PharmPK Discussion - First-order one compartment formulas

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On 14 Feb 1997 at 17:58:08, djtippey.-at-.dbtech.net (Del & Jackie Tippey) sent the message


Greetings;

        I am working on a PK program for my department's aminoglycoside /
vancomycin PK program. I have equations that will give me estimates of
levels and Vd after "n" doses - provided it is the initiation of therapy. I
was wondering if anyone knew of equations that could help me determine
levels after "n" doses if I had a ballpark pre-therapy level. I know that
the steady-state equations probably will remain the same, but I wanted to
know in case levels are drawn before steady-state so we determine expected
levels.

        Thanks in advance...

        -DT-

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On 18 Feb 1997 at 11:48:45, "David Nix" (nix.aaa.tonic.Pharmacy.Arizona.EDU) sent the message


The full equation for concentrations at any time is:

C(t) = D/TI/ke/V*(exp(-k*ts)-exp(-k*t))*(1-exp(-nktau))/(1-exp(-ktau))

       D=dose
       TI=time of infusion
       k=elimination rate constant
       V=volume
       ts=t-TI  :    restrict ts>=0
       tau = dosing interval
       n = # of doses given

There are several bayesian estimation programs commercially available
that will handle 1 or more non-steady-state levels.  However, if a
computer and software are not available, some other methods may be
useful.  Below is how I have handled similar problems:

Single level:
     1.  assume k based on creatinine clearance
     2.  calculate V from the above equation
     3.  If volume is reasonable (.24 to 0.4 L/kg for aminoglycoside)
          then accept new parameters.  Otherwise, you may adjust ke
          by 20-40% and recalculate V.  This method will get parameters in the
         "ball park".

Two levels

     1. Within same dose interval.  Use levels to estimate k, then
          calculate V as above.
     2.  trough-dose-peak -  This senerio provides a better estimate
          of V than ke.  However, you must calculate ke by trial and error.
          Guess at ke and calculate V based on one of the levels.  Then check
          to see if the other level is predicted correctly.  After some
          practice, this process does speed up considerable, but it is still
          time consuming.  Your speed is related to your ability to guess at k
          and revise the estimate, and also how close that you are trying to
          approach the measured concentrations.

The use of computers and baysian approach is recommended.

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On 25 Feb 1997 at 12:36:16, djtippey.aaa.dbtech.net (Del & Jackie Tippey) sent the message


Thanks for the rapid and informative feedback.

-DT-
Del Tippey R.Ph., M.S.S.M.
DCH Regional Medical Center
801 University Blvd. E.
Tuscaloosa,AL 35405
1-205-759-7310
djtippey.aaa.dbtech.net

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