TIS, the mean estimates of both log R, and TIS, and the upper limit of log R, - the lower limit of TIS, do not have a significant effect on the simultaneous optima. On the other hand, both TIS and log R, values gradually increased through the diagonal combinations, such as the lower limits of log R, and TIS, the mean estimates of log R, and TIS, and the upper limits of log R, and TIS, as shown in Figure 5 . The highest possible simultaneous optimum of log R, is required while TIS should

+

+

+

+

Journal of fharmaceufical Sciences / 1371 Vol. 83, No. 9, September 1994

Table 8-Optimal Formulations in Physical Form

a

Formulation Factor ("10)

A

B

C

d-Limonene /-Menthol 1,8-Cineole Ethanol Propylene glycol

0.820 1.42 1.40 16.7 13.6

0.874 1.43 1.42 18.2 13.3

0.972 1.49 1.41 19.3 14.1

Irritation is not serious for formulation A, where the most significant irritation is found to be slight liquefaction and desquamation with no other marked findings. In a trade-off, it is still possible to choose formulation B as the optimum formulation with very low skin irritation and a promising skin penetration rate of 390 pgh. As can be seen from Table 8, where the three optimum formulations A, B, and C are described in physical form, there are only small differences in concentrations of causal factors and it is obvious that it would be impossible to reach these exact combinations using a normal analysis based on a onefactor-at-a-time experiment. In future investigations, the possible differences in these optimum formulations between humans and other animals should be evaluated. However, with respect to preformulation studies, optimization of indomethacin gels containing a combination of three kinds of monoterpenes a s penetration enhancer could be reasonably well performed by means of the optimization method described in this study.

b

References and Notes

Figure 5-Simultaneous optimal values of response variables as a function of individual optima in confidence intervals: (a) log Rp values; (b) TIS values. Table 7-Response Variables of Simultaneous Optimal Formulations Represented as a Function of Individual Optimaa

TIS

log RP

Formulation

Predicted

Experimentalb

Predicted

Experimentalb

A B C

4.9 6.2 7.6

4.6 k 1.7 5.6 f 1.5 8.8k 2.4

2.51 2.59 2.67

2.50 f 0.10 2.57 k 0.10 2.71 k 0.10

a Formulation A was estimated as a function of the lower limits of log Rp and TIS. Formulation B was estimated as a function of the mean estimates of log Rp and TIS. Formulation C was estimated as a function of the upper limits of log Rp and TIS. Experimental data were represented as the mean SD of five animals.

be as low as possible and only by trade-off can a high log R, be achieved. The three diagonal combinations have been investigated in a repeated experiment with 5 replicates. Table 7 shows the predicted values and the experimental results of log R, and TIS. There is excellent agreement between the measured and predicted data for both log R , and TIS responses. The optimum formulation should be chosen between A and B in Table 7, since C has a relatively higher irritation score. 1372 1Journal of Pharmaceutical Sciences Vol. 83, No. 9, September 1994

1. Okabe, H.; Takayama, K.; Ogura, A.; Nagai, T. Drug Des. Delivery 1989, 4, 313-321. 2. Okabe, H.; Obata, Y.; Takayama, K.; Nagai, T. Drug Des. Delivery 1990, 6, 229-239. 3. Obata,-Y.; Takayama, K.; Okabe, H.; Nagai, T. Drug Des. Delivery 1990, 6, 319-328. 4. Williams, A. C.; Barry, B. W. Pharm. Res. 1991,8, 17-24. 5. Obata, Y.; Takayama, K.; Machida, Y.; Nagai, T. Drug. Des. Discovery 1991, 8, 137-144. 6. Kaiho, FI; NomGa, H.; Makabe, E.; Kato, Y. Chem. Pharm. Bull. 1987.35, 2928-2934. 7. Ogiso, T.;' Ito, Y.; Iwaki, M.; Atago, H. J . Pharmacobio-Dyn. 1986, 9, 517-525. 8. Barry, B. W.; Williams, A. C. Proc. Int. Symp. Control. Rel. Bioact. Muter. 1989, 16. 9. Fonner, D. E., Jr.; Buck, J. R.; Banker, G. S. J . Pharm. Sci. 1970, 59,1587-1596. 10. Schwartz, J. B.; Flamholz, J. R.; Press, R. H. J . Pharm. Sci. 1973,62, 1165-1170. 11. Mcleod, A. D.; Lam, F. C.; Gupta, P. K.; Hung, C. T. J . Pharm. Sci. 1988, 77, 704-710. 12. Fenyvesi, E.; Takayama, K.; Szejtli, J.;Nagai, T. Chem.Pharm. B d l . 1984,32, 670-677. 13. Takayama, K.; Imaizumi, H.; Nambu, N.; Nagai, T. Chem. Pharm. Bull. 1985,33,292-300. 14. Khuri, A. I.; Conlon, M. Technornetrics 1981,23, 363-375. 15. Haga, T.; Takeuchi, H.; Okuno, T. Quality J . S . &. C. 1976, 6, 35-40 (In Japanese). 16. Takayama, K.; Nagai, T. Znt. J . Pharm. 1991, 74,115-126. 17. Yamaoka, K.; Tanigawara, Y.; Nakagawa, T.; Uno, T. J . Pharmacobio.-Dyn. 1981, 4 , 879-885. 18. Takayama, K.; Nagai, T. Chem. Pharm. Bull. 1989,37, 160167.

Acknowledgments A supportive research grant from Advance Co., Ltd. is gratefully acknowledged.