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Lesson 2: Parent and Metabolite Kinetics

PML Parent Metabolite Michaelis-Menten

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#1 bwendt@certara.com

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Posted 21 October 2016 - 04:39 PM

Here comes the material of our second session of the PML School. Chris presented a model for simultaneously fitting of parent and metabolite kinetic data where the metabolite clearance follows Michaelis-Menten kinetics.

Textual Model file:

Attached File  Metabolite_Kinetics_PK19.txt   741bytes   624 downloads

Slide Deck:

Attached File  Metabolite_Kinetics_Webinar.pdf   743.17KB   1150 downloads

Link to the recording of the webinar:

https://certara.webex.com/certara/lsr.php?RCID=4f489fbb54678caa1bd5288dd5241fa1


Let me know if there are questions or comments.

Bernd


Edited by bwendt@certara.com, 25 October 2016 - 02:53 PM.


#2 bwendt@certara.com

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Posted 21 October 2016 - 06:04 PM

There was some extra text in the model file. Here is a corrected version: 

 

 

Attached File  Metabolite_Kinetics_PK19.txt   741bytes   414 downloads


Edited by bwendt@certara.com, 25 October 2016 - 02:57 PM.


#3 pypendop

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Posted 22 October 2016 - 06:17 PM

Thank you for an excellent second session. I asked a question but did not get the answer I was looking for, so here it is again with more context:

Are the fixed effects statements the only place where initial estimates (and bounds) can be entered in a PML model? This would make modeling multiple individuals with different initials inconvenient. In the "old" WNL5 ASCII models, the initials could be entered in the normal initial estimates tab (i.e. the same as for library models), so different individuals modeled at the same time could have different initials. Similarly, a different set of constants could be entered for each individual, which is useful in some situations. To give an example, I have a small study in which 3 groups of 2 subjects each received a drug via a target-controlled infusion (so the input is fairly complex - hence the need for a user-written model); the difference between groups was the duration of infusion. In the ASCII model I wrote, this can easily be specified by a constant, and it the parameters used for the TCI input had been different in each individual (we sometimes use individual rather than group parameters), this could also have been easily specified. If we needed different initial estimates for each individual, again, this would have been possible using a single model. From what we have seen in PML so far, it looks like a model would have to be written for each individual.

 

Bruno



#4 dlweiner

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Posted 22 October 2016 - 08:09 PM

Thank you for an excellent second session. I asked a question but did not get the answer I was looking for, so here it is again with more context:

Are the fixed effects statements the only place where initial estimates (and bounds) can be entered in a PML model? This would make modeling multiple individuals with different initials inconvenient. In the "old" WNL5 ASCII models, the initials could be entered in the normal initial estimates tab (i.e. the same as for library models), so different individuals modeled at the same time could have different initials. Similarly, a different set of constants could be entered for each individual, which is useful in some situations. To give an example, I have a small study in which 3 groups of 2 subjects each received a drug via a target-controlled infusion (so the input is fairly complex - hence the need for a user-written model); the difference between groups was the duration of infusion. In the ASCII model I wrote, this can easily be specified by a constant, and it the parameters used for the TCI input had been different in each individual (we sometimes use individual rather than group parameters), this could also have been easily specified. If we needed different initial estimates for each individual, again, this would have been possible using a single model. From what we have seen in PML so far, it looks like a model would have to be written for each individual.

 

Bruno

Bruno, if you enter initial estimates as part of the PML code or via the tabs Parameters/Fixed Effects you are correct that only a single set of initial estimates can be entered and applied to all subjects.  However, if you use the main mapping input, you can enter different values by clicking on the Parameters option (under Setup) and then clicking on rebuild.  Or alternatively you can browse for another file (like NCA output) and map them as initial estimates.  See attached screenshot.

 

Dan W

Attached Files



#5 sethgibbs

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Posted 24 October 2016 - 02:15 PM

I had a question about making the model more complex.  For example, how simple would it be to set up a model where the parent was fit by a 2-compartment model, one metabolite by a 1-compartment model, and a 2nd metabolite by MM model?



#6 dlweiner

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Posted 25 October 2016 - 12:59 PM

I had a question about making the model more complex.  For example, how simple would it be to set up a model where the parent was fit by a 2-compartment model, one metabolite by a 1-compartment model, and a 2nd metabolite by MM model?

Seth,  PK19 is actually a model where 2 compartments were used to model the parent drug, and a single one compartment model was used for the metabolite with MM formation.  Note that volumes for the metabolites cannot be estimated unless the metabolites are measured and modeled as well.  The other consideration is whether or not the formation of the metabolites are reversible or not.  In PK19, it was assumed that the formation of single metabolite was MM and not reversible.  That is why I would consider this a 2 compartment model for the parent.  The limitation of PK19 is that it assumes the only way the parent drug is eliminated is via the formation of the metabolite.  But one could easily add a parallel route of elimination.  Now, what about your question if there is a second metabolite?  You need to know the metabolic pathways and if any are reversible.  You then need to incorporate them into the model (e.g., which clearances are reversible and which are irreversible).  This is straight-forward to do.

