Boomer Manual and Download
PharmPK Listserv and other PK Resources
Previous Page	Course Index	Next Page

Optimal Sampling

Analytical Approach

The analytical method is somewhat more calculus intensive and therefore maybe some what limited. However, the simple example of a one compartment model after an IV bolus is somewhat straightforward.

The steps are:

Differentiate Cp versus each Parameter, P_i, to determine dCp/dP_i
Differentiate dCp/dP_i versus time to determine d²Cp/dP_i.dt
Set d²Cp/dP_i.dt to zero to find the time for the maximum value of dCp/dP_i
Solve for time

Starting with the equation for concentration versus time curve, Equation 21.3.1.

Equation 21.3.1 Concentration versus Time - One Compartment IV Bolus

Differentiating Cp versus kel gives Equation 21.3.2

Equation 21.3.2 dCp/dkel versus time

Next, differentiating dCp/dt versus time gives Equation 21.3.3

Equation 21.3.3 d²Cp/dkel.dt versus time

Rearranging Equation 21.3.3 with kel equal to 0.2 hr^-1 gives a value of 5 hour as the best sample time.

Equation 21.3.4 Best sample time when kel is 0.2 hr^-1

return to the Course index

This page was last modified: Sunday, 28th Jul 2024 at 5:04 pm

Privacy Statement - 25 May 2018

iBook and pdf versions of this material and other PK material is available