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Finite Dose Percutaneous Drug Absorption: Theory and Its Application to In Vitro Timolol Permeation
Finite Dose Percutaneous Drug Absorption: Theory and Its Application to In Vitro Timolol Permeation KIYOSHIKUBOTA'*" AND TAKAO YAMADAS Received June 19, 1989, from the 'Division of Clinical Pharmacology, Clinical Research Institute, National Medical Center, Tokyo, and the %Facultyof Pharmaceutical Sciences, School of Pharmacy, Hoshi Universffy,T o k p Japan. Accepted for publication January 3, 1990. *Present address: Department of Dermatology, University o California, School of Medicine, Box 0989, Surge 110, San Francisco, CA 941434969. Abstract 0 The finite dose in vitro percutaneous absorption kinetics of timolol, a p-blocker, was studied. The flux of timolol across excised human abdominal cadaver skin was measured over a period of 72 h following application of a 40-km thickness patch containing 510, or 20% (w/v) timolol free base. Amountsof timolol in the patch and skin were also determinedat 6,12,24,48, and 72 h after the applicationof the 20% (wlv) patch. The mean diffusion and partition parameters were estimated to be 0.018 h-' and 125.9 pm, respectively, using a newly developed theory. Diffusion and partition parameters were estimated using the values for amounts of a drug eventually partitioning into the perfusing water, as well as two newly proposed conceptual parameter values, AUC, and AUCb which are the AUCs of drug amounts in vehicle and skin, respectively. The dose-dependent skin-timolol interaction is also discussed.
Steady-state drug permeation kinetics have normally been studied in in vitro percutaneous drug absorption experiments using relatively large amounts of a drug in the donor cell.14 The main parameter usually determined is the permeability coefficient, the ratio of the steady-state drug flux to the drug concentration in the donor cell. Although the permeability coefficient may differ with various vehicles, the maximum flux obtained using saturated drug solutions in the donor cell should be independent of the vehicle, providing the vehicles are without direct, enhancing effects on the skin.5 Thus, the permeability coefficient can indicate the maximum permeability of a compound when the solubility of the drug is known.5 Nonetheless, knowing the permeability coefficient and solubility of a drug does not necessarily allow one to predict the actual kinetics of in vivo permeation, except when a transdermal therapeutic system6.7 is used and a constant, unit activity flux is maintained by the device. In this article, a new method is proposed to obtain the two basic kinetic parameters, the partition and diffusion parameters4.8 from the in vitro finite dose drug permeation experiments. The method is used to model the in vitro permeation of timolol, a nonselective P-blocker, from a simple solution matrix through human skin. To study possible dose dependency, three different drug concentrations were employed. Timolol has been used as an antihypertensive.9 It also prevents or reverses ischemic electrocardiographicchanges in patients with angina pectoris.9 Timolol is the only padrenoceptor-blocking drug that has proved to be safe and clinically efficacious in reducing elevated intraocular pressure when used topically.9 In this study, timolol was chosen as a test drug because it has been shown that timolol can be absorbed from the skin and produce the p-blocking action in the normal volunteers.10 0022-3549/90/1100-1015$01.00/0 0 1990, American Pharmaceutical Association
Theoretical Section Method of Determination of the Parameters for the Finite Dose In Vitro Percutaneous Drug Permeation Processes-When the amounts of a drug per unit area in the vehicle and skin are defined as A, and A,,, respectively, and the cumulative amount per unit area of drug excreted into the receptor cell is defined as A,, the following equation holds according to the principle of mass balance:
A,
+ As + A,
= A0
(1)
where A. is the initial amount of a drug per unit area in the where vehicle. Because A, = Jb JBdt and A, + A, = J. and J, are the respective values for the flux from skin to receptor cell and from vehicle to skin per unit area, the following equations are derived:
A,
I,'
+ A, + Jsdt = A0
(3)
The respective Laplace transforms of eqs 2 and 3 are given as:
-
z
A0
s
s
A,+-=-
(4)
By multiplying both sides of eqs 4 and 5 by s and differentiating them with respect to s, the following equations are derived:
-
A,
- -
d-
d-
+ -A, + ds -J, = 0 ds
-:(
:-)
A, + A s + s -A, +-A,
(6)
:-
+ -J,
=0
(7)
Generally, according to the final value theorem, when the Laplace transform of F, a function oft, is given as F,the value for F approaches the AUC and that for -&&F approaches the Journal of Pharmaceutical Sciences I 1015 Vol. 79, No. 11, November 1990
area under the moment curve (AUMCP1 of the F-t curves when s approaches 0. In addition, the AUMC is given as MRT AUC, where MRT is the mean residence time.12 Thus, the following relationships are derived from eqs 6 and 7:
AUCA”+ AUCA, = MRT AUCjl 6
(9)
In the above equations, AUCAYis the AUC of the A,-time curves, AUCA, is the AUC of the A,-time curves, and AUC,” and AUCJa are those for the J , and J , versus time curves, respectively. In eq 8, MRT, is the MRT of a drug through vehicle following application. Similarly, MRT in eq 9 is that for J , and is given
MRT = MRT,
+ MRT,
(10)
where MRT, is the MRT of a drug through skin. When all the initial drug in vehicle is eventually released into the perfusing water, the values for both AUC, and AUC, in eqs 8 and 9 are equal to each other and Ao. In this case, the equation given below is derived from eqs 8 to 10:
In an in vitro condition, where the removal of a drug from the receptor cell by the perfusing solution is sufficiently rapid and skin can be regarded as a simple diffusion membrane, MRT, in eq 11 is given as:13 1
MRT,
I
=-
2kd
uppermost epidermis. However, when the drug is homogeneously soluble14 in the donor matrix, the situation can be described as a simple diffusion membrane. This scenario is explained by the “diffusion-difision model.”l3 In this case, MRT, in eq 8 is given as:
(12)
where k , is the diffusion parameter498 which is defined as D,l1,2 where D,and 1, are the effectivediffusion coefficient and pathlength of diffusion through skin, respectively. From eqs 11 and 12, the following equation is derived:
(13) When A,, in eq 13 is read as the cumulative amount eventually released into the receptor solution, A,(w), the following equation holds for any case where bothA,(m) and AUCA*have finite values [i.e., both A, and J. approach 0 at Km)l:
