Page 190 - Biomedical Engineering and Design Handbook Volume 2, Applications

DESIGN OF CONTROLLED-RELEASE DRUG DELIVERY SYSTEMS 169

The release properties of the device depend highly upon the structure of the matrix whether it is
porous or nonporous. The rate of drug release is controlled by the concentration or solubility of drug
in the polymer and diffusivity of the drug through the polymer for nonporous system. For a porous
matrix, the solubility of the drug in the network and the tortuosity of the network add another dimen-
sion to affect the rate of release. In addition, drug loading influences the release, since high loading
can complicate the release mechanism because of formation of cavities as the drug is leaving the
device. These cavities will fill with fluids and increase the rate of release.
The cumulative amount released from a matrix-controlled device is described by 2

⎛ C ⎞
p
Q = ⎜ C − ⎟ h (6.9)
⎝ A 2 ⎠ p
where C is initial amount of drug, C is solubility of drug in polymer, and h is a time-dependent
A p p
variable defined by
2( C − C D h h 2 CD p
)
p d p
p
A
p
2
h + = t (6.10)
p C C
⎛ C ⎞ p
p
⎜ ⎝ C − 2 ⎠ ⎟ DkK C − 2
A
d
A
where k = the constant for relative magnitude of the concentration in diffusion layer and depletion
zone
D = the diffusivity of drug in the polymer devices
p
and other parameters are the same as described for Eqs. (6.4) to (6.9). At a very early stage of the
release process, when there is a very thin depletion zone, the following will be true:
2( C − C D h h
)
p d p
p
A
2
h <<
p
⎛ C ⎞
p
⎜ C − ⎟ DkK
A
d
⎝ 2 ⎠
Equation (6.10) can be reduced to
CD kK
d
p
h ≈ (6.11)
p
( C − C h ) d
p
A
and placing Eq. (6.11) into Eq. (6.9) gives
Q CD kK ⎛ C ⎞
p
p
d
⎝
A
p
A
t = h d ⎜ if C − C ≈ C − 2 ⎟ ⎠ (6.12)
Since KC = C , Eq. (6.12) becomes
p s
Q = CD k
s
d
t h (6.13)
d
The k term implies that the matrix system is more sensitive to the magnitude of concentration dif-
ference between depletion and diffusion layers.