- On 21 Apr 1998 at 11:44:20, "Philip E. M. Crooker" (pemc.at.bellatlantic.net) sent the message

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I am a grad student taking a first course in PK and have spent a

considerable amount of time discussing the concept of equilibrium

distribution. Unfortunately, the selected text for the course does not

discuss this concept. I have found two references from other texts

which introduce this concept: "Mathematical Approach to Physiological

Problems" by Gerald Riggs, MD, and "Biopharmaceutics and Clinical PK,"

4th ed., by Gibaldi. A quick search of Medline using "equilibrium

distribution" as a keyword did not produce any review articles. Any and

all suggestions for additional references are greatly appreciated.

Thanks very much.

Regards,

Philip Crooker - On 22 Apr 1998 at 14:21:56, "Robert D. Phair, Ph.D." (rphair.at.ix.netcom.com) sent the message

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Philip Crooker wrote to the list asking about the concept of equilibrium

distribution. Concerning references, you might explore Lassen and Perl,

Tracer Kinetic Methods in Medical Physiology, or Jacquez's Compartmental

Analysis in Biology and Medicine.

But I think you would get a lot more from exploring the underlying physical

principles. First, learn to distinguish between equilibrium and steady

state. Many scientists, including a good number of professors lecturing on

kinetics and pharmacokinetics, treat these two terms as interchangeable.

This erroneous interchangeability has led many students astray. Steady

state requires only that nothing be changing with time. Equilibrium is a

thermodynamic concept that requires zero chemical potential gradients.

Hence, at equilibrium, there can be no net fluxes anywhere in the system,

because net fluxes are possible only when there is a nonzero chemical

potential gradient. (Three cheers for Josiah Willard Gibbs!) The difference

between steady state and equilibrium is thus the difference between life

and death. There is a more detailed discussion of this material on the

BioInformatics Services website at

http://www.bioinformaticsservices.com/bis/resources/cybertext/chapter4.html

Once you understand these differences, you are in a much better position to

understand textbooks and colleagues who use these terms loosely. You will

see that an open system, like a living person, cannot be in equilibrium,

only in steady state. You will also see that a closed system that is in

steady state must also be at equilibrium.

This means that the distribution of any constantly infused, metabolized

substance is actually a steady state distribution, not an equilibrium

distribution. The concept of equilibrium is, nevertheless, often loosely

attached to an exchange compartment. The reason this idea survives is that

the ratio of concentrations in the exchanging compartments in a steady

state system is the same as it would be if the two compartments were

completely isolated from the rest of the world and allowed to reach

equilibrium. This leads to the notion of equilibrium subsystems, that is,

systems exchanging with the dynamic system you are considering but

exchanging so fast that the kinetics are invisible and you only need an

equilibrium constant or partition coefficient to adequately characterize

the exchange. Ligand-receptor interactions are often treated in this way,

but there is a danger that in doing so your differential equations will

violate conservation of mass unless you write them carefully. This too is

covered in my web-published tutorial cited above.

Finally, you may want to consider the implications of extravascular

catabolism. If the extravascular exchange compartment is not a pure

exchange, but rather some of the metabolism or elimination of the compound

occurs from the extravascular exchange compartment, then the concept of

equilibrium is clearly inappropriate. In this case, the extravascular

exchange compartment can only achieve a steady state value, and the

so-called equilibrium distribution ratio will depend on metabolic clearance

from the extravascular compartment, not just on the parameters

characterizing the exchange.

I apologize if all this is obvious to you or off the point of your

question, but I know from long experience that these issues trouble many

students. I wish you all the best in your future studies, and I applaud

your search for deeper understanding.

Regards,

Bob

PS The author of the classic text, The Mathematical Approach to

Physiological Problems, is Douglas not Gerald Riggs.

----------

Robert D. Phair, Ph.D. rphair.aaa.bioinformaticsservices.com

BioInformatics Services http://www.bioinformaticsservices.com

12114 Gatewater Drive

Rockville, MD 20854 U.S.A. Phone: 1.301.315.8114

Partnering and Outsourcing for Computational Biology - On 22 Apr 1998 at 14:22:13, Hans Proost (J.H.Proost.at.farm.rug.nl) sent the message

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Dear Philip Crooker,

From your message it is not quite clear what you mean with the term

'distribution equilibrium', nor what you want to know about it.

With respect to a modellistic approach, you might find some useful

information in my paper 'An Extended Pharmacokinetic/Pharmacodynamic

Model describing quantitatively the influence of plasma protein

binding, tissue binding, and receptor binding on the potency and time

course of action of drugs', in Journal of Pharmacokinetics and

Biopharmaceutics 1996;24(1):45-77.

