# PharmPK Discussion - Lag time calculation in WNL

PharmPK Discussion List Archive Index page
• On 23 Aug 2003 at 08:14:43, Vlase Laurian (vlase.at.email.ro) sent the message
`The following message was posted to: PharmPKHelloI have a WNL user-model (first order absorption, 2 comp, first orderelimination)The WNL code I write is:MODELremark   ******************************************************remark   Developer:	remark   Model Date:	08-24-2003remark   Model Version:	1.0remark   ******************************************************remarkremark - define model-specific commandsCOMMANDSNFUNCTIONS 1NDERIVATIVES 3NPARAMETERS 6PNAMES  'v', 'lag', 'k12', 'k21', 'k10', 'ka'ENDremark - define temporary variablesTEMPORARYdose=con(1)t=xENDremark - define differential equations starting valuesSTARTZ(1) = 0Z(2) = 0Z(3) = dose/vENDremark - define differential equationsDIFFERENTIAL   DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)   DZ(2) = Z(1)*k12 - Z(2)*k21   DZ(3) = -ka*Z(3)ENDremark - define algebraic functionsFUNCTION 1F= Z(1)ENDremark - define any secondary parametersremark - end of modelEOMDoes anybody know how to introduce lag time calculation in WNL code?Thank you!Vlase LaurianPhD StudentDept. Pharm. Technol. & BiopharmaceuticsFaculty of PharmacyCluj-NapocaRomania`
Back to the Top

• On 26 Aug 2003 at 23:13:28, Huadong Sun (hd.sun.aaa.utoronto.ca) sent the message
`The following message was posted to: PharmPKIt is tough or almost impossible to incorporate t(lag) in thedifferentialequations. The solution is to try to solve the equations using Laplacetransform and linear algebra (you can facilitate this process using somemathematic software like Maple (commercial available), Maxima(freesoftware)).After you get the explicit form of concentration in every compartment,expressthe time "t" with "t-tlag" and fit your data. Hopefully you will gett-lag.314 Room, 19 Russell StreetFaculty of PharmacyUniversity of TorontoToronto, Ontario M5S2S2(Tel) 416-978-6996(Fax)416-978-8511[It is possible to incorporate an adjustable lag time with differentialequations using Boomer (and possibly other software) but fitting acrossa discontinuity can be a problem not solved by using the integratedform of the equation - or have I got that back to front ;-) - db]`
Back to the Top

• On 27 Aug 2003 at 10:34:21, "A.Heydari" (MDP00AH.-a-.sheffield.ac.uk) sent the message
`The following message was posted to: PharmPKDear Valse LaurianWith respect to the WNL Differential equation model to introduce lagtime, you could use following instruction:   remark - define differential equations   DIFFERENTIAL   if  x < tlag then   DZ(1) = 0   else   DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)   ENDIF   It would be interesting to hear comments on this topic   Thanks   Amir Heydari   PhD Student   Pharmacology Department   Royalle Halamshire Hospital   Sheffield   U.K.`
Back to the Top

• On 27 Aug 2003 at 10:28:47, "Bonate, Peter" (pbonate.at.ilexonc.com) sent the message
`The following message was posted to: PharmPKActually lagtimes can be quite easily handled with differentialequations using a lag compartment.  For example, to include a lag timebetween the absorption compartment (X1) and central compartment (X3)the DiffEqs would bedX1/dt = -ka*X1dX2/dt = ka*X1 - klag*X2dX3/dt = klag*X2 - kel*X3C = X3/VThe lag time is then 1/klag.  The more lag compartments between X1 andthe central compartment the more all or none the lag time becomes.The only price to this method is that as the number of compartmentsincreases the slower the fitting process.Good luck,Peter Bonate`
Back to the Top

• On 27 Aug 2003 at 11:08:58, "Bonate, Peter" (pbonate.at.ilexonc.com) sent the message
`The following message was posted to: PharmPKAmir Heydari writes:"With respect to the WNL Differential equation model to introduce lagtime, you could use following instruction:    remark - define differential equations    DIFFERENTIAL    if  x < tlag then    DZ(1) = 0    else    DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)    ENDIF"I wouldn't recommend this approach because the sum of squares responsesurface is no longer a smooth quadratic function but a discontinuousone, which may make fitting problematic.Pete Bonate`
Back to the Top

