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Kinetics of a drug release from a delayed release device
PII:
Eur. Polym. J. Vol. 34, No. 9, pp. 1283±1293, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0014-3057/98/$ - see front matter S0014-3057(97)00264-4
KINETICS OF A DRUG RELEASE FROM A DELAYED RELEASE DEVICE ALI BICHARA,1,2 JEAN-PIERRE MONTHEARD1 and JEAN-LOUIS TAVERDET2* Laboratoire de Chimie Organique MacromoleÂculaire, Faculte des Sciences et Techniques, 23 Rue Dr Paul Michelon, 42023 Saint-Etienne Cedex 2, France and 2Laboratoire de Chimie et Environnement, Faculte des Sciences et Techniques, 23 Rue Dr Paul Michelon, 42023 Saint-Etienne Cedex 2, France
1
(Received 8 April 1997; accepted in ®nal form 3 July 1997) AbstractÐReaction of sodium salt of benzoic acid with methacryloyl chloride provides an anhydride which is polymerized by the radical method or copolymerized with various percentages of ethylene glycol dimethacrylate to obtain crosslinked products. Hydrolysis reactions of the resulting polymers were carried out in various aqueous solutions and the rate of release of benzoic acid (simulator of drug) seems to depend both on the percentages of crosslinking comonomer and on the pH of the solution. A model of this delayed release of benzoic acid is also proposed. # 1998 Elsevier Science Ltd. All rights reserved
INTRODUCTION
In order to increase the acceptability or ecacy of oral drug therapy, many drugs are presented as controlled release formulation. Several types of devices [1, 2] were used to obtain a controlled release of the organic drug: a drug delivery system may be a matrix of polymer incorporating the organic substance. This drug can be dispersed in the polymer or covalently linked to a polymeric backbone. The attachment of drug to a polymer can be carried out either by a chemical modi®cation of the polymer or, after grafting of the drug onto a monomer, by polymerization or copolymerization of this modi®ed monomer. The controlled release of pesticides in agriculture [3, 4] was also widely studied and used either in a dispersion±dissolution of the bioactive or in an encapsulation into a polymer matrix. Therefore the mechanism of release of the active agent can be explained by a hydrolysis reaction of the organic function when the product is linked to a polymer followed by a diusion in the aqueous medium. In this work, we report some results on the release of benzoic acid (a simulator of an active agent) linked to a methacrylic backbone by an anhydride function. This matrix was crosslinked with various percentages of ethylene glycol dimethacrylate (EDMA) and the time of release, in aqueous medium, basic or acidic, should depend both on the degree of crosslinking and on the pH of the solution. This type of device, called a delayed release system, helps to ensure release of the organic compound by the following two procedures: delayed release and continuous release. A mathematical model, based on a mass transfer coef®cient will be proposed and should allow an opti*To whom all correspondence should be addressed.
mal formulation according to a programmed release rate of the organic molecule. EXPERIMENTAL
Materials The IR spectra of both monomers and polymers were measured with an FT IR 7 Bio-Rad apparatus. Determination of the amount of benzoic acid released was carried out on a JASCO UV/Vis apparatus at the corresponding lmax of the protonated acid or of the sodium salt, in basic medium.
Chemicals Methacryloyl chloride (Aldrich) was distilled before use. EDMA, benzoic acid, tetrahydrofuran (THF) and azobisisobutyronitrile (AIBN) were used as received and distilled water was employed.
Preparation of the monomer A dry 100 ml 3-necked ¯ask equipped with a magnetic stirrer and a re¯ux condenser to which is attached a Drierite-Filled drying tube was used for this synthesis. The mixture of sodium salt of benzoic acid 2 (0.05 mol, 7.2 g) in 10 ml of anhydrous THF and of methacryloyl chloride 1 (0.05 mol, 5.22 g) in 5 ml of dry THF are added into the ¯ask kept between 3 or 68C. After the addition was complete (15 min) a gentle heating follows (during 20 min) and then the mixture was stirred during 4 h. The precipitate of NaCl was ®ltered and washed with dry THF. The solvent was removed from the ®ltrate in a rotary evaporator and the anhydride 3 was obtained with a yield of 84%. The IR spectrum shows peaks at 1784 and 1724 cmÿ1 (carbonyl groups of the anhydride) and at 1635 cmÿ1 (double bond) (Scheme 1).
Preparation of the polymers The monomer (3 g) and AIBN as initiator (9 mg, 3- in weight) were placed in a glass tube which is cooled in liquid nitrogen and connected with a vacuum line (0.1 mm Hg) for 10 min to remove the dissolved air and then sealed. After 72 h at 658C, we obtained the polymer 4
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Scheme 1. Scheme of syntheses of anhydride 3 and polyanhydride 4. which is insoluble in the usual solvents; for this reason, the polymer 4 and copolymers have been washed with methanol and then dried. The yield of 40% was attained.
