- On 30 Apr 1999 at 11:08:43, Cristina Ghiciuc (cghiciuc.-a-.asklepios.umfiasi.ro) sent the message

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Dear Sir,

I'm working for my PhD and I'm very interested if someone could give me

further information about TIME CONSTANT APPROACH. I would greatly

appreciate any help I could get.

Sincerely Yours,

Cristina Ghiciuc - On 7 May 1999 at 11:52:43, "L. Dedik" (DEDIK.-a-.kam1.vm.stuba.sk) sent the message

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>I'm working for my PhD and I'm very interested if someone could give me

>further information about TIME CONSTANT APPROACH. I would greatly

>appreciate any help I could get.

The model in the form of differential equation 1

dC(t)/dt = -k C(t), C(0)=Co, (1)

where C is the drug concentration and t is time,

is frequently used in bio-medicine and the constant k is

called the rate constant. For this model, the reciprocal

value of k

1/k = T

is the time constant T, and the meaning of this time constant

is as follows: The concentration C would reach the zero value at

time T, under the condition that the rate of the

concentration decrease over the interval [0, T] is the same

as that at time zero.

Our study (Durisova M, Dedik L., Balan M,: Bull. Math. Biol.,

57, 1995, 787-808) presents a procedure proposed for building

structured models characterized by several parameters,

including time constants.

Sincerely,

Maria Durisova

and

Ladislav Dedik - On 9 May 1999 at 17:57:10, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message

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"L. Dedik (by way of David_Bourne)" wrote:

[Actually contributed by:

> Maria Durisova

> and

> Ladislav Dedik

> The model in the form of differential equation 1

>

> dC(t)/dt = -k C(t), C(0)=Co, (1)

>

> where C is the drug concentration and t is time,

> is frequently used in bio-medicine and the constant k is

> called the rate constant.

IMHO "frequently used in bio-medicine" should read "*unfortunately* still

used in biomedicine". I would add "A more biologically meaningful

parameterization of this model is:

dC(t)/dt = (-CL C(t))/V, C(0)=Dose/V, (2)

where , CL is clearance, Dose is the amount of drug administered at time 0

and V is the apparent volume of distribution."

The rate constant model is indistinguishable from the clearance/volume

model in the eyes of mathematicians who seem to prefer rate constants

because (maybe it looks simpler to them?) but appear to be blind to trying

to relate the parameters to biology. The rate constant has no *simple*

biological correlate whereas CL is correlated with organ function such as

the liver and kidney and V is correlated with structure such as body size

and composition.

Why do I emphasize "*simple*"? Because by definition k=CL/V and thus k is

determined by both CL and V and thus by both organ function AND body

structure. After clinical pharmacologists adopted the clearance/volume

approach (in the mid-1970s) it then helped to understand and explain

various phenomena that were inadequately described by the rate constant

(half-life) approach e.g. longer half-lives of diazepam in older people are

due to bigger apparent volumes not smaller clearances.

The whole field of population PK is largely concerned with trying to

identify biological factors which predict CL and V. Because very different

biological factors influence CL and V it only makes sense to understand

these parameters as separate entities.

The otherwise excellent PK simulations built by Mohsen Hedayaand discussed recently in this list are an

unfortunate example of the mathematical rather than biological approach to

pharmacokinetics because the student is required to simulate PK in terms of

rate constants rather clearance. I have had a separate correspondence with

Mohsen and have encouraged him to offer the student a choice of PK from

either a mathematical or biological perspective.

> For this model, the reciprocal

> value of k

>

> 1/k = T

>

> is the time constant T, and the meaning of this time constant

> is as follows: The concentration C would reach the zero value at

> time T, under the condition that the rate of the

> concentration decrease over the interval [0, T] is the same

> as that at time zero.

>

I had to read the above definition several times before I understood it (I

think). For me, I am afraid there is no biological interest in such a

definition. An alternative, less mathematically precise definition of the

time constant, is that it is the mean time that each molecule resides in

the body, hence its more commonly used name in pharmacokinetics is the Mean

Residence Time (MRT).

The Time Constant approach suffers from the same difficulties as the rate

constant approach but at least has the advantage that the parameter has

units of time rather than 1/time so that is generally more readily

understood when trying to relate the numerical value to the biological

problem at hand.

--

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 10 May 1999 at 20:54:17, "Bonate, Peter, Quintiles" (pbonate.-at-.qkan.quintiles.com) sent the message

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In regards to more information regarding the time constant approach, refer

to the book by Lee and Amidon from technomic publishing. I copied the

following from their web site. I hope this is what you are looking for.

Pharmacokinetic Analysis

A Practical Approach

Peter I. D. Lee, Ph.D., Janssen Research Foundation, Titusville, New Jersey,

and Gordon L. Amidon, Ph.D., Professor of Pharmaceutics, College of

Pharmacy, University of Michigan, Ann Arbor, Michigan

This insightful new work provides a useful introduction to the very large

and important field of pharmacokinetics. The authors have selected the Time

Constant Approach as a unifying view within which to present important

application areas. In addition to providing consistency, their approach

provides the novice with an intuitive time view that is meaningful from the

outset. This approach allows one to get a "feel" for the data and to relate

it to other data in a direct and accessible manner.

[Rather than include the rest of this description I've included the URL for

the information on the Technomic site

http://www.techpub.com/tech/LibraryIndex_Books.asp?qrystrID=110365 - db]

---

Office Phone: (717) 291-5609 // (800) 233-9936

Publications Office Fax: (717) 295-4538 // Seminar Office Fax: (717)

295-9637

Copyright 1997 Technomic Publishing Co., Inc.

All Rights Reserved

PETER L. BONATE, PhD.

Clinical Pharmacokinetics

Quintiles

POB 9708 (L4-M2828)

Kansas City, MO 64134

phone: 816-767-6084

fax: 816-767-3602

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