Non-linear pharmacokinetic modelsObjectives:
=> To draw the scheme and write the differential equations for compartmental
pharmacokinetic models with non-linear metabolism elimination=> To
understand the process of parallel pathways as it applies with one or more
non-linear pathways
=> To define and use the parameters Vm and Km
=> To design and calculate appropriate dosage regimens when non-linear
pharmacokinetics apply
All of the rate processes discussed so far in this course, except for the
infusion process, follow first order kinetics. In particular the elimination
process has been assumed to follow first order kinetics. However occasionally it
is observed that the elimination of a drug appears to be zero order at high
concentrations and first order at low concentrations. That is 'concentration' or
'dose' dependent kinetics are observed. That is at high doses, which produce
higher plasma concentrations, zero order kinetics are observed, whereas at lower
doses the kinetics are linear, that is first order.
This occurs especially with drugs which are extensively metabolized. A
typical characteristic of enzymatic reactions and active transport is a
limitation on the capacity of the process. There is only so much enzyme present
in the liver, and therefore there is a maximum rate at which metabolism can
occur. A further limitation in the rate of metabolism can be the limited
availability of a co-substance or co-factor required in the enzymatic process.
This might be a limit in the amount of glucuronide or glycine, for example.
Most of our knowledge of enzyme kinetics is derived from in vitro
studies where substrate, enzyme, and co-factor concentrations are carefully
controlled. Many factors are involved in vivo so that each cannot be
easily isolated in detail. However, the basic principles of enzyme kinetics have
application in pharmacokinetics.
Dose dependent pharmacokinetics can often be described by Michaelis-Menten
kinetics with the RATE of elimination approaching some maximum rate, Vm.
Equation 86
with Km a Michaelis-Menten constant. Km is the concentration at which the
rate of metabolism is 1/2 the maximum rate, Vm
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