Controlled-Release Technology - American Chemical Society

Chapter 24

Constant-Release Diffusion Systems Rate Control by Means of Geometric Configuration 1

2

K. G. Nelson , S. J. Smith, and R. M. Bennett

Downloaded by UNIV OF BATH on October 16, 2017 | http://pubs.acs.org Publication Date: September 4, 1987 | doi: 10.1021/bk-1987-0348.ch024

Pharmacy Research, Upjohn Company, Kalamazoo, MI 49001

A device consisting of an array of frustum-shaped cells that contain a drug dispersed in a permeable matrix is shown to obey zero-order release kinetics following an initial burst phase. Geometric shapes of dissolving solids or diffusion systems and the constraints of impermeable barriers influence mass transport and can be exploited as in the constant release wedge- or hemispheric-shaped devices. Equations describing the release characteristics of the frustum-shaped cells correlate quite well with experiments involving the release of the test compound ethyl p-aminobenzoate dispersed in a Silastic matrix. Experimental parameters include diffusivity, solubility, suspension concentration, declination angle, and opening radius. The p h a r m a c o l o g i c a l l y a c t i v e compound i n a dosage form g e n e r a l l y must undergo d i s s o l u t i o n i n o r d e r f o r i t t o be a b s o r b e d i n t h e body. The i m p o r t a n t f a c t o r s which govern t h e t i m e c o u r s e o f t h e d i s s o l u t i o n p r o c e s s a r e s o l u b i l i t y , d i f f u s i o n , and t h e s u r f a c e a r e a o f drug exposed t o t h e d i s s o l u t i o n medium. Whereas most t a b l e t s a r e formul a t e d t o d i s i n t e g r a t e r a p i d l y i n o r d e r t o maximize e x p o s u r e o f t h e p a r t i c u l a t e s t o t h e l i q u i d and hence maximize t h e d i s s o l u t i o n r a t e , c e r t a i n g e o m e t r i c c o n f i g u r a t i o n s o f dosage forms c a n be employed t o c o n t r o l t h e e x t e r n a l o r i n t e r f a c i a l a r e a exposed f o r d i f f u s i o n o r d i s s o l u t i o n and t h e r e b y e f f e c t a means o f c o n t r o l l i n g t h e r a t e o f r e l e a s e o f t h e d r u g . V a r i o u s approaches t o t h i s mode o f r a t e c o n t r o l w i l l be r e v i e w e d f o l l o w e d by a d e s c r i p t i o n , t h e o r e t i c a l development, and e x p e r i m e n t a l e v a l u a t i o n o f a system based on an a r r a y o f frustum-shaped c e l l s . 'Current address: College of Pharmacy, University of Arkansas for Medical Sciences, Little Rock, AR 72205 2

Current address: College of Pharmacy, Medical University of South Carolina, Charleston, SC 29425 0097-6156/87/0348-0324S06.00/0 © 1987 American Chemical Society

Lee and Good; Controlled-Release Technology ACS Symposium Series; American Chemical Society: Washington, DC, 1987.

24.

NELSON ET AL.


