# PharmPK Discussion - Half-life calculations

PharmPK Discussion List Archive Index page
• On 5 Dec 2005 at 08:31:40, "Prof. Stefan Soback" (stefans.-a-.moag.gov.il) sent the message
`I'm sorry, but it appears that I failed to understand this point. CanI get some clarification to these sentences?"The elimination rate constant is clearance divided by volume ofdistribution. If clearance and volume of distribution are normallydistributed, the elimination rate constant is not normally distributed."And then"In particular in the case of wide distributions, the differencesbetween the (harmonic) mean of half-life and the half-life estimatedfrom mean clearance and mean volume of distribution can beconsiderable. And what is the best answer?"As far as I can understand Vss/CL = MRT and MRT =1/K. In other wordsCL/Vss = K. The use of K derived from the ratio of Vss and CL forhalf-life calculation (ln2/K) can be applied only to one-compartmentmodel.In other words, what is meant by "half-life estimated from meanclearance and mean volume of distribution"?Best regardsStefan[The MRT = 1/K refers to a one compartment model only(?). It's notequal to beta (two compartment) is it? A problem (I think) with thenon compartmental approach is that you loose some of the model detail- db]`
Back to the Top

• On 5 Dec 2005 at 11:40:00, "Davies, Brian" (brian.davies.at.roche.com) sent the message
`The following message was posted to: PharmPKSee comments below which I have added to clarify some of the points forProf Soback-----Original Message-----From: david.-a-.boomer.org [mailto:david.aaa.boomer.org] On Behalf Of Prof.Stefan SobackI'm sorry, but it appears that I failed to understand this point. CanI get some clarification to these sentences?"The elimination rate constant is clearance divided by volume ofdistribution. If clearance and volume of distribution are normallydistributed, the elimination rate constant is not normally distributed."And then "In particular in the case of wide distributions, thedifferencesbetween the (harmonic) mean of half-life and the half-life estimatedfrom mean clearance and mean volume of distribution can beconsiderable. And what is the best answer?" >>The volume of distribution referred to above is Vz, the apparentvolume of distribution and not Vss<<As far as I can understand Vss/CL = MRT and MRT =1/K. In other wordsCL/Vss = K. The use of K derived from the ratio of Vss and CL forhalf-life calculation (ln2/K) can be applied only to one-compartmentmodel. >>This is true that K is the elimination rate constant for a 1compartment model.  In the case of the 2 compartment model or higher,CL/Vss = kss, the steady-state rate constant.kss = 0.693/t1/2ss = 0.693 x MRT. T1/2ss or effective half-life is avery useful concept in pharmacokinetics<<In other words, what is meant by "half-life estimated from meanclearance and mean volume of distribution"?Best regardsStefan`
Back to the Top

