Example Calculation:

1. A dose of 200 mg of a drug with V = 30 L and kel = 0.2 hr^-1 was given to a patient. What is the drug concentration imediately and after 2 hours?

The following plasma concentrations can be calculated

Cp = Cp0 * e- kel * t

Thus:

Cp⁰ = 200/30 = 6.7 mg/liter, Cp² = 4.5

2.  The pharmacokinetic parameters kel and V can be determined if we know the dose given and the plasma concentrations at two (or more) times after an IV administration. This is done using Equation 5 in the form:

ln Cp = ln Cp⁰ - kel*t

If Cp¹ = 5.5 mg/liter and Cp⁴ = 2.3 mg/liter after a 200 mg IV dose then:

slope = -kel =  (ln 2.3 - ln5.5) / 4-1

= -.87 / 3 = -0.29 /hr, thus kel = 0.29 /hr.

Now ln Cp ¹ = ln Cp⁰ - kel * t, so

ln 5.5 = ln Cp⁰ - 0.29 x 1

ln Cp⁰ = 1.705 + 0.29 = 1.99

Cp⁰ =  1.99 = Dose / V

V = Dose / V = 200 / 1.99 = 100.5 L

3. A drug with kel = 0.20 hr^{- 1} and V = 30 L was given.  Calculate the dose required by rapid IV, to achieve a plasma concentration of 5.0 ug/ml (= 5.0 mg/L) at 3 hours.

Thus Cp³ = Cp⁰ * e^{- kel*t} or Cp³ = (Dose / V)*e^-kel*t

Substituting in the values we know:

5.0 = (Dose / 30)* e^-.20*3

solving for Dose we get

Dose = 150 / .549 = 273.3 mg.