Biomedical Engineering Reference
In-Depth Information
A network model of the liver was developed [ 10 ] consisting of a square lattice
of vascular bonds connecting two types of sites that represent either sinusoids
or hepatocytes. Random walkers explored the lattice at a constant velocity and
were removed with a set probability from hepatocyte sites. To simulate different
pathological states of the liver, random sinusoid or hepatocyte sites were removed.
For a lattice with regular geometry, it was found that the number of walkers decayed
according to an exponential relationship. For a percolation lattice with a fraction
p of the bonds removed, the decay was found to be exponential for high trap
concentrations but transitioned to a stretched exponential at low trap concentrations.
The models described above are all basic random walk models, and the lattices are
abstract representations of the geometry of the exploration space. Ideally, one would
strive for the incorporation of agent-based lattice models with anatomically correct
fractal-like models of specific organs such as the liver, kidneys, lungs, etc.
2
Nonlinearity in Pharmacokinetics
As stated above, nonlinear pharmacokinetics exists when the parameters are dose- or
time- dependent [ 52 ]. With dose-dependence, an increase in the administered dose
results in a disproportionate increase in the absorbed dose. The most common type
of dose-dependence discussed in the literature follows Michaelis-Menten kinetics,
where the clearance of a drug changes with concentration due to saturation of the
drug action sites. References to time-dependent nonlinearity are much less frequent,
although Levy [ 38 ] lists the following possible sources: absorption and elimination
parameters, systemic clearance, enzymatic metabolic activity, plasma binding, renal
clearance, and cerebrospinal fluid drug concentration. It is also worth mentioning
that both dose and time dependences can be present simultaneously. Because the
body is a complex system, the observed concentration values are the end product of
many intricate interactions.
2.1
Power Laws and Fractals
Complex systems often pose major challenges to applied mathematicians who
model them using various simplifications. Fortunately, sometimes, as is the case
with pharmacokinetic processes taking place in the human body, they can be
described by reasonably simple mathematics due to the presence of scaling rules
which result in power laws. Power laws have been found across scientific disciplines
including ecology, biology, economics, chemistry, physiology, and physics [ 20 ].
Theyaregivenbythesimpleformula:
Ax α .
g
(
x
)=
(13)
Search WWH ::




Custom Search