Download Nuffield Free Standing Mathematics Activity

Nuffield Free-Standing Mathematics Activity
Drug clearance
© Nuffield Foundation 2011
Drug clearance …
…. is concerned with the rate at which an active drug is removed
from your body.
‘For most drugs, the model that works best is that this rate is
proportional to the quantity of the drug remaining in your body.’
Can you write this statement as a differential equation?
Can you solve it?
© Nuffield Foundation 2011
The solution of the differential equation gives a
graph like that shown below.
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The full dose is present at the start.
The amount of drug present
diminishes over time.
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The amount of drug in the blood can be easily measured
and hence what proportion of the original dose is present
It is easy to see when the
drug has reached half the
original quantity
This time is
called the halflife of the drug
© Nuffield Foundation 2011
After you establish the half-life of a drug, there is an
equation from which you can calculate the amount
of drug present at any time.
• Half-lives vary from drug to drug, and from
person to person.
• Ibuprofen has a half-life of 2 to 4 hours, depending
on the size and other characteristics of the person.
• With caffeine, the variation is even greater.
© Nuffield Foundation 2011
Reflection
The rate at which your body removes drugs is proportional to
the quantity of the drug that remains in your body.
What is the differential equation that models this
situation?
What is the typical form of the solution?
Can you sketch a typical graph?
What is meant by the half-life of a drug?
Is the half-life of a drug the same for all people?
© Nuffield Foundation 2011
Explore more at
http://sonet.nottingham.ac.uk/rlos/bioproc/ha
lflife/index.html
© Nuffield Foundation 2011