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Design and Evaluation of Sustained-Release Tablets of Lithium in a Fat Matrix and Its Bioavailability in Humans
Design and Evaluation of Sustained-Release Tablets of Lithium in a Fat Matrix and Its Bioavailability in Humans M. LLABR~S' AND J. 8.FARINA Received August 9, 1988, from the Departamento de Ingenieria Quimica y Tecnologia Farmadutica, Facultad de Farmacia, Accepted for publication January 17, 1991. Universidad de La Laguna, 38200 La Laguna, Tenerife, Spain. Abstract 0 The development of sustained-release lithium (Li) tablets, intended to release the active principleat a rate of 1.OmM/h for 10 h, was undertaken. The parameters used for the control of the releasewere the glycerilpalmite-stearatecontent, the carboxypolymethylene content, and the compression force. The experimental design is based on Hadamard's matrices and is of the adaption by stages type. The formulation seen as optimal from in vitro assays was later assessed in vivo by a crossover study of six subjects. The parameters used to measure the bioavailability were the total amount of Li excreted in the urine in the 96 h following ingestion,the maximum urinary excretion rate, and the time at which this rate was reached. The acceptability interval for the first two parameters was established from the theoretical curve of urinary excretion, which was calculatedby convolution of the desired in vivo release variable (1.O mM/h for 10 h) by the absorption-dispositionvariable obtained after administering the preparation in Li carbonate capsules. The results obtained show that the bioavailability of the formulation is 75% of the immediate-release formulationused as control and that the release rate, although close to the desired value, lasts only 7 or 8 h; these results agree with those given by numerical deconvolution using the mean urinary excretion curves.
Lithium has a long half-life, but it i s characterized by a relatively rapid absorption rate as compared w i t h the distribution rate; this leads t o steady-state plasma levels greater than the tolerable maximum concentration. For this reason, the use o f sustained- or controlled-release oral dosage forms has been recommended.13 This article describes the development and the results o f a single-dose, in vivo evaluation of some fat matrix, sustainedrelease tablets of lithium intended to release lithiumat a rate of 1.0 mhVh for 10 h. The first stage o f the development was the in v i t r o optimization o f the release rate, assuming the release rate to be equal in vivo and in vitro under dissolution test conditions previously established.4 The second part consisted of a single-dose bioavailability assessment of the optimized formulation and verification o f in v i t r o release test. The suitability o f this release rate for multiple-dose therapy and the pharmacokinetic background of the bioavailability assessment have been discussed elsewhere.4.5
glyceryl palmite stearate content; P(2), the carboxypolymethylene content; and P(3), the compression force. The coded levels for each factor were given in the appropriate Hadamard 4 x 4 matrix9
1 1 1 1 1 1 -1 -1 1 -1 1-1 1 - 1 -1 1 where 1 and -1 denote the upper and lower levels of each factor. When this strategy is applied, there are two alternatives. If there is no record of previous experience on the subject, the levels of each factor should coincide with the extreme values that each factor can take, according to the process under study. If, however, earlier data indicating the position of the optimum point are available, the limits of each factor under study should be centered on that point. In this instance, we had some information obtained from assays carried out while the manufacturing method was being perfected, so we adopted the second strategy, establishing the following values for each factor. PU), 260-300 mg; P(2),22-31 mg; P(3),605-977 Kp. In this way, four formulations were prepared and coded, ae shown in Table I. Two batches of formulation F-2 were made in order to assess both the reproducibility of the manufacturing process and in vitro dissolution test. These two batches were coded as F-2 and F-2B. For subsequent calculation of the B values, the average results of these two batches were used. From the mean releasdissolution rates, the effects of each technological factor under study may be calculated using the following equations:
(4)
Experimental Section Design of the Formulations-"he formulations were of the fat matrix type, based on glyceryl palmite-stearate (Precirol Ato, Gatfosse) and carboxypolymethylene (Carbopol 940, Acofarma). Their manufacture basically consisted of melting the glyceryl palmitestearate a t 50 "C, adding lithium carbonate until evenly dispersed throughout the mass, cooling to a dough-like consistency, granulating, and sieving. Pre-sieved carboxypolymethylene (sieve aperture, 0.4 mm), talcum, and magnesium stearate were added to the granulometric fraction (collected between the I- and 0.4-mm sieve sizes). The granulate thus obtained was compressed in a double, singlepunch eccentric tablet press, with 12 mm 4 punches and a system to measure compression force.6 In the search for the optimum composition, an adaptative design by stages was used with three factors being taken into account: PO), the 1012 I Journal of Pharmaceutical Sciences Vol. 80, No. 11, November 1991
Table CComposltion of the Formulations Studiedm 1st Step
Variable Precirol, mg Carbopol 940, mg Lithium carbonate, mg Talc, mg Magnesium stearate, mg Compressionforce, kgf
2nd Step
F-1
F-2
F-3
F-4
F-5
300 31 400 26 12 977
300 22 400 26 12 605
260 31 400 26 12 605
260 22 400 26 12 977
340 40 400 26 12 1350
a The first, second, and sixth variables were used for control release rate purposes.