Influence

Constant-Release Diffusion Systems

325

o f Geometry

S o l i d D i s s o l u t i o n . The d i s s o l u t i o n r a t e of a s o l i d , whether i t be a n o n d i s i n t e g r a t i n g compact o r a powder, g e n e r a l l y d e c r e a s e s w i t h t i m e because o f t h e r e d u c t i o n i n s u r f a c e a r e a as t h e d i s s o l u t i o n p r o ceeds. The f a m i l i a r c u b e - r o o t law f o r d i s s o l u t i o n o f s o l i d s was d e r i v e d by H i x s o n and C r o w e l l (_1) on t h e b a s i s o f d i f f u s i o n away from t h e s u r f a c e o f a s p h e r i c a l l y - s h a p e d s o l i d . The convex s u r f a c e o f a s p h e r e d e c r e a s e s i n a r e a as s o l i d mass i s l o s t from t h e s u r f a c e so t h a t the d i s s o l u t i o n r a t e d e c r e a s e s i n p r o p o r t i o n t o the d e c r e a s e i n a r e a u n t i l t h e s o l i d i s c o m p l e t e l y d i s s o l v e d . By i n c l u d i n g shape f a c t o r s , t h i s model has been extended t o d e s c r i b e t h e d i s s o l u t i o n o f v a r i o u s p r i s m a t i c forms ( 2 ) . As i n t h e c a s e of s p h e r i c a l p a r t i c l e s , t h e d i s s o l u t i o n r a t e s d e c r e a s e w i t h t i m e as t h e d i s s o l u t i o n p r o c e s s p r o g r e s s e s because of t h e d e c r e a s e i n a r e a . In c o n t r a s t t o a convex s u r f a c e , a concave s u r f a c e may increase i n s u r f a c e a r e a as s o l i d mass i s eroded from t h e s u r f a c e . The d i s s o l u t i o n r a t e o f a concave s u r f a c e t h u s i n c r e a s e s w i t h t i m e . Rippie and Johnson (3) s t u d i e d t h e d i s s o l u t i o n c h a r a c t e r i s t i c s o f s o l i d p e l l e t s t h a t were d e s i g n e d t o m i n i m i z e l o s s i n s u r f a c e a r e a d u r i n g dissolution. T h i s was a c c o m p l i s h e d by employing p e l l e t s h a v i n g a c r o s s s e c t i o n s u c h t h a t b o t h convex and concave s u r f a c e s were present. D i s s o l u t i o n r a t e s o f c y l i n d e r s h a v i n g c r o s s shaped and c l o v e r l e a f c r o s s s e c t i o n s were measured and compared w i t h t h a t o f a r i g h t c i r c u l a r c y l i n d e r . A l t h o u g h t h e d i s s o l u t i o n r a t e s of t h e uniquely-shaped p e l l e t s decreased over time, with p a r t i a l l y coated p e l l e t s t h e r a t e s d e c r e a s e d much l e s s t h a n t h a t of t h e c i r c u l a r c y l i n d e r , e.g., a f t e r 60% mass l o s s t h e r a t e s were a p p r o x i m a t e l y 55% g r e a t e r t h a n t h a t of t h e c i r c u l a r c y l i n d e r . I f a h o l e i s p r e s e n t i n a n o n d i s i n t e g r a t i n g t a b l e t , t h e convex s u r f a c e o f t h e h o l e w i l l i n c r e a s e i n a r e a as t h e s u r f a c e d i s s o l v e s . A t h e o r e t i c a l a n a l y s i s by C l e a v e (4) on t a b l e t s i n t h e form o f p a r a l l e l e p i p e d s i n d i c a t e d t h a t t h e p r e s e n c e o f one or more h o l e s i n a t a b l e t can a l t e r s i g n i f i c a n t l y t h e d i s s o l u t i o n r a t e o f t h e t a b l e t over time. I t was c o n c l u d e d t h a t a two-hole t a b l e t i s b a s i c a l l y a b e t t e r c o n f i g u r a t i o n than the others f o r m a i n t a i n i n g a constant dissolution rate. I t should d i s p l a y a reduction i n d i s s o l u t i o n r a t e d u r i n g d i s s o l u t i o n of between 0 and 9.7%, depending on t h e p a r t i c u l a r dimensions. R e l e a s e from M a t r i x . The r e l e a s e of a drug d i s p e r s e d as a s o l i d i n a n o n e r o d a b l e dosage form i n v o l v e s t h e d i s s o l u t i o n o f t h e s o l i d i n t o t h e m a t r i x f o l l o w e d by d i f f u s i o n of t h e s o l u t e t o t h e s u r f a c e o f t h e dosage form. F o r a one d i m e n s i o n a l model o f t h i s p r o c e s s t h e f u n d a m e n t a l e q u a t i o n l i n e a r l y r e l a t e s t h e amount r e l e a s e d w i t h t h e s q u a r e - r o o t o f t i m e ( 5 ) . T h e r e i s a r e c e d i n g boundary t h a t e x i s t s between t h e d e p l e t e d zone and t h e zone c o n t a i n i n g s o l i d d r u g , and t h i s moving i n t e r f a c e e f f e c t i v e l y i n c r e a s e s t h e d i f f u s i o n p a t h l e n g t h as t h e r e l e a s e o f t h e drug o c c u r s . Hence, t h e r e l e a s e r a t e from t h e dosage form d e c r e a s e s w i t h t i m e . This i s a rather general c o n c e p t and, i n d e e d , t h e s q u a r e - r o o t o f t i m e e q u a t i o n was d e r i v e d by H i l l (6) i n 1928 t o d e s c r i b e t h e d i f f u s i o n o f oxygen i n t o f a t i g u e d muscles.