• On 6 Dec 2005 at 08:46:30, "Hans Proost" (j.h.proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Stefan,An explanation of my earlier message: > "The elimination rate constant is clearance divided by volume of > distribution. If clearance and volume of distribution are normally > distributed, the elimination rate constant is not normallydistributed."This refers to the distribution of clearance and volume ofdistribution overthe individuals of a population, often assumed to be a normaldistribution(although a log-normal distribution is likely to be more close to therealsituation, as was the subject of the original thread). For eachindivididualthe elimination rate constant k = CL/V. As a result, the individualvaluesfor k have also some statistical distribution. However, this is not anormaldistribution. > "In particular in the case of wide distributions, the differences > between the (harmonic) mean of half-life and the half-life estimated > from mean clearance and mean volume of distribution can be > considerable. And what is the best answer?"Half-life of each individual is calculated from each individual's k byln(2)/k. Again, the distribution of half-life in the population willnot bea normal distribution. Because of the calculation from the reciprocalof k,it has been suggested to calculate the harmonic mean of half-life as ameasure of 'central tendency'. The harmonic mean is 1 / (1/x1 + 1/x2+ 1/x3+ ...). This results in a 'mean half-life' that is the same ascalculatedfrom ln(2) / 'mean k'. If k is normally distributed, this is areasonableapproach.My point was that if k is not normally distributed (and indeed, it isnot)that this is not a reasonable approach. One can also calculate a meanCL andmean V, and calculate a mean k ( = mean CL / mean V) and mean half-life ( ln(2) / mean k)from these mean values. This results in a different valuefor mean k and mean half-life. And what is the best answer? Without anyknowledge or assumption about the statistical distribution there isnothingto say about that. So one needs to make some reasonable assumptionabout thestatistical distribution. In my opinion, the log-normal distributionis thebest choice, unless there are obvious reasons for something else(e.g. incase of apparent bimodal distributions). Of course one can alwayscalculateand report a mean ('a mean is a mean'), but does not make much senseif this'mean' is not a good descriptor of 'central tendency', i.e. thecentre ofthe distribution. What else is the meaning of a 'mean'? > As far as I can understand Vss/CL = MRT and MRT =1/K. In other words > CL/Vss = K. The use of K derived from the ratio of Vss and CL for > half-life calculation (ln2/K) can be applied only to one-compartment > model.Yes, this refers to the one-compartment model only. But if the volume ofdistribution during the terminal phase V (also denoted V_beta, or Vz) isused, this still works since the terminal rate constant lambda_z(also k_z)= CL / V. And the terminal half-life is (ln2) / lambda_z, so it stillworksfor multi-compartment models. Actually this is a noncompartmentalapproach(only the expression MRT = 1/k does not hold; at least, this k doesnot havea particular meaning).Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.-a-.rug.nl`
Back to the Top

• On 6 Dec 2005 at 10:53:17, "Prof. Stefan Soback" (stefans.-a-.moag.gov.il) sent the message
`Thank you for your answer, but I still have some problems with yourclarification. >>The volume of distribution referred to above is Vz, the apparentvolume of distribution and not Vss<<As long as we have a one-compartment model, it doesn't matter whichvolume term we use. They are all the same. Not so in multi-compartment models. Still I consider the Vss the "true" volume term,but this is obviously not the right place to discuss that. >>This is true that K is the elimination rate constant for a 1compartment model.  In the case of the 2 compartment model or higher,CL/Vss = kss, the steady-state rate constant kss = 0.693/t1/2ss =0.693 x MRT. T1/2ss or effective half-life is a very useful conceptin pharmacokinetics<<The Benet & Galeazzi equation Vss = CL x MRT is about volume ofdistribution at steady state and is valid in any compartment model.I'm not familiar with the kss, so I'm unable to comment on that.However, I seem to have a problem with your equations. The latterpart (0.693 x MRT) is the half-life in one-compartment model. The kss= 0.693/ t1/2ss is obviously O.K., but it doesn't say anything to me.However, 0.693/t1/2ss = 0.693 x MRT I don't understand. When you havean unequivocal MRT, why would you want to translate that to anartificial t1/2?The concept of "effective half-life", whatever it means, as inGibaldi & Perrier (1982) is familiar to me, but I don't know why itis very useful in pharmacokinetics.Best regardsStefan`
Back to the Top

• On 7 Dec 2005 at 11:52:21, "Prof. Stefan Soback" (stefans.at.moag.gov.il) sent the message
`Dear Hans,Thank you for your detailed answer and your patience.As you said:"But if the volume of distribution during the terminal phase V (alsodenoted V_beta, or Vz) is used, this still works since the terminalrate constant lambda_z  (also k_z)= CL / V. And the terminal half-life is (ln2) / lambda_z, so itstill  works for multi-compartment models. Actually this is anoncompartmental  approach (only the expression MRT = 1/k does nothold; at least, this k does not have a particular meaning)."This is clear. When V is determined as the product of CL and 1/beta(or lambda_z) the equation works (and k is the terminal slope), butthen V is a function of elimination. I was thinking of independentlydetermined CL and V (= Vss). I'm sorry for the poorly formulatedquestion.Thanks again,Stefan`
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 "Half-life calculations" as the subject

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