(14) For the steady state, eq 14 reduces to the simple form k , = J,$(2 -A,,), where J,, and A,, are the flux from skin and amount in skin per unit area at steady state, respectively. This is because AJm) and AUC,, will be approximated by J,, * T and A,, T, respectively, as time (T) approaches infinity. Time T is the duration for which the steady state is maintained after the application of a hypothetically infinite amount of a drug in the donor cell and until the removal of a drug from the donor cell (i.e., until the concentration in donor does not significantly change with time). This tquation can be also easily derived if one notices that J,, = C * D$l, and A,, = C’ * 412, where C” is the concentration of a drug in the
(15) where 0,and I , are the effective diffusion coefficient and pathlength of diffusion through vehicle, respectively. The ld value is the “partition parameter”4 or the “apparent length of diffusion of skin”l3 which represents the apparent thickness corresponding to the drug amount in the skin when the drug concentration in the skin at the vehicleskin boundary is considered to be that in vehicle13and is defined as K , * 1. CK, is the skin-vehicle partition coefficient).From eqs 8,13, and 15, the following equation is derived
2 AUCA,
-&)
1,
AUCA” - 1: 30“
(16)
At steady state, eq 16 reduces to 1, = 2 .A& where C is the concentration of a drug in the donor cell when the D, value can be considered to be very large (e.g., when water is used in the donor cell). This is also easily derived if one notices that C = C*lK, and AUCA 11, approaches C T. Method to Predict J,-Vhen the vehicle is a solution and the skin can be regarded as a single simple diffusion membrane, J, is given as:13
-
where Janand A, are decided by the given set of D,,l,, k,, and ld.13 The value of Jacan be also approximated by the following equation:13
(18) where K, >K,, K, is the apparent increasing rate constant of J,, and K, is the apparent decreasing rate constant ofJ,. Both K , and K , are given as complex functions ofD,, l,, I,, and kd.13 The values for K , and K , are estimated by solving the following equations. The details have been given previousiy.13
-+-=-(-+J 2 1
1
Ki K2
1 1 1 ,
kd
2
1,
+ -3 0
(19)
-
1016 I Journal of Pharmaceutical Sciences Vol. 79, No. 11, November 1990
21: -+450:
21, 3 1 d . k:
1 + -6ki
(20)
Experimental Section Skin Preparation and Materials-Full-thickness abdominal cadaver skin, -1.5 x 13 cm2 in size, was obtained at autopsy. All subcutaneous fat was promptly removed. Skin was cut into several 1.5 x 1.5-cm2 pieces and used in experiments within 24 h after autopsy. A therapeutic patch containing timolol free base in the solution matrix, acryl copolymer, was prepared as described previously.14 The diffusion coefficient of timolol in the vehicle, D,,was Patches containing 5,10, and 20% estimated to be -3 x lo-' ~m~ls.14 (w/v)timolol free base, 40 p m in thickness, were used in experiments. Timolol Penetration-A round piece (diameter 6 mm) of patch was applied on the epidermal side of the full-thickness skin. Each patch-skin complex was placed carefully on the diffusion cell (Teflon Flow-Thru Diffusion Cell, Crown Glass Company, Inc., Somerville, NJ).16 Cells were put in a water bath held at 32 "C. Distilled water was pumped into the receptor cell at a flow rate of 2.5 mWh. The perfusate was collected, by fraction collector, for 6 to 72 h. At the end of the experiment, the applied patch and skin were separated and stored at -20 "C until analyzed. Measurement and Stability of Timolol in the Sample--Timolol in the effluent and patch was measured by the HPLC method as previously described.14 A piece of skin was easily homogenized after 3 h of incubation in 4M NaOH at 37°C. Fifteen micrograms of pindolol, an internal standard, and 5 mL of dichloromethane were added to a fraction of homogenized skin and shaken vigorously at basic pH16 for 3 min. After centrifugation (2500 x g, 30 m i d , the organic phase was evaporated to dryness at 37 "C. The residue was reconstructed with 400 pL of mobile phase and measured by HPLC.14 To estimate the recovery rate of timolol from the full-thickness skin, a piece of skin (-10 x 10 mm2)was immersed for 72 h in 400 p L of water containing 50,100, or 200 p g (n = 3, each) of timolol free base. An aliquot of 200 pL of water was then removed and the sum of timolol in the skin and the remaining solution was measured. Timolol absorbed into skin (25.9 rf: 1.3%of the given dose, mean SEM, n = 9) was calculated from the difference in concentrations before and after equilibrium is reached.13-17The recovery rate was estimated to be 92.6 f 2.5%(mean rf: SEM, n = 9). The amounts of timolol in the three patches were within 25% of the calculated values as reported previously.14 When the three different patches were stored at -20 "C for 3 months, the amounts of timolol per unit area in the patches were 98-1048 of the calculated values. The concentrations of timolol in perfusate (0.15 and 0.43 pglmL) were 97 and 98%,respectively, of the initial values when measured after the storage at -20 "C for 3 months. When 100 pg of timolol was s iked into 5 mL of homogenate made from a piece of skin (-2 x 2 cmF and stored at -20 "C for 3 months, the timolol concentration was 96%of the initial value. In addition, no significant change in amount of timolol in the vehicle was observed when stored at room temperature for 12 months. Kinetic A n a l y s i e T h e maximum flux of timolol through the skin, Jsm, and time to Js ,t,,,, were read from the experimental results. The initial amount? timolol, A,, was calculated as the sum of the amount in the vehicle (patch),A,, skin, A,, and effluent, A,, a t 72 h. The amount eventually released into the effluent, AJw), was calculated by extrapolating to infinity using the terminal elimination rate constant (A,) obtained by linear least-squares regression analysis of the logarithm of timolol flux from skin, Js.Assuming the vehicle and excised skin as simple diffusion membranes, diffusion and partition parameters4.8 were estimated. The diffusion parameter, kd,was obtained from eq 14 where AUCAs
*
was estimated from A, values at 0 (A, at 0 h is regarded as A, = O), 6,12,24,48, and 72 h after application of the 20% (wh) timolol patch and extrapolating to infinity using A, of J.. The partition parameter, ld, was obtained fmm eq 16 where AUC,, was estimated from A, values at 0 (A, at 0 h is regarded as A, = A,), 6, 12, 24,48, and 72 h after application of the 20%(w/v) timolol patch. Conversely, Jswas predicted by eqs 17 and 18 and compared with the observed data. StatisticsWilcoxon signed-rank test and analysis of variance (ANOVA),followed by Student-Newman-Keuls test were used where appropriate.
