## Non Compartmental Analysis

Table XIX-2 Typical Cp versus Time Data after IV Bolus Administration

Non compartmental methods can be used to determine certain pharmacokinetic parameters without deciding on a particular compartmental model. The basic calculations are based on the area under the plasma concentration versus times curve (zero moment) and the first moment curve (AUMC). The AUC can be calculated as before using by the trapezoidal rule. The first moment is calculated as concentration times time (Cp * t). The AUMC is the area under the concentration times time versus time curve. Maybe best covered with an example. Consider a drug given both by iv and oral administration. Both the AUC and AUMC were calculated using the trapezoidal rule without making any assumption concerning the number of compartments. The final segment of the AUC curve is calculated as Cp(last)/k, where k is the last exponential (the slowest). The last segment for the AUMC curve is:

From the AUC and AUMC values we can calculate the mean residence time, MRT. This is the average time that the drug stays in the body (or plasma as measured here). It can be related to the average elimination rate constant as 1/MRT. The values from the above data are MRT = 553.21/67.43 = 8.2 hr and k = 1/8.2 = 0.122 hr- 1. Remember we can also calculate the clearance, CL = Dose/AUC = 100/67.43 = 1.48 L.hr- 1. Finally a steady state volume can be calculated as CL * MRT = 1.48 x 8.2 = 12.2 L.

In summary:

Table XIX-3 Typical Cp versus Time Data after Oral Administration

The following data were calculated after a 250 mg oral dose of the same drug. From these data a MRT was calculated as 1360.98/149.78 = 9.08 hr. We can subtract from this MRT(PO) the MRT(iv) to get an idea of the absorption process, the mean absorption time (MAT). That is MAT = MRT(PO) - MRT(iv) = 9.08 - 8.20 = 0.88 hr. From this we can calculate an average absorption rate constant = 1/MAT = 1/0.88 = 1.14 hr-1. Of course we can calculate the bioavailability of the oral dosage form using the dose adjusted AUC ratio.

Thus F = (149.78/67.43) x (100/250) = 0.89.

In summary : MAT = MRT(PO) - MRT(iv)

 Figure XIX-15 Plot of Cp versus Time (IV)
 Figure XIX-16 Plot of Cp x Time versus Time (IV)
 Figure XIX-17 Plot of Cp versus Time (PO)
 Figure XIX-18 Plot of Cp x Time versus Time (PO)

Homework Set 1997