Pharmaceutical Manufacturing Handbook: Production and

MEMBRANE-COATED ORAL EXTENDED RELEASE 1203
release rate will be entered. Ragnarsson et al. [49] have shown that the solid material
disappears earlier as the drug solubility increases and that the third stage with
time - dependent and decreasing release rate appears earlier compared to drugs with
lower solubility.
The contribution of diffusion to the release process can be modeled by using
Fick ’ s fi rst law. For diffusion of a substance through the membrane, it will turn out
as (assuming sink conditions)
dMt
DmKmA D K AC
= JA = ( Cs −Cb)=
dt
h
h
m m s (6)
where K m is the partition coeffi cient for the drug between the membrane and solution,
D m is the diffusion coeffi cient in the membrane, A is the area of the membrane,
h is the thickness of the membrane, and C s and C b are the concentrations on the
inside of the membrane surface and in the bulk, respectively. The equation for diffusion
through pores or cracks resembles Equation (6) :
dM
JA
dt
DKA
t ε
DεKAC = = ( Cs −Cb)=
hτ
hτ
s (7)
where ε and τ are introduced to describe the porosity and tortuosity in the
membrane, respectively. The parameters D m and K m in Equation (6) are replaced
in Equation (7) by D and K , which are the diffusion coeffi cient in the solution
inside the pores and the partition coeffi cient between the solution and materials
surrounding the liquid - fi lled pores, respectively. Equations (6) and (7) depend on
the concentration gradient over the membrane, and both are independent of the
time.
The osmotic contribution to the drug transport is described by the so - called
Kedem – Katchalsky equations (based on nonequilibrium thermodynamics) [50, 51] .
A simplifi ed version is
dMt
ACsLpσΔΠ = JA =
(8)
dt
h
where Δ Π is the osmotic pressure difference over the membrane and L p and σ are
the hydraulic permeability and the refl ection, respectively.
A comparison of Equations (6) – (8) shows important similarities; they depend on
the solubility of the drug, the area of the device, and the thickness of the membrane.
This means that an increased solubility, larger area of the membrane, and thinner
membranes will facilitate the drug release rate. This can be exemplifi ed by a study
by Ragnarsson and Johansson [11] , who showed that, for different salt forms of
metoprolol, an increased solubility also increased the drug release rate, which was
predicted from the equations. Furthermore, Equations (6) – (8) show constant and
time - independent release rates. This constant amount of released drug will be a
biopharmaceutical benefi t since it theoretically makes it possible to achieve a constant
concentration of the drug in the blood plasma.