Chapter 32 Optimal Sampling

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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

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