The polymer 4 shows peaks in IR, at 1784 and 1724 cmÿ1 (anhydride function). A similar procedure was used when EDMA was added as crosslinking product; the insoluble
Fig. 1. Fractional release of hydrolysis product from monomer. In¯uence of the pH on the hydrolysis rate. Q, pH = 8; R, pH = 1.2.
Kinetics of a drug release from a delayed release device
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Fig. 2. Determination of the kinetic order. Ln([M]/[M]0) vs time. (a) pH = 1.2 and (b) pH = 8.
copolymers were washed with methanol then dried. The yields were close to 40%.
Test for determining the rate of drug release Release experiments were conducted in a closed ¯ask (150 cm3), kept at 372 0.58C and at a controlled stirring rate. 75 mg of the polyanhydride, in powder form, were soaked in 50 cm3 of aqueous solution buered at pH = 1.2, 4.2 and 8. Release of benzoic acid was followed by UV spectrophotometry (lmax=230 nm at pH = 1.2). Samples of aqueous solution were taken at dierent time intervals and analysed. Calibration experiments were performed in the same buered solution and led to e = 10825 lmolÿ1 cmÿ1 at pH = 1.2. In all cases, the release of the active agent was studied until equilibrium was reached.
RESULTS AND DISCUSSION
In this drug device, the release of active agent involves two dierent processes: chemical reaction (hydrolysis of benzoic acid) and mass transfer (diffusion of water and benzoic acid through the polymer). The rate of each step may be very dierent and the whole process will be controlled by the slowest step. In order to know whether the rate of chemical reaction may be the slowest step, we have studied the hydrolysis of benzoic acid from the monomer, because in this case, we can consider that there is no mass transfer. Indeed, the monomer is soluble in water and water is in large excess. Consequently the contact between water and the
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Fig. 3. In¯uence of the degree of crosslinking on the release rate of active agent (pH = 1.2). (a) 5% EDMA, (b) 3% EDMA, (c) 1% EDMA and (d) 0% EDMA.
monomer is excellent and permanent. Moreover the solution is stirred. Hydrolysis of benzoic acid from monomer Hydrolysis experiments of benzoic acid from the monomer were performed by dissolving, the branched monomer in (50 cm3) aqueous solution buered at pH = 1.2 and pH = 8 at 310 K. Figure 1 shows fractional release of hydrolysis product vs time. The rate of hydrolysis can be expressed as v
ÿdM kMa H2 Ob dt
where [M] is the concentration of linked monomer, [H2O] is the concentration of water, k is the rate constant and a and b are partial orders.
The rate can be written as follows, v = K'[M]a where k' is a pseudo reaction rate constant, because H2O is in large excess. Figure 2, which represents ln([M]/[M]0) vs time, demonstrates that the hydrolysis is a ®rst order reaction ([M]0 is the concentration of linked monomer at time t = 0). The linear dependence yields k' from the slope (k' = 9.410ÿ5 sÿ1 at pH = 1.2 and k' = 1.410ÿ4 sÿ1 at pH = 8). Hydrolysis of benzoic-acid from polymer Eect of the degree of crosslinking. We have studied hydrolysis in a buered solution at pH = 1.2 from polymer cross-linked with various amounts of ethylene-glycol dimethacrylate (0, 1, 3 and 5% in weight). Figure 3, which represents fractional release C/C0 (C0 would be the concentration of
Kinetics of a drug release from a delayed release device
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Fig. 4. In¯uence of the pH on the release rate of active agent from polymer. (a) Polymer crosslinked with 1% of EDMA and (b) polymer crosslinked with 5% of EDMA.
active agent if hydrolysis reaction was complete) of benzoic acid vs time indicates clearly two steps. During the ®rst one, there is no release of drug. The time of this step increases slowly with crosslinking density. In the second step, active agent is released with a rate that depends on the degree of crosslinking. The higher the concentration of EDMA the slower the rate of drug release. Such an observation is to be expected because the crosslinked matrix leads to a decrease in the active agent mobility [5, 6]. Eect of pH of the buered solution. Hydrolysis of benzoic acid from crosslinked polymer (with 1 and 5% in weight) was studied in a buered sol-
ution at pH = 1.2, 4.2 and 8. Figure 4 shows that pH of the solution has a great in¯uence on the time of delay. At pH = 4.2 this time is divided by about 2 and at pH = 8, there is no delay. The same results are obtained if the polymer is crosslinked with 5% (in weight) of EDMA. On the other hand, after the delay, the rate of release and the benzoic acid concentration at equilibrium were not greatly aected by the pH of the solution. Interpretation We can explain these results by assuming that the whole process involves 4 stages.
