Back to the Top
PharmPK - Discussions about Pharmacokinetics
Pharmacodynamics and related topics
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
College of Pharmacy
Seoul National University
San 56-1, Shillim-Dong, Kwanak-Gu,
Seoul, 151-742, KOREA
Back to the Top
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
Back to the Top
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
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
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (firstname.lastname@example.org)