[R] Michaelis-menten equation

Chun-Ying Lee u9370004 at cc.kmu.edu.tw
Wed Jul 20 04:21:22 CEST 2005


   We are doing a pharmaockinetic modeling.  This model is
described as intravenous injection of a certain drug into
the body.  Then the drug molecule will be eliminated (or decayed)
from the body.  We here used a MM eq. to describe the elimination
process and the changes of the drug conc..  So the diff. eq. would
be: dCp/dt = -Vm/Vd * Cp/(Km+Cp).  Vd is a volume of distribution.
We used lsoda to solve the diff. eq. first and fit the diff. eq.
with optim first (Nelder-Mead simplex) and followed by using nls 
to take over the fitting process of optim.  However, we can not
obtain the correct value for Km if we used the above model.  The
correct Km can be obtained only when we modeled the diff eq. with
dCp/dt= -Vm/Vd * Cp/(Km/vd + Cp).  Now we lost.  The data were
from simulation with known Vm and Km.  Any idea?  Thanks.

--- Chun-ying Lee
> it is not clear to me what you are trying to do:
> you seem to have a time-concentration-curve in PKindex and you seem 
> to set up a derivative of this time dependency according to some 
> model in dCpdt. AFAIKS this scenario is  not directly related to the 
> situation described by the Michaelis-Menten-Equation which relates 
> some "input" concentration with some "product" concentration. If Vm and
> Km are meant to be the canonical symbols,
> what is Vd, a volume of distribution? it is impossible to see (at least
> for me) what exactly you want to achieve.
> (and in any case, I would prefer "nls" for a least squares fit 
> instead of 'optim').
> joerg
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