- On 12 Jun 2001 at 18:49:45, "panteha khalili" (parsiwa.at.hotmail.com) sent the message

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The following message was posted to: PharmPK

Dear readers,

I have a basic question about linearity of pk of drugs or compounds.

We know that if a drug has linear pk characteristics, there will be a

linear relationship between the dose and AUC. Does this linear relationship

have to exist for all the various routes of administeration in order to say

a drug exhibits linear kinetics, or does it only pertain to iv bolus

administration?

What if a drug exhibits linearity for iv-bolus mode of administeration over

a certain range and a non-linear pattern (plateau at higher doses) for oral

dosing?

Thank you for your comments. - On 15 Jun 2001 at 21:30:25, David Bourne (david.-at-.boomer.org) sent the message

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[A few replies - db]

FROM: Nuno Silva

Dear Sir

the nonlinear pharmacokinetics is usually characterized by:

1- elimination of drug does not follow simple first order kinetics - that

is, elimination kinetics are nonlinear

2- the elimination half-life changes as dose is increased, usually due to

saturation of an enzyme system. However, the elimination half-life might

decrease due to self induction of liver biotransformation enzymes.

3- the AUC is not proportional to the amount of bioavailable drug

4- the saturation of capacity-limited processes may be affected by other

drugs that require the same enzyme or carrier-mediated system.

Considering your question, and observing for example two oral formulations:

1- immediate release form -

2- controled release form, controlled (for example) by pH

the drug release kinetics is much different in each case, which will affect

the absortion kinetics. So, if you have a nonlinear drug release from the

formulation you will have a nonlinear absortion and so, a nonlinear kinetics

due to the absortion.

I hope this simple explanation my help you...

---

FROM: khkoz.aaa.czd.waw.pl

Dear Dr Panteha Khalili

I think that;

linearity/nonlinearity in pharmacokinetics only pertains to

specific situation

(f.e. therapeutic doses, therapeutic drug-concentrations,

specific route-administration). Drug possessing linear

kinetics at therapeutic concentrations

frequently possesses nonlinear kinetic at toxic plasma

levels.

Pharmacokinetic process is linear when rate constants or

clearances

a) have first-order nature and b) are not changeable with

the time

Pharmacokinetic process is not-linear when rate constants or

clearances are

a) dose-dependent or

b) concentration-dependent or

c) time-dependent

ad a) pentobarbital in rabbits - linear 2-compartment

kinetics after single i.v. doses

however, AUC

and t1/2 inreasing with dose

ad b) ethanol or diphenylhydantoin in humans:

dCp/dt=-Vmax*Cp/(Km+Cp) after i.v. - disposition rate, and

CLe are concentration-dependent

ad c) kinetic parameters can change with the time

- authoinhibition or authoinduction of the

metabolic processess (cyclophosphamide)

- changeing physiological activity (f.e. blood flow

of the methabolic organs)

- circadian rhytms - parameters changes with the

time of the day or year additionally,

There are different methods - comparison of AUC is the most

popular.

The most effecient is population pharmacokinetics approach -

for comparison

pharmacokinetic parameters.

The influence different physiological or demographic

covariates on

pharmacokinetic parameters can be also nonlinear -

verification with NONMEM

methodology.

mechanisms of nonlinearity:

absorption:

- saturation of absorption process at high doses -

amoxicillin

- selectivity in optical isomerism for absorption

- absorption according to Weibull function (cyclosporin A

p.o-.PAGE2001 symposium, Vitamin A i.m.)

- other, pH dependent, presystemic metabolism

dystribution:

- saturation of protein binding in blood (valproinic acid)

- saturation of dystributional clearance due to protein

binding(Ro 32-3555, PAGE2001 symposium)

- selective protein binding for optical isomers

metabolism:

- saturation or inhibition of metabolic enzymes

- optical isomerism

elimination:

- saturation of tubular excretion

sincerely

Kazimierz H. Kozlowski

---

FROM: Dave Vowles

I guess linearity is always going to be over only a certain dose range,

dependant on the route of administration.

So maybe 'linearity' is only important over the relevant toxicological

(animals) or usual clinical (man) dose ranges

Also what does linear mean ?

if dose is proportional to AUC then

dose=constant x AUC and that constant can be 1 but does not have to be- is

constant =10 still OK ?

Dave

---

FROM: James Hui

It is misleading to designate drugs as either being "linear" or

"non-linear" without qualification. Clinically, what people usually mean

is that in the therapeutic range of doses or plasma concentrations, a drug

exhibits linear PK.

Linearity of PK implies that all absorption (Cmax proportional to dose) and

disposition characteristics (CL, Vd, binding, Renal CL) of a drug remain

unchanged. All drugs will have linear PK only over a certain range of

doses/plasma concentrations - it would be physiologically impossible for a

drug to show linear PK over an infinite dose/plasma concentration range.

Therefore, I would recommend that you always specify both a) the range of

doses/plasma concentrations and b) the route of administration over which

linear PK has been observed for a certain drug.

It is my experience that drugs will commonly exhibit "linear" PK after

I.V. administration but will be "non-linear" after p.o. dosing at the same

doses. This has to do with differences in the amount presented to the

liver, the capacity for GI absorption, the capacity for protein binding,

etc. Obviously, there are many sources for non-linearity in PK and each

source has a different capacity for handling drug. If a drug shows linear

PK in the therapeutic range (i.e. at doses used to treat the disease or

ailment) then for all practical purposes, dosages may be calculated with

this in mind.

James Hui, Ph.D.

Clinical Pharmacology & Drug Metabolism

Triangle Pharmaceuticals, Inc.

