From: Abu Helwa, Ahmad Yousef Mohammad - abuay010
<*ahmad.abuhelwa *>

Date: Thu, 31 Mar 2016 00:29:39 +0000

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

From: owner-nmusers sers

Sent: Thursday, 31 March 2016 4:19 AM

To: Santosh <santosh2005 >

Cc: nmusers

Subject: Re: [NMusers] Calculation of half life

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 GastroPlusâ„˘ User Group<https://www.linkedin.com/grps/GastroPlus-User-Group-5025927/about?> to interact with peers around the world

[cid:image001.jpg

On Wed, Mar 30, 2016 at 11:40 AM, Santosh wrote:

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

Received on Wed Mar 30 2016 - 20:29:39 EDT

Date: Thu, 31 Mar 2016 00:29:39 +0000

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

From: owner-nmusers sers

Sent: Thursday, 31 March 2016 4:19 AM

To: Santosh <santosh2005 >

Cc: nmusers

Subject: Re: [NMusers] Calculation of half life

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 GastroPlusâ„˘ User Group<https://www.linkedin.com/grps/GastroPlus-User-Group-5025927/about?> to interact with peers around the world

[cid:image001.jpg

On Wed, Mar 30, 2016 at 11:40 AM, Santosh wrote:

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

(image/jpeg attachment: image001.jpg)