Non-linearity and Bioavailability

Phoenix Certara Forums Modelling and Simulation
1

Dear Colleagues,

Modeled the PK data from IV and PO (three doses same in both iv and po) dosing in different animals by 2 compartment IV and Oral graphical model with Michaelis-Menten clearance. Got all the parameters V1, V2, Vmax, Km, Cl2, Ka and F.

I am not able to interpret the value of F which is 0.64.

As the drug follows non-linear kinetics the bioavailability will vary with dose (dose dependent) and will be low at lower doses and high (because of enzyme saturation) at higher doses. How to interpret the value of 0.64.

When i perform the NCA of lower dose (both oral and IV) the bioavailability calculated is 0.22 (Mean).

Any thoughts or suggestions.

Thanks in advance

Raghav

2

Dear Raghav

If you know that the bioavailability changes with dose and therefore with concentration, you should model that.

Instead of putting F as a component of the dosepoint, you should not define F there but directly in the differential equation deriv(Aa=-KaAa) and deriv(A1=FKa*Aa…).

Now, instead of F, you put the relationship that includes the predicted concentration and the trend you just defined, for example F=Fbase*(1+emax*C/C+EC50)) . Now this equation is a little bit risky and it is not guaranteed you will be between 0 and 1 at each time.

You could then shift to the logit domain to insure that you stay between 0 and 1

F=ilogit(Fbase*(1+emax*C/(C+EC50)))

Placebo would give you the lower bound, (ilogit(Fbase) and ilogit(Fbase*(1+emax)) the upper bound.

Now the F you got is a sort of average but you can ask the Bayesian estimates by using the add table and click on structural parameters. You will get F for each patient. This can help you establishing the trend.

This is just an idea where you try to model the trend you expect.

I am not sure NCA is the right tool to get that trend but only a model based analysis.

Good luck.

Serge

3

Dear Serge,

The following is the code as suggested by you, and the individual estimates of bioavailability given below :

test(){

deriv(A1 = - (VMax * C / (C + Km))- (Cl2 * (C - C2)) + (F * Aa * Ka))

urinecpt(A0 = (VMax * C / (C + Km)))

deriv(A2 = (Cl2 * (C - C2)))

deriv(Aa = - (Aa * Ka))

C = A1 / V

dosepoint(A1, idosevar = A1Dose, infdosevar = A1InfDose, infratevar = A1InfRate)

C2 = A2 / V2

error(CEps = 0.3)

observe(CObs = C * (1 + CEps))

dosepoint(Aa, idosevar = AaDose, infdosevar = AaInfDose, infratevar = AaInfRate)

stparm(V = tvV * exp(nV))

stparm(VMax = tvVMax * exp(nVMax))

stparm(Km = tvKm * exp(nKm))

stparm(V2 = tvV2 * exp(nV2))

stparm(Cl2 = tvCl2 * exp(nCl2))

stparm(Ka = tvKa)

stparm(F = tvF * exp(nF))

fixef(tvV = c(, 10, ))

fixef(tvVMax = c(, 5636.72, ))

fixef(tvKm = c(, 118.735, ))

fixef(tvV2 = c(, 15.7508, ))

fixef(tvCl2 = c(, 8.82235, ))

fixef(tvKa(freeze) = c(, 15.4021, ))

fixef(tvF = c(, 0.6, ))

ranef(diag(nV, nV2, nCl2, nKm, nVMax, nF) = c(1, 1, 1, 1, 1, 1))

Subject 1 -Oral dose - 3000 ug : F = 0.36

Subject 2 -Oral dose - 3000 ug : F = 0.48

Subject 3 -Oral dose - 3000 ug : F = 0.39

Subject 4 -Oral dose - 10000 ug : F = 0.87

Subject 5 -Oral dose - 10000 ug : F = 0.46

Subject 6 -Oral dose - 10000 ug : F = 0.76

Subject 7 -Oral dose - 30000 ug : F = 0.74

Subject 8 -Oral dose - 30000 ug : F = 0.75

Subject 9 -Oral dose - 30000 ug : F = 0.86

Subject 10 -IV dose - 3000 ug : F = 0.60

Subject 11 -IV dose - 3000 ug : F = 0.57

Subject 12 -IV dose - 3000 ug : F = 0.67

Subject 13 -IV dose - 10000 ug : F = 0.73

Subject 14 -IV dose - 10000 ug : F = 0.66

Subject 15 -IV dose - 10000 ug : F = 0.60

Subject 16 -IV dose - 30000 ug : F = 0.66

Subject 17 -IV dose - 30000 ug : F = 0.67

Subject 18 -IV dose - 30000 ug : F = 0.56

I have few questions around the model :

  1. The bioavailability shows up for subjects dosed i.v also but the value is constant. How to read the F value in subjects dosed with i.v?

  2. In the model i have Vmax and Km parameters for non-linear clearance. Is the ratio of Vmax / Km equals to intrinsic clearance or total clearance ? Please explain ?

  3. I used this model for two species, and scaled up the obtained pk parameters ( V1, V2, Vmax, CL2) to higher species , based on body weight, and put them in the initial estimates to simulate. Now what value should i chose for random effects ? A value of 0.1 for all the parameters is OK?

  4. If i remove the iv data from the model and only model the oral data, Will Vmax be considered as apparent value i.e., Vmax / F ??

  5. Can i estimate the fraction escaping the gut using the above model from intravenous and oral data?

Thanks in advance

Raghav