# PharmPK Discussion - Elimination phase kinetics

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• On 14 Sep 1999 at 22:04:16, Chandrani Gunaratna (prema.-at-.bioanalytical.com) sent the message
`Dear All,I just have a simple question. Do all drugs follow exponential decay in theelimination phase? Can you have a fairly flat curve for some time in thisphase? Are there any exceptions?Thanks for your help.  Chandrani Gunaratna, Ph.D.Senior Research ChemistBioanalytical Systems2701 Kent AvenueWest Lafayette, IN 47906Phone: (765)463-4527E-Mail: prema.aaa.bioanalytical.com`
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• On 16 Sep 1999 at 07:47:24, David_Bourne (david.aaa.boomer.org) sent the message
`[Two replies - db]Date: Wed, 15 Sep 1999 02:06:21 -0700 (MST)X-Sender: ml11439.at.pop.goodnet.comTo: PharmPK.at.boomer.orgFrom: ml11439.aaa.goodnet.com (Michael J. Leibold)Subject: Re: PharmPK Elimination phase kineticsHello Dr.Gunaratna,      Most drugs obey "linear pharmacokinetics" which manifests asexponential decay in the plasma concentration versus time curve.However, some drugs obey "nonlinear pharmacokinetics" where theplasma concentration versus time curve is not "log linear" orexponential in nature. Nonlinear pharmacokinetics is also calledMichaelis-Menten pharmacokinetics and is described by the equation:      dc/dt= -C(Vmax)/(Km + C)    (equation 1) (nonlinear differential                                                 equation)       Vmax= maximal metabolic rate       Km= Michaelis-Menten constant     At high concentrations (C>>Km), the plasma concentrationsdecline at constant rate equal to Vmax (the maximal rate of metabolism).       dc/dt= -Vmax               (equation 2)     At very low concentrations(C<in a log linear, exponential fashion described by the first orderdifferential equation:     dc/dt= -C(Vmax)/(Km)         (equation 3) (linear differential                                                 equation)     dc/dt= -CK  where C= Coe-kt     At intermediate concentrations, the plasma concentrationsdecline at a variable rate as function of the varying plasmaconcentrations themselves (equation 1).     It has been suggested that all drugs which are hepaticallymetabolized are subject to the same Michaelis-Menten enzymepharmacokinetics. That is, at some high concentration all drugswill exhibit enzyme saturable, nonlinear, Michaelis-Mentenpharmacokinetics. Theophyline has been found to exhibit nonlinearpharmacokinetics at higher concentrations, but linear pharmacokineticsat lower concentrations. However, most drugs in the therapeutic rangeare the bottom of the Michaelis-Menten curve and obey linearpharmacokinetics governed by equation 3, and this is why theirplasma concentration versus time curves are exponential.     The plasma concentrations of phenytoin (a drug which obeysMichaelis-Menten pharmacokinetics in the therapeutic range) appears"bowed" on a log plasma concentration versus time curve relative tothe straight line appearance of a drug with linear pharmacokinetics.Phenytoin is the classic Michaelis-Menten drug and various dosageschemes have been devised based on this concept.      I hope that this was helpful!      Mike Leibold, PharmD, RPh      ML11439.aaa.goodnet.com---From: "Barnes, Edward" To: "'PharmPK.at.boomer.org'" Subject: RE: PharmPK Elimination phase kineticsDate: Wed, 15 Sep 1999 09:25:19 -0400Not all drugs follow an exponential decay (1st order).In a saturated system you can have a linear decay (0 order).  This is alsoreferred to as Michaelis-Menten kinetics.  Alcohol (C2H5OH) is an example ofa drug that exhibits 0 order elimination, especially when consumed in largequantities.Ed BarnesTRI3202 Tower Oaks Blvd.Rockville, MD   20852ebarnes.-a-.tech-res.com301-230-4793`
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• On 16 Sep 1999 at 23:11:52, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
`The concept of zero-order elimination is OK as an mathematical entity(See Mike Leibold's equation 2) but it is not a good way to characterizereal concentration time profiles. Ethanol kinetics have been extensivelystudied and a variety of models tested (Holford NHG. The clinicalpharmacokinetics of ethanol. Clinical Pharmacokinetics. 1987;13:273-292). The zero-order fiction might be OK for those who like tomake money crystal ball gazing for drunk driving defendants but there isvery strong evidence that ethanol kinetics are not properly described bya zero-order model. A combination of a mixed order and  first orderelimination pathway is required to describe ethanol PK over a wide rangeof concentrations and this combined model should probably always beconsidered for any drug which appears to have capacity limited kinetics.