Modelling ER data as 3 dept injection using transit model

Phoenix Certara Forums Modelling and Simulation
1

Hello,

I have data of ER injection which would release the drug over longer period of time.I have modelled the data using transit compartment modelling.I am attaching phx prj file in which i have tried 2 different approaches (2cmt_2 depot_estKel_add & 2cmt_3depot_estKel_add)

  1. 2cmt_2 depot_estKel_add: In this approach i have divided the dose into 2 different fractions ie 1 fraction directly reaches the central cmt and another fraction reaches through transit comp and then reaches the central comp. My data fitting using the model seems to be ok.I need help in further optmising this model
  2. 2cmt_3depot_estKel_add: In this approach i have divided the dose into 3 different fractions ie 1 fraction directly reaches the central cmt and another 2 fraction’s reaches through 2 transit comp’s and then reaches the central comp.I have fitted the data to this model but overall the fitting remains the same as that of earlier approach. I need help here in optimising the model and whether my model is correctly written based on my hypothesis stated above.

I need support from people to optmise the models further, your response will be of great help

Regards

HK

ExMS.phxproj (968 KB)

2

Dear HK

Indeed you had a problem with your coding.

You need 4 constraints

0<F1<1

0<F2<1

0<F3<1

F1+F2+F3=1

You code did not guarantee all constraints.

I changed the code to insure these constraints are respected.

Let me know if it helps.

Now for sure all the constraints are respected.

-2LL is better too.

Best Regards

Serge

test(){
transit(Aa2, mtt1, ntr1, max = 50, out = -Aa2 * Ktr1)
transit(Aa3, mtt2, ntr2, max = 50, out = -Aa3 * Ktr2)

need to make sure all F are positive and sum=1

bio1=ilogit(F1_direct)
dosepoint(Aa1, bioavail = bio1)

dosepoint(Aa1, bioavail = F1_direct)

dosepoint(Aa2, bioavail = F2_direct)

bio2=(1-bio1)ilogit(F2_direct)
dosepoint(Aa2, bioavail = bio2)
bio3=1-bio1-bio2
dosepoint(Aa3, bioavail =bio3)
deriv(A1 = - (Kel * A1) +(Aa3Ktr2)+(Aa1 * Ka) + (Aa2 * Ktr1)-(K12A1)+(K21A2))

deriv(Aa1 = - (Aa1 * Ka))
deriv(A2 = (K12A1)-(K21A2))

C = A1 / V1
C2=A2/V2
mtt1=(ntr1+1)/Ktr1
mtt2=(ntr2+1)/Ktr2
error(CEps = 1)
observe(CObs = C + CEps)
stparm(V1 = tvV1 * exp(nV1))
stparm(V2 = tvV2 * exp(nV2))
stparm(Kel = tvKel * exp(nKel))
stparm(Ka = tvKa * exp(nKa))
stparm(K12 = tvK12 * exp(nK12))
stparm(K21 = tvK21 * exp(nK21))
stparm(Ktr1 = tvKtr1 * exp(nKtr1))
stparm(Ktr2 = tvKtr2 * exp(nKtr2))
stparm(ntr1 = tvntr1 * exp(nntr1))
stparm(ntr2 = tvntr2 * exp(nntr2))
stparm(F1_direct = tvF1_direct)
stparm(F2_direct = tvF2_direct)

fixef(tvV1 = c(0, 12,30 ))
fixef(tvV2 = c(0, 211,300 ))
fixef(tvKel= c(0,0.00013, ))
fixef(tvK12 = c(0, 0.744, ))
fixef(tvK21 = c(0, 0.0429, ))
fixef(tvKa = c(0, 0.75, ))
fixef(tvKtr1 = c(0, 0.05, ))
fixef(tvntr1 = c(0, 4, ))
fixef(tvKtr2 = c(0, 0.05, ))
fixef(tvntr2 = c(0, 4, ))
fixef(tvF1_direct = c(, 0,))
fixef(tvF2_direct = c(, 0,))
ranef(block(nV1, nKel) = c(0.060069234, 0.031922021, 0.042022708),
block(nKa, nKtr1) = c(0.32744575, -0.033038011, 0.046767492),
block(nKtr2) = c(0.033038011),
block(nV2) = c(0.32744575),
block(nK12, nK21) = c(0.32744575, -0.033038011, 0.046767492))
ranef(diag(nntr1,nntr2) = c(0.1,0.1))
}

