- On 14 Sep 1999 at 22:04:16, Chandrani Gunaratna (prema.-at-.bioanalytical.com) sent the message

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Dear All,

I just have a simple question. Do all drugs follow exponential decay in the

elimination phase? Can you have a fairly flat curve for some time in this

phase? Are there any exceptions?

Thanks for your help.

Chandrani Gunaratna, Ph.D.

Senior Research Chemist

Bioanalytical Systems

2701 Kent Avenue

West Lafayette, IN 47906

Phone: (765)463-4527

E-Mail: prema.aaa.bioanalytical.com - On 16 Sep 1999 at 07:47:24, David_Bourne (david.aaa.boomer.org) sent the message

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[Two replies - db]

Date: Wed, 15 Sep 1999 02:06:21 -0700 (MST)

X-Sender: ml11439.at.pop.goodnet.com

To: PharmPK.at.boomer.org

From: ml11439.aaa.goodnet.com (Michael J. Leibold)

Subject: Re: PharmPK Elimination phase kinetics

Hello Dr.Gunaratna,

Most drugs obey "linear pharmacokinetics" which manifests as

exponential decay in the plasma concentration versus time curve.

However, some drugs obey "nonlinear pharmacokinetics" where the

plasma concentration versus time curve is not "log linear" or

exponential in nature. Nonlinear pharmacokinetics is also called

Michaelis-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 concentrations

decline 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 order

differential equation:

dc/dt= -C(Vmax)/(Km) (equation 3) (linear differential

equation)

dc/dt= -CK where C= Coe-kt

At intermediate concentrations, the plasma concentrations

decline at a variable rate as function of the varying plasma

concentrations themselves (equation 1).

It has been suggested that all drugs which are hepatically

metabolized are subject to the same Michaelis-Menten enzyme

pharmacokinetics. That is, at some high concentration all drugs

will exhibit enzyme saturable, nonlinear, Michaelis-Menten

pharmacokinetics. Theophyline has been found to exhibit nonlinear

pharmacokinetics at higher concentrations, but linear pharmacokinetics

at lower concentrations. However, most drugs in the therapeutic range

are the bottom of the Michaelis-Menten curve and obey linear

pharmacokinetics governed by equation 3, and this is why their

plasma concentration versus time curves are exponential.

The plasma concentrations of phenytoin (a drug which obeys

Michaelis-Menten pharmacokinetics in the therapeutic range) appears

"bowed" on a log plasma concentration versus time curve relative to

the straight line appearance of a drug with linear pharmacokinetics.

Phenytoin is the classic Michaelis-Menten drug and various dosage

schemes 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 kinetics

Date: Wed, 15 Sep 1999 09:25:19 -0400

Not all drugs follow an exponential decay (1st order).

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.

Ed Barnes

TRI

3202 Tower Oaks Blvd.

Rockville, MD 20852

ebarnes.-a-.tech-res.com

301-230-4793 - On 16 Sep 1999 at 23:11:52, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message

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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 characterize

real concentration time profiles. Ethanol kinetics have been extensively

studied and a variety of models tested (Holford NHG. The clinical

pharmacokinetics of ethanol. Clinical Pharmacokinetics. 1987;

13:273-292). The zero-order fiction might be OK for those who like to

make money crystal ball gazing for drunk driving defendants but there is

very strong evidence that ethanol kinetics are not properly described by

a zero-order model. A combination of a mixed order and first order

elimination pathway is required to describe ethanol PK over a wide range

of concentrations and this combined model should probably always be

considered 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 Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm - On 17 Sep 1999 at 20:25:50, Nils Ove Hoem (n.o.hoem.-at-.farmasi.uio.no) sent the message

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Another way of viewing the 1.order/0.order concepts is simply to view them

as special cases of saturable kinetics. In its simples case saturable

kinetics can be described by the familiar squared hyperbola (as in classical

Michaelis-Menten kinetics. Now if the speed of the process in question (like

elimination) 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 low

saturation (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 approaches

zero.

The point is that those two cases can best be viewed as special cases of

saturation: When the two extreme situations are not present then we have to

describe clearance as a variable dependent on ([X] = Vmax/Km + [X]).

At least in teaching PK to undergraduates I have found this approach an

effective way of structuring those concepts. - On 19 Sep 1999 at 23:51:50, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message

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The mathematical demonstration that the mixed order model

approximates to either a first-order process or a zero-order process

is not in doubt. However, in real life I would argue that one cannot

satisfactorily describe full concentration profiles by using the zero

order eliminaton model because the approximation will necessarily

fail when concentrations become low (in the region of the Km). The

first order approximation on the other hand can work very well, and

has obviously done so for countless drugs, because it is not uncommon

for the highest concentrations to be well under the Km.

A similar situation happens with the limiting case of the organ

clearance model (discussed recently on this list) which predicts

organ clearance is only determined by blood flow when CLint>>Q. This

approximation is very hard to satisfy in real life because it

requires extremely high enzyme activity (quantitated as CLint) in

relation to blood flow. In practice, the organ clearance of high

extraction ratio drugs depends on both blood flow and intrinsic

clearance so that inhibitors (or even inducers) of CLint can be

expected to modify organ clearance. On the other hand, the assumption

that CLint<liver have many different enzymes served by the same blood flow and

it not hard for enzyme activity to be low in relation to Q. The

finding of organ clearance being apparently independent of blood flow

is therefore not unusual.

Fortunately a double dose of foolish approximation (zero-order

elimination and organ clearance only dependent on blood flow) won't

happen because, as Nils points out, when C is much greater than Km,

CLint approaches zero and so the organ clearance cannot be dependent

on blood flow as CLint has to become less than Q.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html - 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

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I have to take issue with the implication that zero-order elimination is

not seen clinically. I have taken care of patients who have overdosed

with phenytoin who have concentrations in the 50 - 60 mcg/ml range. I

can attest that zero order elimination does occur clinically.

Ron Kavanagh, BS Pharm, PharmD, PhD

Office of Clinical Pharmacology and Biopharmaceutics

Food and Drug Administration

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