### T04) Find C0 from Ct, t half 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 193 -kg patient has received an IV bolus injection of a drug. A sample of blood was collected 7.5 hours after the first collection. The drug follows a first order elimination process, and its plasma half life is 3.28 hours. If the plasma concentration was 0.799 mg/L in the second sample, then what was the concentration in the initial sample?

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lb equals 3.89 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) ..... (1)
In the question, k is not provided, but we can derive it from the equation below:
k=0.693/t_{½}=0.693/(3.28 \quad h)=0.211 \quad h^{-1}.
Plugging the values in equation (1), we get:
C_{0}=0.799 × e^(0.211 × 7.5)
∴ C_{0}=3.89
Thus, the initial concentration was: 3.89 mg/L. (Ans).