# PharmPK Discussion - Statistical Moments Theory

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• On 20 Jul 2007 at 17:30:17, habeeb ibrahim (habeebibrahim_ar.at.yahoo.co.in) sent the message

Dear All,

I have 2 qns in the basics. Kindly clarify.

1) What exactly is Statistical Moments Theory? How it is useful in
calculating MRT & AUMC?

2) What is the significance of calculating AUMC in the determination
of Bioavailability of a drug? Where it will be useful?

Thanking you in anticipation

Habeeb Ibrahim
Nicholas Piramal India Ltd.,

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• On 25 Jul 2007 at 19:25:50, "Nadeem Irfan Bukhari" (nadeemirfan_bukhari.-at-.imu.edu.my) sent the message

The following message was posted to: PharmPK

Dear Habeeb
The concept of statistical moments was transfered from chemical
engineering and chromatographic theory and was first used in PK by
Yamaoka Kiyoshi et al, in J. Pharmkin.Biopharm, 6(6). 547-558 (1978).
The author regarded the plasma level time curve as the statistical
distrubution curve and the parameters used to describe the moments of
the cruve were defined as AUC, MRT (mean residence time), and VRT
(variance of residence of drug in the body) are rearded as the zeor,
first normal and second central moments, respectively. Simply the
concept is to define how long on average a drug molecule stay at some
place, in body without making a distiction between elimination by
excretion or elimination by metabolism for example. MRT is a parameter
where the statistical moment theory is particularly employed. It is
because the variability of MRT between drug molecues form a frequency
distribution residence times just like other statistical distribution by
its mean. AUMC is the area under the first moment plasma level time
(ConcentrationXTime vs time) curve. It is used to calculate MRT, time
needed for a molecules to reach the central compartment (MIT) and mean
absorption time (MAT).
One can also find a lot of references one the topic. Some of them are:

Application of statistical moment theory to pharmacokinetics Mayer and
Brazzell J Clin Pharmacol .1988; 28: 481-483.
Willi Cawellow Ed. Parameters for compartment-free pharmacokinetics.
Shaker Verlag, 2003.
Pharmacokinetic book by Milo Gibaldi