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PK Model With Dissolution and Bioavailability

bioavailability PK model dissolution

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#1 littlepetinga

littlepetinga

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Posted 02 September 2022 - 06:48 PM

Hello everyone

 

I am constructing a PK model which is preceded by a dissolution model (a Weibull model) in the GI track. From the dissolved drug in the GI, I pretend that only a fraction (F) is absorbed to the central compartment. However, I have questions on how to do so, since I defined the GI as the dosepoint.

 

Does anyone know how should I proceed?

 

Thank you very much in advance

Sara

 

 

 



#2 Simon Davis

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Posted 03 September 2022 - 06:44 AM

Can you post your project file to see how far you have got?  I assume you have worked through some of the graphical model building examples in the help e.g. https://onlinehelp.c..._Creating_a_two



#3 littlepetinga

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Posted 03 September 2022 - 04:24 PM

Hi Simon

 

Thank you for your reply.

 

I am not using graphical model, I am using PML instead.

You may find below the model text:

test(){

# GI compartment
deriv(Aa = - ((Fmax*(Beta*scB)*(t^((Beta*scB)-1))*exp(-(t^((Beta*scB)))/(Alpha*scA)))/(Alpha*scA)) * Aa)
# Central compartment
deriv(A1_p = ((Fmax*(Beta*scB)*(t^((Beta*scB)-1))*exp(-(t^((Beta*scB)))/(Alpha*scA)))/(Alpha*scA)) * Aa - (Cl_p * C_p)- (Q_p * (C_p - C2_p)) - (VMax_p_m * C_p / (C_p + Km_p_m)))
# Peripheral compartment
deriv(A2_p = (Q_p * (C_p - C2_p)))

# Define Dosepoint
dosepoint(Aa)

# Concentrations definition
C_p = A1_p / V_p
C2_p = A2_p / V2_p

# Model erro
error(CEps_p = 0.1)
observe(Parent = C_p * exp(CEps_p))

# Initial estimates
# Dissolution (Weibull)
fixef(Fmax(freeze) = c(, 1, ))
fixef(Alpha(freeze) = c(, 7, ))
fixef(Beta(freeze) = c(, 1.5, ))
fixef(scA = c(, 80, ))
fixef(scB = c(, 2, ))
# Central compartment
fixef(V_p = c(0, 88, 400))
fixef(Cl_p = c(0, 28, 60))
fixef(F_p = c(0, 0.05, 0.4))
# Peripheral compartment
fixef(V2_p = c(0, 181, 3000))
fixef(Q_p = c(0, 22, 300))
# Metabolite conversion
fixef(VMax_p_m = c(0, 329, 6000))
fixef(Km_p_m = c(0, 700, 5000))
}

 

My idea is, that from the dose dissolved in Aa, only a fraction (F) is absorbed to the central compartment (A1_p).

 

Thank you!

Sara


Edited by littlepetinga, 03 September 2022 - 04:25 PM.


#4 bwendt@certara.com

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Posted 05 September 2022 - 11:59 AM

Hi Sara,

 

I did not check the code in much detail, just used your formulas to do:

 

1. define dissolution rate outside of the deriv statement

2. limit the drate to 0-+Inf

3. added bioavailability (F_p) to the absorption

4. defined the static value Aadose as total dose amount

 

Here is the code:

 

test()
{
 
# GI compartment
deriv(Aa = - drate * F_p * Aadose)
# Central compartment
deriv(A1_p = drate *F_p * Aa - (Cl_p * C_p)- (Q_p * (C_p - C2_p)) - (VMax_p_m * C_p / (C_p + Km_p_m)))
# Peripheral compartment
deriv(A2_p = (Q_p * (C_p - C2_p)))
 
# Define Weibull for dissolution rate
drate=max(0,((Fmax*(Beta*scB)*(t^((Beta*scB)-1))*exp(-(t^((Beta*scB)))/(Alpha*scA)))/(Alpha*scA)))
 
# Define Dosepoint
dosepoint(Aa, idosevar=Aadose)
 
# Concentrations definition
C_p = A1_p / V_p
C2_p = A2_p / V2_p
 
# Model erro
error(CEps_p = 0.1)
observe(Parent = C_p * exp(CEps_p))
 
# Initial estimates
# Dissolution (Weibull)
fixef(Fmax(freeze) = c(, 1, ))
fixef(Alpha(freeze) = c(, 7, ))
fixef(Beta(freeze) = c(, 1.5, ))
fixef(scA = c(, 80, ))
fixef(scB = c(, 2, ))
# Central compartment
fixef(V_p = c(0, 88, 400))
fixef(Cl_p = c(0, 28, 60))
fixef(F_p = c(0, 0.05, 0.4))
# Peripheral compartment
fixef(V2_p = c(0, 181, 3000))
fixef(Q_p = c(0, 22, 300))
# Metabolite conversion
fixef(VMax_p_m = c(0, 329, 6000))
fixef(Km_p_m = c(0, 700, 5000))
}
 
An here are some plots:
 
drate.png
 
compartments.png
 
Let me know if this does not work for you.
 
Bernd
 


#5 littlepetinga

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Posted 09 September 2022 - 04:48 PM

Hi Bernd,

 

Thank you so much! It worked perfectly!

 

If I want the remaining fraction of the dose (1-F_p) to go to a different compartment, can I do it just adding another differential equation?:

deriv(A3 = drate *(1-F_p) * Aa - ....)

 

Thank you so much once again!

Sara



#6 bwendt@certara.com

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Posted 22 September 2022 - 03:12 PM

Hi Sara,

 

absolutely, please go ahead.

 

Bernd







Also tagged with one or more of these keywords: bioavailability, PK model, dissolution

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