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XX Non-linear pharmacokinetic models


=> 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

This page was last modified: 12 February 2001

Copyright 2001 David W.A. Bourne

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