Could anyone know how to get the theoretical Cmax value for a PK study? Can Phoex WNL estimate this value?
Thank you very much,
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Posted 11 January 2020 - 12:06 AM
only for a one-compartment model (with and without lag-time) the exact Cmax can be calculated from the model parameters:
For other models the derivative cannot be obtained analytically. Therefore, you have to use a numeric method to find the maximum and its time.
Instead of paper/pencil/brain use software. In PHX/WNL both Cmax and tmax are given in the outputs as secondary parameters.
Posted 18 January 2020 - 09:32 AM
HI Li, Helmut has already suggested that you can use the models of Phoenix to generate these secondary parameters.
first choose the button to 'set WNL model'
and then use the drop downs to make your selections and then the relevant code will be generated when you click apply.
secondary(Ke = tvCl/tvV)
secondary(Tmax = log(tvKa/Ke)/(tvKa-Ke)+tvTlag)
secondary(AUC = AaDose/tvV/Ke)
secondary(Cmax = AaDose/tvV*exp(-Ke*(Tmax-tvTlag)))
secondary(Ka_hl = log(2)/tvKa)
secondary(Ke_hl = log(2)/Ke)
Remember these are specific to the structural model chosen.
Posted 18 January 2020 - 04:58 PM
I would like to confirm that the exact Cmax in your answer is the theoretical Cmax. Am I right?
As I wrote already in my first post only in a one-compartment model (with and without lag-time) the theoretical Cmax can be derived by calculus/algebra. Hence, it is exact if you like.
For other models numeric methods are required. I don’t know which one is implemented is Phoenix (I’m a user with no access to its source code).
More efficient are e.g., the bisection method or the uniroot algorithm (Brent 1973, 2003) implemented in R and C.
But again, if you really want the exact value, bad luck. The best you can get is a value which deviates not more than the numeric precision of the machine from the theoretical one. If you are not happy with ±3.6·10–16 on 64bit-machines get a number cruncher.
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