T03) Find C0 from Ct, k 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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A 68 -kg patient has received an IV bolus injection of a drug. A sample of blood was collected 3.9 hours after the first collection. The drug follows a first order elimination process, and its elimination rate constant is `0.176 \quad h^{-1}`. If the plasma concentration was 1.48 mg/L in the second sample, then what was the concentration in the initial sample?
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lb equals 2.94 mg/L kg
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For a first order process,
`C_{t}=C_{0}×e^(-kt)`
It may be re-organized as:
`C_{0}=C_{t}/(e^(-kt))`
Or, `C_{0}=C_{t}×e^(kt)`
Plugging the values in above equation, we get:
`C_{0}=1.48 × e^(0.176 × 3.9)`
`∴ C_{0}=2.94`
Thus, the initial concentration was: 2.94 mg/L. (Ans).