- On 12 May 1997 at 15:57:45, Young-Joo Lee (leeyj.aaa.plaza.snu.ac.kr) sent the message

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PharmPK - Discussions about Pharmacokinetics

Pharmacodynamics and related topics

Dear friends:

I have some question on log-trapezoidal rule.

Is there another name(formal name) of "modified log-trapezoidal rule"(in up

phase, linear trapezoidal; in terminal phase, log trapezoidal)?

And I have read one protocol that use log-trapezoidal rule to calculate AUMC.

I don't understand it's meaning.

Is it possible to use log-trapezoidal rule to calculate AUMC?

I think in calculating MRT or Vdss, in spite of using AUC calculated by

log-trapezoidal, AUMC must be calculated by linear trapezoidal rule.

I want to heard your response..

---------------------

Young-Joo Lee, Researcher

Pharmaceutic Lab.

College of Pharmacy

Seoul National University

San 56-1, Shillim-Dong, Kwanak-Gu,

Seoul, 151-742, KOREA

E: leeyj.aaa.snu.ac.kr

--------------------- - On 13 May 1997 at 11:26:03, "Vladimir Piotrovskij" (VPIOTROV.-a-.JANBELC1.SSW.JNJ.COM) sent the message

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Dear Dr. Lee,

Since AUMC is the area under the time*Cp curve, and the tail of the

latter behaves (irrespective to the route of administration) like a

(disturbed) monoexponetial function, the combined trapezoidal rule

(linear in the ascending part and log-linear in the descending part of

the curve) is applicable in general. Of course, the accuracy of this

approximation is significantly less than in case of AUC. Moreover, the

random noise in Cp will disturb the estimates of AUMC obtained by the

trapezoidal rule in much more extent as compared to AUC. Therefore, to get

reliable estimates of MRT and Vss you need much more precise data and more

data points than to estimate CL.

--------

Vladimir Piotrovsky, Ph.D. Fax: +32-14-605834

Janssen Research Foundation Email: vpiotrov.-a-.janbe.jnj.com

Clinical Pharmacokinetics vpiotrov.aaa.janbelc1.ssw.jnj.com

B-2340 Beerse

Belgium - On 14 May 1997 at 15:59:10, Hans Proost (J.H.Proost.at.farm.rug.nl) sent the message

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Dear Colleague,

There is no difference in the way AUC and AUMC should be calculated;

both are areas of a continuous function, which can be calculated

mathematically if the functions are known.

If only data points are known, the areas can be estimated by various

methods; in general, the linear and log trapezoidal rules are the

preferred methods because of their robustness (more sophisticated

methods may be more sensitive to outliers, et cetera).

The choice between the linear and log trapezoidal rule depends ONLY

on the expected profile BETWEEN the data points. If the profile is

expected to be almost linear, or if the profile is expected to be

higher than the linear interpolation, then the linear rule is

preferred. If the profile is expected to follow a curve below the

linear interpolation, the log rule should be used. The latter is

obviously the case during exponential decline.

The simple rule of using the linear rule during the inclining parts,

and the log rule during the declining parts of the curve, can be used

in most cases.

A better criterion for choosing between the linear and log rule can

be found in my paper in J.Pharm.Sci. 1985;74:793-794.

Please note the problems of extrapolation if the last sampling point

is not very low. The extrapolation errors for AUMC are much more

pronounced than for AUC. As a result, the calcuated MRT may be

inaccurate.

Best regards,

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.-at-.farm.rug.nl

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