Although the paper deals with PK/PD in particular, the PK may be

helpful for you (and perhaps the PK/PD part of it, since PK without

PK/PD isn't that interesting, in general, isn't it?).

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.at.farm.rug.nl - On 22 Apr 1998 at 14:23:01, Sri Melethil (smelethil.-at-.cctr.umkc.edu) sent the message

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Dear Philip:

Distribution equilibrium (DE) can be best defined as that point in time

when the ratio of the concentration in a given compartment (or region) to

that in plasma (blood, serum) becomes a constant. For example, in a one

compartment model, one assumes instantaneous achievement of DE. So,

following iv bolus injection of a drug, the concentration ratio (say

heart/blood ) as a function of time will be line horizontal to the X or

time axis (from 0 time). Hence , theoretically, one obtains a

monoexponential decline of concentration in plasma with time (and at any

other sampling site;same slope for all sites) ) Hope this is of help. If

you need more assistance, please contact me.

Sri

Professor, Pharmaceutics and Medicine

Schools of Pharmacy and Medicine

Umiversity of Missouri-Kansas City

203B Katz Hall

Kansas City, Mo 64110

816-235-1794 (fax; 816-235-5190) - On 23 Apr 1998 at 10:17:39, Stephen Duffull (sduffull.at.fs1.pa.man.ac.uk) sent the message

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Dear All

I was interested to read the discussion on steady state and distribution

equilibrium (a term that I do not personally use) from all (especially Sri

Melethil and Robert Phair). Clearly there remains conflicting thoughts

regarding these terms. From my perspective I use "steady state" in a very

simple role to mean that the amount in = amount out. This has specific

connotations to clearance via the basic equation: dose rate = elimination

rate which is only true at "steady state". I try and avoid using the term

"steady state" outside of this definition. With respect to distribution,

which is not specifically included in the "steady state" equation above,

then I do not see a specific problem in using the term equilibrium. In

this case as Sri indicates for a one compartment model the equilibirum (net

balance) between all tissues that the drug distributes is considered

instantaneous, for a two compartment model this equilibrium is delayed

until after the so called initial distribution phase. Clearly the concept

of compartments is a function of our ability to model the time course of a

drug and is subject to various assumptions (eg it is common to use a 1 cpt

model to describe the PK of gentamicin which has been shown to display 3

cpt PK [or perhaps more]). Therefore the simplistic distribution

equilibirum approach described here, based on compartments, will always be

wrong since it is logical that there will always be a net flux of drug to

somewhere in the body (even if we can't [or don't] usually measure it).

Given an understanding of these limitations it does not seem unreasonable

to me to use the term equilibirum (despite that it maybe wrong), to

describe the situation in which the net transfer of drug between various

compartments is essentially zero (or at least very small).

"All models are wrong but some are useful"., Box

I look forward to comments.

Steve

==============

Stephen Duffull

School of Pharmacy

University of Manchester

Ph +44 161 275 2355 - On 23 Apr 1998 at 10:25:28, "Michael Kohn" (kohn.-at-.valiant.niehs.nih.gov) sent the message

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Hooray for Bob Phair!

I am frequently dismayed to see models in which components of a system are

assumed to be in equilibrium for ease of mathematical representation. This

invariably leads to violation of conservation of mass and excessively rapid

metabolic clearance of an infused, inhaled, or ingested material. See my

demonstration of this problem in

M.C. Kohn, The importance of anatomical realism for validation of

physiological models of disposition of inhaled toxicants, Toxicol.

Appl. Pharmacol., 147, 448-458 (1997).

These simplified mathematical models were developed 20-30 years ago when

computer power and accessibility were limited and convenient model-construction

software did not exist. Typically, a modeler had to write a program in FORTRAN

from scratch for each new system to be described. We now have personal

computers that are more powerful than the old mainframes and modeling software

that is optimized for describing kinetic systems. So there's NO EXCUSE for not

doing things the right way!

--

Michael C. Kohn

Laboratory of Computational Biology and Risk Analysis

National Institute of Environmental Health Sciences

P.O. Box 12233, Mail Drop A3-06

Research Triangle Park, NC 27709-2233

Telephone:

919-541-4929 (voice)

919-541-1479 (fax)

e-mail:

kohn.-a-.valiant.niehs.nih.gov

WWW home page:

http://valiant.niehs.nih.gov

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