0022-3549/91/1100-1012$02.50/0 0 1 9 9 1, American Pharmaceutical Association
where q l ) , 8(2), and e(3) are the effects due to the glyceryl palmite stearate content, the carboxypolymethylene content, and the compression force, respectively, and Y(i) is the mean dissolution rate for the ith formulation (i = 1 to 4), which were coded F-1 to F-4, respectively. Once the 0 coefficients had been calculated, the levels of the technological factors could be modified to increase or decrease the release rate. Dissolution Tests-Apparatus I* was used at 100 rpm, with 0.1 M HC1 + 1 O/OO polysorbate 80 as the dissolution medium. As will be discussed below, all the formulations assayed release the active principle following almost zero-order kinetics. However, to avoid problems arising from the different release kinetics of the various formulations, the mean dissolution or release rate was expressed by the quotient between the whole amount dissolved and the length of the assay (8 h). The rationale of this approach was given in an earlier article.9 Analytical Method-Both the dissolution assay samples and the urine samples from the bioavailability assay were evaluated by atomic absorption spectrophotometry (Perkin Elmer, model 603) at 335.8 nm, using an acetylene-air flame. The apparatus was calibrated with a three-point calibration curve for each series of data, When necessary, the samples were diluted with deionized water. Bioavailability Assay-The formulation selected from the dissolution assays (F-5B) was evaluated in vivo in a crossover assay on six volunteers of both sexes, aged 21 to 28 years and randomly distributed in two groups. Lithium carbonate capsules (2 x 200 mg), which utilized the same lot of active ingredient employed to make the sustained-release tablets, were employed a8 reference and coded (3-2. They dissolved almost instantly when 0.1 M HCl was the dissolution medium. The formulation was administered at 8 a.m. with fruit juice, and no food was taken for the 4 h following administration. Urine samples were taken at 1-h intervals for the frst 6 h, every 2 h for the following 6 h, and every 12 h until 96 h in all had elapsed. The parameters used to evaluate the bioavailability were the total amount of lithium excreted in the urine in the 96 h following ingestion [Xu(mar), mM1, the maximum urinary excretion rate observed (V(mar),mM/h), and the time at which this rate was observed (tmax),h). For the statistical evaluation of the bioavailability assay results, the method of Mandallaz and Maul0 was applied. This made it possible to determine the a posteriori probability of the quotient (R) between the means of any given parameter for C-2 and the formulation under assay being found within the following acceptability limits:
P (L(1) IR IL(2))
(5)
where L(1) and L(2) are the lower and upper limits of the interval, respectively. For the parameter Xu(mar), the acceptability limits of R were taken were as f0.75, 1.253. The acceptability limits of the parameter V(,,,=) established in terms of the theoretical value expected for the curve
resulting from the convolution of the desired gastrointestinal release variable (release rate = 1.0 mM/h for 10 h) by the absorptiondisposition variable, as estimated by nonlinear regression11from the mean urinary excretion curve obtained after administering an instant-release formulation.5 As the tCmar)can only be expressed in discrete values, the nonparametric test proposed by Koch" was used. The gastrointestinal release rate was estimated by the numerical deconvolution method proposed by Veng-Pedersen,l3 modified so as to allow the amount of drug released immediately to be estimated and to set limits on the release duration.6
Results and Discussion At the beginning, we had no information about the in vivo-in vitro correlations of this type of lithium tablet to go on and, consequently, no information about the conditions most suited to the optimization of the in vitro release rate. We decided, therefore, to use the same conditions obtained in an earlier bioavailability trial of lithium tablets in which we got a good in vivo-in vitro correlation.4 These conditions, which are described in the paragraph above, were employed until in vivo data were available to validate it. Figure 1shows the mean curves of six experiments for each of the formulations assayed, and Table I1 gives the mean dissolution rates obtained. The four formulations show release rates slightly higher than the desired value, the differences observed between formulations being similar to that between the two batches of the F-2 formulation. The values computed for the coefficients of the technological factors (eqs 2 4 ) are very close to zero "1) = 0.05; 8(2) = 0.005;eI3) = 0.011; that is, a flat region in the response surface has been reached. In order to extend the experimental field, two simple oppositestrategies are possible. First, to reduce all the process variables to the minimum value, which will lead to an increase in the release rate until values similar to capsules are reached. Second, to increase all the process variables until reaching the maximum values permitted by the manufacturing process and tablet press used. We have taken the second way, and two batches of a fifth formulation, coded as F-5 and F-5B, were manufactured. The mean in vitro release rate of lithium was 1.0 mM/h (see Figure l b and Table 11). As all five formulations appear to be bioequivalent from in vitro results, we chose one of them, batch F-5B, for in vivo evaluation. Lot F-5B was evaluated in vivo by the bioavailability assay described above. Table 111 gives the values of the maximum amount of lithium excreted (X(max), mM), the maximum urinary excretion rate (V(max),mM/h), and the time a t which the maximum value was observed (t(max),h), per subject and formulation. Figures 2 and 3 show the mean
8 6
s v
0 . 4 2
2
4
TIME (HOURS)
6
8
2
4
6
8
TIME (HOURS)
Flgure +Mean dissolution curves for the seven formulations assayed. Each point is the average of six assays. The dotted line indicates a zero-order process with a rate of 1 mM/h. A: (V)F-1; (A) F-2; (0)F-2B; (U) F-3; (0)F-4; B: (0)F-5; (W) F-58. Journal of Pharmaceutical Sciences / 1013 Vol. 80, No. 11, November 1991
Table il-Statlstical Descrlptlon of the Flndings of the Dlsaolutlon Tests for Formulations F-1-F-5'
Formulation
Mean
o.6
SD
Max.
Min.
0.0749 0.0511 0.0335 0.0966
1.35 1.29 1.18 1.25 1.25 1.08 1.16
1.11 1.14 1.09 0.99 0.98
1
1
~
1.19 1.21 1.12 1.07 1.08 0.95 1.04
F-1 F-2 F-2B F-3 F-4 F-5 F-5B
0.0950 0.0741 0.0708
0.88 0.99 -
All values expressed as mM/h.