Durham, NC

HuiJ.at.tripharm.com

---

FROM: Silvia Giarcovich

Dear Panthea:

I understand that you have to express in which conditions you find linear pk

characteristics.

You could find linear pk after iv adm. if the elimination follows linear

kinetics but, I think, that you will find non linear pk by the oral route

(for example) if absorption or first pass elimination do not follow linear

kinetics.

Regards, Silvia - On 16 Jun 2001 at 10:28:18, Michael.D.Karol.-at-.abbott.com sent the message

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The answer to your question is complex only because the term "Linear

Pharmacokinetics" is used in different, and contradictory, ways. First I'll

address the context of system analyses. In my opinion, this is the least

confusing, cleanest mathematically, and approach of greatest utility. It is

this definition that I will use to answer your question. It is also the

approach taken in much of the graduate level pharmacokinetic text by Gibaldi

Perrier via Bennets Mammillary Model equation. Note that the mammillary model

equation is a special case of the more general convolution equation - the

equation that mathematically defines linearity.

In this context, the drug is considered to have linear pharmacokinetics if the

systemic pharmacokinetics have the properties of linearity and superposition.

That is to say that the pharmacokinetics are describable by the convolution

equation: c (t) = integral from 0 to t { f(tau) c_d(t-tau) d_tau } where

c_d is the Unit Impulse Response, f(.) is the input function (typically rate

of drug input into the systemic circulation), and c(t) is the resulting

concentration versus time profile. Of particular relevance is the distinction

between the Unit Impulse Response function c_d(.) and the input function f(.).

The Unit Impulse Response function characterizes the underlying drug

pharmacokinetics, whereas, f(.) is the drug input into the systemic

circulation. [Actually, f(.) would be the rate of administration to the input

site of reference when c_d(.) was determined, but this is probably beyond the

scope of the current question.] Since the drug input function and systemic

kinetics are separated, the issue of linearity is independent of the route of

administration.

The alternative use of the term linear pharmacokinetics combines drug input

and systemic pharmacokinetics. It is more of an observation-based definition.

More often than not, we lack intravenous data. The unit impulse response

function can not be determined and f(.) and c_d(.) are inseparable. [A common

obvious exception is the case of in vivo dissolution/drug release where an

oral solution is the reference rather than and intravenous] In this context,

the pharmacokinetics are considered linear if the combine process of drug

input and systemic pharmacokinetics exhibit linearity and superposition.

Now to answer you specific questions. You wrote "We know that if a drug has

linear pk characteristics, there will be a

linear relationship between the dose and AUC." Based on the "linear system -

convolution" definition of linear pharmacokinetics, if the relationship

between dose and AUC is linear, then the pharmacokinetics are likely linear

since it is unlikely that a nonlinearity in drug uptake will be canceled out

by a nonlinearity in systemic kinetics. Important to note; however, is that a

drug with linear pharmacokinetics may exhibit a nonlinear relationship between

dose and AUC if the dose is not administered directly to the site of reference

(usually intravenously) since drug uptake may be nonlinear (ie:nonlinear

absorption) yet the systemic kinetic may still be linear.

Your question was "Does this linear relationship have to exist for all the

various routes of administration in order to say

a drug exhibits linear kinetics, or does it only pertain to iv bolus

administration?" If the drug exhibits linear pharmacokinetics following iv

administration, then the drug has "linear kinetics". The observations

following other routes are a composite of the drugs systemic pharmacokinetics

and input processes. The input into the system is external of the system.

Thus, a nonlinear non-iv dose response relationship does not necessarily imply

nonlinear pharmacokinetics (systemic kinetics).

This "linear system - convolution" approach is the approach I prefer. Of

course, if you use the second definition, your answer will be route dependent.

In either case, I suggest that you define you vocabulary to avoid confusion on

the part of the reader since there is more that one definition in use in

practice.

Hope this helps.

Michael

Michael D. Karol, Ph.D., A.R.F., R.Ph.

Section Manager, Clinical Pharmacokinetics

Center of Clinical Pharmacology and Pharmacokinetics

Abbott Laboratories

AP13A-3, D-4PK

100 Abbott Park Road

Abbott Park, IL 60064-6104

(847) 937-1919 Voice

(847) 938-0178 Fax

Michael.D.Karol.-a-.Abbott.Com - On 25 Jun 2001 at 20:41:36, Janusz Byczkowski (janusz.byczkowski.-a-.usa.net) sent the message

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The following message was posted to: PharmPK

>..."panteha khalili"(by way of David Bourne)

Subject: Linear vs. non-linear PK

Dear readers,

I have a basic question about linearity of pk of drugs or compounds.

We know that if a drug has linear pk characteristics, there will be a

linear relationship between the dose and AUC...">>

Dear Panteha:

"Linear" pharmacokinetic systems should have the rate of transfer of the

chemical from one compartment to another directly proportional to the

total mass of the chemical in this compartment.

However, in reality, pharmacokinetic systems are nonnlinear and cannot

be accurately described by a single elimination rate constant for a wide

range of concentrations.

These nonlinearities, on the other hand, are well handled by PBPK models

but not by classical compartmental PK models, at least not over a wide

range of doses.

I hope, this may help.

Janusz Z. Byczkowski, Ph.D.,D.Sc.,D.A.B.T.

Consultant

212 N. Central Ave.

Fairborn, OH 45324

voice (937)878-5531

office (614)644-3070

FAX (208)330-9302

e-mail januszb.-at-.AOL.com

homepage: http://members.aol.com/JanuszB/index.html

JZB Consulting web site: http://members.delphi.com/januszb/

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