T06) Find half life from C0, Ct and t.
50. Pharmacokinetics 50.2) Plasma concentrations over time 50.2.1) Plasma concentrations over time
T01: Later plasma concentration Normal 1
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For an intravenously administered drug, if the concentration at 2 hr is 3.25 mg/mL, and concentration at 8.3 hr is 0.523 mg/mL, then determine the elimination half life of the drug. Assume that the drug follows a first order kinetics.
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lb equals 2.39 h kg
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For a first order process,
`C_{t}=C_{0}×e^(-kt)`
It may be re-organized as:
`ln(C_{t})=ln(C_{0})-kt`
`∴ k = ln(C_{0}/C_{t})/t`
Difference between two time points (8.3 hr and 2 hr) is 6.3 hr.
`\implies k =(ln(3.25/0.523))/6.3`
Or, `k = 0.29`
Thus, the rate constant is `0.29 \quad h^{-1}`.
Now, to calculate the half life from rate constant: `t_{1/2}=0.693/k=0.693/(0.29 \quad h^(-1))=2.39 \quad h` (Ans).