• On 27 Aug 2003 at 18:37:43, Jurgen Bulitta (bulitta.-at-.ibmp.osn.de) sent the message
`The following message was posted to: PharmPKDear Vlase,it is quite straight forward to include lag time inany kind of nonlin model. The code I attached shouldwork as it is. I would strongly recommend you towatch all compartments you have defined. Thus Iincluded 3 functions, since otherwise sometimesreally funny mistakes in model specificationhappen.If you are not satisfied with the speed of optimization,it is also possible to compile such nonlin models, whataccelerates things by approximately a factor of ~ 10.Hope this helps.Best regardsJuergen Bulitta================================================================== Please find the nonlin model hereMODELremark   ******************************************************remark   Developer:	remark   Model Date:	08-24-2003remark   Model Version:	1.0remark   ******************************************************remarkremark - define model-specific commandsCOMMANDSNFUNCTIONS 3NDERIVATIVES 3NPARAMETERS 6NCON 1PNAMES  'v', 'TLAG', 'k12', 'k21', 'k10', 'ka'ENDremark - define temporary variablesTEMPORARYdose=con(1)T = XENDremark - define differential equations starting valuesSTARTZ(1) = 0Z(2) = 0Z(3) = dose/vENDremark - define differential equationsDIFFERENTIALIF T GE TLAG THEN    DZ(1) = -Z(1)*k10 - Z(1)*k12 + Z(2)*k21 + ka*Z(3)    DZ(2) = Z(1)*k12 - Z(2)*k21    DZ(3) = -ka*Z(3)else    DZ(1) = 0.0    DZ(2) = 0.0    DZ(3) = 0.0endifENDremark - define algebraic functionsFUNCTION 1F= Z(1)ENDFUNCTION 2F= Z(2)ENDFUNCTION 3F= Z(3)ENDremark - define any secondary parametersremark - end of modelEOM=================================================================################################################################## Your data file should look like:# Please note, you need at least one non-missing value# for each function. I would recommend the time point at 0.0h# BQL is my code for Missing value. Any other is also fine.Time	Conc	Function0	0	10.5	BQL	11	BQL	11.5	BQL	12	BQL	12.5	BQL	13	BQL	13.5	BQL	14	BQL	14.5	BQL	15	BQL	15.5	BQL	16	BQL	10	0	20.5	BQL	21	BQL	21.5	BQL	22	BQL	22.5	BQL	23	BQL	23.5	BQL	24	BQL	24.5	BQL	25	BQL	25.5	BQL	26	BQL	20	0	30.5	BQL	31	BQL	31.5	BQL	32	BQL	32.5	BQL	33	BQL	33.5	BQL	34	BQL	34.5	BQL	35	BQL	35.5	BQL	36	BQL	3#################################################################`
Back to the Top

• On 28 Aug 2003 at 12:01:30, fabrice_nollevaux.at.sgs.com sent the message
`Vlase Laurian wrote:"I have a WNL user-model (first order absorption, 2 comp, first orderelimination)"... "Does anybody know how to introduce lag timecalculation in WNL code?"Why do you build a user-model since this model is part of the WNLinternal library of pharmacokinetic models ?-> Model 12 (micro-constants) or Model 14 (macro-constants) inWinNonlin 4.0Fabrice Nollevaux, MScSenior BiostatisticianBiometrics DepartmentSGS Biopharma SA,Vieux Chemin du Poete 10B-1301 Wavre (Belgium)`
Back to the Top

• On 29 Aug 2003 at 11:57:54, Jurgen Bulitta (bulitta.-a-.ibmp.osn.de) sent the message
`The following message was posted to: PharmPKDear Dr. Bonate, dear all,I totally agree with Dr. Peter Bonate's commentthat using tlag without a lag compartment mayhave severe disadvantages on the sum of square surface.It often turns out that tlag is the worst of all fitparameters and that tlag often converges at a pointwhere is should not. One of the reasons is that theabsorption process is often not mirrored by a simplefirst order process.To slightly improve the technical situation during fitting:- It is often helpful to define a cutoff value for tlag,setting tlag to zero if the first estimate is below say 1-3 min.- One should take time in getting realistic initials for tlag.- One should apply rather narrow boundaries on tlag.Does 1/klag or tlag become a much well behaved parameter, ifone specifies a lag compartment? And is it still advisable touse those three improvement suggestions as proposed above?Thanks for any comments.Best regardsJuergen BulittaPharmacokineticistInstitute for Biomedicaland Pharmaceutical ResearchGermany[I agree, setting realistic limits on tlag seem to help - db]`
Back to the Top