Results The mean (+SEM, n = 4) values for AUC,,, AUCA", and AJm), as well as those of J. ,t,,, and the terminal half-life (tlI2) of J, are shown in T a b l a (kd,ld,and the estimated values for D, and K,, supposing 1, = 15 pm, are also shown). The mean (?SEMI A,-,A,-, and J,-time plots (+SEM, n = 4) are shown in Figure 1. In Figure lC, the dotted line indicates the curve predicted from eq 17 using the mean D,, l,, kd,and Id values. The solid line in Figure 1C is that predicted by eq 18. The predicted mean J, -, t,,, and tY2in eq 17 for a 20%(w/v) timolol patch were 1l.f 2 1.5 pg/cm h,13.9 2 3.3 h, and 26.3 f 7.4 h, respectively; no statistically significant differences were observed when compared with the corresponding observed values (Table I). As shown in Tables I and 11, a marked dose dependency was noted. From 5, 10, and 20%(wlv) timolol patches, 40.4,69.1, and 70.3%of the applied dose, respectively, were estimated to be in the effluent (Table I). The difference was statistically significant (p <0.05). In addition, J, /Ao increased and tmax decreased with increasing the dose mable I), although those differences in JsmJAo and t,,, did not reach statistically significant levels. Conversely, for 5, 10, and 20% (w/v) patches, themeanA,values at 72 h were 57.8,28.5, and 22.4% of the applied dose, respectively (Table II), and the difference was statistically significant (p c 0.01). However, there was no statistically significant difference among the mean A, values, which were 13.7, 19.4, and 15.1%,respectively, of the initial doses for 5,10, and 20% (w/v) patches, a t 72 h. The value of D, was calculated to be -1 x cm2/s (Table I), which is smaller than the values for n-alcohol (-lo-' cm2/s) but larger than that for hydrocortisone ( - 1 0 - l ~ cm2/s).1e
Discussion More than 80%of the initial dose was released from each of three kinds of patches into excised skin 72 h post-application. However, the percentage of the initial dose existing in skin at 72 h decreased upon increasing the dose (Table 11). Thus, the dose dependency of the J,-time profiles may be due to a dose-dependent skin-compound interaction. Therefore, for timolol permeation, it would not be correct to regard excised skin as a simple diffusion membrane where A, and J, should be proportional to A, in the solution matrix. This contrasts
Table I-Kinetic Parameters'
5
1.8 f 0.6
41.4 2 5.4
39.7 2 4.6
10
4.7 ? 0.9 12.7 2 1.P
21.0 2 2.4 16.5 ? 2.40
28.2 % 6.6 28.9 f 4 . e
20
-I -
-
84.4 f 20.8 225.9 f 14.8
40.4 14.4 69.1 t 5.9
*
-
-
19200 ? 2673
28860 ? 10410
508.4 t 52.7
70.3 t 7.4
0.018 t 0.004
125.9 f 41.5
-
-
1.14 t 0.26 8.4 t 2.8
/Ao values for three concentrations is not Statistically significant (ANOVA). The a Mean f SEM (n = 4). The difference among the mean J difference among the mean values for three concentrations is not%tistically significant (ANOVA). Calculated supposing Is = 15 pm. The difference is statistically significant (p < 0.05, ANOVA) and the difference between the mean value for the 5% patch and that for the 10% patch is StatiStiCally significant (p C0.05,Student-Newman-Keulstest). 'Not determined. The mean value does not significantly differ from that predicted by eq 17 (Wilcoxon signed-rank test). Q
Journal of Pharmaceutical Sciences I 1017 Vol. 79, No. 11, November 1990
Tabk lclkrr hlmnca at 72 Hours' ~~~~
A,.
Concentration, % 5 10 20
4
A,
P9/CmZ
Yo of d o s e b
Pam2
% of doseC
22.6 k 7.6 64.4 k 17.9 120.1 66.4
13.7 2 4.5 19.4 5 5.2 15.1 2 7.5
95.9 2 10.5 93.6 f 10.7 165.5 f 43.4
57.8 4.7 28.5 2 3.0 22.4 2 4.9
*
*
Mlcm2
% of doseC
46.2 5 13.1 173.4 2 23.4 465.0 2 66.6
28.7 2 8.9 52.0 2 4.4 62.5 2 3.4 ~~~
Mean 2 SEM (n = 4). The difference among the mean values of three concentrations is not statistically significant (ANOVA). The difference among the mean values of three concentrations is statistically signiffcant (p <0.01, ANOVA) and the difference between the mean value for the 5% patch and that for either of the 10 and 20% patches is statistically signifkant (p <0.05, Student-Newman-Keuls test).
