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Dear all,
I have a question regarding the calculation of absorption rate constant (Ka) from plasma concentration-time profile. Method of residuals can be used to calculate the same for a profile having numerous sampling points in the absorption phase before Cmax, however if we have the first sampling point as Cmax what should be our approach to calculate ka?
The first sampling point as Cmax was seen in my experiment at 5 mins after administering drug solution sublingually in an animal model.
Hoping to get some answers/clarifications on the same.
Thanks & regards,
Navdeep Kaur
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The following message was posted to: PharmPK
Dear Navdeep,
You asked:
" I have a question regarding the calculation of absorption rate constant
(Ka) from plasma concentration-time profile. Method of residuals can be
used to calculate the same for a profile having numerous sampling points in
the absorption phase before Cmax, however if we have the first sampling
point as Cmax what should be our approach to calculate ka?
The first sampling point as Cmax was seen in my experiment at 5 mins after
administering drug solution sublingually in an animal model."
Please keep in mind that ka is not a constant. That is an approximation that
is used much too often without considering how wrong it can be in many
instances. The absorption rate in any species is a coefficient - it is
changing with time. Only in cases of very rapid absorption (high solubility
and high permeability) can you feel somewhat constant that treating ka as a
constant is a reasonable assumption. For anything else (and even some of
those) you need to realize that ka can vary over a very wide range. At time
0, ka = 0. For solid dosage forms, it increases as drug goes into solution
and the concentration gradient across the intestinal wall increases. As drug
is absorbed, that concentration gradient decreases, and so does ka.
To properly calculate absorption rate as a function of time, you need a
mechanistic simulation that accounts for the various factors that affect it.
Dissolution, potential precipitation, regionally dependent permeability due
to ionization and other effects, and influx and efflux transporters, for
example, can cause significant changes in ka as a function of time.
GastroPlus has been developed and refined over 14 years with the ACAT
(Advanced Compartmental Absorption and Transit) model as the most
sophisticated example of such simulation software.
Best regards,
Walt
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (NASDAQ: SLP)
42505 10th Street West
Lancaster, CA 93534-7059
U.S.A.
http://www.simulations-plus.com
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Walter
On 9/11/2010 6:44 a.m., Walt Woltosz wrote:
> For anything else (and even some of
> those) you need to realize that ka can vary over a very wide range. At time
> 0, ka = 0. For solid dosage forms, it increases as drug goes into solution
> and the concentration gradient across the intestinal wall increases. As drug
> is absorbed, that concentration gradient decreases, and so does ka.
If I didn't know you were not a beginning pharmaceutics student I would give you zero out of 10 for misunderstanding the difference between absorption rate and the first-order rate constant, Ka.
If you replaced Ka by 'absorption rate' in what you wrote then I would give you a much higher mark. Would you like to explain to us all why you deserve a better mark? :-)
Nick
-- Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology& Clinical Pharmacology
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
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Hi Walt,
Thanks for your comment. However, the case I am referring to here is sublingual absorption so there is no regional variability and drug solution (Drug administered in the form of solution) is rapidly being absorbed i.e. Cmax being obtained at first time point- 5min. In that case what would be the best way to calculate absorption rate coefficient/constant (ka).
Thanks & regards,
Navdeep Kaur
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The following message was posted to: PharmPK
Nick,
Nick,
I'll admit to perhaps typing faster than thinking after returning from 3
weeks on the road and trying to clear over 150 e-mails (that remained even
after doing as many as I could at night in various hotels). :o)
Let me try explaining my point once again:
In GastroPlus, we back calculate the net ka (from the various absorption
rates in all compartments) that would be required to use the classical
equation:
dMabs/dt = ka*Mdiss
i.e., absorption rate = ka x mass dissolved/in solution
thus,
ka(net) = sum across compartments [(dMabs/dt)/(Mdiss)]
When you look at the plots, you see a value that starts at zero, then
typically increases with a shape somewhat like and immediate release plasma
concentration-time curve, peaks, and falls off to a low level. Why?
