ka dependant of dose

Phoenix Certara Forums Modelling and Simulation
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Hi, I am relatively new in the field of NLME and would like to integrate a dose effect on my absorption rate variable. I wonder how I could integrate this in my textual model. In other words, I would like to know how to write an equation to describe a decrease or an increase of my Ka with dose. An example on a 1 or 2 compartment(s) model would be fantastic. Thanks for your help

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Dear boetschc Please see attached a simple project showing you 3 models and their code. The first one shows you an example where Ka increases with concentration. It is better to use C rather than dose as you may want to use your model for extrapolation (single to multiple doses for example). Putting dose as a covariate would do the job only for single dose but you cannot extrapolate to multiple dose while using Concentration in your model for dependence with Ka will enable extrapolations. The second model emulate Ka decreasing with concentration The third model can be accessed using the graphical mode where you assume Ka saturable using a Michaelis Menten type of model for absorption. I hope it helps. If you have data you can share that exhibit Ka dependence on C (or dose), please try it and send it to me for review. best Regards; Serge [file name=ka_dependence_on_dose_or_more_precisely_concentration.phxproj size=217235]Certara | Drug Development Solutions (212 KB)

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Hi Serge and Phoenix Users,

I have a question regarding Micahelis Menten model shared by Serge above.

Updated question:

Can you please explain how doest below mentioned equation represent that as concentration increases, ka (absorption coefficient) decreases?

This equation contains general MM equation, which represent that as conc increases, rate increases and then saturates at Vmax.

deriv(Aa = - (VMax * Aa / (Aa + Km)))
deriv(A1 = - (Cl * C) + (VMax * Aa / (Aa + Km)))

I do not understand which part in equation suggest as concentration increases, rate of absorption decreases, because - signs simply suggest what is coming and going from each compartment. Sorry, I am a bit new to these concepts and will really appreciate some explanation.

Thanks,
Krina

4

Dear Krina,

I do not understand which part in equation suggest as concentration increases, rate of absorption decreases, because - signs simply suggest what is coming and going from each compartment.

sometimes you should not trust your eyes))

You are correct, the right name of this model should be

Model_graphical_Ka_saturating_with_Aa_Michaelis_menten

Please see my corrected code to explain this:

test(){
deriv(A1 = - (Cl * C) + kaAa)
deriv(Aa = - kaAa)
C = A1 / V
dosepoint(Aa, idosevar = AaDose)
error(CEps = 0.1)
observe(CObs = C * (1 + CEps))
stparm(V = tvV * exp(nV))
stparm(Cl = tvCl * exp(nCl))
stparm(VMax = tvVMax)
stparm(Km = tvKm)
fixef(tvV = c(, 50, ))
fixef(tvCl = c(, 5, ))
fixef(tvVMax = c(, 5, ))
stparm(kaAa=(VMax * Aa / (Aa + Km)))
stparm(ka=(VMax * Aa / (Aa + Km))/Aa)
fixef(tvKm = c(, 1, ))
ranef(diag(nV, nCl, nVMax, nKm) = c(0.1, 0.1, 0.1, 1))
}

Select Sim./Pred.check, add kaAa and ka to the variables for simulation and add times seq(0, 2, 0.1). You’ll see that kaAa slightly increases with high Doses (close to zero-order absorption), but increases very fast when dose is small

BR,

Mittyright

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Thanks so much, Mittyright for clarification and code.

The original model fitted my data very well, but I was confused by model name since my model should have increase in Ka with concentration increase and I saw the similar trend with plotting results as well.

All is clear now. Thanks again.