T07) Find t from Ct, C0 and k
50. Pharmacokinetics 50.2) Plasma concentrations over time 50.2.1) Plasma concentrations over time
T01: Later plasma concentration Normal 1
Total tried: Correct: Wrong:
A patient (144 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 3.52 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination rate constant (k) is 0.308 h-1, then how long will it take to reach the plasma concentration to 0.227 mg/L?
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lb equals 8.9 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`
`\implies t = ln(C_{0}/C_{t})/k`
Plugging values in this equation,
`t =(ln(3.52/0.227))/0.308`
Or, `t = 8.9`
Thus, required time is `8.9 \quad h`.(Ans).