Tsbie Ill-Bloavallablllty Assays Resultsa c-2
Subject Sequence
F-58 0
t(max)'
~ ( m s x ) v~m a x ) b
1 3 6 2 4 5
F-5B:C-2
-
-
C-2:F-58
-
10.5 10.8 10.7 10.2 13.2 12.4
0.889 1.33 1.13 0.690 0.922 1.13
2.5
+ma)'
6.11 10.4 8.11 7.15 9.01 10.3
0.5 2.5 2.5 2.5 1.5
vmax)b
t(max?
0.327 0.616 0.397 0.374 0.406 0.490
7 7 7 7 7 7
0
I8
9
21
36
45
54
63
12
81
90
TIME (HOUaS)
Figure %Mean curve of urinary excretion rate for the formulation assayed (tablets F-5B). Key: (-) function resulting from convolution of eqs 6 and 7; (---) ideal rate excretion curve resulting from the convolution of the target release rate (rate = 1.O mM/h for 10 h) with eq 6.
a Maximum amount of lithium excreted in the urine (mM). Maximum urinary excretion rate (mM/h). 'Time of maximum urinary excretion (h).
Table IV-Mean, Standard Deviation, Mean Square Error, Acceptabillty Interval, and A Posterlorl Probablilty of Quotient between the Averages (R) Being wlthin the Acceptability Interval for the Maxlmum Amount of Lithium Excreted and the Maximum Urlnary Excretlon Rate
Parameter
Mean(*'Dl C-2
F-5B
'quare Error
11.3 8.51 1.28 (1.21) (1.72) Ymu)* 1.01 0.435 8.87 x mMol/h (0.226) (0.103)
Acceptability interval
R.
P
0.751.25
0.75 0.50
0.37-0.61b
0.43 0.88
mMol
a Quotient between the means of any given parameter. Normalized to relative bioavailability (0.75) and based on theoretical simulations.
as described above, giving the following for a 1.0-mM dose of lithium:
P
I -
0 ) I
I
I
1
0
9
18
21
I
36
I
I
I
45
54
63
I
1
T
72
81
90
TIHE (HOURS)
Flgure &Mean curve of urinary excretion rate for the control formulation (C-2) and nonlinear regression fit (continuous line; eq 6). The bars show the standard deviation of the mean.
urinary excretion curves for formulations C-2 (reference) and F-5B, respectively, together with the standard deviation of each point and the curves resulting from the fitted functions. Table IV summarizes the results of the descriptive statistics, the three-way ANOVA findings, and the evaluation of bioavailability using the Bayesian method cited above. The acceptability interval for the absorbed fraction in relation to the reference formulation, measured by the quotient between the total amounts of lithium excreted in the urine in the 96 h following administration, was established with a permissible variation of +25% (i.e., 0.75 5 R I1.25). As can be seen, the value found experimentally was 8.51/11.3 = 0.75 (F-5B/C-2), and the probability that this quotient is found within the acceptability limit was 0.50. The acceptability limit for V(,,,=) was obtained as follows. The mean urinary excretion curve obtained for the capsules was fitted to a triexponential function by nonlinear regression 1014 / Journal of Pharmaceutical Sciences Vol. 80, No. 7 7 , November 7997
Figure 2 shows the curve generated by this equation for a dose equal to that administered (10.7 mM).Figure 3 plots the theoretical curve for a gastrointestinal release rate equal to 1.0 mM/h over a period of 10 h, obtained by the convolution of the gastrointestinal release kinetics with eq. 6. The quotient between the Vcrnar)values attained for the two curves, sustained-release (F-5B) and instant-release (C-2), is 0.511 0.79 = 0.65. Moreover, the V(mar)depends linearly on the fraction of absorbed dosage, so the relation of the maxima should be corrected by the value found in the experiments (in this study, 0.751, giving a value of 0.49. If a n interval of 225% is built into this value, the acceptability interval will finally be 0.37-0.61. The probability of the quotient between the averages of the maximum rates being within this interval is 0.88 (see Table IV). As the t(rnax)can only assume discrete values, the same statistical analysis method as used for the other parameters cannot be applied. Kwh12 demonstrated that the nonparametric method of Wilcoxon can be used to analyze the results
from a crossover assay if the effects due to subject and assay times are null, a state which exists in this instance. From the Wilcoxon test, the null hypothesis for difference between the two formulations can be discounted. The mean value for this difference is 4.5h and the 95% confidence interval, calculated by means of the method described by Cornell,14 is 4.5-5.5h. The confidence interval for the difference between the averages of does not include the desired value, -8 h (see Figure 3). However, the quotient between the mean maximal rates is found with a relatively high probability within the acceptability interval. From this we may deduce that the release time is less than desired and/or the release rate is not constant and equal to 1.0 &. The experimental variations of the individual urinary excretion curves precluded their interpretation by pharmacokinetic methods. In spite of having to treat the conclusions drawn from the pharmacokinetic analysis of mean curves with reserve, we decided to estimate the gastrointestinal release variable using the method given above. The best fit was found for the following polynomial in vivo release variable:
X(c) = 0.37 + 0.98 t - 0.031 * @, when 0 It 5 18
(7)
where X(c) is the amount of lithium released in vivo, expressed in millimoles, a t time t, expressed in hours. The maximum value of this equation is 8.1 mM, very close to the estimated average for the total amount of lithium excreted in the urine for formulation F-5B. Figure 3 sets out the curve resulting from the convolution of eq 6 and 7. The determination coefficient (?)la is 0.994, which demonstrates the good fit of the variable to the experimental points, except for those points in the time interval 7-11 h. In this interval, an abrupt change of urinary excretion rate occurs which cannot be interpreted by a low-order polynomial variab1e; using high-order polynomials did not solve the problem since both the release rate and that obtained by convolution showed unlikely fluctuations. While the data obtained do not lend themselves to an in vivwin vitro correlation as such, the mean release rates could be compared. The in vitro mean release rate was equivalent to 1.04mM/h of