Because the ka is different in each region of the gastrointestinal tract,
and the remaining (unabsorbed) drug is distributed and is transiting through
the various regions. Thus, the net ka (i.e., the instantaneous value that
would be back calculated from the actual net absorption rate across all
compartments at a point in time and total amount of drug in solution within
the lumen at that time) changes with time. The individual compartment ka's
would be constant for passive diffusion, but could also be time-dependent if
saturation of transporters was involved. We tend to call this ka by the name
of ka' to distinguish it from the oversimplified concept of a single
constant ka.
Thus, in general, absorption is not first order, and ka is not constant.
Wish that it were that easy!
Best regards,
Walt
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Hi Walt,
I am still unclear as to how to apply this to my situation viz sublingual administration.
The equation you mentioned
dMabs/dt = ka*Mdiss
I am uncertain how we would get the absorption rate without knowing ka- as you mentioned that it can be back calculated using the above equation.
Hoping to get some clarifications on the same.
Thanks & regards,
Navdeep Kaur
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The following message was posted to: PharmPK
Navdeep,
We have an oral cavity dosing option in GastroPlus(tm) which simulates
various aspects of lingual, sublingual, and buccal administration, including
swallowing of a portion of the dose. It can get complicated, depending on
the nature of your drug and dosage form. If you have sufficient data, a
model can be fitted to determine the unknown parameters.
Best regards,
Walt
Walt Woltosz
Chairman & CEO
Simulations Plus, Inc. (NASDAQ: SLP)
42505 10th Street West
Lancaster, CA 93534-7059
U.S.A.
http://www.simulations-plus.com
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The following message was posted to: PharmPK
Navdeep
Having seen how fast fentanyl produces its effects from sublingual
dosing I doubt that a systemic absorption constant would be very
useful if you have a CNS active compound. You may find that rate of
absorption into the brain is more relevant.
Andrew
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The following message was posted to: PharmPK
Hi Navdeep,
The oral cavity dosing option within GastroPlus predicts the permeability of
the drug molecule from its physiochemical properties, using a variant of the
Potts-Guy equation (also used extensively in skin formulation). We are
currently working on updating that with a better correlation.
Hope this helps.
Thanks,
Ray
Siladitya Ray Chaudhuri
Senior Scientist - Simulation Technologies
Simulations Plus, Inc.
42505 10th Street West, Lancaster, CA 93534
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Hi Ray,
You mentioned that 'GastroPlus predicts the permeability of the drug molecule from its physiochemical properties'. Does that mean it is used to calculate absorption rate constant in any way?
Thanks & regards,
Navdeep Kaur
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The following message was posted to: PharmPK
Hi Navdeep,
The predicted permeability is multiplied by the 'Absorption Scale Factor' to
obtain the absorption rate constant (even though I still have trouble
calling it a 'constant' knowing how variable it can be). Simply put, the
absorption scale factor in any compartment is the ratio of the surface area
to the volume, which for a cylinder reduces to 2/R, where R is the radius of
the compartment. However, do note that the absorption rate constant is
different for different compartments i.e. the mouth or any of the 9
compartments of our Advanced Compartmental Absorption and Transit (ACAT)
model. Thus, the rate of drug absorption in any compartment is calculated
directly from this permeability as:
Abs Rate = Permeability x Abs Scale Factor x Volume of Liquid layer (Lumen
for the intestine or saliva layer for the mouth) x (Conc in the liquid layer
- Conc in the cell layer)
Once Abs Rate is computed as Walt pointed out earlier:
"In GastroPlus, we back calculate the net ka (from the various absorption
rates in all compartments) that would be required to use the classical
equation:
dMabs/dt = ka*Mdiss
i.e., absorption rate = ka x mass dissolved/in solution
thus,
ka(net) = sum across compartments [(dMabs/dt)/(Mdiss)]"
In conclusion, it is the permeability (or diffusivity) of the drug that is
calculated from its structure/ physicochemical properties (or correlated
form in vitro measurements) and absorption rate constant is calculated from
this permeability.
Hope this helps.
Kind regards,
Ray
Siladitya Ray Chaudhuri, PhD
Senior Scientist - Simulation Technologies
Simulations Plus, Inc.
42505 10th Street West, Lancaster, CA 93534
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