Purpose
To calculate using rate of change the amount of drug eliminated from the body over time.
Materials
Calculator
Background: The Elimination of Drugs from the Body
Pharmacokinetics provides a functional (mathematical) relationship between the dose of drugs, its effect and way with which to interpret the concentration of drugs in the blood stream. This important issue in pharmacokinetics in most important in patient care, because it can dictate the intervals when the drug doses will be repeated.
The three most important parameters are clearance ( the body's ability to eliminate drugs), volume distribution ( a measure of the space in which the patient's body to contain the drug), bioavailability ( the fraction of the drug that is absorbed in the body).
Clearance of drug is usually constant over the range of concentrations, and can be determined by a linear function. A constant fraction of the drug is eliminated per unit of time.
Clearance (CL) = Rate of elimination / concentration
Since clearance can take place in different organs of the body, the elimination of drugs can be considered as a summative relationship and systemic clearance given by
CL systemic = CL renal + CL liver + CL other
Drugs are eliminated from the body either unchanged or as metabolites. Each excretory organ plays its role in the elimination process. The kidney is the organ that has the responsibility of excreting most of the waste from the body.
Problem: Let C(t) be the concentration of a drug in the blood stream. As the body eliminates the drug C(t) decreases at a rate that is proportional to the amount of the drug that is present at the time. C (t) = - k c(t) where k is a positive number called the elimination constant of the drug.
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a) If c is the concentration at t = 0 find the concentration at time t
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b) If the body eliminates half the drug in 30 hrs, how long does it take to eliminate 90 % of the drug?