## Hula-Hoop references [NCA / SHAM]

Hi Nastia,

Sadistically I throw some more into the arena. A nice quote in Brockmeier’s review 19

In 1958 [sic], F.H. Dost defined the mean life-span (“mittlere Lebensdauer”) of a total number of N molecules as the arithmetic mean of all times “zi” of any one of the N molecules residing in a pharmacokinetic system. This pharmacokinetic characteristic did not attract special interest for several years.

(my emphases)
BTW, Friedrich Hartmut Dost termed “Pharmakokinetik” in 1953 1

Pharmakokinetik ist die Lehre von der quantitativen Auseinandersetzung zwischen Organismus und einverleibten Pharmakon, sonst nichts weiter.
Pharmacokinetics is the science of the quantitative relationship between the organism and incorporated drug, nothing else. (my translation)

Pharmakokinetik is a portmanteau word from ancient Greek φαρμακός (drug) + κινητικός (putting in motion). In the early 1960s (by whom: Gerald Levy, Sidney Riegelman, John Wagner, Milo Gibaldi?) it was translated to pharmacokinetics.

Picky in the list of abbreviations 19

AUC = Area under the curve, most frequently computed by the trapezoidal rule and therefore more appropriately denoted as area under the data (AUD).
AUMC = Area under the first moment curve, i.e. the curve derived by multiplying the concentration by time (C(t)×t). Most frequently computed with the data and integrated by the trapezoidal rule and therefore more appropriately denoted as area under the first moment data (AUMD).

(my emphases)

» » There is a big problem with it. To get a reliable estimate of AUC one has to cover 95% (!) of AUC0–∞ (note that I’m not taking about BE but hard-core PK). For AUMC is should be 99%. I’m quoting Les Benet. Don’t blame me.
»
» Could you please explain this more detaily? What do you mean in getting a reliable estimate of AUC?

I was wrong (not for the first time). 3
$$C_p=\frac{A}{k_a-k_e}(\textrm{e}^{-k_et}-\textrm{e}^{-k_at}) \tag{6}$$

When the time course is measured until the plasma concentration becomes 5% of its maximum, the relative cutoff errors in AUC, MRT, and VRT are smaller than 5%, 10%, and 40%, respectively, and they are independent of the value $$\small{A}$$ in equation 6. If the time course is measured up to the time when plasma concentration becomes 1% of its maximum, the relative errors in AUC, MRT, and VRT are smaller than about 1%, 2%, and 10%, respectively.

1. Dost FH. Der Blutspiegel. Konzentrationsabläufe in der Kreislaufflüssigkeit. Leipzig: VEB Thieme; 1953.
2. Dost FH. Über ein einfaches statistisches Dosis-Umsatz-Gesetz. Klin Wochenschr. 1958; 36(14):655–7. doi:10.1007/bf01488743.
3. Yamaoka K, Nakagawa T, Uno T. Statistical Moments in Pharmacokinetics. J Pharmacokin Biopharm. 1978;6;547–58. doi:10.1007/BF01062109.
4. Cutler DJ. Theory of the mean absorption time, an adjunct to conventional bioavailability studies. J Pharm Pharmacol. 1978;30(8):476–8. doi:10.1111/j.2042-7158.1978.tb13296.x.
5. von Hattingberg HM, Brockmeier D. Standardisierung von Rechenmodellen zur Prüfung der Bioverfügbarkeit von Arzneimitteln. In: Rietbrock N, Schnieders B, editors. Bioverfügbarkeit von Arzneimitteln. Stuttgart, New York: Gustav Fischer; 1979. p. 191–209. ISBN 3-437-10654-6.
6. Riegelman S, Collier P. The application of statistical moment theory to the evaluation of in vivo dissolution time and absorption time. J Pharmacokin Biopharm. 1980;8:509–34. doi:10.1007/BF01059549.
7. Weiss M. Residence Time and Accumulation of Drugs in the Body. Int J Clin Pharm Ther Toxicol. 1981;19(2):82–5. PMID 7216555.
8. Hattingberg HM, Brockmeier D. A Concept for the Assessment of Bioavailability in Complex Systems in Terms of Amounts and Rates. In: Botzler G, van Rossum JM, editors. Pharmacokinetics During Drug Development: Data Analysis and Evaluation Techniques. Stuttgart, New York: Gustav Fischer; 1982. p. 315–23. ISBN 3-437-10654-6.
9. Chan KK, Gibaldi M. Estimation of Statistical Moments and Steady-State Volume of Distribution for a Drug Given by Intravenous Infusion. J Pharmacokin Biopharm. 1982;10(5):551–8. doi:10.1007/BF01059037.
10. Gouyette A. Pharmacokinetics: Statistical Moment Calculations. Drug Res. 1983;33(1):173–6. PMID 6681972.
11. Matis JH, Wehrly TE, Metzler CM. On Some Stochastic Formulations and Related Statistical Moments of Pharmacokinetic Models. J Pharmacokin Biopharm. 1983;11(1);77–92. doi:10.1007/BF01061769.
12. Beal SL. Some Clarifications Regarding Moments of Residence Times With Pharmacokinetic Models. J Pharmacokin Biopharm. 1987;15(1):75–92. doi:10.1007/BF01062940.
13. Brockmeier D, von Hattingberg HM. Mean Residence Time. Methods Find Exp Clin Pharmacol. 1986;8(5):309–12. PMID 3724305.
14. Kasuya Y, Hirayama H, Kubota N, Pang KS. Interpretation and Estimates of Mean Residence Time With Statistical Moment Theory . Biopharm Drug Dispos. 1987;8(3):223–34. doi:10.1002/bdd.2510080304.
15. Nakashima E, Benet LZ. General treatment of mean residence time, clearance, and volume parameters in linear mammillary models with elimination from any compartment. J Pharmacokin Biopharm. 1988;16(5):475–92. doi:10.1007/BF01062381.
16. Purves RD. Optimum Numerical Integration Methods for Estimation of Area-Under-the-Curve (AUC) and Area-under-the-Moment-Curve (AUMC). J Pharmacokin Biopharm. 1992;20(3):211–26. doi:10.1007/BF01062525.
17. Cheng H, Gillespie WR, Jusko WJ. Mean Residence Time Concepts for Non-Linear Pharmacokinetic Systems. Biopharm Drug Disp. 1994;15:627–41. doi:10.1002/bdd.2510150802.
18. Cheng H, Gillespie WR. Volumes of distribution and mean residence time of drugs with linear tissue distribution and binding and nonlinear protein binding. J Pharmacokin Biopharm. 1996;24(4):389–402. doi:10.1007/bf02353519.
19. Brockmeier D. Mean Time Concept and Component Analysis in Pharmacokinetics. Int J Clin Pharmacol Ther. 1999;37(11):555–51. PMID 10584977.

Dif-tor heh smusma 🖖
Helmut Schütz

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