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Fig. 5. Fractional release of active agent as a function of (time)0.5. In¯uence of the pH. (a) EDMA: 5%, pH = 4.2, (b) EDMA: 1%, pH = 4.2, (c) EDMA: 5%, pH = 8 and (d) EDMA: 1%, pH = 8.
I: Penetration of water into polymer. II: Diusion of water and hydrolysis. III: Diusion of active agent (hydrolysis product). IV: Transfer of active agent in solution. Case when there is no delay (pH = 8). When there is no delay before active agent release, the whole process is governed by diusion. This result is con®rmed by Fig. 5(c) and (d). Indeed Fig. 5(c) and (d) indicates that fractional release of the hydrolysis product is linear versus the squared root of
time, for values less than about 0.5. Therefore the release rate is controlled by diusion [7], according to equation (2). Because water is a smaller molecule than benzoic acid, one can suppose that the slowest step is diusion of this second product. Case when there is a delay (pH = 1.2 and pH = 4.2). When there is a delay before release, the slowest step is ®rst by water absorption (during the delay) and then active agent diusion (during the release). In order to explain these results, we should remember that solubility of benzoic acid is greatly in¯uenced by pH of the solution. Indeed
Kinetics of a drug release from a delayed release device
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Fig. 6. Fractional release of active agent as a function of (time)0.5, at pH = 1.2. In¯uence of the degree of crosslinking. (a) 5% EDMA, (b) 3% EDMA, (c) 1% EDMA and (d) 0% EDMA.
benzoic acid is about 160 times less soluble than the basic form at 298 K. Therefore, if pH < pKa (pKa=4.2), the preponderant species is the benzoic acid and if pH>pKa the preponderant species is benzoate. Consequently, if hydrolysis is made at pH < pKa, this reaction into the polymeric matrix depends greatly on the quantity of absorbed water. If this quantity is not sucient, benzoic acid is not soluble and precipitates. This solid form cannot diffuse. Obviously the quantity of absorbed water (and also the time of delay) should be all the more important as the pH of solution is lower. Thus the
time of delay is smaller at pH = 4.2 than at pH = 1.2. Consequently, the time of delay depends mainly on the pH of the solution and not really on the degree of crosslinking. Figure 3, that represents the in¯uence of crosslinking of the active agent release rate, con®rms this result. After this period of time, when no release occurs, Fig. 6 demonstrates that fractional release of the hydrolysis product is linear vs the squared root of time, for values less than about 0.5. This result indicates that the release rate is controlled by the diusion of bigger molecules. The same observation can be made with
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Fig. 7. Ln[C1/(C1ÿC)] as a function of time at pH = 1.2. In¯uence of the degree of crosslinking. (a) EDMA: 5%, (b) EDMA: 3%, (c) EDMA: 1% and (d) EDMA: 0%.
a well known active principle: the salicylic acid and salicylate [8].
MODELLING
Mathematical treatment of diusion Diusion model with Fick's law. The diusion of benzoic acid can be described by the basic equation for unsteady-state diusion, called Fick's second law. If we suppose that polymeric powder is formed
with spherical and isotropic grains of radius R, the equation of diusion of organic substance into polymeric matrix is @C 1 @ @C 2 Dr2 0
Kinetics of a drug release from a delayed release device
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Fig. 8. Ln[C1/(C1ÿC)] as a function of time. In¯uence of the pH with a polymer crosslinked with 5% of EDMA. (a) pH = 4.2, EDMA: 5%, (b) pH = 8, EDMA: 1%, (c) pH = 8, EDMA 5% and (d) pH = 8, EDMA: 1%.