lithium over a period of 8 h (Table 111). The mean in vivo release rate for the same period could be calculated from eq 7 and was shown to be 0.77 mM/h of lithium. Hence, the next step in the optimization p m s s would be to establish an in vitro release rate equal to 1.04/0.77 (i.e., 1.35 mhW. The fact that the in vivo release rate was lower than the figure originally set does not mean that the formulation must be rejected. It is well known that the release-absorption rate and the parameters of disposition kinetics control plasma level fluctuations in the equilibrium, while the mean concentration in the equilibrium is determined by the fraction of dose absorbed, the dose administered, plasma clearance, and the interdosage time interval. Hence, any in vivo release rate below the value needed to keep the plasma level-time fluctuations within the therapeutic interval may be accepted so long as the fraction of absorbed dose is not affected. The findings of this study show the potential of fat-matrix tableta for prolonging the release process. The processes controlling the release of the active principle are complex, including diffusion through the matrix and erosion of the tablet. The porosity of the matrix is due to its carboxypolymethylene content, and this is an excipient which shows pH-dependent gelification. Moreover, one cannot talk of a defined process controlling the release, but, nonetheless, it is possible to reduce the rele ise rate without causing an appreciable increase in the variability of the parameters used to
measure the bioavailability. The problem in the development of a sustained-release formulation is not knowing how the technological factors influence the in vivo release and the in vivo-in vitro correlations. Although both these considerations can be tackled,1618 it requires the evaluation both in vivo and in vitro of groups of formulations made up in accordance with an experimental design, and this is not always feasible. Leeson et al.19 devised an alternative strategy based on four steps: namely, “First, developing one or more formulations which demonstrate a slow release pattern in vitro. Second, studying the system(s)from Step 1 in man and evaluating the resulting plasma level curves. Third, accepting a dosage form if it produced what is defined as an acceptable plasma level cuwe. Fourth, returning to step 1 if no dosage form is considered to be acceptable.” Ifthe in vitro release kinetics required for the first step are defined, and an experimental design is used in the develop ment of formulations which interprets the release rate in terms of the technological factors used to control it, this strategy can be considerably improved upon. This way, if none of the formulations made up meets the in vivo acceptability conditions, one would a t least have relevant information about the relationship between the in vitro release rate and the technological variables used to control the release, as well as about the in vivo-in vitro release relationship. Thus, the first step should be to establish the target release function (i.e., an in vivo release kinetic which permits one to reach drug plasma levels a t steady state in the therapeutic range). To establish such a function, two conditions must be kept in mind. First, the mean absorption rate must be equal to mean plasma levels a t steady state by drug plasma clearance. Second, the maximum time available for release and absorption depends on both the intestinal transit rate of the dosage form and the length of gastrointestinal tract available for absorption. If there is some previous information about the in vivo-in vitro release rate relationship, a provisional target release rate for in vitro development can be established. Another factor which affects this performance of the strategy is the number of formulations to be made up per cycle; in other words, the most suitable experimental design. Obviously if none of the formulations assayed meeta the bioavailability requirements, both the composition of the formulations and the originally assumed in vivo-in vitro correlations must be reassessed. Thus, it appears preferable to increase the number of approximation cycles and reduce the number of formulations made up each time. Experimental designs based on Hadamard matrices, a particular instance of L”-type fractionated factorial designs, are thus more useful than complex designs, such as central composite rotable designs which, while they enable the in vitro release rate to be studied in detail, also require numerous formulations. The designs based on Hadamard matrices have certain limitations when it comes to interpreting the response, as this is assumed to be an increasing or decreasing monotonous function of the variables under study with no interaction taking place between them. The dimensions of Hadamard matrices are also multiples of four. However, the fact that these design-ptimal with the least possible number of assays-can be used7 make this design particularly suitable for this sort of optimization process.
References and Notes 1. Amideen, A. Clin. Phurmacokinet. 1977,2, 73-92. 2. Nielsen-Kudsk, F.; Amdisen, A. Eur. J . Clin. Phrmncokinet. 1978,16, 271-277. 3. Gaillot, V.; Steimer, J. L.; Mallet, A. J.;Thebault, J. J.; Biecher, A. J. J . Phurmacokinet. Biophnrm. 1979, 7, 57-28,
Journal of Pharmaceutical Sciences I 1015 Vol. SO, No. 1 1 , November 1991
4. LlabrBs, M.; Farina, J. B. Drug Dev. Ind. Pharm. 1989, 15, 1827-1841. 5. Llabrbs, M.; Farina, J . B.; Shchez, E.; Evora, C. M. Proceedings 5thInt. ConferenceonPharmaceutical Technology, Vol. 111;Pans, 1989;pp 213-213. 6. Farina, J. B.; Luengo, M., Sdnchez, V.; Llabrbs, M. C J J . 1986,5, 3-6. 7. Hedayat, A.; Wallis, W. D. Ann. Statistics 1978,6,1184-1214. 8. The United States Pharmacopeia, 21st Rev. Mack: Easton, PA, 1985. 9. Farina, J. B.;Llabrbs, M. Drug Dev. Ind. Pharm. 1987, 13, 1107-1118. 10. Mandallaz, D.; Mau, J. Biometrics 1981,37,213-222. 11. Jenrich, R. In BMDP Statistical Soflware; Dixon, W. J., Ed.; University of California: Berkeley, CA, 1981;pp 290404.
