I fear some correspondents may not be interpreting my remarks as IBack to the Top
intended them.
In no way am I suggesting Ka is a single all-encompassing constant
that describes the process from administered drug to appearance in the
blood. I merely wish to emphasise that the movement across a membrane
is proportional to the concentration of drug on either side (depending
on which way you are going) and that this proportionality constant Ka
is not itself dependent on the concentrations. I fully accept that
this Ka is determined by factors such as surface area and these factors
are subject to change, but my main point is that Ka does not vary with
concentration.
Joe Chamberlain
Back to the Top
The following message was posted to: PharmPK At 09:32 AM 2/9/2004, Joe
Chamberlain wrote:
"I fear some correspondents may not be interpreting my remarks as I
intended them.
In no way am I suggesting Ka is a single all-encompassing constant
that describes the process from administered drug to appearance in the
blood. I merely wish to emphasise that the movement across a membrane
is proportional to the concentration of drug on either side (depending
on which way you are going) and that this proportionality constant Ka
is not itself dependent on the concentrations. I fully accept that
this Ka is determined by factors such as surface area and these factors
are subject to change, but my main point is that Ka does not vary with
concentration."
Sometimes . . .
I believe Ka is well-represented as:
Ka = Peff * S / V
where Peff = effective permeability
S = surface area
V = fluid volume in the lumen
Because Peff is a number that is calculated from an observed steady
state condition (wherein the absorption rate is constant during the
measuring time), when we turn it around to calculate absorption, we
need to use the same kind of surface/volume relationship. For a
cylinder, S/V = 2/R, where are is the radius of the lumen. When Hans
Lennernas and Gordon Amidon conducted the human Peff experiments, the
2/R value used was 2/1.75 = 1.143. In other words, an assumed effective
fluid volume radius of 1.75 cm was used.
Thus, the absorption rate in human is:
dMabs/dt = Peff * 1.143 * (Clumen - Centerocyte)
But we must keep in mind that Peff, S, and V all change as the drug
moves from duodenum to jejunum, ileum, and colon.
Peff differs from one region to another for drugs that are subject to
carrier-mediated transport (influx or efflux), those that permeate by
paracellular transport, and those whose ionization changes
significantly with the pH changes along the gastrointestinal tract.
Peff does, in fact, change with concentration for saturable
carrier-mediated transport, so Ka would change with concentration for
such compounds.
Surface area decreases aborally.
The diameter of the small intestine decreases aborally as well,
affecting volume.
So for an accurate prediction of absorption rate along the
gastrointestinal tract, we need to know how Peff changes with position,
and how S/V changes with position. If we divide the gastrointestinal
tract into a series of compartments, then we can treat the Peff and S/V
in each compartment as a constant as long as there are no saturable
carrier-mediated transporters involved. This requires a different Ka in
each compartment.
With this approach, we can look at the absorption rate for the whole
system over time and see that IF we want to use the traditional
constant Ka absorption equation for the entire time:
dMabs/dt = Ka * Mdiss
where Mdiss = total mass of drug in solution at time t
then we would have to modify Ka over time to get the correct result,
accounting for the change in Ka as the remaining unabsorbed drug moves
down the gastrointestinal tract.
In other words, Ka, as it has been traditionally used, would not be a
constant.
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (SIMU)
1220 W. Avenue J
Lancaster, CA 93534-2902
U.S.A.
http://www.simulations-plus.com
Phone: (661) 723-7723
FAX: (661) 723-5524
E-mail: walt.at.simulations-plus.com
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)