Table 1. Characteristics of hydrolysis product releases at pH = 1.2 % of EDMA
K (sÿ1) t0 (h) C1/C0
0
1
3
5
10.410ÿ6 34 60%
6.410ÿ6 37 53%
5.810ÿ6 40 49%
3.010ÿ6 44 41%
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Table 2. Characteristics of hydrolysis product releases at pH = 8
Table 3. Characteristics of hydrolysis product releases at pH = 4.2
% of EDMA 1 ÿ1
5 ÿ6
K (s ) t0 (h) C1/C0
% of EDMA
6.110 0 51.5%
cess is always given by [7]. Mt Dt 1=2 6 pR2 M1
1 ÿ6
ÿ1
5.910 0 38%
K (s ) t0 (h) C1/C0
2
where M1 is the total amount released at equilibrium. Model with mass transfer coecient. One other way to model the release results is to use a mass transfer coecient [9]. In order to obtain this, we write a mass balance on the buered solution V
dC kS C1 ÿ C dt
3
where V is the volume of solution, S is the total area of the polymeric particles, C1 is the active agent concentration at equilibrium and near the solid's surface. C is the concentration in the bulk solution and we assume that C varies only with time. k is a mass transfer coecient. It is equal to D/1 in which D is the diusion coecient of active agent in aqueous medium and 1 an unknown parameter equal to the thickness of unstirred layer [9]. Modelling of released product hydrolysis The description of diusion with Fick's second law gives results of a more fundamental value than the model based on mass transfer coecient. However, in order to use the model with diusion coecient, we must know the dimensions of polymeric grains. Unfortunately, polymeric particles are not regular in shape. Observed under the microscope, they appear like ovoid grains with variable sizes. Moreover a model based on Fick's law should take into account the simultaneous inward water transport and outward active agent release [10±13]. Therefore we have chosen a model with mass transfer coecient and, in this particular case, the two models are equivalent. Indeed, with a drug delivery system, we do not need to know the active agent concentration in the polymer matrix vs both position and time. We should only get to know the active substance release rate. This useful data is given by the model based in a mass transfer coecient. Indeed, the integration of equation (3) between t0 and t gives the expression of C vs time: C C1 1 ÿ expÿK t ÿ t0
4
in which C and C1 are the concentrations of organic substance, respectively, at time t and at equilibrium time in buered solutions, t0 is the period of time during no release occurs. K is equal to kS/V and it is constant if the operative conditions are the same. Figures 7 and 8, which represent ln [C1/ (C1ÿC)] vs time, demonstrates that the model gives results in good agreement with the experimental data. Indeed ln[C1/(C1ÿC)] is linear with time and
5 ÿ6
5.910 15 53%
5.810ÿ6 22 37%
the slope of the straight line yields the coecient K. The values of K are given in Tables 1, 2 and 3. K is aected by the degree of crosslinking only at pH = 1.2, but it is practically the same (about 610ÿ6 sÿ1), when solution is buered at pH = 4.2 or 8. On the other hand, the time of delay is more sensitive to the pH of solution than to the degree of crosslinking. Moreover K is much smaller than k', the pseudo constant rate of hydrolysis (of benzoic acid) from the monomer. This result con®rms that hydrolysis is not the slowest step of the whole process. CONCLUSION
This work showed that it is possible to make a delayed sustained release device with a drug (simulated by benzoic acid) covalently linked to a polymeric backbone. This type of drug delivery system may be used in pharmaceutical or agricultural applications. It allows the drug to perform up to its potential. It involves two major aspects: controlled release and targeting. The control of drug release and the control of distribution are the two most important features of a delivery system [14]. We have investigated the eect of crosslinking density and the eect of pH of the solution. We have showed that it is possible to change the time of delay and the release rate by changing the degree of crosslinking and the pH of the buered solution. A model, based on a mass transfer coecient, allows simulation of the drug release. Indeed the kinetics of drug release obtained by experiments and the calculations are in good agreement, proving the validity of the model. This model may be useful in optimizing a formulation. As a result it is possible to prepare any dosage form able to deliver drug at the desired rate and site. Optimal drug delivery and consequently maximum therapeutic eects may be reached when the characteristics of the device will be previously programmed. REFERENCES
1. Florence, A. T., Chem. Ind. 1993. 2. Ouchi, T. and Ohya, Y., Prog. Polym. Sci., 1995, 20, 211. 3. D'Antone, S., Solaro, R., Chiellini, E., Rehab, A., Akelah, A. and Issa, R., New Polym. Mater., 1992, 3, 223. 4. McCormick, G. L., in Encyclopedia of Polymer Science and Engineering, Vol. 1, 2nd edn. John Wiley, 1984, pp. 611±622. 5. Trigo, R. M., Blanco, M. D., Huerta, P., Olmo, R. and Teijon, J. M., Polym. Bull., 1993, 31, 577. 6. Yean, L., Bunel, C. and Vairon, J. P., Makromol. Chem., 1990, 191, 1119.
Kinetics of a drug release from a delayed release device 7. Crank, J., The Mathematics of Diusion, 2nd edn. Clarendon Press, Oxford, 1975. 8. Farah, N., Bouzon, J., Rollet, M., Taverdet, J. L. and Vergnaud, J. M., Int. J. Pharm., 1987, 36, 81. 9. Cussler, E. L., Diusion Mass Transfer in Fluid Systems. Cambridge University Press, 1985. 10. Petropoulos, J. H., Papadokostaki, K. G. and Amarantos, S. G., J. Polym. Sci. Part B:, 1992, 30, 717.
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11. Blanco, M. D., Rego, J. M. and Huglin, M. R., Polymer, 1994, 35, 3487. 12. Taverdet, J. L. and Vergnaud, J. M., J. Appl. Polym. Sci., 1984, 29, 3391. 13. Taverdet, J. L. and Vergnaud, J. M., J. Appl. Polym. Sci., 1986, 31, 111. 14. Smolen, V. F. and Ball, L. A., Controlled Drug Bioavailability. John Wiley, New York, 1984.