; ;2 5 0 E
'a 2 0 0
-
-" 1 5 0 5
-
8 too
I
5
50
Id-
Time
(h)
Flgum 1-The A,. (A), A. (B), and J. (C) time profiles after application of the patches containing5 (M),10 (A),and 20%(0)of timobl free base. Vertical bars i n d i t e the values for SEM (n = 4). The dotted and solid lines in (C) are predicted by eqs 17 and 18, respectively, in the text.
with the apparent consistency between the observed J,-time profiles and those predicted (Figure 10. Although it is possible that some degradation of timolol occurred in skin after the application of the patch, this possibility cannot account for the decrease in percent of dose -A, observed when the patch with higher concentration was used (Table 11). This is because applied doses for 6, 10, and 20% (w/v)patches with 40-pm thickness should be 200,400, and 800 pg/cm2,respectively, while at 72 h, the sum of A,, A,, and A, reached 82.4,82.9, and 93.8% of these values, respectively. This indicates a difference of >30%of dose a8 A, among the different patches (Table 11) that cannot be attributed to the degradation of timolol in skin. Chandrasekaran, Bayne, and Shawl9 showed that percutaneous scopolamine absorption is well explained by the model where two mechanisms [ ( I ) a simple dissolution producing mobile and freely diffusible molecules and (2) an adsorption process producing nonmobile moleculeel are postulated to occur. However, whether the dose dependency of timolol occurs by the same mechanisms as does that of eoopolarnine is not clear from the current study. The steady1018 I Journal of Pharmaceutical Sciences Vd. 79, No. 11, November 1990
state timolol permeation kinetics determined by equilibrating the epidermis with drug solutions of known concentratiom20 may reveal more detailed mechanisms. In addition, it also awaits further in vivo studies to assess whether similar dose dependency is also observed clinically. Until these issues are scrutinized, the values for kd and Id in Table I should be interpreted carefully. The new method to estimate the diffusion and partition parameters from a finite dose, in vitro drug permeation study advocated in this article is a robust one. When using the well-known parameters which have been employed in steadystate kinetics, the diffusion and partition parameters k d and ld can be calculated as k d = (1/6TL)6J8and ld = P / k d , I 3 where TL and P are lag time and permeability constants, respectively, both of which are estimated from the J,-time profile. However, in the preliminary study we found it is sometimes very difficult to estimate those values exclusively from Jmtime profiles following finite doses of timolol.8 The estimated parameter values (particularly the partition parameter 1,) often show a great intraindividual variance even if several neighboring pieces of the same skin are employed (data not shown). On the other hand, in the method proposed herein, the experimental error does not cause serious derangement of the AUC,,, AUC,,", andA,(a) values in eqs 14 and 16, and the estimated parameter values should be more reliable than those estimated exclusively from the J,-time profiles. To fully appreciate the effect a formulated drug has on the skin barrier function and the relationship thereof to the a b sorbed amount upon repeated application of an ointment21-29 it would be helpful to know the amount of drug in the skin attained after the application of a single finite dose under in vitm conditions. Similarly, to resolve the debate on the dilution of the commercially available topical corticosteroid ointment,= in vitm study of the dose and/or concentration dependency of a drug applied on the skin may provide valuable information. The new method proposed in this article could be used for other drugs, besides tirnolol, to address these clinically important issues.
References and Notes 1. Scheuplein, R. J. J . Invest. Dermatol. 1965,45,334-346. 2. Scheuplein, B. J.; Blank, I. H.; Brauner, G. J.; MacFarlane,D. J. J . Invest. Dermatol. 1969.52, 63-70. 3. Blank, I. H.; McAuliffe, D. J. J . Invest. Dermatol. 1985, 85, 522-4526. 4. Okamoto, H.; Haahida, M.; Sezaki, H. J . Pharm. Sci. 1988, 77, 41-24. 5. Flynn, G. L.; Stewart,B. Drug Dev. Res. 1988,13, 169-185. 6. Monkhouse, D. C.; Huq, A. S. Drug Dev. I d . Pharm. 1988,14, 183-209. 7. Ridout, G.; Santua, G. C.; Guy, R. H. Clin. Pharmacokinet. 1988, 15.114-131. 8. Okamoto,H.; Yamaahita, F.; Saito, K.; Haahida, M. Phurmuceut. Res. 1989, 6, 931-937. 9. Friahman, W. H. N. Eng. J . Med. 1982,306, 145C1462. 10. Vlamea, P. H.; Ribeiro, L. C. T.; Rotmenach, H. H.; Bondi, J. V.; Loper, A. E.; Hichene, M.; Dunlay, M. C.; Fergueon, R. K. J . Cardwvasc. Pharmacol. 1985, 7,245-250. 11. Benet, L. 2.;Galeazzi, R. L. J . Phunn. Sci. 1979,68, 1071-1074.
12. Yamaoka, K.; Nakagawa, T.; Uno, T. J. Pharmacokinet. Biopharm. 1978,6,547-558. 13. Kubota, K.; Ishizaki, T. J.Pharmucokinet. Biophurm. 1986,14, 409-439. 14. Kubota, K.; Yamada, T.; Ogura, A.; Ishizaki, T. J . Phurm. Sci. 1990, 79, 179-184. 15. Bronaugh, R. L.; Stewart, R. F. J . Phurm. Sci. 1985, 74,64-67. 16. Lefebvre, M. A.: Girault, J. J.LW. Chromutogr. 1981,4,483-500. 17. Jetzer, W. E.; Huq, A. S.;Ho, N. F. H.; F1ynn;G. L. J.Phurm. Sci. 1986, 75, i o g a i i o 3 . 18. Scheuplein, R. J.; Blank, I. H. Physwl. Rev. 1971,51,702-747. 19. Chandrasekaran, S. K.; Bayne, W.; Shaw, J. E. J. Pharm. Sci. 1978,67, 1370-1374.
