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When I have modeled iv data using compartmental microconstants I have
often used the following formula to calculate lambda-z: lambda_z = 0.5 *
((k12 + k21 + k10) - ((k12 + k21 +k10)^2 - (4 * k21 *k10))^0.5)
(If the formatting (superscript and symbol font) did not come through
well on the listserve this would be
lambda-z = 0.5 * ((k12 + k21 + k10) - ((k12 + k21 +k10)^2 - (4 * k21
*k10))^0.5) , where the ^ symbol means raised the the power of.)
I have an extravascular two-compartment model with a lag time and want
to compare the lambda-z for it to the iv lambda-z to see if I have a
flip-flop model. Will this formula work for this extravascular model?
(If so, it must indeed have a flip-flop model because the iv and the
oral data rate constants using this formula are quite different.) If
not, is there a formula for calculating lambda-z for two-compartment
extravascular dosings with Tlag?
(Yes, I know there are software programs that would provide lambda-z as
a secondary parameter, but I really would prefer not to learn a new
software program if I can avoid it. If I have to, I might just perform
linear regression on the terminal points without fitting the whole
model; but I'd rather the whole fit be taken into account if possible.)
Thanks,
Cory
-
Cory Langston, DVM, PhD, DACVCP
College of Veterinary Medicine
240 Wise Center Drive
Mississippi State, MS 39762-6100
[How about plotting the data on semi-log graph paper and comparing the slopes visually ;-)
Also, if you have fit the extravascular data with micro-constants you could calculate Cp at
two time points in the 'terminal' phase and calculate the slope. In Boomer I would add these
as data points with zero weight (to not disturb the fit) - db]
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The following message was posted to: PharmPK
Dear Cory,
The calculation of lambda-z from the rate constants will be the same for
iv and oral administration, so I don't think this is a problem. However,
a more problematic question is how you obtained these rate constants. If
you have oral data, fitting the data to a two-compartment model with
first-order absorption will result in two different solutions with
exactly the same predicted concentration profile and objective function
value, analogous to the 'flip-flop' in the case of a one-compartment
model. However, these two solutions have different rate constants k10,
k12 and k21. Since most computer programs provide only one of these two
solutions (usually assuming that the fastest 'macro rate constant' is
the absorption rate constant, without any reasonable argument), you may
not be aware of this. In addition, accurate estimation of the rate
constants is cumbersome, unless the number of measurements is very high.
Therefore, in my view, fitting data to a two-compartment model with
first-order absorption (without information about the PK after
intravenous administration) does not make sense at all.
I agree with David's suggestion: this is the 'classical and reliable'
approach, avoiding the aforementioned problems.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
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The following message was posted to: PharmPK
Dear Cory:
Yes, it does make sense to fit a 2 compartment model with oral
absorption just as you might with a 1 compartment model with oral
absorption. Dr. Proost is correct that you will have the flip-flop. But it
is easy to get around this. Just choose which of the 2 solutions you wish to
estimate. If you want the one where the Ka is faster than the Ke, you simply
parameterize your model by saying that V=V, Ke = Ke, but Ka = Ke + X. Then
your Ka will always be faster. On the other hand, if you have a sustained
release formulation, for example, and you want the Ke to be the faster, then
V=V, Ka = Ka, but Ke = Ka + X. Easy to get around the flip flop this way.
Microconstants are not hard to get. Dr. Proost is correct that it
is always good to start any project with data as rich as possible. But as
you study new subjects (say 5) you can make a pop model. Then you can use
D-optimal design to estimate the optimal times to sample for the model you
think you have. Then do another 5. Remodel with the10 subjects. Do optimal
design again, and so forth, until you get happy or the sampling times get
stable. It is true that this involves circular reasoning that you are
supposed to know the parameter vales from which you develop the optimal
design. But that appears to be the current state of the art.
David Bayard in our lab is also studying a new method of multiple
model optimal design which he has developed for nonparametric PK models
which avoids this circular reasoning. It is being submitted for a poster at
the PAGE meeting in June in Glasgow.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.
Professor of Medicine,
Founder and Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
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