Eur. Polym. J. Vol. 34, No. 9, pp. 1283±1293, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0014-3057/98/$ - see front matter S0014-3057(97)00264-4
KINETICS OF A DRUG RELEASE FROM A DELAYED RELEASE DEVICE ALI BICHARA,1,2 JEAN-PIERRE MONTHEARD1 and JEAN-LOUIS TAVERDET2* Laboratoire de Chimie Organique MacromoleÂculaire, Faculte des Sciences et Techniques, 23 Rue Dr Paul Michelon, 42023 Saint-Etienne Cedex 2, France and 2Laboratoire de Chimie et Environnement, Faculte des Sciences et Techniques, 23 Rue Dr Paul Michelon, 42023 Saint-Etienne Cedex 2, France
1
(Received 8 April 1997; accepted in ®nal form 3 July 1997) AbstractÐReaction of sodium salt of benzoic acid with methacryloyl chloride provides an anhydride which is polymerized by the radical method or copolymerized with various percentages of ethylene glycol dimethacrylate to obtain crosslinked products. Hydrolysis reactions of the resulting polymers were carried out in various aqueous solutions and the rate of release of benzoic acid (simulator of drug) seems to depend both on the percentages of crosslinking comonomer and on the pH of the solution. A model of this delayed release of benzoic acid is also proposed. # 1998 Elsevier Science Ltd. All rights reserved
INTRODUCTION
In order to increase the acceptability or ecacy of oral drug therapy, many drugs are presented as controlled release formulation. Several types of devices [1, 2] were used to obtain a controlled release of the organic drug: a drug delivery system may be a matrix of polymer incorporating the organic substance. This drug can be dispersed in the polymer or covalently linked to a polymeric backbone. The attachment of drug to a polymer can be carried out either by a chemical modi®cation of the polymer or, after grafting of the drug onto a monomer, by polymerization or copolymerization of this modi®ed monomer. The controlled release of pesticides in agriculture [3, 4] was also widely studied and used either in a dispersion±dissolution of the bioactive or in an encapsulation into a polymer matrix. Therefore the mechanism of release of the active agent can be explained by a hydrolysis reaction of the organic function when the product is linked to a polymer followed by a diusion in the aqueous medium. In this work, we report some results on the release of benzoic acid (a simulator of an active agent) linked to a methacrylic backbone by an anhydride function. This matrix was crosslinked with various percentages of ethylene glycol dimethacrylate (EDMA) and the time of release, in aqueous medium, basic or acidic, should depend both on the degree of crosslinking and on the pH of the solution. This type of device, called a delayed release system, helps to ensure release of the organic compound by the following two procedures: delayed release and continuous release. A mathematical model, based on a mass transfer coef®cient will be proposed and should allow an opti*To whom all correspondence should be addressed.
mal formulation according to a programmed release rate of the organic molecule. EXPERIMENTAL
Materials The IR spectra of both monomers and polymers were measured with an FT IR 7 Bio-Rad apparatus. Determination of the amount of benzoic acid released was carried out on a JASCO UV/Vis apparatus at the corresponding lmax of the protonated acid or of the sodium salt, in basic medium.
Chemicals Methacryloyl chloride (Aldrich) was distilled before use. EDMA, benzoic acid, tetrahydrofuran (THF) and azobisisobutyronitrile (AIBN) were used as received and distilled water was employed.
Preparation of the monomer A dry 100 ml 3-necked ¯ask equipped with a magnetic stirrer and a re¯ux condenser to which is attached a Drierite-Filled drying tube was used for this synthesis. The mixture of sodium salt of benzoic acid 2 (0.05 mol, 7.2 g) in 10 ml of anhydrous THF and of methacryloyl chloride 1 (0.05 mol, 5.22 g) in 5 ml of dry THF are added into the ¯ask kept between 3 or 68C. After the addition was complete (15 min) a gentle heating follows (during 20 min) and then the mixture was stirred during 4 h. The precipitate of NaCl was ®ltered and washed with dry THF. The solvent was removed from the ®ltrate in a rotary evaporator and the anhydride 3 was obtained with a yield of 84%. The IR spectrum shows peaks at 1784 and 1724 cmÿ1 (carbonyl groups of the anhydride) and at 1635 cmÿ1 (double bond) (Scheme 1).
Preparation of the polymers The monomer (3 g) and AIBN as initiator (9 mg, 3- in weight) were placed in a glass tube which is cooled in liquid nitrogen and connected with a vacuum line (0.1 mm Hg) for 10 min to remove the dissolved air and then sealed. After 72 h at 658C, we obtained the polymer 4
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Scheme 1. Scheme of syntheses of anhydride 3 and polyanhydride 4. which is insoluble in the usual solvents; for this reason, the polymer 4 and copolymers have been washed with methanol and then dried. The yield of 40% was attained.