20. Chandrasekaran, S. K.; Michaels, A. S.;Campbell, P. S.; Shaw, J. E. Am. Inst. Chem. Eng. J . 1976,22,828-832. 21. Courtheoux, S.; Pechenot, D.; Bucks, D. A.; Marty, J. P.; Maibach, H. I.; Wepierre, J. Br. J. DermatoI. (Suppl.) 1986, 115, 4952. 22. Bucks, D. A. W.; Maibach, H. I.; Guy, R. H. J.Phurm. Sci. 1985, 74,1337-1339. 23. Bucks, D. A. W.; Maibach, H.I.; Guy, R. H. In Percutaneous Absorption, 2nd ed., Bronaugh, R. L.;Maibach, H. I., Eds; Marcel Dekker: New York, 1989; pp 633-651. 24. Cornarakis-Lentzos, M.; Cowin, P. R. J. Phurmuceut. Biomed. Anal. 1987,5, 707-716.
Journal of Pharmaceutical Sciences I 1019 Voi. 79, No. 11, November 1990
Steady-state drug permeation kinetics have normally been studied in in vitro percutaneous drug absorption experiments using relatively large amounts of a drug in the donor cell.14 The main parameter usually determined is the permeability coefficient, the ratio of the steady-state drug flux to the drug concentration in the donor cell. Although the permeability coefficient may differ with various vehicles, the maximum flux obtained using saturated drug solutions in the donor cell should be independent of the vehicle, providing the vehicles are without direct, enhancing effects on the skin.5 Thus, the permeability coefficient can indicate the maximum permeability of a compound when the solubility of the drug is known.5 Nonetheless, knowing the permeability coefficient and solubility of a drug does not necessarily allow one to predict the actual kinetics of in vivo permeation, except when a transdermal therapeutic system6.7 is used and a constant, unit activity flux is maintained by the device. In this article, a new method is proposed to obtain the two basic kinetic parameters, the partition and diffusion parameters4.8 from the in vitro finite dose drug permeation experiments. The method is used to model the in vitro permeation of timolol, a nonselective P-blocker, from a simple solution matrix through human skin. To study possible dose dependency, three different drug concentrations were employed. Timolol has been used as an antihypertensive.9 It also prevents or reverses ischemic electrocardiographicchanges in patients with angina pectoris.9 Timolol is the only padrenoceptor-blocking drug that has proved to be safe and clinically efficacious in reducing elevated intraocular pressure when used topically.9 In this study, timolol was chosen as a test drug because it has been shown that timolol can be absorbed from the skin and produce the p-blocking action in the normal volunteers.10 0022-3549/90/1100-1015$01.00/0 0 1990, American Pharmaceutical Association
Theoretical Section Method of Determination of the Parameters for the Finite Dose In Vitro Percutaneous Drug Permeation Processes-When the amounts of a drug per unit area in the vehicle and skin are defined as A, and A,,, respectively, and the cumulative amount per unit area of drug excreted into the receptor cell is defined as A,, the following equation holds according to the principle of mass balance:
A,
+ As + A,
= A0
(1)
where A. is the initial amount of a drug per unit area in the where vehicle. Because A, = Jb JBdt and A, + A, = J. and J, are the respective values for the flux from skin to receptor cell and from vehicle to skin per unit area, the following equations are derived:
A,
I,'
+ A, + Jsdt = A0
(3)
The respective Laplace transforms of eqs 2 and 3 are given as:
-
z
A0
s
s
A,+-=-
(4)
By multiplying both sides of eqs 4 and 5 by s and differentiating them with respect to s, the following equations are derived:
-
A,
- -
d-
d-
+ -A, + ds -J, = 0 ds
-:(
:-)
A, + A s + s -A, +-A,
(6)
:-
+ -J,
=0
(7)
Generally, according to the final value theorem, when the Laplace transform of F, a function oft, is given as F,the value for F approaches the AUC and that for -&&F approaches the Journal of Pharmaceutical Sciences I 1015 Vol. 79, No. 11, November 1990
area under the moment curve (AUMCP1 of the F-t curves when s approaches 0. In addition, the AUMC is given as MRT AUC, where MRT is the mean residence time.12 Thus, the following relationships are derived from eqs 6 and 7:
AUCA”+ AUCA, = MRT AUCjl 6
(9)
In the above equations, AUCAYis the AUC of the A,-time curves, AUCA, is the AUC of the A,-time curves, and AUC,” and AUCJa are those for the J , and J , versus time curves, respectively. In eq 8, MRT, is the MRT of a drug through vehicle following application. Similarly, MRT in eq 9 is that for J , and is given
MRT = MRT,
+ MRT,
(10)
where MRT, is the MRT of a drug through skin. When all the initial drug in vehicle is eventually released into the perfusing water, the values for both AUC, and AUC, in eqs 8 and 9 are equal to each other and Ao. In this case, the equation given below is derived from eqs 8 to 10:
In an in vitro condition, where the removal of a drug from the receptor cell by the perfusing solution is sufficiently rapid and skin can be regarded as a simple diffusion membrane, MRT, in eq 11 is given as:13 1
MRT,
I
=-
2kd
uppermost epidermis. However, when the drug is homogeneously soluble14 in the donor matrix, the situation can be described as a simple diffusion membrane. This scenario is explained by the “diffusion-difision model.”l3 In this case, MRT, in eq 8 is given as:
(12)
where k , is the diffusion parameter498 which is defined as D,l1,2 where D,and 1, are the effectivediffusion coefficient and pathlength of diffusion through skin, respectively. From eqs 11 and 12, the following equation is derived:
(13) When A,, in eq 13 is read as the cumulative amount eventually released into the receptor solution, A,(w), the following equation holds for any case where bothA,(m) and AUCA*have finite values [i.e., both A, and J. approach 0 at Km)l:
(14) For the steady state, eq 14 reduces to the simple form k , = J,$(2 -A,,), where J,, and A,, are the flux from skin and amount in skin per unit area at steady state, respectively. This is because AJm) and AUC,, will be approximated by J,, * T and A,, T, respectively, as time (T) approaches infinity. Time T is the duration for which the steady state is maintained after the application of a hypothetically infinite amount of a drug in the donor cell and until the removal of a drug from the donor cell (i.e., until the concentration in donor does not significantly change with time). This tquation can be also easily derived if one notices that J,, = C * D$l, and A,, = C’ * 412, where C” is the concentration of a drug in the