CONTROLLED-RELEASE TECHNOLOGY


326

C o n s t a n t R e l e a s e Conf i g u r a t i o n s . The i d e a o f a r e c e d i n g boundary has been c o u p l e d w i t h t h e i n c r e a s i n g boundary a r e a o f a concave s u r f a c e by Brooke and Washkuhn (7-10) t o produce a d e v i c e t h a t w i l l r e l e a s e drug a t a c o n s t a n t o r z e r o - o r d e r r a t e f o r an extended p e r i o d of time. The d e v i c e c o n s i s t s o f a nonpermeable c y l i n d e r w i t h a c a v i t y h a v i n g a c i r c u l a r s e c t o r c r o s s s e c t i o n . The c e n t e r o f t h e c i r c u l a r sector l i e s j u s t outside the c y l i n d e r , thereby producing a s l i t f o r r e l e a s e o f t h e s o l u t e . The c a v i t y i s f i l l e d w i t h drug i n s o l i d form o r suspended i n a permeable m a t r i x . When exposed t o an aqueous medium, t h e drug d i f f u s e s o u t t h e o p e n i n g . As t h e mass i s l o s t from t h e d e v i c e t h e d i f f u s i o n p a t h l e n g t h becomes g r e a t e r , which n o r m a l l y would d e c r e a s e t h e r a t e o f d i f f u s i o n . Because o f t h e g e o m e t r i c shape, however, as t h e mass i s l o s t from t h e d e v i c e t h e i n t e r f a c i a l area increases. These c o u n t e r a c t i n g e f f e c t s e s s e n t i a l l y b a l a n c e each o t h e r and l e a d t o a r e l a t i v e l y c o n s t a n t r a t e o f release. R e p o r t e d e x p e r i m e n t a l d a t a d i s p l a y good l i n e a r i t y w i t h t i m e f o l l o w i n g an i n i t i a l l y h i g h e r r a t e . A system h a v i n g t h e g e o m e t r i c shape o f a hemisphere has been d e s c r i b e d r e c e n t l y (11-13) t h a t i s a l s o based on t h e i d e a o f a s i m u l t a n e o u s l y i n c r e a s i n g p a t h l e n g t h and i n c r e a s i n g i n t e r f a c i a l area. A drug-polymer m a t r i x was p r e p a r e d i n t h e shape o f a hemisphere having a s m a l l c a v i t y a t t h e center f a c e . An impermeable c o a t i n g was l a m i n a t e d over t h e d e v i c e e x c e p t f o r t h e c a v i t y . I n an aqueous medium t h e drug was r e l e a s e d t h r o u g h t h e c a v i t y and t h e d i f f u s i o n p r o p e r t i e s o f t h i s u n i q u e i n w a r d l y - r e l e a s i n g shape p r o v i d e d a c o n s t a n t r e l e a s e r a t e f o l l o w i n g an i n i t i a l l y h i g h e r r a t e . T h i s t y p e o f d e v i c e has been shown t o d e l i v e r a t e s t compound a t a c o n s t a n t r a t e f o r 60 days. Frustum A r r a y

