# PharmPK Discussion - Morphine

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• On 4 Aug 2000 at 15:23:45, ml11439.-a-.goodnet.com sent the message
`Dr.Paepe,    One compartment equations that describe the plasma concentrationsof a drug following an IV bolus or infusion, and the companion equationsdescribing 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-kmtb) 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)Vmc) 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-1d) Simulations     The above pharmacokinetic equations and parameters can beused to simulate a hypothetical case where the concentrationof a metabolite 5 minutes after a bolus exceeds that of theparent, but after a 20minute infusion, the concentration ofthe metabolite is less than the parent, but only to exceed thatof 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= 2.91e) Conclusion     It would seem from this hypothetical case that the situationyou describe could be explained by the rapid metabolism of morphineto a metabolite with a longer half-life. To accomplish this, theformation constant of the metabolite would have to be high (~5)toallow for the rapid accumulation of the metabolite after the bolus,and the metabolites elimination constant would have to be less thanthe parent drug to allow for a relative accumulation in plasmalevels of the metabolite relative to the parent drug during anIV infusion. The volumes of distribution of the parent drug andmetabolite were assumed be similar in the above simulations, butthis could have an influence as well.                            Mike Leibold, PharmD, RPh                            ML11439.-at-.goodnet.comReferences1) Gibaldi, M., Perrier, D., Pharmacokinetics, New York, Marcel Dekker    19752) Gibaldi, M., Perrier, D., Pharmacokinetics 2nd ed, New York, Marcel Dekker   19823) Wagner, J., Fundamentals of Clinical Pharmacokinetics, Hamilton, Drug    Intelligence Publications 19754) Godfrey, Keith, Compartment Models and Their Application, New York,    Academic Press 1983`
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