(15) where 0,and I , are the effective diffusion coefficient and pathlength of diffusion through vehicle, respectively. The ld value is the “partition parameter”4 or the “apparent length of diffusion of skin”l3 which represents the apparent thickness corresponding to the drug amount in the skin when the drug concentration in the skin at the vehicleskin boundary is considered to be that in vehicle13and is defined as K , * 1. CK, is the skin-vehicle partition coefficient).From eqs 8,13, and 15, the following equation is derived
2 AUCA,
-&)
1,
AUCA” - 1: 30“
(16)
At steady state, eq 16 reduces to 1, = 2 .A& where C is the concentration of a drug in the donor cell when the D, value can be considered to be very large (e.g., when water is used in the donor cell). This is also easily derived if one notices that C = C*lK, and AUCA 11, approaches C T. Method to Predict J,-Vhen the vehicle is a solution and the skin can be regarded as a single simple diffusion membrane, J, is given as:13
-
where Janand A, are decided by the given set of D,,l,, k,, and ld.13 The value of Jacan be also approximated by the following equation:13
(18) where K, >K,, K, is the apparent increasing rate constant of J,, and K, is the apparent decreasing rate constant ofJ,. Both K , and K , are given as complex functions ofD,, l,, I,, and kd.13 The values for K , and K , are estimated by solving the following equations. The details have been given previousiy.13
-+-=-(-+J 2 1
1
Ki K2
1 1 1 ,
kd
2
1,
+ -3 0
(19)
-
1016 I Journal of Pharmaceutical Sciences Vol. 79, No. 11, November 1990
21: -+450:
21, 3 1 d . k:
1 + -6ki
(20)
Experimental Section Skin Preparation and Materials-Full-thickness abdominal cadaver skin, -1.5 x 13 cm2 in size, was obtained at autopsy. All subcutaneous fat was promptly removed. Skin was cut into several 1.5 x 1.5-cm2 pieces and used in experiments within 24 h after autopsy. A therapeutic patch containing timolol free base in the solution matrix, acryl copolymer, was prepared as described previously.14 The diffusion coefficient of timolol in the vehicle, D,,was Patches containing 5,10, and 20% estimated to be -3 x lo-' ~m~ls.14 (w/v)timolol free base, 40 p m in thickness, were used in experiments. Timolol Penetration-A round piece (diameter 6 mm) of patch was applied on the epidermal side of the full-thickness skin. Each patch-skin complex was placed carefully on the diffusion cell (Teflon Flow-Thru Diffusion Cell, Crown Glass Company, Inc., Somerville, NJ).16 Cells were put in a water bath held at 32 "C. Distilled water was pumped into the receptor cell at a flow rate of 2.5 mWh. The perfusate was collected, by fraction collector, for 6 to 72 h. At the end of the experiment, the applied patch and skin were separated and stored at -20 "C until analyzed. Measurement and Stability of Timolol in the Sample--Timolol in the effluent and patch was measured by the HPLC method as previously described.14 A piece of skin was easily homogenized after 3 h of incubation in 4M NaOH at 37°C. Fifteen micrograms of pindolol, an internal standard, and 5 mL of dichloromethane were added to a fraction of homogenized skin and shaken vigorously at basic pH16 for 3 min. After centrifugation (2500 x g, 30 m i d , the organic phase was evaporated to dryness at 37 "C. The residue was reconstructed with 400 pL of mobile phase and measured by HPLC.14 To estimate the recovery rate of timolol from the full-thickness skin, a piece of skin (-10 x 10 mm2)was immersed for 72 h in 400 p L of water containing 50,100, or 200 p g (n = 3, each) of timolol free base. An aliquot of 200 pL of water was then removed and the sum of timolol in the skin and the remaining solution was measured. Timolol absorbed into skin (25.9 rf: 1.3%of the given dose, mean SEM, n = 9) was calculated from the difference in concentrations before and after equilibrium is reached.13-17The recovery rate was estimated to be 92.6 f 2.5%(mean rf: SEM, n = 9). The amounts of timolol in the three patches were within 25% of the calculated values as reported previously.14 When the three different patches were stored at -20 "C for 3 months, the amounts of timolol per unit area in the patches were 98-1048 of the calculated values. The concentrations of timolol in perfusate (0.15 and 0.43 pglmL) were 97 and 98%,respectively, of the initial values when measured after the storage at -20 "C for 3 months. When 100 pg of timolol was s iked into 5 mL of homogenate made from a piece of skin (-2 x 2 cmF and stored at -20 "C for 3 months, the timolol concentration was 96%of the initial value. In addition, no significant change in amount of timolol in the vehicle was observed when stored at room temperature for 12 months. Kinetic A n a l y s i e T h e maximum flux of timolol through the skin, Jsm, and time to Js ,t,,,, were read from the experimental results. The initial amount? timolol, A,, was calculated as the sum of the amount in the vehicle (patch),A,, skin, A,, and effluent, A,, a t 72 h. The amount eventually released into the effluent, AJw), was calculated by extrapolating to infinity using the terminal elimination rate constant (A,) obtained by linear least-squares regression analysis of the logarithm of timolol flux from skin, Js.Assuming the vehicle and excised skin as simple diffusion membranes, diffusion and partition parameters4.8 were estimated. The diffusion parameter, kd,was obtained from eq 14 where AUCAs
*
was estimated from A, values at 0 (A, at 0 h is regarded as A, = O), 6,12,24,48, and 72 h after application of the 20% (wh) timolol patch and extrapolating to infinity using A, of J.. The partition parameter, ld, was obtained fmm eq 16 where AUC,, was estimated from A, values at 0 (A, at 0 h is regarded as A, = A,), 6, 12, 24,48, and 72 h after application of the 20%(w/v) timolol patch. Conversely, Jswas predicted by eqs 17 and 18 and compared with the observed data. StatisticsWilcoxon signed-rank test and analysis of variance (ANOVA),followed by Student-Newman-Keuls test were used where appropriate.
