# PharmPK Discussion - Extravascular lambda-z from micro-constants

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• On 5 Mar 2013 at 13:16:32, Cory Langston (Langston.at.cvm.msstate.edu) sent the message
`When I have modeled iv data using compartmental microconstants I haveoften 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 throughwell on the listserve this would belambda-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 wantto compare the lambda-z for it to the iv lambda-z to see if I have aflip-flop model. Will this formula work for this extravascular model?(If so, it  must indeed have a flip-flop model because the iv and theoral data rate constants using this formula are quite different.)  Ifnot, is there a formula for calculating lambda-z for two-compartmentextravascular dosings with Tlag?(Yes, I know there are software programs that would provide lambda-z asa secondary parameter, but I really would prefer not to learn a newsoftware program if I can avoid it. If I have to, I might just performlinear regression on the terminal points without fitting the wholemodel; but I'd rather the whole fit be taken into account if possible.)Thanks,Cory-Cory Langston, DVM, PhD, DACVCPCollege of Veterinary Medicine240 Wise Center DriveMississippi 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 attwo time points in the 'terminal' phase and calculate the slope. In Boomer I would add theseas data points with zero weight (to not disturb the fit) - db]`
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• On 7 Mar 2013 at 15:15:55, "J.H.Proost" (j.h.proost.-a-.rug.nl) sent the message
`The following message was posted to: PharmPKDear Cory,The calculation of lambda-z from the rate constants will be the same foriv and oral administration, so I don't think this is a problem. However,a more problematic question is how you obtained these rate constants. Ifyou have oral data, fitting the data to a two-compartment model withfirst-order absorption will result in two different solutions withexactly the same predicted concentration profile and objective functionvalue, analogous to the 'flip-flop' in the case of a one-compartmentmodel. However, these two solutions have different rate constants k10,k12 and k21. Since most computer programs provide only one of these twosolutions (usually assuming that the fastest 'macro rate constant' isthe absorption rate constant, without any reasonable argument), you maynot be aware of this. In addition, accurate estimation of the rateconstants is cumbersome, unless the number of measurements is very high.Therefore, in my view, fitting data to a two-compartment model withfirst-order absorption (without information about the PK afterintravenous 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 ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 7 Mar 2013 at 14:47:15, Roger Jelliffe (jelliffe.aaa.usc.edu) sent the message
`The following message was posted to: PharmPKDear Cory:Yes, it does make sense to  fit a 2 compartment model with oralabsorption just as you might with a 1 compartment model with oralabsorption. Dr. Proost is correct that you will have the flip-flop. But itis easy to get around this. Just choose which of the 2 solutions you wish toestimate. If you want the one where the Ka is faster than the Ke, you simplyparameterize your model by saying that V=V, Ke = Ke, but Ka = Ke + X. Thenyour Ka will always be faster. On the other hand, if you  have a sustainedrelease formulation, for example, and you want the Ke to be the faster, thenV=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 itis always good to start any project with data as rich as possible. But asyou study new subjects (say 5) you can make a pop model. Then you can useD-optimal design to estimate the optimal times to sample for the model youthink you have. Then do another 5. Remodel with the10 subjects. Do optimaldesign again, and so forth, until you get happy or the sampling times getstable. It is true that this involves circular reasoning that you aresupposed to know the parameter vales from which you develop the optimaldesign. But that appears to be the current state of the art.David Bayard in our lab is also studying a new method of multiplemodel optimal design which he has developed for nonparametric PK modelswhich avoids this circular reasoning. It is being submitted for a poster atthe PAGE meeting in June in Glasgow.Very best regards,Roger JelliffeRoger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.Professor of Medicine,Founder and Co-Director, Laboratory of Applied Pharmacokineticswww.lapk.orgUSC Keck School of Medicine2250 Alcazar St, Room 134-BLos Angeles CA 90033`
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