• On 1 Sep 2003 at 16:58:31, "Hans Proost" (j.h.proost.at.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Peter Bonate and Juergen Bulitta,The suggestion of Peter Bonate to replace lagtimes by a delay using anadditional compartment is very good. Using the traditional concept of anabrupt change in absorption rate, results in problems in finding thebestfitting value, as was stated correctly. I have a few comments:> The lag time is then 1/klag.  The more lag compartments between X1 and> the central compartment the more all or none the lag time becomes.What is the lag time in case of n compartments with rate constantsklag? Isit n/klag?> The only price to this method is that as the number of compartments> increases the slower the fitting process.The model using an additional compartment is a different modelresulting ina different absorption profile and a different plasma concentrationprofile(unless the number of lag compartments is very high). Therefore theresultscannot be compared, and lagtimes will be somewhat different from thoseusingthe traditional abrupt change in absorption rate.Juergen Bulitta wrote:>  One of the reasons is that the absorption process is often not> mirroredby a> simple first order process.Yes, one might argue that the absorption profile described by a few lagcompartments (small n) is more realistic than the abrupt change of thetraditional lag time concept; in fact, the latter is ratherunrealistic: azero absorption rate after ingestion of a drug formulation, and then anabrupt change to the maximum absorption rate, decliningmonoexponentially.Ever seen this in practice?> - One should apply rather narrow boundaries on tlag.This may indeed avoid getting unrealistic values for tlag, but what todo ifthe estimated lag time reaches the bounderies (usually asumptotically,depending of the software)? Bounderies do not guarantee correct results.A further comment: be careful if the first measurable concentration isrelatively low compared to the next one or to the peak concentration.Suchvalues may affect the fitting considerably, and are actualllyincompatiblewith the traditional lag time approach. I think that Peter Bonate's lagcompartments will give much better results in such cases, which are notuncommon in my experience.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.at.farm.rug.nl`
Back to the Top

• On 6 Sep 2003 at 22:43:09, Jurgen Bulitta (bulitta.-a-.ibmp.osn.de) sent the message
`The following message was posted to: PharmPKDear Dr. Proost, dear Dr. Bonate, dear all,I believe the discussion about lag time has gone to a pointwhere we should reconsider the final goal. Is ita) to define the absorption phase as precisely as possible tryingto interpret all possible effects of influence.b) to find a reasonable input function that allows drawingconclusions on any disposition or PK/PD issue.The lag-compartment approach is certainly an elegant and muchsmoother way to describe the absorption phase. For solid oraldosage forms the following processes may influence the kineticsof drug absorption:- disintegration- dissolution- local pH changes along the GI-tract- de-/protonation equilibria according to local pH- gastric emptying time- different rate constants of drug absorption between stomach andduodenum etc. due to physiological differences- first pass metabolism, possibly saturable- and sometimes enterohepatic recirculation (as a source foradditional drug up-take)What one hopes during modelling with a single rate constant ka is,that one of these processes is predominant. This is most oftenuntrue.What I would like to say is: If one is really interested in allthose processes, he/she might possibly better use deconvolutionor Wagner Nelson, Loo-Riegelman etc. to study the absorptionphase in detail. This can usually only reliably be done with an(intraindividual) iv reference.As one usually is not in the rich situation to have anintraindividual iv reference, I guess the followingsolutions apply:1) introducing lag time (as a rough approximation)2) specifying absorption rate constant as a function of time3) introducing lag compartments (as a better approximation)4) specifying direct input functions like a Weibull function.To 1) As you asked what to do, if Tlag reaches its boundaries.It may be feasible to adjust the boundaries from run to run, sothat the minimum distance between fitted Tlag and its e.g. upperboundary is at least 0.5 h, factor 2 x estimate (or whatever).This also helps for other fitting parameters. If it is no longernecessary to adjust any boundaries, self-convergence of theparameters is achieved. This technique is often used in quantumchemistry.To 2) As Hans Proost proposed, this approach is certainly muchmore realistic and often observed in (part of) the subjects'profiles. Whether one uses ka(t) or zero-order followed byfirst order depends on the situation. So this approach may reallyhelp, but often suffers from interindividual variability and itis sometimes difficult to fit the switch-time (--> error surfaceissue), if one uses a stepwise function for ka. It may happen,that some subjects show a switch while others do not have anyinformation about a switch.To 4) Specifying the input as function of time (not as adifferential term) may sometimes be a big improvementduring fitting.All these approaches are subject to the following practicalproblems:A) I seldom saw that there was one solution applicable to allsubjects, although the lag-compartment approach may be the mostrobust in this case.B) Even intra-individually there is sometimes large variationin the absorption process especially for sustained release products.C) Specifying the input as a function of time may severelyinfluence the disposition parameters. The same applies tospecifying ka as a function of time.Therefore, if one is not primarily interested in the absorptionprocess, it might be a reasonable choice simply using ka and Tlag.These parameters are often highly correlated with each other andthey tend to be imprecise and difficult to fit, but they mightinfluence the disposition parameters not as much as allother approaches.Our problem is that the window of watching theabsorption process - plasma concentrations - is pretty late. Soone should really ask, how many parameters do I want to spend onthe absorption process and do (all) my profiles contain enoughinformation for my preferred model, at least if one appliesindividual PK?I would be interested, if anyone has successfully applied the kaas a function of time approach for a set of say > 10 subjectsand how much inter-/intra-individual variability was involved there.Has anyone experience with Pop-PK and such extended absorptionmodels?Thanks very much in advance.Best regardsJuergen Bulitta`
Back to the Top