Results The mean (+SEM, n = 4) values for AUC,,, AUCA", and AJm), as well as those of J. ,t,,, and the terminal half-life (tlI2) of J, are shown in T a b l a (kd,ld,and the estimated values for D, and K,, supposing 1, = 15 pm, are also shown). The mean (?SEMI A,-,A,-, and J,-time plots (+SEM, n = 4) are shown in Figure 1. In Figure lC, the dotted line indicates the curve predicted from eq 17 using the mean D,, l,, kd,and Id values. The solid line in Figure 1C is that predicted by eq 18. The predicted mean J, -, t,,, and tY2in eq 17 for a 20%(w/v) timolol patch were 1l.f 2 1.5 pg/cm h,13.9 2 3.3 h, and 26.3 f 7.4 h, respectively; no statistically significant differences were observed when compared with the corresponding observed values (Table I). As shown in Tables I and 11, a marked dose dependency was noted. From 5, 10, and 20%(wlv) timolol patches, 40.4,69.1, and 70.3%of the applied dose, respectively, were estimated to be in the effluent (Table I). The difference was statistically significant (p <0.05). In addition, J, /Ao increased and tmax decreased with increasing the dose mable I), although those differences in JsmJAo and t,,, did not reach statistically significant levels. Conversely, for 5, 10, and 20% (w/v) patches, themeanA,values at 72 h were 57.8,28.5, and 22.4% of the applied dose, respectively (Table II), and the difference was statistically significant (p c 0.01). However, there was no statistically significant difference among the mean A, values, which were 13.7, 19.4, and 15.1%,respectively, of the initial doses for 5,10, and 20% (w/v) patches, a t 72 h. The value of D, was calculated to be -1 x cm2/s (Table I), which is smaller than the values for n-alcohol (-lo-' cm2/s) but larger than that for hydrocortisone ( - 1 0 - l ~ cm2/s).1e
Discussion More than 80%of the initial dose was released from each of three kinds of patches into excised skin 72 h post-application. However, the percentage of the initial dose existing in skin at 72 h decreased upon increasing the dose (Table 11). Thus, the dose dependency of the J,-time profiles may be due to a dose-dependent skin-compound interaction. Therefore, for timolol permeation, it would not be correct to regard excised skin as a simple diffusion membrane where A, and J, should be proportional to A, in the solution matrix. This contrasts
Table I-Kinetic Parameters'
5
1.8 f 0.6
41.4 2 5.4
39.7 2 4.6
10
4.7 ? 0.9 12.7 2 1.P
21.0 2 2.4 16.5 ? 2.40
28.2 % 6.6 28.9 f 4 . e
20
-I -
-
84.4 f 20.8 225.9 f 14.8
40.4 14.4 69.1 t 5.9
*
-
-
19200 ? 2673
28860 ? 10410
508.4 t 52.7
70.3 t 7.4
0.018 t 0.004
125.9 f 41.5
-
-
1.14 t 0.26 8.4 t 2.8
/Ao values for three concentrations is not Statistically significant (ANOVA). The a Mean f SEM (n = 4). The difference among the mean J difference among the mean values for three concentrations is not%tistically significant (ANOVA). Calculated supposing Is = 15 pm. The difference is statistically significant (p < 0.05, ANOVA) and the difference between the mean value for the 5% patch and that for the 10% patch is StatiStiCally significant (p C0.05,Student-Newman-Keulstest). 'Not determined. The mean value does not significantly differ from that predicted by eq 17 (Wilcoxon signed-rank test). Q
Journal of Pharmaceutical Sciences I 1017 Vol. 79, No. 11, November 1990
Tabk lclkrr hlmnca at 72 Hours' ~~~~
A,.
Concentration, % 5 10 20
4
A,
P9/CmZ
Yo of d o s e b
Pam2
% of doseC
22.6 k 7.6 64.4 k 17.9 120.1 66.4
13.7 2 4.5 19.4 5 5.2 15.1 2 7.5
95.9 2 10.5 93.6 f 10.7 165.5 f 43.4
57.8 4.7 28.5 2 3.0 22.4 2 4.9
*
*
Mlcm2
% of doseC
46.2 5 13.1 173.4 2 23.4 465.0 2 66.6
28.7 2 8.9 52.0 2 4.4 62.5 2 3.4 ~~~
Mean 2 SEM (n = 4). The difference among the mean values of three concentrations is not statistically significant (ANOVA). The difference among the mean values of three concentrations is statistically signiffcant (p <0.01, ANOVA) and the difference between the mean value for the 5% patch and that for either of the 10 and 20% patches is statistically signifkant (p <0.05, Student-Newman-Keuls test).
; ;2 5 0 E
'a 2 0 0
-
-" 1 5 0 5
-
8 too
I
5
50
Id-
Time
(h)
Flgum 1-The A,. (A), A. (B), and J. (C) time profiles after application of the patches containing5 (M),10 (A),and 20%(0)of timobl free base. Vertical bars i n d i t e the values for SEM (n = 4). The dotted and solid lines in (C) are predicted by eqs 17 and 18, respectively, in the text.
