Polymeric Drugs and Drug Delivery Systems - American Chemical

Chapter 16

Kinetics of Controlled Release from Acid-Catalyzed Matrices Abhay Joshi and Kenneth J. Himmelstein

1

Downloaded by UNIV OF PITTSBURGH on July 2, 2013 | http://pubs.acs.org Publication Date: August 15, 1991 | doi: 10.1021/bk-1991-0469.ch016

Allergan Pharmaceuticals, 2525 Dupont Drive, Irvine, CA 92715-1599

A mathematical model for the analysis of basic physicochemical determinants that yields experimentally verifiable predictions of erosion characteristics and controlled release of bioactive agents from bioerodible matrices is presented. There is considerable experimental information in the literature on the detailed performance of the poly(ortho ester) system, covering a wide range of system characteristics, and therefore making a good test case for mathematical analysis. The analysis shows that the dynamic changes in polymer matrix properties, namely, simultaneous reaction-diffusion-transport of matrix constituents, moving diffusion and water front, water-polymer partition coefficients, solubility of water and diffusivity of matrix components as a function of extent of acid catalyzed matrix hydrolysis, play a significant role in regulating the release kinetics of bioactive agents. The model predicts experimentally measureable quantities: release characteristics of incorporated bioactive agents, water penetration into the matrix, and catalytic degradation of the polymer matrix. Further, a good estimate of the concentration of unbroken polymer backbone linkages and hence the molecular weight of the polymer disc with time is obtained using random scission kinetics.

Drug release in a controlled fashion for a variety of applications from a single generalized system has long been a substantial goal of drug delivery research. One of the approaches taken to achieve this goal has been the use of hydrolytically unstable polymers which contain drug. To achieve a wide range of delivery durations in these systems, the rate of hydrolysis can be altered by choice of copolymer to give intrinsically different reaction rates and (by virtue of different glass transition 1

Current address: Himmelstein and Associates, Pearl River, NY 10965

0097-6156/91/0469-0170S06.00/0 © 1991 American Chemical Society

In Polymeric Drugs and Drug Delivery Systems; Dunn, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


16. JOSHI & HIMMELSTEIN

Kinetics of Controlled Release

171

temperatures) different water permeation rates, and by including erosion accelerating acid groups or core stabilizing basic excipients. It is desirable that the rate of drug release from these systems be controlled by the hydrolysis of the polymer itself. The kinetics of reaction, however, depend on many different physical and chemical processes that occur in tandem: diffusion of water into the matrix, reaction with the polymer, physical degradation of the polymer, diffusion of the drug through the degrading matrix, and secondary processes such as the production and diffusion of secondary molecules like catalysts and stabilizers. In order to assess the effect of all these interrelated processes on the performance of these eroding polymeric release systems, a means of systematically studying them is required. Therefore, a mathematical model which includes all of the important reaction and transport properties in a mechanistic fashion can be a useful tool to study the performance of these complex systems. A previous model (7) was developed for this purpose. This model was able to predict the general performance characteristics of a polymeric delivery system which used a small diffusible molecule to act as a catalyst to accelerate the erosion rate. However, this model was never applied to the simulation of experimental data using independently measured parameters such as rate constants and diffusivities to determine its quantitative predictive capabilities. Secondly, to determine whether or not a system is really performing as believed, a more rigorous method than simply calculating the rate of drug release should be employed, since many different sets of processes can lead to very similar release characteristics. The previously developed model had as its major dependent variable, the concentration of hydrolyzable polymeric linkages at any position and time. While this variable was useful for simulations, it is not an easily verifiable measure to describe experimental systems. Thus in aris paper, the model is extended to the calculation of polymer molecular weight distribution as a function of time and position using random degradation kinetics. This variable is then used to calculate the average molecular weight for these systems. In addition, the model is updated to include a position dependent water partition coefficient at the model-defined polymer-environmental barrier. Finally, it is desirable to relate gross erosion characteristics - bulk or surface erosion to an easily defined characteristic of the system. The Thiele modulus, an indicator that determines the regimes of diffusion and reaction controlled kinetics of the system, is used to describe the overall system performance. In this paper, then, the previously developed model (7) is extended to the calculation of erosion characteristics of a well described polymeric delivery system, the acid-catalyzed erosion of poly(ortho ester)s (2-6). This system is chosen as the example system because of the completeness of the data package in the open literature. It is expected that this modelling approach is also useful for other hydrolytically unstable polymeric drug delivery systems. Experimental Model Structure. As one of the main goals of the present effort is to use the extended mathematical analysis to model experimentally described results, the model