Device

Concept. A d e v i c e has been d e v e l o p e d t h a t i n c o r p o r a t e s t h e i d e a o f geometric c o n t r o l of d i f f u s i o n a l r e l e a s e i n t o a f l a t c o n f i g u r a t i o n which i s b e t t e r s u i t e d f o r c e r t a i n t y p e s o f dosage forms t h a n i s a p e l l e t o r c y l i n d e r . I t r e l e a s e s drug a t a z e r o o r d e r r a t e f o l l o w i n g an i n i t i a l b u r s t p e r i o d . The d e v i c e c o n s i s t s o f a t w o - d i m e n s i o n a l a r r a y o f cone-shaped c e l l s i n a r e l a t i v e l y f l a t nonpermeable m a t r i x ( F i g u r e 1 ) . Because each c e l l i s open a t t h e lower s u r f a c e o f t h e c e l l - c o n t a i n i n g l a y e r and does n o t i n c l u d e t h e v e r t e x , t h e shape i s a c t u a l l y t h e f r u s t u m o f a cone. The frustum-shaped c e l l s c o n t a i n t h e drug i n t h e form o f a p a r t i c u l a t e s o l i d d i s p e r s e d i n a permeable matrix. A nonpermeable b a c k i n g i s p r o v i d e d t o complete t h e system. The drug i s r e l e a s e d by d i f f u s i o n t h r o u g h t h e s m a l l h o l e s a t t h e lower s u r f a c e and r e s u l t s i n an i n c r e a s e d p a t h l e n g t h and i n c r e a s e d i n t e r f a c i a l a r e a w i t h i n each c e l l i n a manner s i m i l a r t o t h e c y l i n d e r and hemisphere d e s c r i b e d p r e v i o u s l y . The p r e s e n c e o f suspended s o l i d a t t h e i n t e r f a c e m a i n t a i n s a c o n s t a n t d r i v i n g f o r c e for diffusion. The g e o m e t r i c c o n f i g u r a t i o n f o r an i n d i v i d u a l c e l l i s shown i n F i g u r e 2 and d e p i c t s a d e p l e t e d zone between a and r . A l t h o u g h t h e g e o m e t r i c shape d e v e l o p e d i n t h e p r e s e n t work i s a f r u s t u m o f a cone, o t h e r g e o m e t r i c c o n f i g u r a t i o n s f o r t h e i n d i v i d u a l c e l l s a r e p o s s i b l e , e.g., a pyramid ( 1 4 ) . A multiple-hole device d e s c r i b e d r e c e n t l y (15) f u n c t i o n s , i n e f f e c t , as i f i t had hemispherically-shaped cells.


24.

NELSON ET AL.

327

Constant-Release Diffusion Systems

BACKING


Q

Q

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Q

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V;;/

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Q

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s

Q

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CELL-CONTAINING LAYER FRUSTUMSHAPED CELL F i g u r e 1.

F i g u r e 2.

Frustum-array

Partially

depleted

device.

frustum-shaped

cell.


328

CONTROLLED-RELEASE

T E C H N O L O G Y


Theoretical. The t h e o r y o f s t e a d y s t a t e d i f f u s i o n i n a h o l l o w s p h e r e has been d e s c r i b e d by Crank ( 1 6 ) . Because e a c h f r u s t u m shaped c e l l i n t h e system c l o s e l y a p p r o x i m a t e s a s p h e r i c a l s e c t o r of a h o l l o w s p h e r e , a t h e o r e t i c a l model can be d e v e l o p e d on t h i s b a s i s t o p r e d i c t t h e r e l e a s e c h a r a c t e r i s t i c s f o r t h i s sytem. T h i s assump t i o n s h o u l d be v a l i d u n t i l t h e p o i n t i s r e a c h e d such t h a t t h e c u r v e d i n t e r f a c e ( r i n F i g u r e 2) t o u c h e s t h e f l a t impermeable b a c k i n g , w h i c h s h o u l d r e p r e s e n t c a . 90% o f t h e r e l e a s e . The s t e a d y s t a t e d i f f u s i o n e q u a t i o n i n s p h e r i c a l p o l a r c o o r d i n a t e s r e l a t e s c o n c e n t r a t i o n c t o o n l y t h e r a d i u s r because o f s p h e r i c a l symmetry:

3?[*'£]-° T h i s has

(1

the general

>

solution

c = β + St r

(2)

where α and β a r e c o n s t a n t s o f i n t e g r a t i o n . F o r d i f f u s i o n i n a h o l l o w s p h e r e where t h e c o n c e n t r a t i o n i s z e r o a t t h e i n n e r r a d i u s r = a and C a t t h e o u t e r r a d i u s r = b, i t can be shown t h a t s

α =

a-b

To e v a l u a t e f i r s t law

C

(3)

sa

the r a t e of r e l e a s e a t the

J = -DA

i n n e r s u r f a c e r = a,

— dr

Ficks

(A)

i s combined w i t h E q u a t i o n s 2 and 3. J i s the f l u x , A i s the area, and D i s t h e d i f f u s i v i t y . This r e s u l t s i n a release rate R at r = a of

R = AnD

If

b »

a,

b-a

C

(5)

ss

then

R = Απϋ3ΰ

(6)

Controlled-Release Technology - American Chemical Society

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