Biomedical Engineering Reference
In-Depth Information
Hence, we find for bioavailability that
exp
−
fCL
int
Q
=
.
F
(10)
This is the simplest mode which captures sinusoid structure of transport and
metabolism in the liver but has been met with only mixed success in predicting
physiological data.
The Distributed Tube Model assumes that the distribution of tubes satisfies a
statistical profile regarding their geometries and enzyme densities. The variance in
this distribution,
2
, depends on both path length and enzyme statistics and hence is
substrate dependent. It can be measured from a quadratic fit of log
ε
(
F
)
to 1
/
Q
.Bya
series expansion one finds
e
−<
xi
>
1
1
2
<
e
−
xi
x
i
2
F
=
<
F
i
>
=
<
>
=
+
>
+
...
,
(11)
which results in the following relation
1
2
exp
−
2
fCL
int
Q
fCL
int
Q
1
2
ε
F
=
+
,
(12)
2
2
where
ε
=
∑
i
[(
CL
int
,
i
/
CL
int
)
/
(
Q
i
/
Q
)]
and the index i runs over all individual
tubes.
Comparative studies of these models [
56
] revealed that the choice of a liver
model has most important effects for drugs with high clearance. All models have
reasonable correlation for most drugs at low clearance, but exhibit a systematic
discrepancy at high clearance, especially for the well-stirred model. The distributed
model corrects this discrepancy without altering low clearance behavior.
At a more fundamental level of model development, agent-based and fractal-
geometry-based models have been proposed and investigated. For example, a
stochastic random walk model for the drug molecules was studied [
67
], a model
of convective-diffusive transit behavior in the liver [
52
], a gamma-distributed
drug residence time model [
61
], transient fractal kinetics studies [
1
], and fractal
Michaelis-Menten kinetics [
45
] were all undertaken to come up with a more
realistic description of physiological processes involving drug molecules.
To take into account the organ heterogeneity and simulate enzyme kinetics in
disordered media, lattice models have been introduced by investigators. Berry [
7
]
performed Monte Carlo simulations of a Michaelis-Menten reaction on a two-
dimensional lattice with a varying density of obstacles to simulate the barriers to
diffusion caused by biological membranes. He found that fractal kinetics resulted at
high obstacle concentrations. Kosmidis et al. [
35
] performed Monte Carlo simula-
tions of a Michaelis-Menten enzymatic reaction on a two-dimensional percolation
lattice at criticality. They found that fractal kinetics emerged at long times.
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