172

POLYMERIC DRUGS AND DRUG DELIVERY SYSTEMS

was set up to simulate the physical system studied by Nguyen, et al. (2). In these experiments, an acid producing species, phthalic anhydride, is mixed into the poly(ortho ester) matrix, along with the drug to be released. The general system is shown in Figure 1. In operation, water (A) from the environment diffuses into the poly(ortho ester) disc to react with the acid producing species (B) to produce the acid catalyst (C). The catalyst is free to react with the hydrolytically unstable polymer linkage (D) to form an activated unstable intermediate complex (D*) which then can further react with water (A) to break the backbone linkages. As the polymer erodes, there is a subsequent loss of physical integrity of the polymeric system and drug (E), along with small degradation products, is free to diffuse out. The rate of drug release (E) from the eroding matrix is controlled by: (a) the chemical properties of the system - the hydrolytic and the neutralizing process at the boundary of the device, catalytic degradation of the polymer and the intrinsic backbone reactivity, and (b) several concomitant physical processes such as water diffusivity, water solubility, water partitioning, etc. Mathematical Model. The assumptions which make up the core of the model are as follows: 1. A slab geometry of the polymer matrix with center line at x=0 and outer surface atx=a. See Figure 1. 2. The drug and other molecules are assumed to be in a single phase with the polymeric structure. 3. No volume change of the system as water diffuses in. Poly(ortho ester)s are rather hydrophobic (3). 4. Perfect sink conditions externally with finite mass transfer boundary layers. 5. Transport in the polymeric system is assumed to be by Fickian diffusion, although the diffusivity of the various species depends on the extent of hydrolysis of the polymeric linkages. 6. The chemical reactions are assumed to be elementary and the overall reaction scheme is given in Figure 1. The mathematical model then is a set of coupled, nonlinear, one dimensional, unsteady-state mass balances of the form

where Cj is the concentration of the 1 species, Dj is the diffusivity of the 1 species, χ is the position, t is the time, and V j is the net sum of the rate of production and degradation of the 1 species given by the reaction scheme as shown in Figure 1. Since the diffusivity is dependent on the extent of hydrolysis, the diffusivity is assumed to take the form (7) th

th

t h

D? = i ? f e x p [ ^ c

C p )

],

i = A,B,C,E


(2)


16. JOSHI & HIMMELSTEIN

X =0

Kinetics of Controlled Release

X:8

Figure 1. Scheme depicting erosion process of polymer disc containing acid labile linkages. (Reproduced with permission from ref. 7. Copyright 1991 Elsevier Science Publishers.)


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POLYMERIC DRUGS AND DRUG DELIVERY SYSTEMS

174

where O is the diffusivity of the 1 species, Dj° is the diffusivity through unreacted polymer, and μ is a proportionality constant. The boundary conditions for the system are then: 1. Symmetry at the centerline: t h

i

A ( 0 , t ) ^ ( 0 , r ) = 0,


2.

0 < * , i = A,B,C,E

(3)

Finite mass transfer into the bulk environment which approximates sink conditions:

A ( 0 , t ) ^ ( a , 0 =

fc,(C,,6u/ib-C,(a,0),

0 < * , i = B,C,E

(4)

where Cj is the concentration of 1 species at time zero in the bulk of the aqueous phase. 3. For water, there is local equilibrium between the water in the disk and in the environment at the surface. th

b u l k

C (a,t) A

=

K(C )C° D

A

where C ° is the concentration of water in the aqueous phase and Κ is the partition coefficient. The initial conditions are: A

C,(*,0) = 0 for 0 < χ < a , i = C , ( * , 0 ) = C ? for0

Polymeric Drugs and Drug Delivery Systems - American Chemical

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