 

Dan



#7 sethgibbs

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Posted 25 October 2016 - 01:18 PM

Seth,  PK19 is actually a model where 2 compartments were used to model the parent drug, and a single one compartment model was used for the metabolite with MM formation.  Note that volumes for the metabolites cannot be estimated unless the metabolites are measured and modeled as well.  The other consideration is whether or not the formation of the metabolites are reversible or not.  In PK19, it was assumed that the formation of single metabolite was MM and not reversible.  That is why I would consider this a 2 compartment model for the parent.  The limitation of PK19 is that it assumes the only way the parent drug is eliminated is via the formation of the metabolite.  But one could easily add a parallel route of elimination.  Now, what about your question if there is a second metabolite?  You need to know the metabolic pathways and if any are reversible.  You then need to incorporate them into the model (e.g., which clearances are reversible and which are irreversible).  This is straight-forward to do.

 

Dan

Thanks,

So I would need to add an equation for the elimination of the unmetabolized parent compound along with a second set of equations and for the second metabolite (similar to what was needed for the first metabolite), assuming that I have data for both metabolites.  Additionally, do I need to add secondary equations to the code in order for the model to include those parameters in the output for both parent and metabolite(s)? 



#8 dlweiner

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Posted 25 October 2016 - 01:38 PM

Thanks,

So I would need to add an equation for the elimination of the unmetabolized parent compound along with a second set of equations and for the second metabolite (similar to what was needed for the first metabolite), assuming that I have data for both metabolites.  Additionally, do I need to add secondary equations to the code in order for the model to include those parameters in the output for both parent and metabolite(s)? 

Seth, for a model like this you would need to add your own secondary parameters.

 

Dan



#9 bwendt@certara.com

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Posted 26 October 2016 - 08:57 AM

I had a question about making the model more complex.  For example, how simple would it be to set up a model where the parent was fit by a 2-compartment model, one metabolite by a 1-compartment model, and a 2nd metabolite by MM model?

 

Seth,

 

if you are still somewhat unfamiliar with PML code you may want to start building your model using the graphical model builder. There you can add:

  • new compartments for each of your metabolites
  • link it to the central compartment for the parent compound
  • add elimination compartments for your metabolites
  • link it to the metabolite compartments
  • determine reversible (2-way) or irreversible (1-way) pathways

Here is a snapshot of what you were asking for:

 

complex_model.png

 

This model assumes that you have metabolite data along with parent data.

 

Bernd 



#10 pypendop

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Posted 27 October 2016 - 04:24 PM

Bruno, if you enter initial estimates as part of the PML code or via the tabs Parameters/Fixed Effects you are correct that only a single set of initial estimates can be entered and applied to all subjects.  However, if you use the main mapping input, you can enter different values by clicking on the Parameters option (under Setup) and then clicking on rebuild.  Or alternatively you can browse for another file (like NCA output) and map them as initial estimates.  See attached screenshot.

 

Dan W

Dan, thank you very much for your answer. One (somewhat) related question: can you specify constants in PML as was possible in WNL5 ASCII?



#11 dlweiner

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Posted 27 October 2016 - 06:31 PM

Dan, thank you very much for your answer. One (somewhat) related question: can you specify constants in PML as was possible in WNL5 ASCII?

Buno,

 

It is implemented differently.  For WNL5 the input constants were generally dosing related, and this has been replaced via dose mapping in Phoenix WNL.  If you need values other than dosing data in the model, you would have to hard code them into the model or create a column on the data set with the values and specify them as covariates (e.g. covariate(BW) ).  These "covariates" could then be used in your PML model code.

 

Dan



#12 pypendop

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Posted 27 October 2016 - 07:35 PM

Buno,

 

It is implemented differently.  For WNL5 the input constants were generally dosing related, and this has been replaced via dose mapping in Phoenix WNL.  If you need values other than dosing data in the model, you would have to hard code them into the model or create a column on the data set with the values and specify them as covariates (e.g. covariate(BW) ).  These "covariates" could then be used in your PML model code.

 

Dan

Thank you. To make sure I understand - my current example is a model I wrote in which the input is a TCI, i.e. an exponentially decreasing infusion rate over time according to the equation Rate at time t = target*V1*(k10+k12*exp(-k21*t)+k13*exp(-k31*t). In my WNL5 model, I entered duration of infusion, target, V1, and the microrate constants as constants (which made adjusting them when using the model for various drugs and therefore various sets of constants easy). What you are saying is that the equation itself (i.e. the values for these constants) would have to be coded in the model?



