## Prof. Keller vs. Yamaoka [NCA / SHAM]

❝ I was wrong (not for the first time).^{ 1}

❝ $$C_p=\frac{A}{k_a-k_e}(\textrm{e}^{-k_et}-\textrm{e}^{-k_at}) \tag{6}$$

❝ 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.

Prof. Keller disagrees

^{ 2}:

`<...>for an acceptable estimate of the MRT`_{trunc} the last concentration to be measured should be 1.096 % of the initial concentration value or less. Accordingly, the concentration curve must be followed for approximately a 2 log decline (10^{–2}*C_{0} <= C_{n}). Thus, the truncation at a concentration that is 1 % of the initial concentration will result in a 5 % error of the cut MRT estimate and not 2 % as stated by Yamaoka et al. According to mono-exponential kinetics, the near 2 log period lasts for 6.51 times the elimination half-life<...>

By the way I couldn't follow Yamaoka's logic regarding that magic cut-off errors. How did they find it?

Regarding prof.Keller's note: he's using IV data for cut-off errors estimation, so it is not clear why he did compare it with 1-cpt model with oral first-order absorption in Yamaoka's article.

- Yamaoka K, Nakagawa T, Uno T.
*Statistical Moments in Pharmacokinetics.*J Pharmacokin Biopharm. 1978;6;547–58. doi:10.1007/BF01062109.

- Keller F, Hartmann B, Czock D.
*Mean residence time as estimated from cropped and truncated moments.*Arzneimittelforschung. 2009;59(7):377-381. doi:10.1055/s-0031-1296411.

Kind regards,

Mittyri

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