ExMS.phxproj (1.35 MB)

3

Dear Serge,

As always your insight is always helpful

Thanks for your minor tweakings to the code

Regards

HK

4

there is several ways to constrain the entities into what Serge mentions:

0<F1<1

0<F2<1

0<F3<1

F1+F2+F3=1

one way is this TvF1 >0 ,TvF2 >0 ,TvF3 >0 and the sum is 1

F1 = tvF1 / ( 1+ TvF1 + TvF2)

F2 = tvF2 / ( 1+ TvF1 + TvF2)

F3 = 1/(1 + tvF1 + tvF2 )

take an example tvF1 0.25 tvF2 = 0.5

F1 = 0.25 / ( 1+0.25 +0.5) = 0.25 / 1.75 = 0.142…

F2 = 0.5 / ( 1+0.25 +0.5) = 0.5/ 1.75 = 0.285

F3 = 1/(1 + 0.25 +0.5 ) = 1/ 1.75 =] 0.5714286

F1 + F2 + F 3 = (1 + 0.25 +0.5 ) /(1 + 0.25 +0.5 ) = 1

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1003686

https://cs.brown.edu/research/pubs/theses/ugrad/2013/mcerlean.pdf

5

Dear smouksassi1 & Serge,

Thanks for your suggestion’s,

I have landed into a trouble, i have sc injection formulation which shows 4 different peaks, you can see the plot in the phx project attached

  • I have tried fitting the data using my earlier hypothesis that dose is distributed into 3 different fractions ie 1 fraction directly reaches the central cmt and another 2 fraction’s reaches through 2 transit comp’s and then reaches the central comp

  • i have also tried to increase another transit comp, ie assuming that now dose is distributed into 4 different fractions ie 1 fraction directly reaches the central cmt and another 3 fraction’s reaches through 3 transit comp’s and then reaches the central comp

but in both cases iam facing an issue in fitting, can any one help me

Regards

HK

MS.phxproj (774 KB)

6

Dear Colleague

Here is the new code.

First your initial estimates were bad. In addition, in the mass balance for A1, (Aa4*Ktr3) term was missing.

Now I got I think a very good fit.

Best Regards

Serge

test(){
transit(Aa2, mtt1, ntr1, max = 50, out = -Aa2 * Ktr1)
transit(Aa3, mtt2, ntr2, max = 50, out = -Aa3 * Ktr2)
transit(Aa4, mtt3, ntr3, max = 50, out = -Aa4 * Ktr3)
bio1=ilogit(F1_direct)
dosepoint(Aa1, bioavail = bio1)
bio2=(1-bio1)ilogit(F2_direct)
dosepoint(Aa3, bioavail = bio3)
bio3=(1-bio1-bio2)ilogit(F3_direct)
dosepoint(Aa2, bioavail = bio2)
bio4=1-bio1-bio2-bio3
dosepoint(Aa4, bioavail = bio4)
deriv(A1 = - (Kel * A1) +(Aa3Ktr2)+(Aa1 * Ka) + (Aa2 * Ktr1)-(K12A1)+(K21A2)
+(Aa4Ktr3))

deriv(Aa1 = - (Aa1 * Ka))
deriv(A2 = (K12A1)-(K21A2))

