Chemistry Reference
In-Depth Information
One model currently used at our organization is as follows. The states in the model
include the mass of undissolved drug in the GI tract (
M
), the concentration of dissolved
drug (
C
), and the fraction of the dose absorbed (
A
). The dissolution rate scales with the
amount of undissolved drug in the GI tract and the concentration gradient between
the diffusion boundary layer around the undissolved particles
—
a zone that is taken to be
saturated with respect to drug
and bulk
C
. The solubility of the API, which is also its
concentration in the boundary layer, is
s
, and its mass transfer rate is the constant
h
.
V
is
the volume of the
—
fluid in the GI tract.
D
is the dose. The dissolution rate admits two
xed
points:
C
0. (In other words, dissolution ceases when the concentration in the
bulk reaches the thermodynamic solubility of the material or when all of the solid has
dissolved.) Finally, the model assumes first-order absorption with a constant permeation
rate
k
. The last equation below de
=
s
and
D
=
nes the cumulative amount of drug absorbed.
d
M
d
t
hM
s
C
;
V
d
C
d
t
hM
s
C
kC
;
D
d
A
d
t
kC
:
Initial conditions are
M
0
D
;
C
0
A
0
0
:
Next, we can introduce the following nondimensionalization scheme:
M
D
;
CV
D
;
A
D
;
t
T
;
M
C
A
t
s
D
=
V
;
kT
V
;
σ
η
hsT
;
ξ
where
T
is the transit time of the drug through the GI tract,
σ
is solubility normalized by
the maximum theoretical concentration in the GI tract,
η
is the dimensionless mass
transfer rate, and
ζ
is a dimensionless permeation rate. The absorption model becomes
;
d
M
d
t
η
M
1
C
σ
ξ
C
d
C
d
t
η
M
1
C
;
σ
d
A
d
t
ξ
C
:
M
0
1
;
C
0
A
0
0
:
