PharmPK Discussion - Morphine

PharmPK Discussion List Archive Index page

On 4 Aug 2000 at 15:23:45, ml11439.-a-.goodnet.com sent the message


Dr.Paepe,

    One compartment equations that describe the plasma concentrations
of a drug following an IV bolus or infusion, and the companion equations
describing the plasma concentrations of a metabolite are as follows:

a) IV bolus
     i) Cp parent drug  Cp= (Xo/Vd)e-ket

     ii) Cp metabolite=[ KfXo/Vm(ke-km)][e-kmt - e-ket]

     iii) when Ke>>Km  Cp metabolite~= [KfXo/(Vm(ke-km))]e-kmt

b) IV infusion
     i) Cp parent drug  Cp= [Ko/KeVd][1-e-ket]

     ii) Cp metabolite = KfKo/kekmVm + (KfKo)e-ket/-k(km-ke)Vm+
                        (KfKo)e-kmt/-km(ke-km)Vm

     iii) Ke>>Km
         Cp metabolite~= KfKo/kekmVm - (KfKo)e-kmt/km(ke-km)Vm

c) Pharmacokinetic Parameters

     Ke= 8.326 hr-1   T1/2= .0833 hr (5 min)
     Vd= 25ml= .025 Liter
     Xo= 5mg
     Ko= 10mg/hr

     Km= 1.0 hr-1   T1/2= .693 hrs
     Vm= 25ml= .025 liter
     Kf= 5 hr-1

d) Simulations

     The above pharmacokinetic equations and parameters can be
used to simulate a hypothetical case where the concentration
of a metabolite 5 minutes after a bolus exceeds that of the
parent, but after a 20minute infusion, the concentration of
the metabolite is less than the parent, but only to exceed that
of the parent at 60 minutes into the infusion.

     i) Cp parent drug 5 minutes following 5mg IV bolus

     Cp parent = [Xo/Vd]e-ket= 99.96 mg/l

     ii) Cp metabolite 5 minutes following 5mg IV bolus

      Cp metabolite~= [KfXo/(Vm(ke-km))]e-kmt= 125.59 mg/l

      Ratio metabolite/Parent drug= 125.59/99.96= 1.256

     iii) Cp parent drug after 20minute infusion

      Cp parent= [Ko/KeVd][1-e-ket]= 45.04 mg/l

      After 60 minute infusion Cp parent= 48.031 mg/l

     iv) Cp metabolite after 20 minute infusion

      Cp metabolite~= KfKo/kekmVm - (KfKo)e-kmt/km(ke-km)Vm= 44.532 mg/l

      After 60 minute infusion Cp metabolite= 139.78 mg/l

     v) Ratios of metabolite/parent after 20 min and 60min:

       Ratio 20min= 44.532/45.04= .988

       Ratio 60min= 139.78/48.031= 2.91

e) Conclusion

     It would seem from this hypothetical case that the situation
you describe could be explained by the rapid metabolism of morphine
to a metabolite with a longer half-life. To accomplish this, the
formation constant of the metabolite would have to be high (~5)to
allow for the rapid accumulation of the metabolite after the bolus,
and the metabolites elimination constant would have to be less than
the parent drug to allow for a relative accumulation in plasma
levels of the metabolite relative to the parent drug during an
IV infusion. The volumes of distribution of the parent drug and
metabolite were assumed be similar in the above simulations, but
this could have an influence as well.

                            Mike Leibold, PharmD, RPh
                            ML11439.-at-.goodnet.com

References
1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker
    1975
2) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker
   1982
3) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug
    Intelligence Publications 1975
4) Godfrey, Keith, Compartment Models and Their Application, New York,
    Academic Press 1983

Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Morphine" as the subject

PharmPK Discussion List Archive Index page