#13 cerebellars

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Posted 27 October 2016 - 08:43 PM

Thank you very much for the excellent presentation. It is very informative.

 

Michelle



#14 dlweiner

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Posted 28 October 2016 - 01:15 PM

Thank you. To make sure I understand - my current example is a model I wrote in which the input is a TCI, i.e. an exponentially decreasing infusion rate over time according to the equation Rate at time t = target*V1*(k10+k12*exp(-k21*t)+k13*exp(-k31*t). In my WNL5 model, I entered duration of infusion, target, V1, and the microrate constants as constants (which made adjusting them when using the model for various drugs and therefore various sets of constants easy). What you are saying is that the equation itself (i.e. the values for these constants) would have to be coded in the model?

Bruno,

 

This is pretty easy to do.    Convert your model to text / PML.  Then edit the dosepoint statement to read something like 

 

dosepoint(A1,rate=myrate)
myrate= target*V1*(k10+k12*exp(-k21*t)+k13*exp(-k31*t))
 
If your original model had extravascular input A1 above would be Aa.  Note that you will need to add fixef statements to define k10, k12, k13 and k31 (although these will already be in your model if you started with such a model before you converted to pml).  And somewhere you need to define "target".
 
Dan W


#15 pypendop

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Posted 31 October 2016 - 05:14 PM

 

Bruno,

 

This is pretty easy to do.    Convert your model to text / PML.  Then edit the dosepoint statement to read something like 

 

dosepoint(A1,rate=myrate)
myrate= target*V1*(k10+k12*exp(-k21*t)+k13*exp(-k31*t))
 
If your original model had extravascular input A1 above would be Aa.  Note that you will need to add fixef statements to define k10, k12, k13 and k31 (although these will already be in your model if you started with such a model before you converted to pml).  And somewhere you need to define "target".
 
Dan W

 

Hi Dan,

 

Thank you again for your response. One more question: when you talk about converting to PML, is there a way to actually convert WNL5 ASCII models to PML, or do you mean re-writing the model in PML? I looked in the documentation and did not find a process to convert.

 

Bruno



#16 dlweiner

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Posted 31 October 2016 - 05:39 PM

Hi Dan,

 

Thank you again for your response. One more question: when you talk about converting to PML, is there a way to actually convert WNL5 ASCII models to PML, or do you mean re-writing the model in PML? I looked in the documentation and did not find a process to convert.

 

Bruno

Bruno,

 

I mean rewriting the model using PML.  But note that since you can convert both library and graphical models to PML this is generally pretty easy to do.  In your case, if I understand your model correctly, after converting the appropriate closest library model you only need to add/modify the couple of statements I mentioned in my email.

 

Dan W



#17 pypendop

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Posted 08 November 2016 - 09:07 PM

Bruno,

 

I mean rewriting the model using PML.  But note that since you can convert both library and graphical models to PML this is generally pretty easy to do.  In your case, if I understand your model correctly, after converting the appropriate closest library model you only need to add/modify the couple of statements I mentioned in my email.

 

Dan W

Dan,

 

Thank you for your continuing explanations. I have tried unsuccessfully to re-write my model in PML. I copy the code below. The model runs, but does not estimate anything. Is there something obviously wrong? Should there be an "else" statement after the "if" statement? If so, how should it be written (from the PML documentation, it looks like it should be [else {dosepoint(A1, rate=0)}], but this is not recognized by the program)? Also, can tinf (infusion time) be entered as a fixed effect, or does it mean that it would be estimated by the model? The reason I did it this way is that I have 6 subjects and 3 infusion times (2 subjects for each), and would like to run the model in population mode; the fixed effect statement allows me to enter a value for each subject as an initial estimate. I have tried to run the same model for a single subject, specifying the value of tinf in the model, but it still does not estimate anything. I have also tried to enter the initial estimates in the fixed effect statements, which again, does not solve my problem.

 

Bruno

 

test(){
target=7.6
Vi=126.7
k10=0.2091
k12=0.3298
k13=0.01462
k21=0.1334
k31=0.0071415
deriv(A1 = - Cl * C - Cl2 * (C - C2) - Cl3 * (C - C3))
deriv(A2 = Cl2 * (C - C2))
deriv(A3 = Cl3 * (C - C3))
if (t<=tinf) {dosepoint(A1, rate=TCI)}
TCI=target*Vi*(k10+k12*exp(-k21*t)+k13*exp(-k31*t))
C = A1 / V
C2 = A2 / V2
C3 = A3 / V3
error(CEps = 1)
observe(CObs = C + CEps)
fixef(V)
fixef(V2)
fixef(V3)
fixef(Cl)
fixef(Cl2)
fixef(Cl3)
fixef (tinf)
}


#18 dlweiner

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Posted 08 November 2016 - 09:21 PM

Bruno,

 

Replace 

if (t<=tinf) {dosepoint(A1, rate=TCI)}

with

dosepoint(A1, rate=TCI)

 

since you have separately entered the dose (via the dose window) and the program knows the rate (TCI), tinf is implicit and already accounted for in the dosepoint statement.  Also delete the fixef statement for tinf.

