# PharmPK Discussion - Time constant approach

PharmPK Discussion List Archive Index page
• On 30 Apr 1999 at 11:08:43, Cristina Ghiciuc (cghiciuc.-a-.asklepios.umfiasi.ro) sent the message
`Dear Sir,I'm working for my PhD and I'm very interested if someone could give mefurther information about TIME CONSTANT APPROACH. I would greatlyappreciate any help I could get.Sincerely Yours,Cristina Ghiciuc`
Back to the Top

• On 7 May 1999 at 11:52:43, "L. Dedik" (DEDIK.-a-.kam1.vm.stuba.sk) sent the message
`>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 1dC(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  iscalled  the rate  constant.  For  this model,  the reciprocalvalue of k1/k = Tis the  time constant T, and  the  meaning of this time  constantis as follows: The concentration  C would reach the zero value attime   T,  under   the  condition   that  the   rate  of  theconcentration decrease  over the interval [0, T] is the sameas that at  time zero.Our study (Durisova M, Dedik L., Balan M,: Bull. Math. Biol.,57, 1995, 787-808) presents  a procedure proposed for buildingstructured   models  characterized   by  several  parameters,including time constants.Sincerely,Maria DurisovaandLadislav Dedik`
Back to the Top

• On 9 May 1999 at 17:57:10, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`"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* stillused in biomedicine". I would add "A more biologically meaningfulparameterization 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 0and V is the apparent volume of distribution."The rate constant model is indistinguishable from the clearance/volumemodel in the eyes of mathematicians who seem to prefer rate constantsbecause (maybe it looks simpler to them?) but appear to be blind to tryingto relate the parameters to biology. The rate constant has no *simple*biological correlate whereas CL is correlated with organ function such asthe liver and kidney and V is correlated with structure such as body sizeand composition.Why do I emphasize "*simple*"? Because by definition k=CL/V and thus k isdetermined by both CL and V and thus by both organ function AND bodystructure. After clinical pharmacologists adopted the clearance/volumeapproach (in the mid-1970s) it then helped to understand and explainvarious phenomena that were inadequately described by the rate constant(half-life) approach e.g. longer half-lives of diazepam in older people aredue to bigger apparent volumes not smaller clearances.The whole field of population PK is largely concerned with trying toidentify biological factors which predict CL and V. Because very differentbiological factors influence CL and V it only makes sense to understandthese parameters as separate entities.The otherwise excellent PK simulations built by Mohsen Hedaya and discussed recently in this list are anunfortunate example of the mathematical rather than biological approach topharmacokinetics because the student is required to simulate PK in terms ofrate constants rather clearance. I have had a separate correspondence withMohsen and have encouraged him to offer the student a choice of PK fromeither 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 (Ithink). For me, I am afraid there is no biological interest in such adefinition. An alternative, less mathematically precise definition of thetime constant, is that it is the mean time that each molecule resides inthe body, hence its more commonly used name in pharmacokinetics is the MeanResidence Time (MRT).The Time Constant approach suffers from the same difficulties as the rateconstant approach but at least has the advantage that the parameter hasunits of time rather than 1/time so that is generally more readilyunderstood when trying to relate the numerical value to the biologicalproblem at hand.--Nick Holford, Dept Pharmacology & Clinical PharmacologyUniversity of Auckland, Private Bag 92019, Auckland, New Zealandemail:n.holford.aaa.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html`
Back to the Top

• On 10 May 1999 at 20:54:17, "Bonate, Peter, Quintiles" (pbonate.-at-.qkan.quintiles.com) sent the message
`In regards to more information regarding the time constant approach, referto the book by Lee and Amidon from technomic publishing.  I copied thefollowing from their web site.  I hope this is what you are looking for.Pharmacokinetic AnalysisA Practical ApproachPeter I. D. Lee, Ph.D., Janssen Research Foundation, Titusville, New Jersey,and Gordon L. Amidon, Ph.D., Professor of Pharmaceutics, College ofPharmacy, University of Michigan, Ann Arbor, MichiganThis insightful new work provides a useful introduction to the very largeand important field of pharmacokinetics. The authors have selected the TimeConstant Approach as a unifying view within which to present importantapplication areas. In addition to providing consistency, their approachprovides the novice with an intuitive time view that is meaningful from theoutset. This approach allows one to get a "feel" for the data and to relateit to other data in a direct and accessible manner.[Rather than include the rest of this description I've included the URL forthe information on the Technomic sitehttp://www.techpub.com/tech/LibraryIndex_Books.asp?qrystrID=110365 - db]---Office Phone: (717) 291-5609 // (800) 233-9936Publications Office Fax: (717) 295-4538 // Seminar Office Fax: (717)295-9637Copyright 1997 Technomic Publishing Co., Inc.All Rights ReservedPETER L. BONATE, PhD.Clinical PharmacokineticsQuintilesPOB 9708  (L4-M2828)Kansas City, MO  64134phone:  816-767-6084fax:  816-767-3602`
Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Time constant approach" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)