The polymer 4 shows peaks in IR, at 1784 and 1724 cmÿ1 (anhydride function). A similar procedure was used when EDMA was added as crosslinking product; the insoluble
Fig. 1. Fractional release of hydrolysis product from monomer. In¯uence of the pH on the hydrolysis rate. Q, pH = 8; R, pH = 1.2.
Kinetics of a drug release from a delayed release device
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Fig. 2. Determination of the kinetic order. Ln([M]/[M]0) vs time. (a) pH = 1.2 and (b) pH = 8.
copolymers were washed with methanol then dried. The yields were close to 40%.
Test for determining the rate of drug release Release experiments were conducted in a closed ¯ask (150 cm3), kept at 372 0.58C and at a controlled stirring rate. 75 mg of the polyanhydride, in powder form, were soaked in 50 cm3 of aqueous solution buered at pH = 1.2, 4.2 and 8. Release of benzoic acid was followed by UV spectrophotometry (lmax=230 nm at pH = 1.2). Samples of aqueous solution were taken at dierent time intervals and analysed. Calibration experiments were performed in the same buered solution and led to e = 10825 lmolÿ1 cmÿ1 at pH = 1.2. In all cases, the release of the active agent was studied until equilibrium was reached.
RESULTS AND DISCUSSION
In this drug device, the release of active agent involves two dierent processes: chemical reaction (hydrolysis of benzoic acid) and mass transfer (diffusion of water and benzoic acid through the polymer). The rate of each step may be very dierent and the whole process will be controlled by the slowest step. In order to know whether the rate of chemical reaction may be the slowest step, we have studied the hydrolysis of benzoic acid from the monomer, because in this case, we can consider that there is no mass transfer. Indeed, the monomer is soluble in water and water is in large excess. Consequently the contact between water and the
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Fig. 3. In¯uence of the degree of crosslinking on the release rate of active agent (pH = 1.2). (a) 5% EDMA, (b) 3% EDMA, (c) 1% EDMA and (d) 0% EDMA.
monomer is excellent and permanent. Moreover the solution is stirred. Hydrolysis of benzoic acid from monomer Hydrolysis experiments of benzoic acid from the monomer were performed by dissolving, the branched monomer in (50 cm3) aqueous solution buered at pH = 1.2 and pH = 8 at 310 K. Figure 1 shows fractional release of hydrolysis product vs time. The rate of hydrolysis can be expressed as v
ÿdM kMa H2 Ob dt
where [M] is the concentration of linked monomer, [H2O] is the concentration of water, k is the rate constant and a and b are partial orders.
The rate can be written as follows, v = K'[M]a where k' is a pseudo reaction rate constant, because H2O is in large excess. Figure 2, which represents ln([M]/[M]0) vs time, demonstrates that the hydrolysis is a ®rst order reaction ([M]0 is the concentration of linked monomer at time t = 0). The linear dependence yields k' from the slope (k' = 9.410ÿ5 sÿ1 at pH = 1.2 and k' = 1.410ÿ4 sÿ1 at pH = 8). Hydrolysis of benzoic-acid from polymer Eect of the degree of crosslinking. We have studied hydrolysis in a buered solution at pH = 1.2 from polymer cross-linked with various amounts of ethylene-glycol dimethacrylate (0, 1, 3 and 5% in weight). Figure 3, which represents fractional release C/C0 (C0 would be the concentration of
Kinetics of a drug release from a delayed release device
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Fig. 4. In¯uence of the pH on the release rate of active agent from polymer. (a) Polymer crosslinked with 1% of EDMA and (b) polymer crosslinked with 5% of EDMA.
active agent if hydrolysis reaction was complete) of benzoic acid vs time indicates clearly two steps. During the ®rst one, there is no release of drug. The time of this step increases slowly with crosslinking density. In the second step, active agent is released with a rate that depends on the degree of crosslinking. The higher the concentration of EDMA the slower the rate of drug release. Such an observation is to be expected because the crosslinked matrix leads to a decrease in the active agent mobility [5, 6]. Eect of pH of the buered solution. Hydrolysis of benzoic acid from crosslinked polymer (with 1 and 5% in weight) was studied in a buered sol-
ution at pH = 1.2, 4.2 and 8. Figure 4 shows that pH of the solution has a great in¯uence on the time of delay. At pH = 4.2 this time is divided by about 2 and at pH = 8, there is no delay. The same results are obtained if the polymer is crosslinked with 5% (in weight) of EDMA. On the other hand, after the delay, the rate of release and the benzoic acid concentration at equilibrium were not greatly aected by the pH of the solution. Interpretation We can explain these results by assuming that the whole process involves 4 stages.
