Dear David, WaltBack to the Top
Are we going to let Walt get away with asserting Ka is not a constant?
Perhaps if he says it often enough people will think it is true.
As Walt so eloquently argues the absorption rate constant is determined
by several physiological parameters and the physical chemistry of the
drug, but it is not dependent on the drug concentration. Similarly the
reabsorption rate constant (if I can call it that) depends on
physiological parameters and the physicochemistry of the drug but does
not depend on the blood concentration of the drug. Fick's Law does
indeed state the rate of absorption is proportional to the difference
in concentrations either side of the membrane, but this refers to the
net transfer. Walt appears to think that movement across the membrane
ceases when the concentrations are equal. It doesn't; we just have a
dynamic equilibrium and there is no need to invoke a variable Ka. It
is Fick's Law which is the simplification, not the concept of Ka being
So let's keep the Ka just like the Ka we all know and love - that is
it's a constant!
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I think Walt is completely right. Ka is not a constant. It's a
theoretical concept conveniently applied by many modellers. It assumes
that the amount absorbed is immediate and maximum at time=0 (unless
there is a lag time, the immediate release is shifted to time tlag). It
may be a good approximation for a clean and very fast absorption (e.g
oral solution). However, for many other formulations absorption is not
that immediate, but more progressive with time. For such formulations
it is therefore not a good approximation.
We did some deconvolution work on 6 different formulations (caps and
tabs) for one compound. Not a single input rate vs time curve followed
that of constant Ka. It rather followed the patterns like that of a
chromatogram: the result of passing trough a chromotagraphic column.
The gastrointestinal track can be regarded as an absorption column,
sometimes with tailing, sometimes with double peaks due to different
absorption characteristics at different places in the intestines. It
might be an idea to first apply a deconvolution (if you have enough
data) and get a rough impression of your input rate vs time. Than
select an absorption model that mimics that pattern.
Kees Bol, PhD
Director Clinical Pharmacokinetics
Lage Mosten 29
4822 NK Breda
tel: +31 (0) 76 54 80 621
gsm: +31 (0) 65 31 26 153
fax: +31 (0) 76 54 21 777
Dear PharmPK colleagues,Back to the Top
Do we mean that Ka is constant with respect to time, with respect to
concentration, or with respect to distance down the GI tract?
Ka is a function of the permeability x surface area coefficient at the
level of the epithelial membrane. Both vary down the length of the GI
tract as both Papp and SA. It may appear as constant with a simple
model when averaged out for any one subject (if insufficient data is
collected on the absorption phase of the timecourse). Both Papp and SA
can vary with time, disease state or genetic disposition. Papp varies
as a function of transporter expression (inward and outward), opening
up the possibilities of concentration, time and comedication/excipient
dependence of Ka.
Best regards, Phil.
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Some days ago there was a comment on whether the absorption rate
constant (ka) is constant or not. I have lost the mail but the author
argued that ka is not a constant since physiological properties that
affect the rate of absorption change during the passage of the drug
through the intestine.
I have no doubt about the changing GI-environment. And I am certain
these changes can have an impact on the absorption rate of a compound.
However, I imho the notion of ka does not (and is not meant to)
reflect the time course of the absorption rate but rather an average
rate. In a similar way, one could say that liver blood flow or the
enzyme activity changes constantly and thus CL cannot be constant.
Although true, the average CL still can be used to describe the
elimination of a compound by hepatic metabolism.
PK/PD modeling is simplification of what really is happening in a very
complex biological system. Since we cannot measure the rate of
absorption at any moment, we use an average term (ka) to describe the
rate of absorption of a compound over a period of time. We cannot
measure the exact liver blood flow or enzyme activity but still can
describe the elimination of a compound by an average value for the CL.
We are aware that these terms are not the true estimates at any
specific time, but it does not make their use in describing the time
course of a drug from intake to elimination redundant.
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