Bioequivalence and Bioavailability Forum

Hi BE-proff,

❝ I do understand that I am asking stupidity but I can't catch the idea why AUMC is required?

I think good explanation you can find here and here.

AFAIK it is just a way to calculate MRT.
BTW may be PK Guru can clarify it more precisely

BE-proff,

❝ […] I can't catch the idea why AUMC is required?

In the BE-context you generally don’t need it at all. It’s only an intermediate step in calculating MRT. Who asked for it?

❝ Can anybody explain me?

We can see plasma profiles as the result of a stochastic process (drug molecules are absorbed, distributed, and metabolized/excreted). At any given time point a certain fraction is in the cir­cu­la­tion. Hey, that’s a sta­tis­tical distribution!

Distributions can be described by ‘statistical moments’

\(S_0=\int f(x)dx\)
\(S_1=\int x\cdot f(x)dx\)
\(S_2=\int x^2\cdot f(x)dx\)

where \(\small{S_0}\) is the AUC and \(\small{S_1}\) the AUMC (Area Under the Moment Curve). In PK \(\small{x=t}\) and \(\small{f(x)=C}\). We need the AUMC to calculate the MRT (Mean of Residence Times), which is for

• iv bolus
      MRT = AUMC / AUC
  
• and for infusion (of length t_inf)
      MRT = AUMC / AUC – ½t_inf

Rule of thumb: After MRT ~⅔ of the drug is eliminated.

S₂ is rarely used (for the calculation of the ‘Variance of Residence Times’): VRT = S₂/S₀ – (S₁/S₀)². MRT and VRT are the coordinates (x|y) of the ‘center of gravity’ of the profile. Try it: Plot a PK-curve on cardboard and stick a pin through x|y. Makes a nice children’s wind wheel.