Page 191 - Biomedical Engineering and Design Handbook Volume 2, Applications

170 MEDICAL DEVICE DESIGN
If

2( C − C D h h
)
A
p
p d p
2
h >>
p
⎛ C ⎞
p
⎜ ⎝ C − 2 ⎠ ⎟ DkK
d
A
where the depletion zone is much larger and the system has a very thin diffusion layer, Eq. (6.10)
becomes
/
12
⎛ 2 CD p ⎞
p
h ≈ t (6.14)
p ⎜ C p ⎟
⎜ ( C − ) ⎟
⎝ A 2 ⎠
and placing Eq. (6.14) into Eq. (6.9) makes
Q = [( 2 C − C C D ] 12 /
)
t 12 / A p p p (6.15)
Equation (6.15) indicates that after the depletion zone is large enough, the cumulative amount of
drug released (Q) is proportional to the square root of time (t ).
1/2
6.6 DISSOLUTION/COATING-CONTROLLED DELIVERY SYSTEMS
Controlled release of drug can be achieved by utilizing the rate-limiting step in the dissolution
process of a solid drug with relatively low aqueous solubility. The dissolution rate can be quantita-
tively described by Noyes-Whitney equation as follows:

dC DA
= ( C − C ) (6.16)
0
t
dt h
where dC/dt = rate of drug dissolution
D = diffusion coefficient of drug in diffusion layer
h = thickness of diffusion layer
A = surface area of drug particles
C = saturation concentration of the drug in diffusion layer
0
C = concentration of drug in bulk fluids at time t
t
The surface area A of the drug particle is directly proportional to the rate of dissolution. For a
given amount of drug, reducing particle size increases its surface area and dissolution rate. However,
small particles tend to agglomerate and form aggregates. Using a specialized milling technique with
stabilizer and other excipients, aggregation can be prevented to make microparticles smaller than
400 nm in diameter to improve the dissolution of the drug in the body.
The saturation solubility C can also be manipulated to change the rate of dissolution. Both the
0
physical and chemical properties of a drug can be modified to alter the saturation solubility. For
example, salt form of a drug is much more soluble in aqueous environment than the parent drug. The
solubility of a drug can also be modified when the drug forms complex with excipients, resulting in
a complex with solubility different from the drug itself.
Controlled or sustained release of drug from delivery systems can also be designed by enclosing
drug in a polymer shell/coating. After the dissolution or erosion of the coating, drug molecules