> From: ml11439.-at-.goodnet.com (Michael J. Leibold)> Subject: Re: PharmPK Elimination phase kinetics>      At high concentrations (C>>Km), the plasma concentrations> decline at constant rate equal to Vmax (the maximal rate of metabolism).>        dc/dt= -Vmax               (equation 2)> From: "Barnes, Edward" > Subject: RE: PharmPK Elimination phase kinetics> In a saturated system you can have a linear decay (0 order).  This is also> referred to as Michaelis-Menten kinetics.  Alcohol (C2H5OH) is an example of> a drug that exhibits 0 order elimination, especially when consumed in large> quantities.--Nick Holford, Dept Pharmacology & Clinical PharmacologyUniversity of Auckland, Private Bag 92019, Auckland, New Zealandemail:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm`
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• On 17 Sep 1999 at 20:25:50, Nils Ove Hoem (n.o.hoem.-at-.farmasi.uio.no) sent the message
`Another way of viewing the 1.order/0.order concepts is simply to view themas special cases of  saturable kinetics. In its simples case saturablekinetics can be described by the familiar squared hyperbola (as in classicalMichaelis-Menten kinetics. Now if the speed of the process in question (likeelimination) is decribed by:                 dX/dt = (Vmax/(Km + [X])) * [X]       and Clearance =Vmax/Km  (a constant)Then in the case that [X]<                 dX/dt ~ (Vmax/Km) * [X]and thus aproaches 1.order kinetics. So any facilitated process will at lowsaturation (of course) be satisfactorily described as a 1.order process.The other special case of saturation kinetics when [X]>>Km when (Km+[X])}~[X]of course gives dX/dt ~ Vmax thus 0.0rder kinetics. Clearance approacheszero.The point is that those two cases can best be viewed as special cases ofsaturation: When the two extreme situations are not present then we have todescribe  clearance as a variable dependent on ([X] = Vmax/Km + [X]).At least in teaching PK to undergraduates I have found this approach aneffective way of structuring those concepts.`
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• On 19 Sep 1999 at 23:51:50, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message
`The mathematical demonstration that the mixed order modelapproximates to either a first-order process or a zero-order processis not in doubt. However, in real life I would argue that one cannotsatisfactorily describe full concentration profiles by using the zeroorder eliminaton model because the approximation will necessarilyfail when concentrations become low (in the region of the Km). Thefirst order approximation on the other hand can work very well, andhas obviously done so for countless drugs, because it is not uncommonfor the highest concentrations to be well under the Km.A similar situation happens with the limiting case of the organclearance model (discussed recently on this list) which predictsorgan clearance is only determined by blood flow when CLint>>Q. Thisapproximation is very hard to satisfy in real life because itrequires extremely high enzyme activity (quantitated as CLint) inrelation to blood flow. In practice, the organ clearance of highextraction ratio drugs depends on both blood flow and intrinsicclearance so that inhibitors (or even inducers) of CLint can beexpected to modify organ clearance. On the other hand, the assumptionthat CLint<liver have many different enzymes served by the same blood flow andit not hard for enzyme activity  to be low in relation to Q. Thefinding of organ clearance being apparently independent of blood flowis therefore not unusual.Fortunately a double dose of foolish approximation (zero-orderelimination and organ clearance only dependent on blood flow) won'thappen because, as Nils points out, when C is much greater than Km,CLint approaches zero and so the organ clearance cannot be dependenton blood flow as CLint has to become less than Q.--Nick Holford, Dept Pharmacology & Clinical PharmacologyUniversity of Auckland, Private Bag 92019, Auckland, New Zealandemail:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html`
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• On 20 Sep 1999 at 11:14:01, Ronald Kavanagh 301-827-6408 FAX 301-443-9282 (KAVANAGHR.at.cder.fda.gov) sent the message
`I have to take issue with the implication that zero-order elimination isnot seen clinically. I have taken care of patients who have overdosedwith phenytoin who have concentrations in the 50 - 60 mcg/ml range. Ican attest that zero order elimination does occur clinically.Ron Kavanagh, BS Pharm, PharmD, PhDOffice of Clinical Pharmacology and BiopharmaceuticsFood and Drug Administration`
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