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PharmacokineticsSingle intravenous bolus injection into one compartmentLet us revert to the example described previously where the initial concentration was 10mg/L and K = 0.1h -1 and calculatethe concentration 12 hours after injection (See Figure 5.3).C t= C 0x e -KtC t= C 0x exp(-Kt)= 10mg/L x exp(-0.1h -1 x 12h)= 10mg/L x exp(-1.2) [The exponential is now unitless as h -1 and h cancel out]If we now use a calculator to obtain a value for exp(-1.2) as described above, it will be 0.301. The calculation becomes:C t= 10mg/L x 0.301= 3.01mg/LSo, given an initial concentration of 10mg/L and an elimination rate constant of 0.1h -1 , the concentration remaining after12h should be 3.01mg/L. This agrees with Figure 5.3.10C 0 = 10 mg/L9Concentration (mg/L)8765432Conc at 12 hours (C t )100 5 10 15 20 25 30Time (Hours)Figure 5.3 Calculating concentration at 12 hours post dosing.5.2.2 Time at which concentration falls to a particular levelWe may want to calculate how long it will take for drug concentrations to fall to some specified figure. For example, indrug overdose, we might want to know how long it would take for concentrations to fall to a safe level.Consider the following scenario: Current drug concentration (C 0) is 35mg/L and concentrations below 20mg/L are likelyto be safe. The drug has an elimination rate constant of 0.045h -1 . In the absence of any special measures, how long wouldwe have to wait for levels to fall low enough to be non-toxic?51Download free ebooks at bookboon.com