Calculation of half life

Dear all, I am looking for ways to calculate t[1/2,lamda,z] the elimination phase half life, using a 3-compartment model. ADVAN 12 and TRANS6 seems to be a way. However, I am using the intercompartment clearance and volumes based parameterization, e.g. Q3,V3 etc.. half.life = log(2)/gamma Could anyone please share NONMEM code to compute the half-life based on gamma? Thanks so much in advance. Best regards, Santosh

Dear Santosh, there are formulas to make the conversions, and I normally use the spreadsheet that you can download at this link: http://cognigencorp.com/nonmem/nm/CONVERT.XLS It is not very convenient If you want to do things in batches, but I guess you can do some "reverse engineering" and implement the code in NONMEM. I have done it for two-compartments, but I never needed it for three (which is a lot of coding). If you do work out the NONMEM code - or anyone else already has it - please post it here, it could be useful. Best regards, Paolo

Santosh Perhaps a more pertinent question is – Why do you want to know half-life? Steve ………………………………………………………………………………………………………………………..……………………..……………………………………… Stephen Duffull I Professor of Clinical Pharmacy | Dean Otago Pharmacometrics Group New Zealand’s National School of Pharmacy | Te Kura Mātauraka Wai-whakaora University of Otago | Te Whare Wānanga o Otāgo Dunedin | Ōtepoti Ph: 64 3 479 5044 Website | http://www.pharmacometrics.co.nz/

You can add formulas to NONMEM code. All individual noncompartmental parameters can be calculated within NONMEM. An example of the NONMEM code is below. tH DADT(6) = A(8) ;calculates AUC if A is concentration DATD(8) = [put here the right part of the differential equation which calculates concentration] CONC=A(8) AUC =A(6) AUCT=A(12) IF (CONC.GT.1E-20) THEN LAM=-([put here the right part of the differential equation which calculates concentration]/CONC ELSE LAM=666666666 ENDIF IF (AUC.GT.1E-20) THEN MRT=AUCT/AUC ELSE MRT=666666666; ENDIF IF (AUC.GT.1E-20.AND.MWT.GE.0.000001) THEN CL =DKG*BIO/(AUC*MWT) ELSE CL =666666666 ENDIF VSS=MRT*CL IF (DABS(LAM).GT.1E-20) THEN IHL=0.693147/LAM ELSE LAM=666666666 IHL=666666666 ENDIF IF (DABS(LAM).GT.1E-10.AND.AUC.GE.1E-10) THEN VZ =DKG*BIO/(LAM*AUC*MWT) ELSE VZ =666666666 ENDIF AQ=1; BQ=K23+K32+KED; CQ=K32*KED; DQ=BQ**2-4*AQ*CQ; BET2=666666666 IF (DQ.GE.0) BET2=(-BQ+SQRT(DQ))/(2*AQ); BHLK= KED*(K32/(K32 + K23)) IF (BET2.LT.-1E-10) THEN BHL=-LOG(2)/BET2; ELSE BHL=666666666 ENDIF IF (DABS(A1).GE.1E10) A1=6666666 IF (DABS(A2).GE.1E10) A2=6666666 IF (DABS(A3).GE.1E10) A3=6666666 IF (DABS(A4).GE.1E10) A4=6666666 IF (DABS(A5).GE.1E10) A5=6666666 IF (DABS(IHL).GE.1E10) IHL=6666666 IF (DABS(MRT).GE.1E10) MRT=6666666 IF (DABS(CL).GE.1E10) CL=6666666 IF (DABS(VSS).GE.1E10) VSS=6666666 IF (DABS(LAM).GE.1E10) LAM=6666666 IF (DABS(VZ).GE.1E10) VZ=6666666 IF (DABS(BHL).GE.1E10) BHL=6666666 IF (DABS(BHLK).GE.1E10) BHLK=6666666

Santosh, There is an article that provides the equations that I think you are looking for. Calculating the hybrid (macro) rate constants of a three-compartment mamillary pharmacokinetic model from known micro-rate constants. Richard Upton Journal of Pharmacological and Toxicological Methods 49 (2004) pg. 65-68 Best regards, Luann Luann Phillips Director, Pharmacometrics Buffalo Office: +1-716-633-3463 ext. 236 | Website < http://www.cognigencorp.com > For news and events, follow us on: LinkedIn < https://www.linkedin.com/company/simulations-plus-inc > | Twitter < https://twitter.com/SimulationsPlus > | YouTube < https://www.youtube.com/channel/UCT4wMdIEnI95nlyLfRJY7Ww > | Facebook < https://www.facebook.com/SimulationsPlus/ > Join the GastroPlus™ User Group < https://www.linkedin.com/grps/GastroPlus-User-Group-5025927/about ?> to interact with peers around the world http://www.simulations-plus.com/Default.aspx

Hi Santosh: You can calculate half life for a 3-compartment model using the following R code example. This is based on the article published by Richard Upton Richard Upton Journal of Pharmacological and Toxicological Methods 49 (2004) pg. 65-68 #------------------------------------------------------------------- #Three compartment model CL <- 2 V1 <- 10 Q12 <- 0.5 V2 <- 30 Q13 <- 0.3 V3 <- 40 #Rate constant parameterization k10 <- CL/V1 k12 <- Q12/V1 k21 <- k12*V1/V2 k13 <- Q13/V1 k31 <- k13*V1/V3 #Half-lives j <- k12+k10+k21+k31+k13 k <- k12*k31+k10*k21+k10*k31+k21*k31+k13*k21 l <- k10*k21*k31 m <- (3*k - j^2)/3 n <- (2*j^3 - 9*j*k + 27*l)/27 Q <- (n^2)/4 + (m^3)/27 alpha <- sqrt(-1*Q) beta <- -1*n/2 rho <- sqrt(beta^2+alpha^2) theta <- atan2(alpha,beta) lambda1 <- j/3 + rho^(1/3)*(cos(theta/3) + sqrt(3)*sin(theta/3)) lambda2 <- j/3 + rho^(1/3)*(cos(theta/3) - sqrt(3)*sin(theta/3)) lambda3 <- j/3 -(2*rho^(1/3)*cos(theta/3)) thalf_alpha <- log(2)/lambda1 thalf_beta <- log(2)/lambda2 thalf_gamma <- log(2)/lambda3