1016 I Journal of Pharmaceutical Sciences Vol. 80, No. 1 7 , November 1991
12. Koch, G.G.Biometrics 1972,28,577.-584. 13. Veng-Pederaen, P. J. Pharm. Sci. 1980,69, 312-318. 14. Cornell, R.G. In Drug Abso tion and Dis sition: Statistical Considerations;Albert, K. S.,Fd.; A.Ph.A.: a h i n g t o n , 1980;pp 5147. 15. Draper, N.; Smith, H. Applied Regression Analysis, 1st Ed.; J . Wiley & Sons; New York, 1981;pp 458-517. 16. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J.Pharm. Sci.1982, 71,924-927. 17. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J . Pharm. Sci. 1982, 71,927-930. 18. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J.Pharm. Sci.1982, 71,930-933. 19. Leeson, L. J.; Adair, D.; Clevenger, J.; Chiang, N. Pharmacokinet. Biophnrm. 1985,13,493-514.
Lithium has a long half-life, but it i s characterized by a relatively rapid absorption rate as compared w i t h the distribution rate; this leads t o steady-state plasma levels greater than the tolerable maximum concentration. For this reason, the use o f sustained- or controlled-release oral dosage forms has been recommended.13 This article describes the development and the results o f a single-dose, in vivo evaluation of some fat matrix, sustainedrelease tablets of lithium intended to release lithiumat a rate of 1.0 mhVh for 10 h. The first stage o f the development was the in v i t r o optimization o f the release rate, assuming the release rate to be equal in vivo and in vitro under dissolution test conditions previously established.4 The second part consisted of a single-dose bioavailability assessment of the optimized formulation and verification o f in v i t r o release test. The suitability o f this release rate for multiple-dose therapy and the pharmacokinetic background of the bioavailability assessment have been discussed elsewhere.4.5
glyceryl palmite stearate content; P(2), the carboxypolymethylene content; and P(3), the compression force. The coded levels for each factor were given in the appropriate Hadamard 4 x 4 matrix9
1 1 1 1 1 1 -1 -1 1 -1 1-1 1 - 1 -1 1 where 1 and -1 denote the upper and lower levels of each factor. When this strategy is applied, there are two alternatives. If there is no record of previous experience on the subject, the levels of each factor should coincide with the extreme values that each factor can take, according to the process under study. If, however, earlier data indicating the position of the optimum point are available, the limits of each factor under study should be centered on that point. In this instance, we had some information obtained from assays carried out while the manufacturing method was being perfected, so we adopted the second strategy, establishing the following values for each factor. PU), 260-300 mg; P(2),22-31 mg; P(3),605-977 Kp. In this way, four formulations were prepared and coded, ae shown in Table I. Two batches of formulation F-2 were made in order to assess both the reproducibility of the manufacturing process and in vitro dissolution test. These two batches were coded as F-2 and F-2B. For subsequent calculation of the B values, the average results of these two batches were used. From the mean releasdissolution rates, the effects of each technological factor under study may be calculated using the following equations:
(4)
Experimental Section Design of the Formulations-"he formulations were of the fat matrix type, based on glyceryl palmite-stearate (Precirol Ato, Gatfosse) and carboxypolymethylene (Carbopol 940, Acofarma). Their manufacture basically consisted of melting the glyceryl palmitestearate a t 50 "C, adding lithium carbonate until evenly dispersed throughout the mass, cooling to a dough-like consistency, granulating, and sieving. Pre-sieved carboxypolymethylene (sieve aperture, 0.4 mm), talcum, and magnesium stearate were added to the granulometric fraction (collected between the I- and 0.4-mm sieve sizes). The granulate thus obtained was compressed in a double, singlepunch eccentric tablet press, with 12 mm 4 punches and a system to measure compression force.6 In the search for the optimum composition, an adaptative design by stages was used with three factors being taken into account: PO), the 1012 I Journal of Pharmaceutical Sciences Vol. 80, No. 11, November 1991
Table CComposltion of the Formulations Studiedm 1st Step
Variable Precirol, mg Carbopol 940, mg Lithium carbonate, mg Talc, mg Magnesium stearate, mg Compressionforce, kgf
2nd Step
F-1
F-2
F-3
F-4
F-5
300 31 400 26 12 977
300 22 400 26 12 605
260 31 400 26 12 605
260 22 400 26 12 977
340 40 400 26 12 1350
a The first, second, and sixth variables were used for control release rate purposes.