with the apparent consistency between the observed J,-time profiles and those predicted (Figure 10. Although it is possible that some degradation of timolol occurred in skin after the application of the patch, this possibility cannot account for the decrease in percent of dose -A, observed when the patch with higher concentration was used (Table 11). This is because applied doses for 6, 10, and 20% (w/v)patches with 40-pm thickness should be 200,400, and 800 pg/cm2,respectively, while at 72 h, the sum of A,, A,, and A, reached 82.4,82.9, and 93.8% of these values, respectively. This indicates a difference of >30%of dose a8 A, among the different patches (Table 11) that cannot be attributed to the degradation of timolol in skin. Chandrasekaran, Bayne, and Shawl9 showed that percutaneous scopolamine absorption is well explained by the model where two mechanisms [ ( I ) a simple dissolution producing mobile and freely diffusible molecules and (2) an adsorption process producing nonmobile moleculeel are postulated to occur. However, whether the dose dependency of timolol occurs by the same mechanisms as does that of eoopolarnine is not clear from the current study. The steady1018 I Journal of Pharmaceutical Sciences Vd. 79, No. 11, November 1990
state timolol permeation kinetics determined by equilibrating the epidermis with drug solutions of known concentratiom20 may reveal more detailed mechanisms. In addition, it also awaits further in vivo studies to assess whether similar dose dependency is also observed clinically. Until these issues are scrutinized, the values for kd and Id in Table I should be interpreted carefully. The new method to estimate the diffusion and partition parameters from a finite dose, in vitro drug permeation study advocated in this article is a robust one. When using the well-known parameters which have been employed in steadystate kinetics, the diffusion and partition parameters k d and ld can be calculated as k d = (1/6TL)6J8and ld = P / k d , I 3 where TL and P are lag time and permeability constants, respectively, both of which are estimated from the J,-time profile. However, in the preliminary study we found it is sometimes very difficult to estimate those values exclusively from Jmtime profiles following finite doses of timolol.8 The estimated parameter values (particularly the partition parameter 1,) often show a great intraindividual variance even if several neighboring pieces of the same skin are employed (data not shown). On the other hand, in the method proposed herein, the experimental error does not cause serious derangement of the AUC,,, AUC,,", andA,(a) values in eqs 14 and 16, and the estimated parameter values should be more reliable than those estimated exclusively from the J,-time profiles. To fully appreciate the effect a formulated drug has on the skin barrier function and the relationship thereof to the a b sorbed amount upon repeated application of an ointment21-29 it would be helpful to know the amount of drug in the skin attained after the application of a single finite dose under in vitm conditions. Similarly, to resolve the debate on the dilution of the commercially available topical corticosteroid ointment,= in vitm study of the dose and/or concentration dependency of a drug applied on the skin may provide valuable information. The new method proposed in this article could be used for other drugs, besides tirnolol, to address these clinically important issues.
References and Notes 1. Scheuplein, R. J. J . Invest. Dermatol. 1965,45,334-346. 2. Scheuplein, B. J.; Blank, I. H.; Brauner, G. J.; MacFarlane,D. J. J . Invest. Dermatol. 1969.52, 63-70. 3. Blank, I. H.; McAuliffe, D. J. J . Invest. Dermatol. 1985, 85, 522-4526. 4. Okamoto, H.; Haahida, M.; Sezaki, H. J . Pharm. Sci. 1988, 77, 41-24. 5. Flynn, G. L.; Stewart,B. Drug Dev. Res. 1988,13, 169-185. 6. Monkhouse, D. C.; Huq, A. S. Drug Dev. I d . Pharm. 1988,14, 183-209. 7. Ridout, G.; Santua, G. C.; Guy, R. H. Clin. Pharmacokinet. 1988, 15.114-131. 8. Okamoto,H.; Yamaahita, F.; Saito, K.; Haahida, M. Phurmuceut. Res. 1989, 6, 931-937. 9. Friahman, W. H. N. Eng. J . Med. 1982,306, 145C1462. 10. Vlamea, P. H.; Ribeiro, L. C. T.; Rotmenach, H. H.; Bondi, J. V.; Loper, A. E.; Hichene, M.; Dunlay, M. C.; Fergueon, R. K. J . Cardwvasc. Pharmacol. 1985, 7,245-250. 11. Benet, L. 2.;Galeazzi, R. L. J . Phunn. Sci. 1979,68, 1071-1074.
12. Yamaoka, K.; Nakagawa, T.; Uno, T. J. Pharmacokinet. Biopharm. 1978,6,547-558. 13. Kubota, K.; Ishizaki, T. J.Pharmucokinet. Biophurm. 1986,14, 409-439. 14. Kubota, K.; Yamada, T.; Ogura, A.; Ishizaki, T. J . Phurm. Sci. 1990, 79, 179-184. 15. Bronaugh, R. L.; Stewart, R. F. J . Phurm. Sci. 1985, 74,64-67. 16. Lefebvre, M. A.: Girault, J. J.LW. Chromutogr. 1981,4,483-500. 17. Jetzer, W. E.; Huq, A. S.;Ho, N. F. H.; F1ynn;G. L. J.Phurm. Sci. 1986, 75, i o g a i i o 3 . 18. Scheuplein, R. J.; Blank, I. H. Physwl. Rev. 1971,51,702-747. 19. Chandrasekaran, S. K.; Bayne, W.; Shaw, J. E. J. Pharm. Sci. 1978,67, 1370-1374.
20. Chandrasekaran, S. K.; Michaels, A. S.;Campbell, P. S.; Shaw, J. E. Am. Inst. Chem. Eng. J . 1976,22,828-832. 21. Courtheoux, S.; Pechenot, D.; Bucks, D. A.; Marty, J. P.; Maibach, H. I.; Wepierre, J. Br. J. DermatoI. (Suppl.) 1986, 115, 4952. 22. Bucks, D. A. W.; Maibach, H. I.; Guy, R. H. J.Phurm. Sci. 1985, 74,1337-1339. 23. Bucks, D. A. W.; Maibach, H.I.; Guy, R. H. In Percutaneous Absorption, 2nd ed., Bronaugh, R. L.;Maibach, H. I., Eds; Marcel Dekker: New York, 1989; pp 633-651. 24. Cornarakis-Lentzos, M.; Cowin, P. R. J. Phurmuceut. Biomed. Anal. 1987,5, 707-716.
Journal of Pharmaceutical Sciences I 1019 Voi. 79, No. 11, November 1990