Chapter 32 Optimal Sampling

return to the Course index
previous | next

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 32.3.1.

Equation 32.3.1 Concentration versus Time - One Compartment IV Bolus

Differentiating Cp versus kel gives Equation 32.3.2

Equation 32.3.2 dCp/dkel versus time

Next, differentiating dCp/dt versus time gives Equation 32.3.3

Equation 32.3.3 d²Cp/dkel.dt versus time

Rearranging Equation 32.3.3 with kel equal to 0.2 hr^-1 gives a value of 5 hour as the best sample time.

Equation 32.3.4 Best sample time when kel is 0.2 hr^-1

This page was last modified: Sunday, 28th Jul 2024 at 5:11 pm

Privacy Statement - 25 May 2018

Material on this website should be used for Educational or Self-Study Purposes Only

Bird Count
An iPhone app that facilitates the geotagging of Bird Count stops
and the return to the same stops during the next
and subsequent Bird Count sessions