We can calculate the line (in Figure VIII-1) using the integrated form of the equation. Starting with the differential equation we can substitute Xg = Xg *e-ka * t. The integration process won't be described here but a reference, which describes the Laplace transform method of integration , can be presented. This method makes integration as easy as the logarithmic transform makes multiplication and division easier.
If we use F * DOSE for Xg0 where F is the fraction of the dose absorbed, the integrated equation for Cp versus time is :-
Notice that the right hand side of this equation (Equation VIII-4) is a constant multiplied by the difference of two exponential terms. A biexponential equation.
We can plot Cp as a constant times the difference between two exponential curves (see Figure II-1). If we plot each exponential separately.
Figure VIII-3, Linear Plot of e-ka x t versus Time for Two Exponential Terms
Notice that the difference starts at zero, increases, and finally decreases again.
Plotting this difference by
gives Cp versus time.
We can calculate the plasma concentration at anytime if we know the values of all the parameters of Equation VIII-4.
We can also calculate the time of peak concentration using the equation:-
As an example we could calculate the peak plasma concentration given that F = 0.9, DOSE = 600 mg, ka = 1.0 hr-1, kel = 0.15 hr-1, and V = 30 liter.
= 2.23 hour
= 21.18 x [ 0.7157 - 0.1075] = 12.9 mg/L
As another example we could consider what would happen with ka = 0.2 hr-1 instead of 1.0 hr-1
= 5.75 hour
= 72 x (0.4221 - 0.3166) = 7.6 mg/L lower and slower than before
Copyright 2001 David W.A. Bourne