More useful equations can be derived from this general equation. These are equations to calculate the maximum and minimum plasma concentration after many doses. That is as n ---> and t = 0 or t = t. These are the limits of the PLATEAU CONCENTRATIONS.
Equation XIV-17 Cp Immediately after Many Doses
Equation XIV-18 Cp Immediately before Many Doses
An example may be helpful: t1/2 = 4 hr; IV dose 100 mg every 6 hours; V = 10 liter
What are the Cpmax and Cpmin values when the plateau values are reached
kel = = 0.17 hr-1
R = e-kel * = e-0.17 x 6 = 0.35
therefore the plasma concentration will fluctuate between 15.5 and 5.4 mg/liter during each dosing interval when the plateau is reached.
We can now calculate the plasma concentration at any time following multiple IV bolus administration and we can calculate the Cpmax and Cpmin values.
Figure XIV-11, Plot of Cp Versus Time showing Time to Approach 50% of Plateau during Multiple Dose Regimen
Plasma Concentration versus Time Plots
In the previous example Cpmax = 15.5 mg/liter
A suitable loading dose would be Cpmax * V
155 mg as a bolus would give Cp = 15.5 mg/liter, followed by 100 mg every 6 hours to maintain the Cpmax and Cpmin values at 15.5 and 5.5 mg/liter respectively.
The loading dose is Cpmax * V
(see Equation XIV-17, page XIV-11)
Equation XIV-19 Loading Dose
Maintenance DOSE = Loading DOSE * (1 - R)
We can try another example of calculating a suitable dosing regimen.
Consider V = 25 liter; kel = 0.15 hr-1 for a particular drug and we need to keep the plasma concentration between 35 mg/liter (MTC) and 10 mg/liter (MEC).
What we need is the maintenance dose, the loading dose, and the dosing interval.
R = e-kel * = 0.2857
- kel * = -1.2528 or
= 8.35 hour; the dosing interval.
A dosing interval of 8 hours would be more reasonable. Thus with = 8 hr and kel = 0.15 hr-1
R = e-kel * = e-8 x 0.15 = 0.3012
If we use Cpmax =
Maintenance dose = Cpmax * V * (1 -R) = 35 x 25 x (1 -0.3012) = 611 mg
Again a more realistic dose would be 600 mg every 8 hours.
Cpmax = = 34.3 mg/L
Cpmin = Cpmax * R = 10.3 mg/L
This regimen would be quite suitable as the maximum and minimum values are still within the limits suggested. All that remains is to calculate a suitable loading dose.
Loading dose = Cpmax * V = 35 x 25 = 875 mg either 875, 850 or 800 mg
This answer can be expressed graphically.
Figure XIV-11. Plasma Concentration after Multiple IV Bolus Doses
Copyright 2002 David W.A. Bourne