0022-3549/91/1100-1012$02.50/0 0 1 9 9 1, American Pharmaceutical Association
where q l ) , 8(2), and e(3) are the effects due to the glyceryl palmite stearate content, the carboxypolymethylene content, and the compression force, respectively, and Y(i) is the mean dissolution rate for the ith formulation (i = 1 to 4), which were coded F-1 to F-4, respectively. Once the 0 coefficients had been calculated, the levels of the technological factors could be modified to increase or decrease the release rate. Dissolution Tests-Apparatus I* was used at 100 rpm, with 0.1 M HC1 + 1 O/OO polysorbate 80 as the dissolution medium. As will be discussed below, all the formulations assayed release the active principle following almost zero-order kinetics. However, to avoid problems arising from the different release kinetics of the various formulations, the mean dissolution or release rate was expressed by the quotient between the whole amount dissolved and the length of the assay (8 h). The rationale of this approach was given in an earlier article.9 Analytical Method-Both the dissolution assay samples and the urine samples from the bioavailability assay were evaluated by atomic absorption spectrophotometry (Perkin Elmer, model 603) at 335.8 nm, using an acetylene-air flame. The apparatus was calibrated with a three-point calibration curve for each series of data, When necessary, the samples were diluted with deionized water. Bioavailability Assay-The formulation selected from the dissolution assays (F-5B) was evaluated in vivo in a crossover assay on six volunteers of both sexes, aged 21 to 28 years and randomly distributed in two groups. Lithium carbonate capsules (2 x 200 mg), which utilized the same lot of active ingredient employed to make the sustained-release tablets, were employed a8 reference and coded (3-2. They dissolved almost instantly when 0.1 M HCl was the dissolution medium. The formulation was administered at 8 a.m. with fruit juice, and no food was taken for the 4 h following administration. Urine samples were taken at 1-h intervals for the frst 6 h, every 2 h for the following 6 h, and every 12 h until 96 h in all had elapsed. The parameters used to evaluate the bioavailability were the total amount of lithium excreted in the urine in the 96 h following ingestion [Xu(mar), mM1, the maximum urinary excretion rate observed (V(mar),mM/h), and the time at which this rate was observed (tmax),h). For the statistical evaluation of the bioavailability assay results, the method of Mandallaz and Maul0 was applied. This made it possible to determine the a posteriori probability of the quotient (R) between the means of any given parameter for C-2 and the formulation under assay being found within the following acceptability limits:
P (L(1) IR IL(2))
(5)
where L(1) and L(2) are the lower and upper limits of the interval, respectively. For the parameter Xu(mar), the acceptability limits of R were taken were as f0.75, 1.253. The acceptability limits of the parameter V(,,,=) established in terms of the theoretical value expected for the curve
resulting from the convolution of the desired gastrointestinal release variable (release rate = 1.0 mM/h for 10 h) by the absorptiondisposition variable, as estimated by nonlinear regression11from the mean urinary excretion curve obtained after administering an instant-release formulation.5 As the tCmar)can only be expressed in discrete values, the nonparametric test proposed by Koch" was used. The gastrointestinal release rate was estimated by the numerical deconvolution method proposed by Veng-Pedersen,l3 modified so as to allow the amount of drug released immediately to be estimated and to set limits on the release duration.6
Results and Discussion At the beginning, we had no information about the in vivo-in vitro correlations of this type of lithium tablet to go on and, consequently, no information about the conditions most suited to the optimization of the in vitro release rate. We decided, therefore, to use the same conditions obtained in an earlier bioavailability trial of lithium tablets in which we got a good in vivo-in vitro correlation.4 These conditions, which are described in the paragraph above, were employed until in vivo data were available to validate it. Figure 1shows the mean curves of six experiments for each of the formulations assayed, and Table I1 gives the mean dissolution rates obtained. The four formulations show release rates slightly higher than the desired value, the differences observed between formulations being similar to that between the two batches of the F-2 formulation. The values computed for the coefficients of the technological factors (eqs 2 4 ) are very close to zero "1) = 0.05; 8(2) = 0.005;eI3) = 0.011; that is, a flat region in the response surface has been reached. In order to extend the experimental field, two simple oppositestrategies are possible. First, to reduce all the process variables to the minimum value, which will lead to an increase in the release rate until values similar to capsules are reached. Second, to increase all the process variables until reaching the maximum values permitted by the manufacturing process and tablet press used. We have taken the second way, and two batches of a fifth formulation, coded as F-5 and F-5B, were manufactured. The mean in vitro release rate of lithium was 1.0 mM/h (see Figure l b and Table 11). As all five formulations appear to be bioequivalent from in vitro results, we chose one of them, batch F-5B, for in vivo evaluation. Lot F-5B was evaluated in vivo by the bioavailability assay described above. Table 111 gives the values of the maximum amount of lithium excreted (X(max), mM), the maximum urinary excretion rate (V(max),mM/h), and the time a t which the maximum value was observed (t(max),h), per subject and formulation. Figures 2 and 3 show the mean
8 6
s v
0 . 4 2
2
4
TIME (HOURS)
6
8
2
4
6
8
TIME (HOURS)
Flgure +Mean dissolution curves for the seven formulations assayed. Each point is the average of six assays. The dotted line indicates a zero-order process with a rate of 1 mM/h. A: (V)F-1; (A) F-2; (0)F-2B; (U) F-3; (0)F-4; B: (0)F-5; (W) F-58. Journal of Pharmaceutical Sciences / 1013 Vol. 80, No. 11, November 1991
Table il-Statlstical Descrlptlon of the Flndings of the Dlsaolutlon Tests for Formulations F-1-F-5'
Formulation
Mean
o.6
SD
Max.
Min.
0.0749 0.0511 0.0335 0.0966
1.35 1.29 1.18 1.25 1.25 1.08 1.16
1.11 1.14 1.09 0.99 0.98
1
1
~
1.19 1.21 1.12 1.07 1.08 0.95 1.04
F-1 F-2 F-2B F-3 F-4 F-5 F-5B
0.0950 0.0741 0.0708
0.88 0.99 -
All values expressed as mM/h.
Tsbie Ill-Bloavallablllty Assays Resultsa c-2
Subject Sequence
F-58 0
t(max)'
~ ( m s x ) v~m a x ) b
1 3 6 2 4 5
F-5B:C-2
-
-
C-2:F-58
-
10.5 10.8 10.7 10.2 13.2 12.4
0.889 1.33 1.13 0.690 0.922 1.13
2.5
+ma)'
6.11 10.4 8.11 7.15 9.01 10.3
0.5 2.5 2.5 2.5 1.5
vmax)b
t(max?
0.327 0.616 0.397 0.374 0.406 0.490
7 7 7 7 7 7
0
I8
9
21
36
45
54
63
12
81
90
TIME (HOUaS)
Figure %Mean curve of urinary excretion rate for the formulation assayed (tablets F-5B). Key: (-) function resulting from convolution of eqs 6 and 7; (---) ideal rate excretion curve resulting from the convolution of the target release rate (rate = 1.O mM/h for 10 h) with eq 6.
a Maximum amount of lithium excreted in the urine (mM). Maximum urinary excretion rate (mM/h). 'Time of maximum urinary excretion (h).