• On 6 Sep 2003 at 21:28:41, "Michael B. Bolger" (bolger.-a-.usc.edu) sent the message
`I've been meaning to weigh in on the lag time compartment issue for awhile now. Juergen Bulitta has nicely defined most of thecharacteristics that should be accounted for in properly consideringabsorption modeling. A lag time compartment does not shed any light onthe physiological and biochemical processes involved in absorption, notthe least of which is saturable gut metabolism and transport. Seereferences below:The lag-compartment approach is certainly an elegant and muchsmoother way to describe the absorption phase. For solid oraldosage forms the following processes may influence the kineticsof drug absorption:- disintegration- dissolution- local pH changes along the GI-tract- de-/protonation equilibria according to local pH- gastric emptying time- different rate constants of drug absorption between stomach andduodenum etc. due to physiological differences- first pass metabolism, possibly saturable- and sometimes enterohepatic recirculation (as a source foradditional drug up-take)Please check the following references that describe applications of theAdvanced Compartmental Absorption and Transit (ACAT) model to thesimulation of almost all of the factors described above. We have notpublished on enterohepatic recirculation (EhRc) yet, but the latestversion of our software "GastroPlus" has an implementation of EhRc.Agoram B, Woltosz WS, and Bolger MB: (2001) Predicting the impact ofphysiological and biochemical processes on oral drug bioavailability.Adv. Drug. Deliv. Rev. 50:S41-S67.Hendriksen BA, Sanchez MF, and Bolger MB: (2003) The CompositeSolubility Versus pH Profile and its Role in Intestinal AbsorptionPrediction. AAPS Pharm. Sci. 5(1):Article 4, 2003(http://www.aapspharmsci.org/view.asp?art=ps050104).Bolger MB, Gilman TM, Fraczkiewicz R, Steere B, and Woltosz W: (2002)“Predicting drug absorption by computational methods.” In “Cell CultureModels of Biological Barriers: In-vitro test systems for DrugAbsorption and Delivery“, ed. C.M. Lehr, Saarbrücken, Germany; byTaylor & Francis, London, UK.Bolger MB, Agoram B. Fraczkiewicz R, and Steer B: (2002) “Simulation ofabsorption, metabolism, and bioavailability.” In “DrugBioavailability. Estimation of Solubility, Permeability andBioavailability, for the Series Methods and Principles in MedicinalChemistry “, ed. Han van de Waterbeemd , published by WileyPublishers 2002.Bolger MB, Woltosz WS, Chittenden J, Fraczkiewicz G (2003) AccurateSimulation of the Non-linear Dose Dependence for Absorption ofValacyclovir and Amoxicillin: Influence of PepT1 and HPT1Intestinal Distribution. AAPS Drug Transport Meeting, Peachtree City,GA, February 2003.Michael B. Bolger, Ph.D.USC School of Pharmacy and Simulations Plus, Inc.`
Back to the Top

• On 8 Sep 2003 at 09:34:20, JELASSAI.at.PRDBE.jnj.com sent the message
`The following message was posted to: PharmPKDear Juergen,[...Has anyone experience with Pop-PK and such extended absorptionmodels?...]Please look at the NonMem news archive:http:/gaps.cpb.uokhsc.edu/nm/5may0895.html [if you can't open it,google to"nonmem absorption", than look in "cached"]andhttp://www.cognigencorp.com/nonmem/nm/98oct042001.htmlThe combination of zero-order and first-order rates makes for aflexible fitto the absorption phase.Best regards,Jeroen`
Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Lag time calculation in WNL" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)