Results and Discussion
Continued
By:
Kristin Ackermann
Amanda Rohs
Blanca Skelding
Determining Intrinsic Permeation Rate


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Saturated drug solution, Cs, in donor
compartment
Monitor permeation of drug through
membrane by sampling receptor
compartment
Permeation rate is a function of:


Partition coefficient of drug toward
membrane
Thickness of diffusion boundary layer (on
both sides of membrane)
Schematic of Drug Conc. Profile
Permeation Rate Per Unit Area
dQ
DK
C1  C2   km C2  C 
 k m Cs  C1  
dt
l

(Eq. 9)
In Equation (9) above:








D = diffusivity of drug through membrane
K = partition coefficient
l = membrane thickness
km = mass transfer coef.
C1 = conc. of drug in donor phase boundary
C2 = conc. of drug in receptor phase boundary
C = conc. Of drug in bulk soln.
Q = cumulative amount of drug permeated
Explanation of Terms
Term 1
Term 2
Term 3
dQ
DK
C1  C2   km C2  C 
 k m Cs  C1  
dt
l



(Eq. 9)
Term 1: Solute diffusion in receptor
solution mass balance
Term 2: Diffusivity through membrane
Term 3: Solute diffusion in donor
solution mass balance
More Explanation

Rearranging Eqn (9) results in Eqn (10):
dQ k m (C s  C )

dt 2  k m l / DK

(Eq. 10)
If the mixing is so vigorous that diffusion
boundary layer can be eliminated, Eqn
(10) is simplified to:
DK (Cs  C )
 dQ 



l
 dt  Sh
(Eq. 11)
Effect of Diffusion Boundary Layer

The effect of diffusion boundary layer on rate of
drug permeation can be represented in Eqn (12a).
dQ
  dt
Where


 dQ 


 dt  Sh
(Eq. 12a)
γ represents the permeation rate per area when
boundary layer is present divided by the permeation
rate when the boundary layer is negligible
Sh->∞ represents the mass transfer coef.
approaching infinity, which would cause the
boundary layer effects to be negligible.
Effect of D.B.L. (continued)

Substituting Eqns (10) and (11) into Eqn
(12a), Eqn (12c) results:

1
2K
Shl
(Eq. 12c)
1
Where Shl is the Sherwood number in
terms of membrane thickness

Since Sh = Shl(D/Df )(d/l), Eqn (12c)
becomes Eqn (13):

  1  2
D
Df

K
Sh  l 
d
1
(Eq. 13)
Effect of D.B.L. (continued)


From Eqn (13), the effect of the
diffusion boundary layer on the rate of
drug permeation can be evaluated
It can be observed that large partition
coefficient and a small Sh will cause
significant effect on intrinsic permeation
rate
Example

When water is used as elution media
and a polymeric membrane, 2 drugs of
similar molecular weight have the
following parameters:
Drug I
D = 4.5 X 10-7 cm2/s
Df = 7 X 10-6 cm2/s
K = 50.2
L = 0.05 cm
D = 0.9 cm
Drug II
D = 4.5 X 10-7 cm2/s
Df = 7 X 10-6 cm2/s
K = 0.05
L = 0.05 cm
D = 0.9 cm
Example
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For both drugs, Sh = 229
For Drug I, g = 0.063
For Drug I, g = 0.995
Experimental permeation rate = 1.0
mg/(cm2h)
Intrinsic permeation rate is:


Drug I = 1.5mg/(cm2h)
Drug I = 1.0mg/(cm2h)
Example (continued)
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
Experimental permeation rate for
drugs I and II is approx. 33% and
0% less than intrinsic rate
Examples illustrate importance of
partition coefficient in determination
of permeation rate
Conclusion
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Mass transfer characteristics of benzoic acid
from a disk surface were investigated to
calibrate in vitro membrane permeation cell
Solution solubility and dissolution rate of
benzoic acid were measured in aqueous PEG
400
Correlating equation for mass transfer
coefficients was established using Sh-Re-Sc
equation
Effect of diffusion boundary layer on rate of
controlled drug release can now be evaluated
accurately using correlation obtained in study
Questions??