Table IV-Mean, Standard Deviation, Mean Square Error, Acceptabillty Interval, and A Posterlorl Probablilty of Quotient between the Averages (R) Being wlthin the Acceptability Interval for the Maxlmum Amount of Lithium Excreted and the Maximum Urlnary Excretlon Rate
Parameter
Mean(*'Dl C-2
F-5B
'quare Error
11.3 8.51 1.28 (1.21) (1.72) Ymu)* 1.01 0.435 8.87 x mMol/h (0.226) (0.103)
Acceptability interval
R.
P
0.751.25
0.75 0.50
0.37-0.61b
0.43 0.88
mMol
a Quotient between the means of any given parameter. Normalized to relative bioavailability (0.75) and based on theoretical simulations.
as described above, giving the following for a 1.0-mM dose of lithium:
P
I -
0 ) I
I
I
1
0
9
18
21
I
36
I
I
I
45
54
63
I
1
T
72
81
90
TIHE (HOURS)
Flgure &Mean curve of urinary excretion rate for the control formulation (C-2) and nonlinear regression fit (continuous line; eq 6). The bars show the standard deviation of the mean.
urinary excretion curves for formulations C-2 (reference) and F-5B, respectively, together with the standard deviation of each point and the curves resulting from the fitted functions. Table IV summarizes the results of the descriptive statistics, the three-way ANOVA findings, and the evaluation of bioavailability using the Bayesian method cited above. The acceptability interval for the absorbed fraction in relation to the reference formulation, measured by the quotient between the total amounts of lithium excreted in the urine in the 96 h following administration, was established with a permissible variation of +25% (i.e., 0.75 5 R I1.25). As can be seen, the value found experimentally was 8.51/11.3 = 0.75 (F-5B/C-2), and the probability that this quotient is found within the acceptability limit was 0.50. The acceptability limit for V(,,,=) was obtained as follows. The mean urinary excretion curve obtained for the capsules was fitted to a triexponential function by nonlinear regression 1014 / Journal of Pharmaceutical Sciences Vol. 80, No. 7 7 , November 7997
Figure 2 shows the curve generated by this equation for a dose equal to that administered (10.7 mM).Figure 3 plots the theoretical curve for a gastrointestinal release rate equal to 1.0 mM/h over a period of 10 h, obtained by the convolution of the gastrointestinal release kinetics with eq. 6. The quotient between the Vcrnar)values attained for the two curves, sustained-release (F-5B) and instant-release (C-2), is 0.511 0.79 = 0.65. Moreover, the V(mar)depends linearly on the fraction of absorbed dosage, so the relation of the maxima should be corrected by the value found in the experiments (in this study, 0.751, giving a value of 0.49. If a n interval of 225% is built into this value, the acceptability interval will finally be 0.37-0.61. The probability of the quotient between the averages of the maximum rates being within this interval is 0.88 (see Table IV). As the t(rnax)can only assume discrete values, the same statistical analysis method as used for the other parameters cannot be applied. Kwh12 demonstrated that the nonparametric method of Wilcoxon can be used to analyze the results
from a crossover assay if the effects due to subject and assay times are null, a state which exists in this instance. From the Wilcoxon test, the null hypothesis for difference between the two formulations can be discounted. The mean value for this difference is 4.5h and the 95% confidence interval, calculated by means of the method described by Cornell,14 is 4.5-5.5h. The confidence interval for the difference between the averages of does not include the desired value, -8 h (see Figure 3). However, the quotient between the mean maximal rates is found with a relatively high probability within the acceptability interval. From this we may deduce that the release time is less than desired and/or the release rate is not constant and equal to 1.0 &. The experimental variations of the individual urinary excretion curves precluded their interpretation by pharmacokinetic methods. In spite of having to treat the conclusions drawn from the pharmacokinetic analysis of mean curves with reserve, we decided to estimate the gastrointestinal release variable using the method given above. The best fit was found for the following polynomial in vivo release variable:
X(c) = 0.37 + 0.98 t - 0.031 * @, when 0 It 5 18
(7)
where X(c) is the amount of lithium released in vivo, expressed in millimoles, a t time t, expressed in hours. The maximum value of this equation is 8.1 mM, very close to the estimated average for the total amount of lithium excreted in the urine for formulation F-5B. Figure 3 sets out the curve resulting from the convolution of eq 6 and 7. The determination coefficient (?)la is 0.994, which demonstrates the good fit of the variable to the experimental points, except for those points in the time interval 7-11 h. In this interval, an abrupt change of urinary excretion rate occurs which cannot be interpreted by a low-order polynomial variab1e; using high-order polynomials did not solve the problem since both the release rate and that obtained by convolution showed unlikely fluctuations. While the data obtained do not lend themselves to an in vivwin vitro correlation as such, the mean release rates could be compared. The in vitro mean release rate was equivalent to 1.04mM/h of lithium over a period of 8 h (Table 111). The mean in vivo release rate for the same period could be calculated from eq 7 and was shown to be 0.77 mM/h of lithium. Hence, the next step in the optimization p m s s would be to establish an in vitro release rate equal to 1.04/0.77 (i.e., 1.35 mhW. The fact that the in vivo release rate was lower than the figure originally set does not mean that the formulation must be rejected. It is well known that the release-absorption rate and the parameters of disposition kinetics control plasma level fluctuations in the equilibrium, while the mean concentration in the equilibrium is determined by the fraction of dose absorbed, the dose administered, plasma clearance, and the interdosage time interval. Hence, any in vivo release rate below the value needed to keep the plasma level-time fluctuations within the therapeutic interval may be accepted so long as the fraction of absorbed dose is not affected. The findings of this study show the potential of fat-matrix tableta for prolonging the release process. The processes controlling the release of the active principle are complex, including diffusion through the matrix and erosion of the tablet. The porosity of the matrix is due to its carboxypolymethylene content, and this is an excipient which shows pH-dependent gelification. Moreover, one cannot talk of a defined process controlling the release, but, nonetheless, it is possible to reduce the rele ise rate without causing an appreciable increase in the variability of the parameters used to