 

Lastly, all of the remaining fixef statements need to be modified.  For example, 

fixef(V)

needs to be something like 

fixef(V = c(, !!!, ))

 

where !!! should be replaced by whatever your initial estimate is for V.  You need to make similar changes to all of the fixef statements.

 

If you still have problems, email me the model at dlweiner@gmail.com and I will take a look at it.

 

Dan W

 

Dan,

 

Thank you for your continuing explanations. I have tried unsuccessfully to re-write my model in PML. I copy the code below. The model runs, but does not estimate anything. Is there something obviously wrong? Should there be an "else" statement after the "if" statement? If so, how should it be written (from the PML documentation, it looks like it should be [else {dosepoint(A1, rate=0)}], but this is not recognized by the program)? Also, can tinf (infusion time) be entered as a fixed effect, or does it mean that it would be estimated by the model? The reason I did it this way is that I have 6 subjects and 3 infusion times (2 subjects for each), and would like to run the model in population mode; the fixed effect statement allows me to enter a value for each subject as an initial estimate. I have tried to run the same model for a single subject, specifying the value of tinf in the model, but it still does not estimate anything. I have also tried to enter the initial estimates in the fixed effect statements, which again, does not solve my problem.

 

Bruno

 

test(){
target=7.6
Vi=126.7
k10=0.2091
k12=0.3298
k13=0.01462
k21=0.1334
k31=0.0071415
deriv(A1 = - Cl * C - Cl2 * (C - C2) - Cl3 * (C - C3))
deriv(A2 = Cl2 * (C - C2))
deriv(A3 = Cl3 * (C - C3))
if (t<=tinf) {dosepoint(A1, rate=TCI)}
TCI=target*Vi*(k10+k12*exp(-k21*t)+k13*exp(-k31*t))
C = A1 / V
C2 = A2 / V2
C3 = A3 / V3
error(CEps = 1)
observe(CObs = C + CEps)
fixef(V)
fixef(V2)
fixef(V3)
fixef(Cl)
fixef(Cl2)
fixef(Cl3)
fixef (tinf)
}

 



#19 raghava choudary

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Posted 10 December 2016 - 01:39 PM

Hi Dan,

 

Greetings.......

 

All the examples dealing with Parent and Metabolite kinetics are from intravenous dosing ?

 

I have an example where the parent is dosed orally and the formation of two metabolites was monitored. Created a graphical model where parent (Aa) is absorbed to central compartment (Ka) and metabolite formed from parent (CLpar2M1) central compartment, and Metabolite M2, formed from parent central compartment (CLpar2M2). The clearance of metabolites is represented as CLmet1 and CLmet2.  I have few questions from this exercise. I understand all the clearance and volume parameters are apparent i.e., CL/F and V/F. 

 

 

01) How to graphically represent if the parent is converted to metabolite in the gut (some fraction is converted to metabolite in the absorption compartment and then absorbed to systemic circulation) ?

 

02) I am trying to model the parent and metabolite with the parameter like Fm (fraction metabolized to metabolite M1 and fraction metabolized to M2) ? Can this be acheived in a different way ? How to estimate the parameter fm of each pathway?

 

Thanks in advance

 

With best regards,

 

Raghav



#20 dlweiner

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Posted 10 December 2016 - 03:12 PM

Hi Dan,

 

Greetings.......

 

All the examples dealing with Parent and Metabolite kinetics are from intravenous dosing ?

 

I have an example where the parent is dosed orally and the formation of two metabolites was monitored. Created a graphical model where parent (Aa) is absorbed to central compartment (Ka) and metabolite formed from parent (CLpar2M1) central compartment, and Metabolite M2, formed from parent central compartment (CLpar2M2). The clearance of metabolites is represented as CLmet1 and CLmet2.  I have few questions from this exercise. I understand all the clearance and volume parameters are apparent i.e., CL/F and V/F. 

 

 

01) How to graphically represent if the parent is converted to metabolite in the gut (some fraction is converted to metabolite in the absorption compartment and then absorbed to systemic circulation) ?

 

02) I am trying to model the parent and metabolite with the parameter like Fm (fraction metabolized to metabolite M1 and fraction metabolized to M2) ? Can this be acheived in a different way ? How to estimate the parameter fm of each pathway?

 

Thanks in advance

 

With best regards,

 

Raghav

Raghav,  I'm not sure I have immediate answers to your questions but I'm happy to work through them with you.  Can you email me at dlweiner@gmail.com with any working model you have?  And I'll try to work through this modeling exercise with you.

 

Dan







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