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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.
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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.
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"L. Dedik (by way of David_Bourne)" wrote:
[Actually contributed by:
> Maria Durisova
> 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
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 Hedaya
and 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
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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.
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)
Copyright 1997 Technomic Publishing Co., Inc.
All Rights Reserved
PETER L. BONATE, PhD.
POB 9708 (L4-M2828)
Kansas City, MO 64134
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