measure the bioavailability. The problem in the development of a sustained-release formulation is not knowing how the technological factors influence the in vivo release and the in vivo-in vitro correlations. Although both these considerations can be tackled,1618 it requires the evaluation both in vivo and in vitro of groups of formulations made up in accordance with an experimental design, and this is not always feasible. Leeson et al.19 devised an alternative strategy based on four steps: namely, “First, developing one or more formulations which demonstrate a slow release pattern in vitro. Second, studying the system(s)from Step 1 in man and evaluating the resulting plasma level curves. Third, accepting a dosage form if it produced what is defined as an acceptable plasma level cuwe. Fourth, returning to step 1 if no dosage form is considered to be acceptable.” Ifthe in vitro release kinetics required for the first step are defined, and an experimental design is used in the develop ment of formulations which interprets the release rate in terms of the technological factors used to control it, this strategy can be considerably improved upon. This way, if none of the formulations made up meets the in vivo acceptability conditions, one would a t least have relevant information about the relationship between the in vitro release rate and the technological variables used to control the release, as well as about the in vivo-in vitro release relationship. Thus, the first step should be to establish the target release function (i.e., an in vivo release kinetic which permits one to reach drug plasma levels a t steady state in the therapeutic range). To establish such a function, two conditions must be kept in mind. First, the mean absorption rate must be equal to mean plasma levels a t steady state by drug plasma clearance. Second, the maximum time available for release and absorption depends on both the intestinal transit rate of the dosage form and the length of gastrointestinal tract available for absorption. If there is some previous information about the in vivo-in vitro release rate relationship, a provisional target release rate for in vitro development can be established. Another factor which affects this performance of the strategy is the number of formulations to be made up per cycle; in other words, the most suitable experimental design. Obviously if none of the formulations assayed meeta the bioavailability requirements, both the composition of the formulations and the originally assumed in vivo-in vitro correlations must be reassessed. Thus, it appears preferable to increase the number of approximation cycles and reduce the number of formulations made up each time. Experimental designs based on Hadamard matrices, a particular instance of L”-type fractionated factorial designs, are thus more useful than complex designs, such as central composite rotable designs which, while they enable the in vitro release rate to be studied in detail, also require numerous formulations. The designs based on Hadamard matrices have certain limitations when it comes to interpreting the response, as this is assumed to be an increasing or decreasing monotonous function of the variables under study with no interaction taking place between them. The dimensions of Hadamard matrices are also multiples of four. However, the fact that these design-ptimal with the least possible number of assays-can be used7 make this design particularly suitable for this sort of optimization process.
References and Notes 1. Amideen, A. Clin. Phurmacokinet. 1977,2, 73-92. 2. Nielsen-Kudsk, F.; Amdisen, A. Eur. J . Clin. Phrmncokinet. 1978,16, 271-277. 3. Gaillot, V.; Steimer, J. L.; Mallet, A. J.;Thebault, J. J.; Biecher, A. J. J . Phurmacokinet. Biophnrm. 1979, 7, 57-28,
Journal of Pharmaceutical Sciences I 1015 Vol. SO, No. 1 1 , November 1991
4. LlabrBs, M.; Farina, J. B. Drug Dev. Ind. Pharm. 1989, 15, 1827-1841. 5. Llabrbs, M.; Farina, J . B.; Shchez, E.; Evora, C. M. Proceedings 5thInt. ConferenceonPharmaceutical Technology, Vol. 111;Pans, 1989;pp 213-213. 6. Farina, J. B.; Luengo, M., Sdnchez, V.; Llabrbs, M. C J J . 1986,5, 3-6. 7. Hedayat, A.; Wallis, W. D. Ann. Statistics 1978,6,1184-1214. 8. The United States Pharmacopeia, 21st Rev. Mack: Easton, PA, 1985. 9. Farina, J. B.;Llabrbs, M. Drug Dev. Ind. Pharm. 1987, 13, 1107-1118. 10. Mandallaz, D.; Mau, J. Biometrics 1981,37,213-222. 11. Jenrich, R. In BMDP Statistical Soflware; Dixon, W. J., Ed.; University of California: Berkeley, CA, 1981;pp 290404.
1016 I Journal of Pharmaceutical Sciences Vol. 80, No. 1 7 , November 1991
12. Koch, G.G.Biometrics 1972,28,577.-584. 13. Veng-Pederaen, P. J. Pharm. Sci. 1980,69, 312-318. 14. Cornell, R.G. In Drug Abso tion and Dis sition: Statistical Considerations;Albert, K. S.,Fd.; A.Ph.A.: a h i n g t o n , 1980;pp 5147. 15. Draper, N.; Smith, H. Applied Regression Analysis, 1st Ed.; J . Wiley & Sons; New York, 1981;pp 458-517. 16. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J.Pharm. Sci.1982, 71,924-927. 17. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J . Pharm. Sci. 1982, 71,927-930. 18. Llabrbs, M.; Vila, J. L.; Martinez-Pacheco, R. J.Pharm. Sci.1982, 71,930-933. 19. Leeson, L. J.; Adair, D.; Clevenger, J.; Chiang, N. Pharmacokinet. Biophnrm. 1985,13,493-514.