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Fig. 5. Fractional release of active agent as a function of (time)0.5. In¯uence of the pH. (a) EDMA: 5%, pH = 4.2, (b) EDMA: 1%, pH = 4.2, (c) EDMA: 5%, pH = 8 and (d) EDMA: 1%, pH = 8.
I: Penetration of water into polymer. II: Diusion of water and hydrolysis. III: Diusion of active agent (hydrolysis product). IV: Transfer of active agent in solution. Case when there is no delay (pH = 8). When there is no delay before active agent release, the whole process is governed by diusion. This result is con®rmed by Fig. 5(c) and (d). Indeed Fig. 5(c) and (d) indicates that fractional release of the hydrolysis product is linear versus the squared root of
time, for values less than about 0.5. Therefore the release rate is controlled by diusion [7], according to equation (2). Because water is a smaller molecule than benzoic acid, one can suppose that the slowest step is diusion of this second product. Case when there is a delay (pH = 1.2 and pH = 4.2). When there is a delay before release, the slowest step is ®rst by water absorption (during the delay) and then active agent diusion (during the release). In order to explain these results, we should remember that solubility of benzoic acid is greatly in¯uenced by pH of the solution. Indeed
Kinetics of a drug release from a delayed release device
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Fig. 6. Fractional release of active agent as a function of (time)0.5, at pH = 1.2. In¯uence of the degree of crosslinking. (a) 5% EDMA, (b) 3% EDMA, (c) 1% EDMA and (d) 0% EDMA.
benzoic acid is about 160 times less soluble than the basic form at 298 K. Therefore, if pH < pKa (pKa=4.2), the preponderant species is the benzoic acid and if pH>pKa the preponderant species is benzoate. Consequently, if hydrolysis is made at pH < pKa, this reaction into the polymeric matrix depends greatly on the quantity of absorbed water. If this quantity is not sucient, benzoic acid is not soluble and precipitates. This solid form cannot diffuse. Obviously the quantity of absorbed water (and also the time of delay) should be all the more important as the pH of solution is lower. Thus the
time of delay is smaller at pH = 4.2 than at pH = 1.2. Consequently, the time of delay depends mainly on the pH of the solution and not really on the degree of crosslinking. Figure 3, that represents the in¯uence of crosslinking of the active agent release rate, con®rms this result. After this period of time, when no release occurs, Fig. 6 demonstrates that fractional release of the hydrolysis product is linear vs the squared root of time, for values less than about 0.5. This result indicates that the release rate is controlled by the diusion of bigger molecules. The same observation can be made with
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Fig. 7. Ln[C1/(C1ÿC)] as a function of time at pH = 1.2. In¯uence of the degree of crosslinking. (a) EDMA: 5%, (b) EDMA: 3%, (c) EDMA: 1% and (d) EDMA: 0%.
a well known active principle: the salicylic acid and salicylate [8].
MODELLING
Mathematical treatment of diusion Diusion model with Fick's law. The diusion of benzoic acid can be described by the basic equation for unsteady-state diusion, called Fick's second law. If we suppose that polymeric powder is formed
with spherical and isotropic grains of radius R, the equation of diusion of organic substance into polymeric matrix is @C 1 @ @C 2 Dr2 0
Kinetics of a drug release from a delayed release device
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Fig. 8. Ln[C1/(C1ÿC)] as a function of time. In¯uence of the pH with a polymer crosslinked with 5% of EDMA. (a) pH = 4.2, EDMA: 5%, (b) pH = 8, EDMA: 1%, (c) pH = 8, EDMA 5% and (d) pH = 8, EDMA: 1%.
