# PharmPK Discussion - Absorption rate constant

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• On 6 Nov 2010 at 13:56:19, Navdeep Kaur (kaurnavy.-a-.gmail.com) sent the message
`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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• On 8 Nov 2010 at 09:44:07, Walt Woltosz (walt.-a-.simulations-plus.com) sent the message
`The following message was posted to: PharmPKDear Navdeep,You asked:" I have a question regarding the calculation of absorption rate constant(Ka)  from plasma concentration-time profile. Method of residuals can beused to calculate the same for a profile having numerous sampling points inthe absorption phase before Cmax, however if we have the first samplingpoint as Cmax what should be our approach to calculate ka?The first sampling point as Cmax was seen in my experiment at 5 mins afteradministering drug solution sublingually in an animal model."Please keep in mind that ka is not a constant. That is an approximation thatis used much too often without considering how wrong it can be in manyinstances. The absorption rate in any species is a coefficient - it ischanging with time. Only in cases of very rapid absorption (high solubilityand high permeability) can you feel somewhat constant that treating ka as aconstant is a reasonable assumption. For anything else (and even some ofthose) you need to realize that ka can vary over a very wide range. At time0, ka = 0. For solid dosage forms, it increases as drug goes into solutionand the concentration gradient across the intestinal wall increases. As drugis absorbed, that concentration gradient decreases, and so does ka.To properly calculate absorption rate as a function of time, you need amechanistic simulation that accounts for the various factors that affect it.Dissolution, potential precipitation, regionally dependent permeability dueto ionization and other effects, and influx and efflux transporters, forexample, 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 mostsophisticated example of such simulation software.Best regards,WaltWalt WoltoszChairman & CEOSimulations Plus, Inc. (NASDAQ: SLP)42505 10th Street WestLancaster, CA  93534-7059U.S.A.http://www.simulations-plus.com`
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• On 9 Nov 2010 at 07:30:52, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`WalterOn 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 PharmacologyDept Pharmacology&  Clinical PharmacologyUniversity of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand`
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• On 8 Nov 2010 at 10:44:24, Navdeep Kaur (kaurnavy.at.gmail.com) sent the message
`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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• On 8 Nov 2010 at 15:15:28, Walt Woltosz (walt.at.simulations-plus.com) sent the message
`The following message was posted to: PharmPKNick,Nick,I'll admit to perhaps typing faster than thinking after returning from 3weeks on the road and trying to clear over 150 e-mails (that remained evenafter 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 absorptionrates in all compartments) that would be required to use the classicalequation:  dMabs/dt = ka*Mdissi.e., absorption rate = ka x mass dissolved/in solutionthus,ka(net) = sum across compartments [(dMabs/dt)/(Mdiss)]When you look at the plots, you see a value that starts at zero, thentypically increases with a shape somewhat like and immediate release plasmaconcentration-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 throughthe various regions. Thus, the net ka (i.e., the instantaneous value thatwould be back calculated from the actual net absorption rate across allcompartments at a point in time and total amount of drug in solution withinthe lumen at that time) changes with time. The individual compartment ka'swould be constant for passive diffusion, but could also be time-dependent ifsaturation of transporters was involved. We tend to call this ka by the nameof ka' to distinguish it from the oversimplified concept of a singleconstant 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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• On 9 Nov 2010 at 09:39:58, Navdeep Kaur (kaurnavy.-at-.gmail.com) sent the message
`Hi Walt,I am still unclear as to how to apply this to my situation viz  sublingual administration.The equation you mentioneddMabs/dt = ka*MdissI 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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• On 9 Nov 2010 at 11:45:41, Walt Woltosz (walt.-a-.simulations-plus.com) sent the message
`The following message was posted to: PharmPKNavdeep,We have an oral cavity dosing option in GastroPlus(tm) which simulatesvarious aspects of lingual, sublingual, and buccal administration, includingswallowing of a portion of the dose. It can get complicated, depending onthe nature of your drug and dosage form. If you have sufficient data, amodel can be fitted to determine the unknown parameters.Best regards,WaltWalt WoltoszChairman & CEOSimulations Plus, Inc. (NASDAQ: SLP)42505 10th Street WestLancaster, CA  93534-7059U.S.A.http://www.simulations-plus.com`
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• On 9 Nov 2010 at 20:55:49, andrew sutton (drandrewsutton.-at-.gmail.com) sent the message
`The following message was posted to: PharmPKNavdeepHaving seen how fast fentanyl produces its effects from sublingualdosing I doubt that a systemic absorption constant would be veryuseful if you have a CNS active compound. You may find that rate ofabsorption into the brain is more relevant.Andrew`
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• On 9 Nov 2010 at 14:31:11, Siladitya Ray Chaudhuri (ray.-at-.simulations-plus.com) sent the message
`The following message was posted to: PharmPKHi Navdeep,The oral cavity dosing option within GastroPlus predicts the permeability ofthe drug molecule from its physiochemical properties, using a variant of thePotts-Guy equation (also used extensively in skin formulation). We arecurrently working on updating that with a better correlation.Hope this helps.Thanks,RaySiladitya Ray ChaudhuriSenior Scientist - Simulation TechnologiesSimulations Plus, Inc.42505 10th Street West, Lancaster, CA 93534`
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• On 9 Nov 2010 at 23:00:07, Navdeep Kaur (kaurnavy.-at-.gmail.com) sent the message
`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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• On 10 Nov 2010 at 09:48:36, Siladitya Ray Chaudhuri (ray.-a-.simulations-plus.com) sent the message
`The following message was posted to: PharmPKHi Navdeep,The predicted permeability is multiplied by the 'Absorption Scale Factor' toobtain the absorption rate constant (even though I still have troublecalling it a 'constant' knowing how variable it can be). Simply put, theabsorption scale factor in any compartment is the ratio of the surface areato the volume, which for a cylinder reduces to 2/R, where R is the radius ofthe compartment. However, do note that the absorption rate constant isdifferent for different compartments i.e. the mouth or any of the 9compartments of our Advanced Compartmental Absorption and Transit (ACAT)model. Thus, the rate of drug absorption in any compartment is calculateddirectly from this permeability as:Abs Rate = Permeability x Abs Scale Factor x Volume of Liquid layer (Lumenfor 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 absorptionrates in all compartments) that would be required to use the classicalequation: dMabs/dt = ka*Mdissi.e., absorption rate = ka x mass dissolved/in solutionthus,ka(net) = sum across compartments [(dMabs/dt)/(Mdiss)]"In conclusion, it is the permeability (or diffusivity) of the drug that iscalculated from its structure/ physicochemical properties (or correlatedform in vitro measurements) and absorption rate constant is calculated fromthis permeability.Hope this helps.Kind regards,RaySiladitya Ray Chaudhuri, PhDSenior Scientist - Simulation TechnologiesSimulations Plus, Inc.42505 10th Street West, Lancaster, CA 93534`
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