Page 189 - Biomedical Engineering and Design Handbook Volume 2, Applications

168 MEDICAL DEVICE DESIGN

Analysis of diffusion-controlled reservoir or matrix drug delivery systems require few assumptions:
(1) the diffusion coefficient of a drug molecule in a medium must be constant; (2) the controlled drug
release must have a pseudosteady state; (3) dissolution of solid drug must occur prior to the drug
release process; and (4) the interfacial partitioning of drug is related to its solubility in polymer and
in solution as defined by

C
K = s (6.4)
C
p
where K = partition coefficient of the drug molecule from polymer to solution
C = solubility of drug in the solution phase
s
C = solubility of drug in polymer phase
p
With the above assumptions, the cumulative amount Q of drug released from a diffusion-controlled
2
reservoir-type drug delivery device with a unit surface area can be described as follows :
CKD D m DD t t
d
p
Q = t − d m ∫ C bt () dt (6.5)
KD h + D h KD h + D h
dm
m d
dm
m d 0
where D = diffusivity of drug in polymer membrane with thickness h
m m
D = diffusivity of hydrodynamic diffusion layer with thickness h
d d
C = concentration of drug in reservoir side
b
t = time
Under sink condition, where C ≈ 0or C 〉〉 C , Eq. (6.5) is reduced to
bt() s bt()
CKD D m
p
d
Q = t (6.6)
KD h + D h
m d
dm
This relationship shows that release of drug can be a constant, with rate of drug release being
Q = CKD D m
p
d
t KD h + D h (6.7)
m d
dm
In extreme cases, the rate of release may depend mainly on one of the layers, either polymer
membrane layer or hydrodynamic diffusion layer. If the polymer membrane is the rate-controlling
layer, KD h >> D h , the equation can be simplified to
dm m d
Q CD m
p
t = h m (6.8)
which shows that the release rate is directly proportional to its solubility of the drug in polymer and
inversely proportional to thickness of the polymer membrane.
Delivery systems designed on this principle can be administered by different routes: intrauterine
such as Progestasert, implants such as Norplant, transdermal such as Transderm-Nitro, and ocular
such as Ocusert.
A matrix system, often described as monolithic device, is designed to uniformly distribute the
drug within a polymer as a solid block. Matrix devices are favored over other design due to their
simplicity, low manufacturing costs, and lack of accidental dose dumping which may occur with
reservoir systems when the rate-controlling membrane ruptures.