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 103 -kg patient has received an IV bolus injection of a drug. A sample of blood was collected 4.4 hours after the first collection. The drug follows a first order elimination process, and its elimination rate constant is `0.239 \quad h^{-1}`. If the plasma concentration was 0.318 mg/L in the second sample, then what was the concentration in the initial sample?


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lb equals 0.91 mg/L kg

    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}=0.318 × e^(0.239 × 4.4)`
    `∴ C_{0}=0.91`
    Thus, the initial concentration was: 0.91 mg/L. (Ans).