11 Controlled Release of Delmadinone Acetate from Silicone
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Polymer Tubing: In Vitro-In Vivo Correlations to Diffusion Model JOHN S. KENT Institute of Pharmaceutical Sciences, Syntax Research, Palo Alto, Calif. 94304 Introduction Over the past decade, there has been a great interest i n silicone polymers as substances for controlling the release of a drug or chemical substance. The research i n this area has been summarized at a Symposium (1). The present report deals with silicone polymer (Silastic®) tubing as a substance for controlling the release of a steroid, delmadinone acetate. I t has been discussed (1, p. 103) that silicone polymer tubing packed with drug crystals leads to variable and unpredicably low results. To avoid this it has been suggested i n our laboratory and elsewhere (2-5) that the drug be present i n the tube i n the form of a suspension. This allows a uniform supply of the drug to the tubing inner wall, assuming that the suspending medium provides s o l u b i l i t y for the drug and does not rapidly diffusion from the tube. A device such as this was developed and used i n the following experiments. The experiments reported here determine the long term release characteristics of a drug-suspension silicone polymer tube implanted i n vivo, determine i f the drug release i s membrane and/or diffusion layer controlled and examine i f there i s a correlation between i n vivo and i n vitro release. Theoretical The mathematical relationship for diffusion i n a cylinder has been discussed (6). I t was of interest to determine i f the steroid released from the silicone polymer tubing devices studied here was controlled by the tubing thickness and/or a boundary diffusion layer. The physical model i s shown i n Figure l a . The symbols are defined as: C = the saturation concentration of drug i n the suspension medium; Ci = concentration of drug i n the silicone polymer tubing at the suspension - inner wall interface; C2 • concentration of drug i n the silicone polymer tubing at the outer tubing wall - receptor interface; C3 = s
157
Paul and Harris; Controlled Release Polymeric Formulations ACS Symposium Series; American Chemical Society: Washington, DC, 1976.
Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on October 31, 2017 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0033.ch011
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CONTROLLED RELEASE POLYMERIC
FORMULATIONS
concentration of drug i n the receptor at the outer tubing wall receptor interface; A = inner tube radius; Β = outer tube radius; Ε = outer radius of boundary diffusion layer. Certain assumptions are necessary in the derivation of the mathematical model: 1. Steady state i s established such that the flux, J, i s constant through every concentric cylindrical s h e l l ; 2. There i s no significant boundary layer within the cylindrical tubing. The diffusional resistance comprises the tubing and the external boundary diffusion layer, hence no interfacial barriers; 3. There i s no significant diffusion through the ends of the tubing sections; 4. The diffusion layer i s symmetrical over entire tubing surface. The derivation of this model has been recently discussed in detail (7). However, for convenience the derivation i s included here. The general case for diffusion through a cylinder can be written as: Flux = J = -2π rhD ^ Eq. 1 3r where r = cylinder radius, h = cylinder length, D = diffusion coefficient and C = diffusing species concentration. By rearrangement of this equation and defining D m as the apparent diffusion coefficient in the silicone polymer tubing, the following equation i s obtained.
3r
-2 Trille 3C
m
2
r J By integration between the inner (A) and outer (B) r a d i i and between Ci and C2, equation 2 becomes: J
J
In (B/A) If the same derivation i s applied to the cylindrical boundary diffusion layer, with integration between Β and Ε and con centrations C3 and CQ the resulting equation i s : (C0-C3) In (E/B) ' * Equations 3 and 4 are combined by using the partition coefficients defined as follows: τ
-2
=
TThD
a
E L q
J
4
Κχ
= Partition coefficient between the core suspending medium and the silicone polymer tubing (C /Ci). II Partition coefficient between the silicone polymer tubing and the receptor phase (C2/C3 = C i / C ) . Where C = solubility of the drug i n the receptor phase. The equation i s then: s
K
=
sr
s r
Paul and Harris; Controlled Release Polymeric Formulations ACS Symposium Series; American Chemical Society: Washington, DC, 1976.
11.
KENT
Delmadinone
DK a
x
159
Acetate
ln(B/A) + ϋ ^ Κ χ !
ln(E/B)
q
*
The product of Κχ and K n can be defined as KJ-Q which i s the partition coefficient between the suspension medium and the receptor phase. Equation 5 defines the flux, J, as being dependent on tubing thickness and the boundary diffusion layer. The equation i s simplified i f one or the other diffusional resistances predominates. If D Ki ln(B/A) i s greater than ^m^III ln(E/B), the diffusion process is membrane (tubing thickness) controlled. The resulting equation being:
Downloaded by UNIV OF CALIFORNIA SAN FRANCISCO on October 31, 2017 | http://pubs.acs.org Publication Date: June 1, 1976 | doi: 10.1021/bk-1976-0033.ch011
a
2TrhD C 27rhD C Ki ln(B/A) ln(B/A) ** where Ci • C = saturation solubility of the diffusing species in the silicone polymer. If the opposite i s true, the diffusional process i s boundary layer controlled. That equation i s then: m
m
s
m
m
J
6
q
0
m
K
m
ln(E/B)
ln(E/B)
q
Experimental Materials. Delmadinone acetate (DA; 6-chloro-17a hydroxypregna-l,4,6-triene-3,20-dione acetate) was used i n the micronized form. For some partitioning and s o l u b i l i t y studies tritium labeled delmadinone acetate with a specific activity of 0.152 uCi/mg was used. Deionized water was used i n the i n vitro diffusion studies. Silicone polymer (Silastic®) tubing and Silastic® Medical Grade Adhesive Type A (Dow Corning, Medical Products Division) was used throughout the experiment. The suspending f l u i d used i n the silicone polymer tube devices was polysorbate 80 (Tween 80, ICI-United States). Preparation of F i l l e d Silicone Polymer Tubes. Specified lengths of the various sizes of silicone tubing were washed with acetone and dried. One end was then plugged with Silastic® Medical Adhesive Type A and allowed to cure. The tubes for the i n vivo study were then weighed and then again after f i l l i n g with the steroid suspension so the f i l l weight could be calculated. The steroid suspension was composed of 50% micron ized delmadinone acetate and 50% polysorbate 80 except as noted under the i n vivo studies. After the tubes were f i l l e d with the steroid suspension, they were sealed with the Silastic® Medical Grade Adhesive. A summary of the materials and tubing devices used i n the i n vivo and i n vitro studies i s found i n Tables I and I I . In Vitro Diffusion Studies. The DA suspension f i l l e d silicone polymer tubes (DA tubes) were fastened between an upper
Paul and Harris; Controlled Release Polymeric Formulations ACS Symposium Series; American Chemical Society: Washington, DC, 1976.
160
CONTROLLED RELEASE POLYMERIC
FORMULATIONS
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