# Mixed absorption modeling

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### #1 gwchoi

gwchoi

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Posted 22 August 2019 - 10:14 AM

Dear all,

I have developed a parent and metabolites PK model.

My model building strategy is a stepwise approach.

In the first step, I just have developed parent PK model.

The absorption of the parent drug is modeled using mixed absorption model (first and zero-order absorption).

In this approach, dose is divided by a fraction of dose absorbed by the zero-order absorption (FR).

Although I used 'ilogit' function, however, a range of post-hoc parameter of FR is -1.08 to 2.97.

My first question is how can I code the FR with a range of 0 to 1.

In the second step, I am developing a metabolite PK model with fixing the parameters from parent PK model.

When I use (freeze) function to "error" and "fixef" of parents drug PK parameters, the CV% of metabolite PK parameters is not calculated.

How can I handle these issues?

I've attached the model code.

Thanks!

test(){
#------------Parent PK model----------------------------#

dosepoint(A1, duration=(D), bioavail=ilogit(FR))
dosepoint(Aa, bioavail=ilogit(1-FR))

deriv(Aa = -Ka*Aa)
deriv(A1 = - (CL * C)+Ka*Aa )
C = A1 / V

error(CEps(freeze) =  0.544783)
observe(CObs = C * (1 + CEps))

stparm(V = THETA1 * exp(nV)) # Volume of distribution
stparm(CL = THETA2 * exp(nCL))   # CL/F
stparm(D = THETA3 * exp(nD)) # Duration of Parent for zero order absorption to the central compartment
stparm(Ka = THETA4 *exp(nKa))    # First order absorption rate constant
stparm(FR = THETA5 +nFR )    # Fraction of dose directly go to the central compartment with zero order absorption

fixef(THETA1 (freeze)= c(0, 2.98014, ))
fixef(THETA2 (freeze)= c(0, 2.38676, ))
fixef(THETA3 (freeze)= c(0, 0.589064, ))
fixef(THETA4(freeze) = c(0, 0.538162,))
fixef(THETA5(freeze) = c(0, 0.811779,1))

ranef(diag(nV, nCL, nD, nKa, nFR) = c(0.12097657, 0.13467876, 0.1054329, 0.14217843, 3.7403325))

#--------------M1 modeling----------------------------------#

deriv(Am1 = CL*C - CLm1*Cm1)
Cm1 = Am1/V

observe(CObs_M1 = Cm1 * (1+CEps1))
error(CEps1 = 0.1)

stparm(CLm1 = THETA6 * exp(nCLm1))
fixef(THETA6 = c(0,100,))

ranef(diag(nCLm1) = c(0.1))
}

### #2 Simon Davis

Simon Davis

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Posted 26 August 2019 - 10:46 AM

I'd recommend to look into the other posts where ilogit and its application is discussed

https://support.cert...etween-0-and-1/

support.certara.com/forums/topic/964-modeling-and-simulating-fraction-metabolized/

I beleive the correct way would be

dosepoint(A1, duration=(D), bioavail=(FR))

dosepoint(Aa, bioavail=(1-FR))

stparm(FR = ilogit(THETA5 +nFR ))

regarding second question - it is difficult to say. We see that Theta6 has some unplausible high value. Is that intended?

What do your diagnostic plots say? How far are your results from good fit?

Since including data regarding metabolite you are adding some info into the model, the estimates of the parent thetas/etas also could change, so you can try to fit it simultaneously ?

Simon

### #3 gwchoi

gwchoi

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Posted 18 September 2019 - 01:39 AM

Dear Simon

After all, I selected the first order absorption.

Could I get comments regarding PK models that I've developed? (attached project file)

This model has three observations.

After parent drug (P) is administered via IV or SC route, it is metabolized to M1 and then M2 (P->M1->M2). Although there are other metabolites, M1 and M2 have pharmacological activities.

I've been tried to fit the parent and metabolites after IV or SC administration simultaneously using several models.

1. Empirical compartment PK model

In this approach, one or two compartments model were used to fit the parent drug data set. The metabolites are linked as the one-compartment model.

The -2LL value is lower in the two-compartment model than the one-compartment regarding parent drug.

Although it is obvious that IV administration group has biexponential elimination phase, SC groups have monoexponential elimination.

Q1) How can I interpret the discrepancy between each administration groups and which model do I have to select?

2. Michaelis-Menten equation

In this approach, the elimination of parent drug is described using MM equation since AUC exponentially increase as ascending dose escalation.

3. Semiphysiological PK model

This model is aimed for extrapolation from rats to humans.

The compartment model is expended by adding liver compartment where elimination occurs.

Q2) Diagnostic plots of IVAR vs CWRES from all the models have an obvious trend in M1 and M2. This means the models have a structure error. However, it is hard to find a key error. How can I handle tish issue?