C = A1 / V1
C2=A2/V2
mtt1=(ntr1+1)/Ktr1
mtt2=(ntr2+1)/Ktr2
mtt3=(ntr3+1)/Ktr3
error(CEps = 1)
observe(CObs = C + CEps)
stparm(V1 = tvV1 * exp(nV1))
stparm(V2 = tvV2 * exp(nV2))
stparm(Kel = tvKel * exp(nKel))
stparm(Ka = tvKa * exp(nKa))
stparm(K12 = tvK12 * exp(nK12))
stparm(K21 = tvK21 * exp(nK21))
stparm(Ktr1 = tvKtr1 * exp(nKtr1))
stparm(Ktr2 = tvKtr2 * exp(nKtr2))
stparm(Ktr3 = tvKtr3 * exp(nKtr3))
stparm(ntr1 = tvntr1 * exp(nntr1))
stparm(ntr2 = tvntr2 * exp(nntr2))
stparm(ntr3 = tvntr3 * exp(nntr3))
stparm(F1_direct = tvF1_direct)
stparm(F2_direct = tvF2_direct)
stparm(F3_direct = tvF3_direct)

fixef(tvV1 = c(0, ,100 ))
fixef(tvV2 = c(0, 126,500 ))
fixef(tvKel= c(0,0.000121,10 ))
fixef(tvK12 = c(0, 0.02,5 ))
fixef(tvK21 = c(0, 0.001855,5 ))
fixef(tvKa = c(0, 1.25, ))
fixef(tvKtr1 = c(0, 0.05, ))
fixef(tvntr1 = c(0, 4, ))
fixef(tvKtr2 = c(0, 0.05, ))
fixef(tvntr2 = c(0, 4, ))
fixef(tvKtr3 = c(0, 0.05, ))
fixef(tvntr3 = c(0, 4, ))
fixef(tvF1_direct = c(,-4, ))
fixef(tvF2_direct = c(,-4, ))
fixef(tvF3_direct = c(,-4, ))
ranef(block(nV1, nKel) = c(0.060069234, 0.031922021, 0.042022708),
block(nKa, nKtr1) = c(0.32744575, -0.033038011, 0.046767492),
block(nKtr2) = c(0.033038011),
block(nKtr3) = c(0.033038011),
block(nV2) = c(0.32744575),
block(nK12, nK21) = c(0.32744575, -0.033038011, 0.046767492))
ranef(diag(nntr1,nntr2,nntr3) = c(0.1,0.1,0.1))
}

MS.phxproj (1.49 MB)

7

Dear Serge,

Accepted my minor oversight while writing the code,

Thanks for correcting it, however when iam trying to run this in NLME/naive pooled mode/FOCE method with full all subjects data (n=6) the run time is going into many hours.

Is it because of my system configuration or just the model is too complex because of differential equations

Iam attaching the full data (n=6) for you to try at your end and check for me

Regards

Harish

FULL of removing_t_0_data_mean bydURUEON MS data1234.xls (38 KB)

8

Dear Harish

To me your model is way much too overparametrized.

I suggest you to try to limit the number of transit compartments and not using the max=50.

When using naive pool, the fit was excellent but ntr1 was 178 which means 178 transit compartments, non sense to me. I believe this transit compartments is not necessary. If you change the number for ntr1, you get the same graph, completely insensitive.

Try to start with a simpler model and may be without transit compartments but only 3 extra vascular inputs.

Transit compartments is testing too many scenarios and it can take forever.

Best Regards

Serge

9

Dear Serge,

Thanks for your suggestion, i tried doing it with simple model using 3 depot extravascular inputs, but the model didn’t fit the data well

I was wondering is there any way we can use transit compartment to model the data based on the figure below

Regards

Harish

10

Dear Serge,

Thanks for your suggestion, i tried doing it with simple model using 3 depot extravascular inputs, but the model didn’t fit the data well

I was wondering is there any way we can use transit compartment to model the data based on the figure below

Regards

Harish

transit.jpg
transit.jpg999×580 58.3 KB