Integrated equation

If we use F • DOSE for Xg⁰ where F is the fraction of the dose absorbed, the integrated equation for Cp versus time is shown in Equation 17.3.1.

Equation 17.3.1 Drug Concentration after an Oral Dose

Notice that the right hand side of this equation (Equation 17.3.1) 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 2.2.1). If we plot each exponential separately.

Figure 17.3.1 Linear Plot of e^{-k' 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.

Figure 17.3.2 Linear Plot of Drug Concentration versus Time

We can calculate the plasma concentration at anytime if we know the values of all the parameters of Equation 17.3.1.

By setting the rate of change of Cp versus time, dCp/dt, to zero and after some rearranging an equation for the time of peak can be derived.

Equation 17.3.2 Time of Peak Concentration after an Oral Dose

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.

As another example we could consider what would happen with ka = 0.2 hr^-1 instead of 1.0 hr^-1

lower and slower than before.

References

• Mayersohn, M and Gibaldi, M. 1970 Mathematical Methods in Pharmacokinetics. I Use of the Laplace Transform for Solving Differential Rate Equations, Amer. J. Pharm. Education, 34, 608-614

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Copyright 2001-3 David W. A. Bourne (david@boomer.org)