Table 1. Characteristics of hydrolysis product releases at pH = 1.2 % of EDMA
K (sÿ1) t0 (h) C1/C0
0
1
3
5
10.410ÿ6 34 60%
6.410ÿ6 37 53%
5.810ÿ6 40 49%
3.010ÿ6 44 41%
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Table 2. Characteristics of hydrolysis product releases at pH = 8
Table 3. Characteristics of hydrolysis product releases at pH = 4.2
% of EDMA 1 ÿ1
5 ÿ6
K (s ) t0 (h) C1/C0
% of EDMA
6.110 0 51.5%
cess is always given by [7]. Mt Dt 1=2 6 pR2 M1
1 ÿ6
ÿ1
5.910 0 38%
K (s ) t0 (h) C1/C0
2
where M1 is the total amount released at equilibrium. Model with mass transfer coecient. One other way to model the release results is to use a mass transfer coecient [9]. In order to obtain this, we write a mass balance on the buered solution V
dC kS C1 ÿ C dt
3
where V is the volume of solution, S is the total area of the polymeric particles, C1 is the active agent concentration at equilibrium and near the solid's surface. C is the concentration in the bulk solution and we assume that C varies only with time. k is a mass transfer coecient. It is equal to D/1 in which D is the diusion coecient of active agent in aqueous medium and 1 an unknown parameter equal to the thickness of unstirred layer [9]. Modelling of released product hydrolysis The description of diusion with Fick's second law gives results of a more fundamental value than the model based on mass transfer coecient. However, in order to use the model with diusion coecient, we must know the dimensions of polymeric grains. Unfortunately, polymeric particles are not regular in shape. Observed under the microscope, they appear like ovoid grains with variable sizes. Moreover a model based on Fick's law should take into account the simultaneous inward water transport and outward active agent release [10±13]. Therefore we have chosen a model with mass transfer coecient and, in this particular case, the two models are equivalent. Indeed, with a drug delivery system, we do not need to know the active agent concentration in the polymer matrix vs both position and time. We should only get to know the active substance release rate. This useful data is given by the model based in a mass transfer coecient. Indeed, the integration of equation (3) between t0 and t gives the expression of C vs time: C C1 1 ÿ expÿK t ÿ t0
4
in which C and C1 are the concentrations of organic substance, respectively, at time t and at equilibrium time in buered solutions, t0 is the period of time during no release occurs. K is equal to kS/V and it is constant if the operative conditions are the same. Figures 7 and 8, which represent ln [C1/ (C1ÿC)] vs time, demonstrates that the model gives results in good agreement with the experimental data. Indeed ln[C1/(C1ÿC)] is linear with time and
5 ÿ6
5.910 15 53%
5.810ÿ6 22 37%
the slope of the straight line yields the coecient K. The values of K are given in Tables 1, 2 and 3. K is aected by the degree of crosslinking only at pH = 1.2, but it is practically the same (about 610ÿ6 sÿ1), when solution is buered at pH = 4.2 or 8. On the other hand, the time of delay is more sensitive to the pH of solution than to the degree of crosslinking. Moreover K is much smaller than k', the pseudo constant rate of hydrolysis (of benzoic acid) from the monomer. This result con®rms that hydrolysis is not the slowest step of the whole process. CONCLUSION
This work showed that it is possible to make a delayed sustained release device with a drug (simulated by benzoic acid) covalently linked to a polymeric backbone. This type of drug delivery system may be used in pharmaceutical or agricultural applications. It allows the drug to perform up to its potential. It involves two major aspects: controlled release and targeting. The control of drug release and the control of distribution are the two most important features of a delivery system [14]. We have investigated the eect of crosslinking density and the eect of pH of the solution. We have showed that it is possible to change the time of delay and the release rate by changing the degree of crosslinking and the pH of the buered solution. A model, based on a mass transfer coecient, allows simulation of the drug release. Indeed the kinetics of drug release obtained by experiments and the calculations are in good agreement, proving the validity of the model. This model may be useful in optimizing a formulation. As a result it is possible to prepare any dosage form able to deliver drug at the desired rate and site. Optimal drug delivery and consequently maximum therapeutic eects may be reached when the characteristics of the device will be previously programmed. REFERENCES
1. Florence, A. T., Chem. Ind. 1993. 2. Ouchi, T. and Ohya, Y., Prog. Polym. Sci., 1995, 20, 211. 3. D'Antone, S., Solaro, R., Chiellini, E., Rehab, A., Akelah, A. and Issa, R., New Polym. Mater., 1992, 3, 223. 4. McCormick, G. L., in Encyclopedia of Polymer Science and Engineering, Vol. 1, 2nd edn. John Wiley, 1984, pp. 611±622. 5. Trigo, R. M., Blanco, M. D., Huerta, P., Olmo, R. and Teijon, J. M., Polym. Bull., 1993, 31, 577. 6. Yean, L., Bunel, C. and Vairon, J. P., Makromol. Chem., 1990, 191, 1119.
Kinetics of a drug release from a delayed release device 7. Crank, J., The Mathematics of Diusion, 2nd edn. Clarendon Press, Oxford, 1975. 8. Farah, N., Bouzon, J., Rollet, M., Taverdet, J. L. and Vergnaud, J. M., Int. J. Pharm., 1987, 36, 81. 9. Cussler, E. L., Diusion Mass Transfer in Fluid Systems. Cambridge University Press, 1985. 10. Petropoulos, J. H., Papadokostaki, K. G. and Amarantos, S. G., J. Polym. Sci. Part B:, 1992, 30, 717.
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11. Blanco, M. D., Rego, J. M. and Huglin, M. R., Polymer, 1994, 35, 3487. 12. Taverdet, J. L. and Vergnaud, J. M., J. Appl. Polym. Sci., 1984, 29, 3391. 13. Taverdet, J. L. and Vergnaud, J. M., J. Appl. Polym. Sci., 1986, 31, 111. 14. Smolen, V. F. and Ball, L. A., Controlled Drug Bioavailability. John Wiley, New York, 1984.