Where did the Poison come from?

Forensic Pharmacokinetics

A few years ago a prominent politician was found to be suffering from chemical poisoning. The poison detected in their blood was not a single compound but a group of related compounds. Each of the compounds has slow linear elimination kinetics that appear to follow one compartment pharmacokinetics. Topical absorption is relatively rapid and complete and since elimination was quite slow calculations can be based on IV bolus equations. The blood sample was carefully assayed and three components were quantitated.

Component Fraction Found in
the Blood Sample
Elimination
half life
A 16.32% 17.9 days
B 68.96% 37.9 days
C 14.72% 13.9 days

The most likely time that the politician was poisoned was 60 days before the blood sample was collected. There were three possible sources of the poison. Solid samples from each of these sources were available. Also, because the synthetic process used to prepare these sample was different they contained different proportions of each marker compound. The samples were carefully assayed to determine the amount of each marker component and the amounts were expressed as a present in the table below.

Component Fraction Found
in Sample 1
Fraction Found
in Sample 2
Fraction Found
in Sample 3
A 25% 31% 44%
B 31% 44% 25%
C 44% 25% 31%

Your objective as the forensic pharmacokineticist in charge is to determine the sample most likely to have poisoned the politician! Estimate the fractions present when the posion was administered


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Graph Paper Resources

Graph Paper in PDF Format. If you have Adobe Reader installed or Preview in Mac OS X clicking on the links below will provide the graph paper indicated.

Some Equations:

Amount at time t

kel from the semi-log slope equation


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