Purpose
To investigate the concentration of medication in the blood
To calculate the re-medication times for a given medication
To graph the concentration of medication with respect to time
Materials
Graph paper
Calculator
Background
All drugs have a serum half life, or the time it takes for excretion processes to lower the serum concentration by half. To maintain the effect of the drug the patient must receive regular fixed doses, this enables the drug to maintain its concentration. Pharmacokinetic models can be used to regulate the administration of drugs for the patient so that the concentration of drugs can remain at a certain peek. The half life t1/2 of a drug is the time for the plasma concentration or the amount of the drug in the body to be reduced by 50%> In some cases the disease may affect the half life of the drug, therefore the formula t1/2 = 0.693 (V/CL) gives the relationship between the half life, clearance and the volume of distribution.
Steady State
Steady state concentration will be reached when the drug is administered at a constant rate.
Drug Elimination: CL = (Rateofconcentration/ concentration) or Drug Elimination = Clearance x concentration.
During each dosage of a drug the concentration of the drug rises and falls, therefore steady state rises and falls and is identical in each interval.
Activities
1. After an 8 mg injection of a drug, the readings of the drug concentration after 2 seconds intervals are given in the table.
(table available in print form)
Graph the concentration of this drug over time. Then use the graph to respond to the following questions;
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a) What was the concentration of the drug at t(2)
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b) When was the concentration at its peak?
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c) At what times if any was the concentration the same?
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d) At what time was the concentration at its lowest?
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e) To be effective the concentration of the drug should be between 7.00 and 5.00 what times should the drug be re-administered?
2. The half- life of a certain cancer drug is 4 hours. Suppose a patient is given 10mg of this drug.
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a) Find an equation that can be used to model the amount remaining after t hours
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b) When will there be 8 mg of drugs remaining?
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c) After how long will there be only 2 mg?
3. A patient is given a drug intravenously at a rate of 43.2 mg/ hr to relieve her headache. If the drug is entering a component of volume 35,000 ml (this is the volume of the part of the body through which the drug circulates). The rate at which the drug leaves the patient is proportional to the quantity entered, with the proportionality constant 0.080.
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a) Make a table and graph the concentration of the drug in the patient for 5 hours.
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b) Write a differential equation that can be used to satisfy the concentration of the drug.