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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.
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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
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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
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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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