Area under the moment curve AUMC

The numerator of Eq. (4) is the integral of the derived function t x f(t), usually called the area under the moment curve (AUMC) (7,8). The denominator is the AUC according to Eq. (2). As visualized by the top plot of Figure 2, the mean as center of gravity represents the time value where the profile (when cut from cardboard) would be in perfect balance. 

Traditionally, linear pharmacokinetic analysis has used the n-compartment mammillary model to define drug disposition as a sum of exponentials, with the number of compartments being elucidated by the number of exponential terms. More recently, noncompartmental analysis has eliminated the need for defining the rate constants for these exponential terms (except for the terminal rate constant, Xz, in instances when extrapolation is necessary), allowing the determination of clearance (CL) and volume of distribution at steady-state (Vss) based on geometrically estimated Area Under the Curves (AUCs) and Area Under the Moment Curves (AUMCs). Numerous papers and texts have discussed the values and limitations of each method of analysis, with most concluding the choice of method resides in the richness of the data set. 

Purves, R.D. (1992) Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and area-under-the-moment curve (AUMC). Journal of Pharmacokinetics and Biopharmaceutics, 20, 211-226. 

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See also in sourсe #XX -- [ ]

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